The information in this document
is intended for use in hobbyist, experimental, research, and other
applications where a bug in the hardware, firmware, or software, will not
have a significant impact on the future of the Universe or anything else.
We will not be responsible for any consequences
of such bugs including but not limited to damage to the $100,000,000
wafer FAB that was purchased on eBay for $1.98 + shipping, financial
loss from the waste of
28 spools of ABS due to the office 3-D printer fabricating a part with
random dimensions due to loss of lock, or bruising to your pet's ego
from any number of causes directly or indirectly related to
the implementation and use of this system. ;-)
The only safety issues with the experiments to be performed using this kit
are with respect to the low power Helium-Neon (HeNe) laser. Sure, you could
drop the breadboard on your foot, but that's outside our control. :( :-)
The first one is with respect to
laser light and your vision. The output power of the laser is
between 0.5 and slightly over 1.0 mW which is less than that of
a typical laser pointer. Nonetheless, one should avoid looking directly
into the beam or specular (shiny) reflections of it. However a
momentary flash will not cause any permanent harm, only perhaps an
afterimage that should go away in a few minutes at most. A 1 mW laser
beam is similar in brightness to that of the noonday Sun. So treat it
like a little red Sun in a cylinder. :)
The other one is electrical. The laser runs on a High Voltage (HV) low
current power supply. As long as the laser cable is undamaged and securely
attached to the power supply, the HV is safety tucked away inside. However,
if the laser head is unplugged just after being on, there can be an annoying,
though harmless charge retained on the HV connector due the capacitance
of the laser tube, feeling like the shock
from a static buildup when walking across a carpet on a dry day.
But tossing the laser head across the room from a reflex reaction is
bad form (and probably won't help your grade). So just don't touch
the metal prongs for a few minutes, or short between
the prongs with the metal-end of an insulated tool like a screwdriver.
Even though this laser is not likely to cause any harm, one should always
take laser safety seriously. Someday you may be working with one that is
truly dangerous.
The Michelson interferometer is one of the most widely used configurations
in a variety of applications including metrology (precision measurement).
An experimental setup is presented which allows for several types of
interferometers to be easily implemented and without requiring any special
tools or test equipment. The behavior of various interferometer
configurations will be explored as well as how the characteristics of
the laser impact performance. Various enhancements are also described for
both the laser and detector, as well as extensions to actual
measurements like displacement (change in position) down to nm precision.
The set of parts may be easily duplicated
and/or modified for specific interests.
For the combined kit (heterodyne + homodyne), both of the relevant
manuals will need to be referred to, though there is a lot of overlap.
Interferometers are the key technology is numerous applications in
manufacturing and testing where the very minute wavelength of light
is the "yardstick" providing non-contact measurements down to nanometer
precision. In short, a light source is split into two parts that may
travel different paths and then recombined at some type of detector.
Where the path lengths differ by an integer number of wavelengths, the
result will be constructive interference and the output of the detector
will be high; where it differs by an integer number of wavelengths plus
one half wavelength, the result will be destructive interference and the
output of the detector will be low. In between, the output will vary
sinusoidally. With suitable detectors and electronics, remarkably
precise measurements can be performed. For example, nearly every microchip
manufactured in the explored universe has been done with wafer steppers whose
stages were positioned using interferometry based on HeNe lasers.
While interferometers are employed in a wide array of applications,
the general emphasis for these experiments relate to the use of interferometery
in metrology - precision measuremens of physical characteristics like
displacement, velocity, angle, straightness, and more.
Therefore unlike numerous interferometer experiments that may be found via
a Web search, the emphasis here is on the signals that the setup provides,
not so much on the interference patterns. (Though nothing precludes the
observation of these.
The experimental setups will enable various interferometer configuration
to be easily implemented and then tested with one arm being on a micrometer
linear stage and/or with some other device or material that can vary
the path length precisely. The light source is a Class II 633 nm
Helium-Neon laser (HeNe for short) with an output power of between 0.4 and
just over 1 mW. The basic detector is a biased photodiode connected to
a dual channel digital oscilloscope. Variations and enhancements to these
will be offered as options.
Among the areas that can be explored with the basic setups are:
Techniques for aligning the interferometer.
Impact on performance of the coherence length of the laser source.
Inserting optics in one of the beam paths.
Using the interferometer as a pressure and/or temperature sensor.
There is no need to construct all of the interferometer
configurations described below. Doing the Linear Interferometer (LI)
first makes sense
since there are detailed instructions on its construction, alignment, testing.
Building the High Stability Plane Mirror Interferometer (HSPMI)
would be the logical next step moving from cube corners
to plane mirrors. It also permits the loudspeaker and/or PZT actuators
to be added. Then after that one of the others. Perhaps coordinate with
the other project students using this same kit so that each of
you do different ones.
This minimal set of experiments can all be done using parts in the Basic Kit:
Construction of Linear Interferometer (LI).
Evaluating and explaining fringe response for various path length
differences with respect to lasing modes.
Interferometer as air pressure or index of refraction of air sensor.
Interferometer as temperature and/or gas sensor.
Construction of Quad-Sin-Cos detector for displacement measurements.
Homodyne measurement display using µMD0.
The following additional projects can be done using parts in the Deluxe kit:
Construction and testing of other types of interferometers including the
PMI, HSPMI, and SBI.
Construction of Original Michelson Interferometer (BMI) and comparison
with the LI.
Resolution of the various interferometer configurations.
Sensitivity to alignment based on configuration.
Interferometer as earthquake and/or vibration detector.
PZT actuator for sub-wavelength-scale movement.
Loudspeaker actuator for wavelength scale movement and "interferometer
microphone".
Analysis of interferometer behavior as a function of the laser modes.
The following are more advanced projects, but they
may require additional parts and/or different parts including the laser
that are not included in the either kit:
Interferometer as gas partial pressure sensor.
Substitution of random polarized HeNe laser for the linearly polarized
laser.
Construction of the laser itself using a bare laser tube, power supply,
and mounts.
Stabilizing the laser for single frequency operation using analog
circuits or µSLC1.
Implementation of stabilized two frequency Zeeman HeNe laser. (Requires
suitable random polarized laser.)
Heterodyne measurement display using µMD1 or µMD2.
There is some information on these in this manual and links will be
provided to learn more.
As of Summer 2021, there are 3 versions of the setups. Around 5 each of
V1.0 and V1.5 (which differ in minor details) have been built and are
being used for in-person and remote project labs at a local college;
V2.0 is preferred going forward and will come in several flavors.
For the two in the field (V1.0 and V1.5), the
differences will be identified in the assembly instructions or whereever
else needed. Differences for V2.0 will eventually be added.
Various configurations of V2.0 are or will be available on eBay under my
user ID siliconsam or by searching for "Sam's Michelson Interferometer
Experimental Setups for Education-Signal Oriented". Or directly from
me with more options and slightly lower cost. If interested, contact me
via Sci.Electronics.Repair
FAQ Email Links Page.
Note: Off-page links (including any clickable graphics)
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All of the measurements performed by these systems are based on variations
of the Michelson interferometer, invented over 100 years ago by Albert
Michelson. This is one of the simplest interferometer configurations but
also one of the most widely used. The textbook version is shown below:
In short, a light beam is split into two parts which
are bounced off of a pair of reflectors and recombined at a detector. Any
change in the relative path lengths of the two "arms" formed by the
reflectors results in a phase shift between the waves in the two beams
resulting in constructive or destructive interference,
which can be measured and converted to displacement (change in position)
down to nanometer precision. All other types of measurements made by
these systems are based on opto-mechanical configurations designed
such that changes in the measured variable are detectable by what is
in essense a Michelson interferometer.
Where the Path Length Difference (PLD) between the two arms is small, the
requirements for the laser are not very stringent. In fact, for very
small PLDs, an LED or even a totally incoherent source like an incandescent
lamp may be substituted for the laser. However, to be useful for the PLDs
necessary for most applications (millimeters to 10s of meters), the light
source must be a laser. And not just any laser, but one
that has a narrow "linewidth". While the popular concept of a
laser is of a light source that is monochromatic (single color
or wavelength), in reality most lasers do not even come close.
It takes careful design and implementation to achieve that.
For these metrology applications the laser should ideally
produce an output that is a single optical frequency with a linewidth
approaching zero. In practice, it isn't that narrow but can result in
a linewidth of much less than 1 MHz, resulting in a usable PLD of 100s
of meters. This is usually a low power stabilized HeNe laser.
However, for PLDs of a few inches, a common (much less expensive)
unstabilized HeNe laser will be adequate. Within this range, all the
modes will be sufficiently correlated and the fringe contrast/signal
amplitude will be acceptable.
Engrave PLD on your brain. It will be used throughout this manual. :)
The simple Michelson interferometer setup can be used in a metrology system,
but it has severe limitations which make it impractical for most applications.
Alignment is extremely critical. Even the slightest deviation from
perfect alignment will result in a reduction or loss of signal. Yet when
perfectly aligned, one half of the optical power from the laser reflects
directly back into the laser - which may destabilize it resulting in
erratic fluctuations of its output in amplitude, optical phase, optical
frequency, and polarization.
Near the end of this manual is an experimental setup similar to the original
Michelson Interferometer configuration adapted for the PBSC. So you
can see these various issues for yourself.
The diagrams below show some variations on the angles of the Beam-Splitter
(BS) and Mirrors (M1, M2).
The first one is essentially the same as the diagram, above. The
"Single Angled" one does nothing to prevent back-reflections.
And while the "Double Angled" version does eliminate back-reflections, the
two beams are angled at the detector which means their relative phase will
vary across the detector. That is undesirable for our experiments
in at least two ways: First, it will mean that the detector won't see a clean
fringe signal. In fact there may be little or no signal depending on
how the fringes average across its face. Second, alignment
will change as either mirror is moved making testing with respect
to PLD very tricky. But can you suggest an application where it may
be useful?
The first enhancement of the Michelson interferometer is to add a means of
separating the outgoing and return beams so that there is vitrually no
optical power returned to the laser. The simplest way to do this is to
replace the mirrors with Retro-Reflectors (RRs), typically cube-corner
(trihedral) prisms, which have the property of returning the beam directly back
parallel with the outgoing beam, but which may have an offset. In this way,
virtually none of the reflected light ends up back at the laser.
The use of the RRs also greatly reduces the
sensitivity to alignment as any change in their angle is converted to a
small change in the distance between the outgoing and return beams, but
they remain parallel.
All of the practical interferometer configurations include at least
one cube corner retro-reflector.
The second enhancement is to use a Polarizing Beam-Splitter Cube (PBSC) in
place of the 45 degree partially reflecting mirror. While a plate
beam-splitter could be used, the PBSC is much more common.
The beams reflected to the two
arms of the interferometer then have orthogonal polarization which effectively
makes them independent until they are combined at the detectors.
The result is then one of the most widely used
configurations - the Linear Interferometer (LI),
which was the first one used by HP in their original 5500A
laser interferometer displacement measuring system. (As an aside, I do NOT
know where that name "Linear Interferometer"
comes from except perhaps that the inital configuration
was in-line with the laser and thus "linear".) In practice, Arm 1 is
used as the reference and is made as short as possible with the Cube Corner
(CC) attached directly to the PBS cube. Both arms can move where differential
measurements are required.
With the use of the PBS, the maximum amount of the laser optical power is
available - virtually nothing exits
out the unused side of the beam-splitter as it would in the original Michelson
setup, above. However, at least half the power is lost in the detection
scheme that is typically used so it would end up being similar.
In principle, this wasted power
can be diverted to a second detector. Their difference will then have twice
the amplitude and the signal-to-noise ratio will nearly double (but
opposite phase). This is
rarely, if ever, done though. But for the more complex interferometer
configurations described later as well as for use with two frequency
lasers, the use of the PBS is essential to avoid incurring very large
losses, or for the schemes to work at all.
However, since the laser used in these experimental setups are not single
frequency, the PLD between Arm 1 and Arm 2 should be minimized for the initial
setup. The effects of larger PFDs may be explored once "first signal" is
achieved. Alternatively, a single mode laser can be built. Much more on
all this below.
Single Beam Interferometer (SBI): Compact, small cube corner for
remote reflector, single pass: resolution X1.
High Stability Plane Mirror Interferometer (HSPMI): Plane mirror
for remote reflector, sensitivity to temperature changes <1/10th that of
PMI, double pass: resolution X2.
Modified Linear Interferometer (MLI): Same architecture as SBI
but beam paths separated, cube corner for remote reflector,
single pass: resolution X1. It really only has "linear" in
its name because it uses cube corners like the basic LI.
Double Pass Linear Interferometer (DPLI): Similar to the HSPMI
but with cube corners for the arm reflectors, double pass, resolution X2.
Like the MLI, it really only has "linear" in its name because it uses cube
corners like the basic LI.
Single Pass Plane Mirror Interferometer (SPPMI): Uses NO cube
corners, single pass: resolution X1. The SPPMI may also be called the
"No Cube Corner" interferometer. It is most similar to the original
Michelson interferometer but uses QWPs to avoid back-reflections. However,
it is similarly very sensitive to misalignment and useful only over
short changes in PLD.
High Resolution Plane Mirror Interferometer (HRPMI): Doubles the
resolution compared to the PMI or HSPMI but is much more complex and
tricky to align. Quadruple pass, resolution x4. Additional parts
and determination may be required to construct this.
When used in a displacement measuring system with a 633 nm HeNe laser, 1X
represents a full cycle resolution of 1/2 wavelength or ~316 nm; 2X of ~158 nm,
and 4X of ~79 nm. For a homodyne system with a Quad-A-B deterctor, there are
4 counts per cycle so that gets multiplied by 4. The very commonly used PMI
will have a resolution of 40 nm and interpolation techniques can extend it
down to under 1 nm.
Either a Thorlabs DET110 (or equivalent) or a custom detector are used here.
Both perform the same function: A silicon photodiode (PD) when reverse biased
by a positive DC voltage (battery or power supply) is essentially a current
source providing Ipd with a sensitivity measured in amps / watt (A/W) or
for our purposes, mA/mW of incident laser power. The sensitivity for
silicon at 633 nm is typically between 0.3 and 0.4 mA/mW and linear
up to several mW for the types of PDs used here. This relationship
holds even when a load resistor R-Load is installed between the PD
and circuit common (negative of the bias supply),
resulting in an output voltage that is linear with respect to
incident laser power based on Ipd * R-Load.
For example, with a laser power of 0.5 mW, a PD sensitivity of 0.35 mA/mW,
and R-Load of 10K ohms, Vo would be 1.75 V.
Note the polarity of the PD with its cathode connected to the positive of the
power supply and thus reverse biased. With no light incident on the PD,
only the so-called "dark current" will flow, which is generally small enough
to be ignored (nanoamps or less).
Thorlabs DET110: This is typical of a commercial biased detector
(without amplification). More information may be found at
Thorlabs DET110 Spec Sheet.
R-Protect PD BNC Center
+-------/\/\----------+----|<|------<<-----------------+------o Scope or DMM
| 1K | +-<<-------------+ |
o | | BNC Shield | /
\ Power _|_ C-Bypass | | \ R-Load
o --- | | /
| 12 V Battery | | | \
| +| |- | | | |
+---------||||--------+-----------+ +---+------o GND
| |
|<--------- Thorlabs DET110 -------->|<---- Output Wiring ---->
R-Protect limits current should the battery be installed backwards
or should the PD fail shorted. C-Bypass improves the high frequency
response by eliminating the other components from the AC signal path.
The DET110 mounts on a standard post using an 8-32 setscrew. Threads
on the front allow accessories to be easily attached.
Custom single channel detector: For the purposes of these kits, a
much lower cost approach will have similar performance and more flexibility,
being easily extended to two channels for the Quad-Sin-Cos decoder. And it
will be educationally more rewarding. ;-) The circuit
is virtually identical to that of the DET110:
R-Protect PD Yellow
+-----/\/\-------|<|----<<----------------------+---------o Scope Channel 1
| |
| /
| \ R-Load
| /
| DC Power \
| Red +| |- Black |
+-----------------------<<---------||||---------+---------o Scope Ground
| |
|<--- SBB or QDx PCB --->|<---- Scope / Power Wiring ---->
PD Pins: Facing Front of PD with Legs Down: Anode on left, Cathode on right.
DC power comes from either a wall adapter or USB +5 V, so no power switch is
needed. And for the low signal bandwidth, no C-Bypass is required, though
there is a spot on the QCx PCBs for one.
A couple of resistors will be required for the detector and elsewhere so
here is info on reading the color codes:
Resistor Color Code Chart (from the Digikey Web site)
Construction is most easily done using a small Solderless BreadBoard (SBB).
This has 17 columns of two sets of 5 bussed holes. Short #20 to #24 AWG wires
are used as jumpers where the busses aren't convenient. The SBB has a
double-sided sticky pad on the bottom which enables it to be attached
to a standard post using the "Detector adapter plate" and
an 8-32 setscrew.
For the single channel detector, only two wires need to attach to the SBB:
+DC power and the signal output. The load resistor can be external, or on
the SBB with an additional wire to scope GND and -DC. The wire colors are
suggestions. ;-)
Basic testing of either detector can be done using the laser or even a
flashlight to confirm sensitivity to light. However, even a super-bright
flashlight will likely result in only a small signal compared to the laser.
These only use the custom detector. It would be silly, space consuming -
and expensive - to require two DET110s! So, for two channels, all parts
except for the power source and protection resistor are replicated:
R-Protect PD1 Yellow
+-----/\/\----+--|<|---<<-----------------------+----------o Scope Channel 1
| | |
| | PD2 Blue |
| +--|<|---<<---------------------------+------o Scope Channel 2
| | |
| / /
| R-Load1 \ \ R-Load2
| / /
| DC Power \ \
| Red +| |- Black | |
+-----------------------<<---------||||---------+---+-------o Scope Ground
| |
|<--- SBB or QDx PCB --->|<----- Scope / Power Wiring ------>
PD Pins: Facing Front of PD with Legs Down: Anode on left, Cathode on right.
Although HP called the combination of the PBSC and reference CC attached to
it, the "Linear Interferometer", the term "LI" here will refer to the entire
setup. And to enable the PLD to be set to zero, the CC normally attached
directly to the PBSC will be mounted a few inches away.
The designations m-n show the paths taken by the Arm 1 and Arm 2 beams where
"m" is the Arm and "n" is the sequence number.
The diagram below shows the general arrangement of the laser, beam splitter,
cube corners, and detector used for all the interferometer configurations.
The other configurations will have a few additional or substitute parts and
small variations in the horizonatal position of the laser
and placement of the detector but are otherwise similar.
Therefore the LI setup will be described in more detail.
The photo below shows the actual setup used for initial testing. There are
minor variations in the actual kits depending on version and whether they
are the "Basic" or "Deluxe" versions. These will be noted below.
Where the total path length and PLD is small, no beam expander is
needed for the laser, which may result in a larger signal since
the entire beam hits the detector.
MIPM Linear Interferometer Assembly with Thorlabs
Detector
Baseplate: This is a custom 8x18x0.5 inch aluminum optical
"breadboard" with an array of 144 1/4-20 tapped holes on one inch
centers to which all the components are attached with cap-head screws
or set-screws. (We may use the terms "baseplate" and "breadboard"
interchangeably.)
HeNe laser: This is a ~1.25" cylindrical laser "head"
mounted within a pair of aluminum rings each with 4 screws to allow
for its position and alignment to be easily adjusted. A separate high
voltage power supply which plugs into the AC line drives the laser tube
safely enclosed in the aluminum cylinder. The laser is of very high quality
from JDS Uniphase or Melles Griot. It is the only somewhat fragile item
so please don't drop it or use it to hammer nails. Your instructor (and I),
and perhaps your grades won't like that. :( :)
The photo shows a laser without a beam expander but the laser in the kit
will either come with a beam expander already attached to convert the
~0.5 mm beam from the laser tube into a ~4 mm beam with low divergence,
or the expander which can be attached and centered with 3 screws.
The raw beam is
is a bit trickier to align and to maintain alignment as the stage in Arm 2
is moved, but it is quite adequate for a small range of PLD.
But where the PLD is large (e.g., for use as an earthquake sensor),
the beam expander eases the alignment and
is required so that the divergence of the beam doesn't affect the
detector response (e.g., the fringe contrast). Since the beam expander
is secured by 3 screws (see below) it can be removed to explore how the
raw beam behaves. However, two cautions: (1) Do NOT remove the plastic
bezel of the laser head as that will expose the high voltage connected
to the laser tube and (2) careful lateral adjustment of the beam expander
will be required when reattached to center the beam.
If using the beam expander, the posts/rings for the laser should probably
be mounted one hole to the left of where they are in the photo to
provide more clearance.
Installing the optional beam expander: The black beam expander
itself attaches to the "Beam Expander Adapter" which is a circular plate
around 1-1/4". The threaded end of the beam expander will need to be glued
to the adapter ring unless it is a tight enough fit to stay in place.
If too loose, use a small amount of 5-Minute Epoxy attach it. Make sure it
is centered and straight.
Once cured (give it 15 minutes to be safe), it attached to the front of
the laesr head using three M2.5 capscrews, which may already be installed.
If not, they will be in one of the hardware bags or with the beam expander
or adapter ring. The holes in the adapter ring are large enough so that
there is (hopefully) enough adjustment range to center the beam, which must
be done "live" - with the laser powered. Thread the M2.5 screws in just
snug and adjust the centering until the beam is nice and round - this
can also be confirmed by looked at the scatter off the front lens of the
beam expander and centering there. Then tighten the screws just enough
so it won't move around but it is metal in plastic so overtightening may
strip the threads.
The heart of the setup is an assembly using optical
components from Hewlett Packard (HP), Agilent, or Keysight. These may
be configured in a variety of ways to create several types of
interferometers:
HP/Agilent 10702A or 10706A Polarizing Beam Splitter Cube (PBSC).
(The two part numbers are physically and functionally identical except for
the label.) It is a high quality 1 inch PBSC
mounted in a precision stainless steel frame.
HP/Agilent 10703A Cube Corner (CC) retro-reflector. This
is a glass trihedral prism installed in a stainless steel cylidrical case.
It can be attached directly to the PBSC. Not in basic kit.
A pair of HP/Agilent 10722A or equivalent Quarter WavePlates
(QWPs) can also be attached to the PBSC. Not in basic kit.
As a point of interest (or trivia), these parts cost
something like $4,000 if purchased new. Fortunately for us,
eBay is much less expensive. :-)
This assembly is either on a slightly adjustable metal mount (as in the
photo) that gets attached to a precision machined wood block, or attaches
directly to a precision machined wood block with pedestal. They are
functional equivalent since the adjustment capability of the metla mount is
redundant.
Two unmounted glass cube corner retro reflector
trihedral prisms: These can be secured in the
one inch Thorlabs KM100 kinematic mirror mounts with the KM100s rotated
180 degrees so the knobs face the PBSC.
For some of the other interferometer configurations, these will be replaced
either with 1" planar mirrors installed in the KM100s, or with a thinner
mirror glued to a loudspeaker or PZT. (More on these later.)
The turning mirror: is simply a small rectangular high
quality planar first surface aluminized mirror that redirects the
output beam to the detector if needed. The exit direction of the
beam depends on the specific interferometer configuration but most
of them direct the output to the left so to get it to the detector
requires a right angle reflection.
The single channel detector shown in the photo
is a Thorlabs DET110 biased photodiode which generates
a current proportional to the amount of light (i.e., optical power).
It's in a nice shielded case feeding a nice shielded BNC cable
for the output and has its own own battery. It also costs a fortune. ;-)
At 633 nm, the relationship is approximately 0.3 mA / mW of laser power.
An external load resistor sets the sensitivity in terms of V/mW. For
example, with a 10K ohm load resistor, the effective
sensitivity is approximately 3 V / mW. Other commercial
detectors may be substituted for the DET110. But parts are
included in the kit to construct a detector that will serve
the same purpose with essentially the same performance (for
our needs) and can be modified for two channels to
generate both amplitdue and position signals (Quad-Sin-Cos)
outputs for displacement measurements. It just doesn't look
as cool unless perhaps you choose to install it in a
3-D-printed case. :)
Going forward, only parts for this home-built single or two channel
detector will be included in the kits. At the very least, building the
thing is more educational. ;-)
There are either one or two types of Polarizers:
All kits include one or more pieces of Circular Polarizer (CP) which is
a Linear Polarizer (LP) combined with a Quarter WavePlate (QWP). The LP
axis is at 45 degrees to the sides.
Some kits also include a square piece of Linear Polarizer (LP) sheet
with its polarization axis lined up with one of the sides.
The CP type can be used for most purposes in place of an LP. Specifically
here for placing in front of the detector and/or photodiodes. And if using
a random polarized HeNe laser, the CP can be used to force it to be
linearly polarized with the circular polarized output sent to the PBSC,
which works fine. That's why some kits may not have an LP at all. But
where an LP is present, it will probably be larger since the LP is used
for most experiments. Only a very small piece of CP is required for the
Quadrature Detector. For everything else, the LP is simpler to deal with
since which side is the input doesn't matter.
Do NOT remove the protective film until ready to use. Also note that the
CP sheet has a weak adhesive on the QWP surface and it will attract dust and
debris (including grubby fingerprints!) Cleaning can be done with
isopropyl alcohol but the adhesive will still be there when it evaporates.
Only small pieces of these are required for any given purpose so they can be
cut as desired. Four or 9 equal pieces of each is probably a decent choice.
Use masking tape to stick them whever they need to be stuck to. ;-)
A variety of mounting schemes are used:
Laser: As noted above, the laser head cylinder is secured in a
pair of 4-screw adjustable ring mounts so that it can be moved horizontally
and vertically, and have its alignment fine tuned. For the interferometers,
it will need to be positioned at a height of 3-1/4 inches above
the baseplate and either centered or offset approximately 1/4 inch toward
the back of the setup (as shown above) depending on the specific
interferometer being implemented.
PBSC assembly: The mount for this is either a metal platform
attached to a wood block, just a wood block with pedestal.
Wood is just as good as a much more costly metal mount, weighs less,
and can have holes for screws drilled easily. (If it really bothers you
that such a primitive material is used, feel free to paint it
your choice of decorator colors. ;-) But don't get paint on anything
else!) The required pilot holes
for wood screws will already be drilled. ;-) The turning mirror stuck
to an angle bracket with tape or adhesive also attaches to this wood block
with a single screw. The PBS is attached either to an HP 10711A mount
with 4-40 machine screws directly to the wood block with pedestal using
#4 wood screws. The 10711A provides a roll adjustment but that isn't
really needed here as the alignment of the laser and reflectors can have
the same effect.
Interferometer Arm 1: This would normally be the "Reference Arm"
in the basic Linear Interferometer. A CC is installed in a one inch Thorlabs
KM100 adjustable mount on a post in a post holder which allows for height and
rotation about the vertical axis, and also fine adjustment pan and tilt
of the CC itself via the knobs on the KM100. Either a high quality
one inch first surface mirror or a Corner Cube (CC) can install in the KM100.
Interferometer Arm 2: This is what the "Tool" of a displacement
measureing system (for example) would mount on. It has a similar KM100 for a
mirror or CC, but mounted on a micrometer controlled linear stage so that its
position can be adjusted very precisely. A loudspeaker with a mirror
glued to its cone to be used as an electrically driven actuator or as
a laser microphone can also be installed in the KM100.
Detector: There are currently two types of detectors: The
Thorlabs DET110 (or equivalent) and a simple custom single or two channel
detector. Functionally, they are equivalent, but the custom detector can
be easily extended to two channels for providing the Quad-sin-cos displacement
information. They both mount on a Thorlabs post.
Thorlabs DET110: The Thorlabs DET110 is attached to a post on a
post holder on a BA1S "Holddown". That way, it's horizontal position can
be adjusted to accommodate whether the beam is coming from the turning mirror
or direct from the PBSC.
The 3.6x3.6 mm active area of the DET110 is similar in diameter to the
central region of the expanded laser beam.
If a ~1 inch threaded ring is included, it can be used to mount the CP or LP
on the DET110 so it can be rotated easily.
Custom detector: For the kits, this is a small solderless
breadboard (though a prototyping board or even a custom PCB may be
used instead). For the single channel version, a photodiode and its
protection resistor to the bisa supply are installed, along with an LP (or CP
used as an LP) at 45 degrees in front of the PD. For the
interferometer setup, the performance is more than adequate and
indistinguishable from the DET110. And the ~100:1
cost advantage :) makes it likely to be the default going forward.
This same platform will also be used for the quadrature decoder.
The following diagram shows the relationships of the various mounts
for setting the heights during assembly. The specific heights used aren't
critical but 3-1/4 inches places the laser in the center of the rings
vertically:
Original Version 1.0 (Left) and Version 1.5 using Block with Pedestal and Arm 2 on Rail
(Right)
Clicking on this diagram will open a high resolution version in the other
window or tab. The heights of any retro-reflectors in the setup will be
what really determines the beam height. For most configurations, the
critical RR will be the one installed on the PBSC since its height is
not adjustable. So everything will be aligned to that.
The following procedure may be used to install each of the parts and then
get to the point of "first signal" using the oscilloscope. The procedure for
the other interferometers will be virtually identical in most respects, but
may be trickier depending on the type.
It is assumed that nothing has been mounted, but depending on the previous use,
some of these steps have already been completed.
Parts attached with fasterners should be snug but don't overtighten.
It is also assumed that the laser is linearly polarized. Slight
changes are required if it is random polarized.
There are minor differences in the assembly procedure depending on the
version of the kit (V1.0 or V1.5); specifically the mounting of the PBS
and whether Arm 2 uses a rail. These will be address below. The use
of a detector other than the Thorlabs DET110 or equivalent will be dealt
with separately. There will be a separate procedure for V2.0 (coming soon).
Laser mount posts: Attach two 2 inch posts to the breadboard
using 1/4-20 set screws.
If the laser head has a beam expander, or it is anticipated that one will
be added later, it is recommended that the posts be mounts 1 hole to the
left of where the are in the photo.
Note: To assure that there are ample threads engaged in both parts
here and in subsequent steps with set-screws,
the set-screw should be installed approximately half-way
into the baseplate or mounting plate and then a thin tool or
even the edge of a metal plate or stiff cardboard can be used to keep
the set-screw from turning as the post or post holder is threaded onto it
before tightening.
Laser mount rings: Secure to the top of the posts with 8-32 cap
head screws.
Laser head: These steps secure and align the laser head cylinder.
Install the Nylon thumbscrews in the ring mounts if not already present.
If there are two different lengths of thumbscrews (e.g., 1 and 1-1/4 inch),
the longer ones should be in the front side of the rings.
Slip the laser head into the rings. Initially set it to
approximately centered. Then shift it 1/4 inch toward the back
of the baseplate.
Plug the big white male "Alden" connector of the laser head into the
female Alden connector of the power supply. Make sure it is seated fully,
usually against the shoulder with no part of the prongs sticking out.
If the power supply is "lab style" - a chessy plastic box with keylock
switch and power indicator, then it plugs into the AC line. An IEC type
line cord will be included if in the USA; you will have to provide the
approriate like cord if elsewhere. If there is a voltage switch on the
back of the supply, confirm that it is set corretly for your location.
If set wrong, the power supply may be damaged.
If the power supply is a bare "brick", it requires 12, 15, or 24 VDC
from a matching wall adapter that should be included. Confirm that the
voltage ratings match. There may be more than one wall adapter in the
kit that appears similar. Check the labels! Using the wrong one may
damage the brick and/or wall adapter. The wiring is probably
already done via a barrel to screw terminal adapter, but confirm that the
wires are secure and attached to the correct terminals. Positive is red
and negative is black. If there is a yellow wire, it should be attached
to the black wire and thus negative as well.
Power up the laser by turning the keylock switch or plugging in the
wall adapter. It may take a few seconds to light. DO NOT stare
into the beam with your remaining good eye. :-)
Confirm that the laser is polarized: The model number should be 1107P,
1108P, or 05-LHP-211. There should be an alignment mark near the front
of the laser. If not or just to confirm, rotate a LP or LP/CP in front of
the laser. If the laser is polarized, there will be orientations where
virtually no light gets through at all times. Add an alignment mark if
there is none. (If it is random polarized, this
orientation will swap by 90 degrees over a few seconds as the laser
warms up. More on this below in the section on linear versus randon
polarized lasers.) DO NOT assume the yellow arrow of the safety sticker
(if present) identifies the polarization orientation. Check it!
Orient the laser head so the polarization
axis is at +45 degrees (counterclockwise) from vertical when
viewed from the front. What differences will there be if it is at
-45 degrees?
Using the thumbscrews, adjust the position so that the beam is at a height
of exactly 3-1/4 inches (centered vertically in the rings) and perfectly
horizontal, and 1/4 inch toward the back of the setup. DO NOT overtighten
the thumbscrews - just enough so the laser head won't rotate on its own.
Doing this accurately is critical to the ease with which the subsequent
alignnment can be performed since not all mounts have sufficient degrees
of freedom to accomodate an arbitrary beam location and direction.
Fabricating an "alignment plate" out of carboard may be useful. This would
have a hole at the optimal height offest 1/4" toward one side from a
mark at the bottom.
V1.0 or V1.5 with wood block (plain or with pedestral): Secure
the wood block using a 1 inch 1/4-20 cap-head
screw. The location should have the laser beam passing over it 1/4 inch
back of center with the wider part to the left. Carefully align it parallel
to the X-Y axis before tighening the screw. It won't be accessible once
the PBSC is installed.
One inch Polarizing Beam Splitter Cube (PBSC) in stainless steel
frame: This will probably be labeled 10702A or 10706A.
Remove any optics that may be attached to
the PBSC. They will not be required for the LI. Store them wrapped in
soft paper towels, bubble wrap, etc., to protect the optical surfaces.
There are two variations on the PBSC mounting depending on the
design of the wood block:
V1.0 with simple rectangular block: The PBSC may be attached to an
HP 10711A mount or a 1/2" adapter plate. If not, locate the 10711A
or adapter plate and secure the PBSC to it with four 4-40 1-3/4" caphead
screws so the side with the beam path diagram is visible and the "In"
arrow points to the right facing the long dimension of the mount.
Attach the mounted PBSC to the wood block using two 3/4" wood screws.
Center them in the slots with the PBSC aligned with the X-Y axes. The
diagonal of the PBSC should be facing front-left to back-right with the
"In" arrow pointing left-to-right. If it cannot be mounted this way,
rotate the PBSC 90 degrees on its mount.
V1.5 with wood block with pedestal: The PBSC should be attached
with four #4 2 inch wood screws. The diagonal of the PBSC should be facing
front-left to back-right with the "In" arrow pointing left-to-right.
The laser beam should pass through the PBSC centered vertically and 1/4
inch toward the back. It should be at the same location relative to
the breadboard at the far end. If not, fine tune alignment. :) Getting
this dialed in will greatly simplifiy alignment later.
Turning mirror: Use tape or a *tiny* bit of adhesive to attach the
turning mirror to the right angle "Turning Mirror Bracket" centered
vertically with respect to the PBSC and flush with the right edge. Attach
the bracket to the Wood Block with a single 3/4 inch
#5 wood screw in the pilot hole already drilled. If the bracket has an
elongated hole, center the screw for now.
Arm 1: These steps assemble the components of Arm 1.
Attach a 2 inch post holder to the baseplate using a 1/4-20
set-screw.
KM100 or similar mirror mount: Secure to a 2 inch post with an 8-32
3/8 inch cap-head screw. Slip the post into the Arm 1 post holder and
hand tighten the its thumbscrew. Adjust the two alignment knobs so that
the mounting plate is parallel to the base in both directions. If the
adjustments are too tight, check that any locking screws are not tightened.
Else, total removal, cleaning, and lubricating with a tiny amount of
light grease or machine oil will be required.
Cube Corner (CC) trihedral prism: Install a CC in the KM100 with
its apex facing out and oriented so that a flat is at the top or bottom.
It should be secured with either a soft-tipped set-screw
or Nylon wide-head screw. DO NOT overtighten - it should be snug enough not
to fall out (these are fragile!) but not so tight as to smash the CC!
Note that the CCs mount backwards from what might be expected so that their
edge can be secured securely. :) They thus face through the mount.
Adjust the height and orientation of the adjustable mount so that the
return beam hits the PBSC at the same height as the incident beam, and offset
approximately 1/4 inch to the left of center. The spacing between the
centers of the two beams should then be approximately 1/2 inch.
Place a piece of paper where the detector would be for the beam from the
turning mirror. Adjust the orientation and height of the mirror mount
so there is a bright return beam there from Arm 1.
Arm 2: These steps assemble the components of Arm 2.
The first part of the procedure differs slightly for the original
version with the linear stage and adapter plates, and the upgraded
version with the six inch Thorlabe rail:
Orignal version with linear stage and adapter plates:
Attach a 1 inch post holder to the linear stage top adapter
plate using a short 1/4-20 set-screw. The set-screw must not protrude
through the plate.
Attach the plate with post holder to the linear stage via the slots
with two M3x8mm cap head screws.
Attach the linear stage to the bottom adapter plate using four 4-40 1/4
inch screws. It will be necessary to push or adjust the moving part of
the linear stage to access the corner holes.
Secure the bottom adapter plate to the baseplate,
lining it up with a set of holes such that the PLD between the CCs in the
two arms can be adjusted to be zero using the micrometer. Two 1/2 inch
1/4-20 cap-screws are required at diagonal corners, four may be used if
desired.
Adjust the micrometer so the distance to the center of the PBS cube
is the same ±0.1 inch (2.5 mm) for Arms 1 and 2 for a PLD near 0.
Version with rail:
Attach a 1 inch post holder to the Parker linear stage with a 4-40 3/8"
flat head or Philips head screw through the hole in the bottom of the post
holder. The heads of either type screw should be large enough not to
pass through the 1/4-20 hole in the post holder. If it does, a washer will
need to be added.
CAUTION: Make sure the tip of the screw does NOT contact the fixed part of
the linear stage. If it does, an addition washer may need to be added. Or
the screw can be shortened slightly with a metal file or grinding wheel.
Attach the Parker linear stage to the Thorlabs RC1 rail carrier with
a 4-40 3/8" or 1/2" cap head screw slipped through the base
of the linear stage secured with a large #4 washer or standard #5 or
#6 washer and nut.
Add stops at both ends using a 8-32 3/8" cap head screw and #10 washer
positioned as high as possible.
Secure the rail to the baseplate / breadboard with 1/4x20 3/8" cap head
screws in the end holes.
Install the RC1 carrier with Parker stage and post holder onto the rail.
Adjust the micrometer so the stage is approximately in the center of
its travel range.
Position the RC1 carrier so the distance to the center of the PBS cube
is the same ±0.1 inch (~±2.5 mm) for Arms 1 and 2 for a PLD
near 0.
After confirming that the post holder and RC1 fit the stage without
issues, a *small* amount of 5 minute Epoxy may be added between them
to reduce the chance them loosening while adjusting the alignment.
Common to both:
KM100 or similar mirror mount: Secure to a 3/4 inch post with an
8-32 3/8 inch cap-head screw. Slip the post into the Arm 2 post holder and
hand tighten its thumbscrew. Adjust the two alignment knobs so that
the mounting plate is parallel to the base in both directions. If the
adjustments are too tight, check that any locking screws are not tightened.
Else, total removal, cleaning, and lubricating with a tiny amount of
light grease or machine oil will be required.
Cube Corner (CC) trihedral prism: Install the CC in the KM100 with
its apex facing out and oriented to that a flat is at the top or bottom.
(This reduces the change of the beams hitting an edge of the prism.)
It should be secured with either a soft-tipped set-screw
or Nylon wide-head screw. DO NOT overtighten - it should be snug enough not
to fall out (these are fragile!) but not so tight as to smash the CC!
Note that the CCs mount backwards from what might be expected so that their
edge can be secured properly. It's flat surface is facing through the mount.
Adjust the height and orientation so that the return beam
hits the PBSC at the same height as the incident beam, and offset
approximately 1/4 inch to the left of center. The spacing between the
centers of the two beams should then be approximately 1/2 inch.
With the rail setup, this may occur a slight distance below the lowest
possible height of the mirror mount. In that case, raise the laser and
Arm 1 mount by approximatley double that distance. It should be less than
0.1" and will be well within the height adjustment range of the laser and
the clear aperture of the PBSC. If you'd prefer to raise the laser
mounting rings in the interest of purity :), add a few washers between
the rings and posts.
Using your piece of paper, there should now be two spots corresponding
to the returns from Arms 1 and 2.
Adjust the height and orientation of the CCs to superimpose the return
beams from Arm 1 and Arm 2. Fine tuning can be done with the mount knobs.
As a quick test, place a linear polarizer (LP or LP/CP with the
non-adhesive facing the beam) with the polarization axis at 45 degrees in
the combined return beam. If the alignment is close, very slight
rotation of the linear stage micrometer should result in the intensity
varying dramatically. Further fine tuning of the alignment may be required
to maximize the variation and uniformaty of the fring pattern. The
optimal alignment will be where it goes almost totally dark to light.
Of course, much more more can be done using
these simple observations including effects of alignment, expansion using
a lens, display using a Webcam, etc.
Set up the oscilloscope: (If using a USB scope, this assumes that
the required software and device drivers have already been installed on your
PC or MAC.) For input, use one of the scope probes on the 1X setting
(there is a slide switch on its body).
Single Channel Detector: These steps assemble the components of the
fringe detector using the Thorlabs DET110 or home-built equivalent.
Attach a BA1S Holddown to a 2 inch post holder with a 1/4-20 3/8 inch
cap-head screw.
Install a 2 inch post into the post holder with the small (8-32) tapped
hole at the top with the lock screw just snug.
Clamp the assembly down loosely with a 1/4-20 1/2 inch cap head screw.
Thorlabs DET110 (or equivalent) detector: Attach a BNC cable to
the DET110 and the other end with BNC "T" and screw terminal adapter to
Channel 1 of the scope. Jumper wires may be convenient between the scope
probe and screw terminals.
Custom detector: Install a photodiode, 1K ohm resistor, and
male-male jumper wires to the solderless breadboard based on the circuit
in the section: Single Channel Detectors.
install a 10K ohm resistor for R-Load. 10K is probably an
acceptable value but depending on laser power and alignment, a higher
(most likely) or lower resistance may be desirable.
Tape or place a piece of LP or LP/CP to the front of the sensor with its
polarizaiton axis at 45 degrees (edges at 0/90 degrees). If using the CP,
remove the protective film from both sides and the sticky side can be stuck
directly to the DET100 or PD.
Flip the toggle switch on the DET110 to On (up) or apply power to
the home-built detector.
Adjust the position of the detector so that the combined return beams are
centered on the active area of the sensor.
If alignment is close, the amplitude of the signal on the scope should
vary dramatically as the micrometer is rotated by the smallest amount.
The wavelengths of light are TINY! Each full cycle is 1/2 wavelength or
around 316.5 nm. The micrometer moves the stage by 0.5 mm per full
rotation, or around 1,389 nm/degree.
The amplitude can be maximized using the knobs on the KM100s or other
adjustable mounts. The signal amplitude may vary slightly (up to ~20
percent) in a periodic cycle over a time scale of seconds to minutes
in addition to it probably increasing slightly as the laser warms up.
The time scale will depend on how long the HeNe has been on. Why?
There can be several causes.
And for those new to interferometers, the optimal alignment will also be
where the signal instability is maximized. ;-) Almost ANYTHING will
affect it from touching the apparatus or table on which it is on,
to just walking across the floor. The wavelength of light is really
really small. ;-) To put this in
some perspective, a full cycle of the signal with the Linear Interfemeter
is a change in PLD of 316.4 µm (1/2 wavelength of 632.8 nm or
1/3,160th of a mm). That's about 1/158th the
diameter of an average human hair (~50 µm) or 1/22th the diameter
of a human red blood cell (7 µm). Street traffic will be detectable,
as will drafts from the A/C, changes in temperature, and siesmic
events. Some of these effects can be further explored using parts in
these kits.
Now you're set to explore all sorts of exciting aspects of
interferometry. ;-)
The tests above were done with the PLD near 0. What happens otherwise?
If the laser were Single Longidudinal Mode (SLM), the PLD would not matter
up to a very large number in the 100s of meters or more. However, the
laser used in the has 1 or 2 modes depending on its cavity length, which
changes due to thermal expansion during warmup as the modes sweep through
the neon gain curve. (There is much more on this in the section:
Linear polarized versus random polarized laser.)
For the first of the following tests,
the laser must be linearly polarized with its polarization
axis (indicated by the alignment line near the front)
oriented at 45 degrees. If your laser is random polarized, it should
be oriented so the two outer lines near the front are aligned horizontally
and vertically. A CP should be mounted in the beam
with its LP side facing the laser
and its polarization axis at 45 degrees. If the CP is stuck to a
microscope cover slip, this means the LP (shiny) side of the sandwich is
facing the laser and the cover slip is out. *Gently* tape it in place,
cover slips are fragile.
For all these tests, it will be better to shut off the laser for a few minutes
before starting. Then when it is turned on, the mode sweep due to cavity
expansion will be fastest.
Check behavior with the PLD set as close to 0 as possible by
measurements of the distance from the PBSC to the CCs in each arm.
±1 mm will be acceptable. Monitor the
behavior of the detected signal over time by twiddling the micrometer
periodically over a few minutes. Note any significant change in
signal amplitude. A change of 10 or 15 percent can be attributable to
the normal variation in total power during mode sweep and warmup, but anything
more will be due to the interferometer.
The cavity length of the laser tube is around 137.6 mm or 5.417 inches.
One half of this is 68.8 mm or 2.7085 inches.
Change the location of the mirror in Arm 2 so the PLD is within
±1 mm of one half the cavity length by relocating the stage
and/or adjusting its position using the micrometer.
Now observe the fringe signal again and describe what you see
over the course of a few minutes. (Turn off the laser again and
allow it to cool for a few minutes as above.)
Try intermediate locations for the Arm 2 mirror.
If the Arm 1 adjustable mount is positioned as close as possible to the
PBS cube (using a BA1S holddown instead of direct attechment to the
breadboard if necessary) it will be possible to achieve a PLD of at
least the tube cavity length. See how the signal amplitude there compares
with the one with a PLD of 0. If it's noticeably lower, why might that be?
There are several factors involved.
Now explain the behevior in each case. And what is special about a PLD of
zero and one half the cavity length?
If your laser is random polarized, it is possible to perform the following
additional tests with the CP removed from the front of the laser:
Repeat the above tests with the laser oriented so the outer lines are
aligned with the horizontal and vertical axes.
Repeat with the lines on the laser oriented at ±45 degrees.
Explain your results with respect to the longitudinal mode behavior.
What would happen if the PLD could be extended to more than the cavity length
of the laser?
All of these tests can also be done with the other interferometer
configurations. Predict how the results would change, if at all.
High Stability Plane Mirror Interferometer (HSPMI)
The basic Plane Mirror Interferometer (PMI) as its name implies uses a
plane mirror instead of a cube corner for the remote reflector. It has
a double pass architecture which halves the distance for a full fringe
cycle at the detector for a movement of the reflector in
Arm 2 (called the "measurement arm"). However, it is not
desirable to use a PMI here because it
is double-pass only for Arm 2 but single pass for Arm 1. Thus
while the PLD can be set to zero, the spacings or lengths of the
two arms (as well as the change in displacement) are not the same,
which at the very least is confusing. (More on this in the section
on the PMI.)
The HSPMI on the other hand is perfectly symmetric: The beam paths for both
Arms 1 and 2 are double pass and go through the CC. However, the change
in PLD is double the change in position of the mirror in either arm. Thus
it could also be used as a differential HSPMI where the relative displacement
of Arms 1 and 2 is to be measured.
Normally, the Arm 1 mirror would be mounted along with the QWP on the PBSC
as the reference since absolute PLD doesn't matter with the single
frequency or two frequency lasers used in metrology applications.
But as with the LI, we need the PLD to be close to zero or ohter specific
value for experiments using a multi-longitudinal mode laser. (The "other
specific value" would normally be a small integer multiple of the laser's
internal cavity length. Why?)
As with the LI, above, the designations m-n show the paths taken by the
Arm 1 and Arm 2 beams where "m" is the Arm and "n" is the sequence number.
Assuming the LI was already built, not many changes/additions are required:
Install the HP retro-reflector (10703A) on the PBSC face closest to the
detector. The orientation should be such that the beam doesn't hit an apex.
This usually means the serial number (if present) runs up and down.
Install QWPs (HPO 10722A or unmarked) on the faces toward the Arms. Their
orientation does not matter as long as the screw slots are used.
Replace the unmounted cube corner retro-reflectors with circular
1" planar mirrors. The mirror mounts can be rotated 180 degrees to make
them easier to adjust.
Adjust the location of the Arm 2 planar mirror so that the PLD is close
to zero. Since the Arm 1 and Arm 2 beam paths are identical,
distances from the mirrors to the faces of the PBSC block can be used.
Alignment will be similar to that for the LI, differ in some respects
due to the planar mirrors and double pass architecture:
Adjustment will be more finicky. This includes setup at a PLD of
0 as well as with respect to changes in PLD. While grabbing and
manipulating the entire mirror mounts may be acceptable for the LI,
the knobs should probably be used for the HSPMI. Why?
The signal level will be lower by as much as a factor of 2 or more.
Trace the beam paths and compare them to those of the LI.
A loudspeaker consists of a coil of fine wire ("voice coil") on a cardboard
form suspended within the field of a strong magnet in such a way that it
can only move along its axis. This is attached to the speaker cone.
Applying a voltage to the voice coil moves the cone in or out
depending on polarity.
The mini loudspeaker 4 ohm woofer can move its cone a couple of mm with
1.5 V at 0.375 A. But for these tests, it only needs to move a few µm.
One of the interferometer configurations using planar mirrors must be
used for this since it's not practical to attach a cube corner to the
loudspeaker. The HSPMI is recommended.
To use it:
The 1 inch diameter 1/4 inch thick "Speaker Mounting Disk"
should be glued to the back of the loudspeaker with Epoxy. This will permit
it to be installed in a KM100 mount just like a 1 inch diameter mirror.
One of the small mirrors should be attached to the front of the
loudspeaker with the tiniest of tiny dots of Epoxy at the corners.
as shown below. Position it to be as parallel as possible to the
loudspeaker frame.
For seeing how its movement will affect the interferometer,
the loudspeaker can be driven with a 1.5 V battery (not included) and
series resistor. Even with a fairly high resistor value like 10K ohms,
the mirror will move decent amount, probably much more than one fringe
cycle. Or it can be driven through a resistor via the 10K ohm potentiometer
and 10K ohm series resistor from a 9 V battery or 12 VDC power supply.
+ o--------+
|
Battery / 10K
or Power 10K \<---/\/\---> +
Supply /
\ Loudspeaker
|
- o--------+-----------> -
Calculate the sensitivity of movement in nm with respect to loudspeaker
voice coil current.
DO NOT connect the loudspeaker directly to the
12 VDC power supply or 9 V battery as they both may be damaged or destroyed.
No more than 1.5 V should ever be applied to the speaker. This can be
done using a series resistor between it and the power supply or battery
or with the potentiometer and series resistor as shown above.
Only a very small current will be needed to move the mirror enough to
be readily detected and it won't be visible by eye.
An electronic function generator with simple buffer amplifier and current
limiting resistor can also be used to drive the loudspeaker over a larger
range as long as the voltage to
the loudspeaker doesn't exceed around 1.5 V. With a triangle wave and
µMD0, it should be possible to demonstrate the linearity (or
non-linearity) of the loudspeaker cone with respect to voltage.
The loudspeaker will also be sensitive as a microphone so monitoring the
detector output on the scope should result in a fairly sensitive response to
voice and music, though the frequency response will be terrible due to the
large mass of the mirror. Input that to the line input of a stereo system
and listen to it on headphones. Why? The quality will be terrible but it
will demonstrate possibly the most complex way of going from acoustic
sound to electronic sound. ;-)
A PieZo Transducer (PZT) can be used to move
a mirror where only a small displacement is required.
(The acronym PZT is actually based on the active material which deforms
as a function of voltage,
an inorganic compound of Lead (Pb), Zirconium (Zr), Titanium (Ti),
and oxygen). Look it up. But our abbreviation is easier to remember. ;-)
The PZT beeper element in the kit is 27 mm in diameter with an active area
of around 20 mm in diameter. It is what's called a "drum head" PZT because the
surface moves in and out at its center when a voltage is applied.
It can move a few µm with 15 V at essentially no current - it
has some capacitance but an infinite resistance, which for slow movement
is all that matters.
As with the loudspeaker, one of the interferometer configurations using
planar mirrors must be used for this since it's not practical to attach
a cube corner to the PZT. The HSPMI is recommended.
A small platform should be fashioned from a washer or something similar so
that one of the small mirrors can be glued to the center ONLY of the PZT.
This is necessary because a large mounting area may impede its movement.
The PZT can be mounted directly on one of the KM100s with three tiny
dots of Epoxy around the edges, or taped in place. Take care attaching
the wires as the solder connections are fragile. Putting a small amount
of Epoxy over them (but only in their vicinity so as not to impede
movement) would be useful.
A 9 V battery or the 12 VDC power supply can be used along with the 10K ohm
potentiometer to vary its voltage:
+ o--------+
|
Battery / 10K
or Power 10K \<---/\/\/\---> +
Supply /
\ PZT
|
- o--------+-------------> -
(The 10K ohm series resistor is not required for the PZT but using it makes
the circuit identical and safe for the speaker.)
Calculate the sensitivity of mirror movement in nm with respect to PZT voltage.
As with the speaker, an electronic function generator
can be used to drive the PZT. With a typical output voltage swing of
20 V peak-peak, the change in position will be several
wavelengths. By using a triangle wave and µMD0, it should be possible
to observe how good the linearity of movement of the PZT is with
respect to voltage, though there will be fewer full cycles compared
to the speaker.
Or it can driven from the loudspeaker output of an audio amplifier through
a step-up transformer.
The PZT may be sensitive enough to act as a microphone as well.
This may be the niftiest experiment and demonstrates the sensitivity of the
interferometer to changes in the index of refraction of air.
It may be done using any of the interferometer configurations, though the
sensitivity will depend on which one is used.
The concept is that an increase in air pressure will change its index
of refraction, and while this is totally invisible to the human eye, the
interferometer should be able to easily detect it as a shift in the
fringe signal. In fact many fringe cycles even for a space of a couple
inches. With some simple calculations, it is possible to
corelate the pressure reading on the gauge with the phase change of
the fringe signal. If it's sealed well enough, even warming the
gas cell by holding it tightly should result in a detectable fringe
shift. However, doing that without introducing vibrations that
totally swamp any change due to the expansion would be a challenge.
The Gas Cell Compensator (GCC) consists of a ~2 inch length of 1" inch OD
Acrylic tube, a pair of planar windows sealed to the ends,
the pressure bulb and gauge for a blood pressure cuff
(sphygmomanometer), and some simple plumbing. It can mount on a Thorlabs
post and post holder using a BA1S hold-down.
GCC Assembly:
The Acrylic tube will already be cut to length and drilled and
tapped for the 10/32 hose barb and 8-32 set-screw to attach it to
a Thorlabs post. The ends will have been ground to be close enough
for government work. :) They don't need to be perfectly perpendicular
to the tube or parallel to each-other. Nor do they need be polished - the
rough cut surface is better for gluing. Only that they can seal to
the windows.
The windows are 1-1/8 inch in diameter and made of either glass or Acrylic.
The Acrylic will have paper protective brown paper on both sides.
If there is more than one hose barb with threads, one of them may
have the threads shortened so as not to protrude inside the Acrylic cylinder.
Partially thread it into its 10-32 hole. Mix
the tiniest amount of 5 minute Epoxy and apply it to the exposed threads.
Then rotate it clockwise until fully seated. Wipe off any excess Epoxy
and allow time to cure.
Apply a small amount of the remaining Epoxy to the threads of a 8-32
1/2" set-screw. Intstall it in the 8-32 tapped hole so that no more
3/8" is exposed. Apply some more Epoxy at the threads where they meet the
tube. (Since this one is vertical and can't interfere with the beams, some
portion of it protruding inside the Acrylic tube is OK. Add
an 8-32 nut as shown in the diagram for added strength with the Epoxy
joining the nut to the cylinder.
Clean one window end one end of the 2" tube with
alcohol if available. Soap and water is also acceptable. DO NOT use
anything stronger. Make sure it is completely dry and dust-free by
shining a bright light through it before proceeding. Repeat as needed.
Carefully place the tube on top of the cleaned window. Put a weight
on top of it or use some other means to prevent it from moving accidentally.
Prepare a small amount of 5 minute Epoxy and apply the tiniest
bead all around the outside of the joint between the 2" tube
and window.
Avoid getting any Epoxy inside the tube, especially
on the windows, as much of their area may need to be unobstructed
depending on the type of interferometer and/or whether the laser has
a beam expander.
If it gets messed up before curing, the Epoxy can be careully wiped off and
then the glass and/or Acrylic can be cleaned with alcohol (but nothing
stronger!). After curing, a single edge razor blade can be used to remove
Epoxy, then cleaned with alcohol. Take care to avoid scratching the
window(s).
Repeat the previous three steps for the other end. A cotton swab can
still be used to clean the previously attached window if necessary.
It's especially important that the inner surfaces of both windows
be clean as they will be inaccessible once the second window is installed.
Wait an hour or so before proceeding to allow the Epoxy to fully cure.
Connect the hose barb on the tube with the pressure gauge and bulb
using the rubber tubing. Test to confirm the connections are reasonably
gas-tight and correct if necessary. For this experiment, a small leak
may be preferred as it will allow for a controlled pressure decline which
can be used to correlate with the fringe signal.
The photo on the left shows the prototype using a 3/4" OD PVC tube
installed in Arm 1 of the interferometer. The ends are covered with
pieces of heat shrink to hide the ugly cut microscope slide windows.
Yours will be (1) shorter, (2) made of 1" OD clear Acrylic (Plexiglas)
instead of PVC, (3) use circular windows, and (4)
hopefully nicer looking when completed. ;-)
The photo on the right shows the complete setup (with the extended PLD rail
option) and a scope trace with showing the GCC loosing presure some of its
pressure over 20 seconds or so.
Closeup of GCC Assembly using a Piece of PVC Pipe (left),
Overall Setup Showing the Fringe Signal as the Pressure Declines
Note: If doing this using one of the plane mirror interferometers, the
Arm 1 mirror mount may need to face away from the PBSC (with the mirror
installed backwards) as with the CCs in the LI to provide enough clearance
for the GCC. Then adjust the Arm 2 mirror position so the PLD is 0.
The blood pressure gauge reads up to 300 mm/Hg (almost 6 psi),
but there should be no need to go anywhere near the
extreme hypertension region for these tests! :) 100 mm/Hg will be more
than enough.
The gas cell can be mounted in either arm of the interferometer, though
using Arm 1 is probably better as it has nothing else. It can be positioned
so that either one or both beams (where present) pass through it. (How
will this change the calculations?) Avoid
aligning the gas cell so that the windows are perfectly perpendicular
to the beam paths - angle it slightly so the reflections from the surfaces
of the windows do not coincide with the main beams.
The Arm 1 and Arm 2 path lengths should be set as close to equal as possible
for these experiments taking into consideration the increase in optical
path length due to the 1 mm glass microscope slide windows. How much does
this affect the total path length?
Fine tune the alignment of the interferometer to maximize signal amplitude.
Close the bleeder valve and slowly pump up the bulb while watching the
scope display and pressure gauge. The index of refraction, n, will be
approximately equal to 1 + P * k. By measuring the number of cycles and
partial cycles as the pressure is changed, it is possible to calculate k.
Check it against a value found in a search. Why might it not be the same?
Knowing k, an arbitrary pressure can be measured with the interferometer.
Based on the NIST
Refractive Index of Air Calculator using Ciddor Equation, the index
of refraction of air at 1 atm (760 mm/Hg), 20°C, and 50%RH, is 1.000271372.
As an example, at a pressure above 1 atm of 100 mm/Hg, it is 1.00030715.
What is the value of "k"? Over
the 3 inches (76.2 mm) inside the GCC, the change in path length is
approximately 2.73 µm or 4.31 full wavelengths at 633 nm. You
can complete the calculations. ;-) Perform the test with 100 mm/Hg
and your favorite interferometer configuration. Explain your results.
What are the possible sources of error? Hint: What effect will reflections
from the parallel surfaces of the windows have on transmission?
You might be wondering if it would be possible for the interferometer to
act as a microphone using only the change in air pressure from sound waves
in one arm. This could be done in principle, but the sensitivity would be
extremely poor. In fact to get a detectable response from the Thorlabs DET110
due only to the air pressure variations
would require sound levels similar to what might be found a few feet from a
jet engine or directly in front of the loudspeaker array at a rock concert.
Of course the entire interferometer would be vibrating (assuming it didn't
totally disintegrate) and that would dominate any response.
Original equipment human ears are extremely sensitive. ;-)
See, for example: Engineering
Toolbox: Sound Pressure.
This shows how a change in temperature of an object undetectable by
eye can produce a noticeable effect if in one arm of the
interferometer. A glass block with two polished surfaces actually
called a "compensator plate" is included in the kit, along with 1 or 2
power resistors to heat it.
It may be done using any of the interferometer configurations, though the
sensitivity will depend on which one is used.
Thermal Assembly Assembly:
Thread the wood chip (~1x2x3/16" block) with 8-32 stud into a Thorlabs
post and install it in a post holder attached to the breadboard for
convenience in mounting the other parts. (V2.0 dimensions ~1x1-1/4x1/4".)
There are either two 10 ohm power resistors or one 25 ohm power resistor.
Use a drop of Epoxy to secure one of the resistors to the wood chip
using its flat unlabeled surface. There may be some
Epoxy residue from a previous life but this shouldn't affect anything.
Wait at least 15 minutes for the Epoxy to cure.
Use a drop of Epoxy to secure a long frosted surface of the compensator
plate to the top (labeled side)
of the power resistor. Wait at least 15 minutes for
the Epoxy to cure.
If there is a second resistor, attach its flat unlabeled side
to the top of the compensator plate with another drop of Epoxy.
Wait at least 15 minutes for the Epoxy to cure.
This stack can then be installed in Arm 1 of the interferometer using
a Thorlabs 1" or 1.5" post, post holder, and BA1S Holddown. Angle the
broad polished faces of the compensator plate very slightly to avoid
back-reflections into the beam paths.
The 12 VDC power pack is used to do the heating. DO NOT use a 9 V battery,
it won't last very long. The power into the resistor(s) is 12*12/R - 7.2 or
5.76 watts for the 2x10 ohm or 25 ohm resistors, respectively.
The Coefficient of Thermal Expansion (CTE) for optical glass is
around 8x10-6/°C. (It varies slightly depending on
the specific type, which is not known for the compensator block.) That means
a 1 °C change in temperature will result in its length changing by 8 ppm
(parts per million or 0.000008 x its length).
Assume that the index of refraction of optical glass, ng,
is approximately 1.5. (Again not precisely known .)
Calculate the expected number of full cycles from the detector
for a 10 °C change in block
temperature. Don't forget that it's the net change in PLD
that matters.
Monitor the fringe signal as the block heats or cools and use the results
above to estimate the temperature of the glass block based on its length.
Without actually knowing the temperature of the block throughout its
volume, and knowing it actual CTE and ng. it is not possible
to be precise. That's OK.
The effect will not be as dramatic as with the GCC, above, but with care,
should be easily detectable.
CAUTION: Do NOT leave the resistors plugged into the power pack continuously
for too long as bad things may happen.
What else may be impacting the PLD change besides
the block itself? For example, is there any detectable response to
the heating if the block is rotated and/or offset so it just
misses both beams?
This one may be a bit more challenging but no additional special parts
are required. (And it's related to the last question, above.)
The index of refraction of air, n, varies by just under -1 ppm/°C.
Or more precisely, according to the same NIST Web site,
-9.517x10-7.
So heated air in one of the interferometer arms should change the
path length due to its change in n.
This can be tested with the same Gas Cell Compensator assembly and
interferometer configuration used
for the air pressure measurements. Heat it with a blow dryer with the
inlet port unplugged from the hose so that the pressure won't be affected.
Do this well away from in the interferometer to avoid heating other
components. Then quickly install it in Arm 1 and wait a few seconds for
the vibrations to die away. Watch the signal as its temperature
(and that of the air inside) declines.
The heating could also be put into an oven on LOW.
Just don't get it so hot that the Epoxy decomposes (which could be as
low as 160 °C). :( :) While the sensitivity of n with
respect to temperature compared to the effect on the glass block is
around 1/10th as great, the GCC is ~5 times as long, so it should still
produce an easily detectable signal.
Note that the expansion of the Acrylic cylinder itself is not a significant
factor for these measurements. Why?
In addition to temperature and pressure, other gases mixed in with air.
or in pure form affect the index of refraction. A variety of common
substances have a significantly higher index of refraction than air and
thus could result in a detectable effect even at low percentages of
partial pressure. These include carbon dioxide, acetone, alcohol,
chloroform, and ether. Thus, if one of these is introduced into an
arm of the interferometer, there should be a detectable change in PLD.
It's probably not a good idea to be messing with chloroform or ether,
and even acetone has its risks (both to bodily internal organs and
to plastics including acrylic), but certainly CO2 (from carbonated
beverages, a CO2 gas canister, or even exhaled breath) and isopropyl
(rubbing or medicinal) alcohol or ethyl alcohol (wine, whiskey)
can be suitable for tests. :-)
Parts to do these tests are not included in the kits, but with a bit of
resourcefulness, it should be possible to provide a suitable vessel
either for a gas or liquid (with its vapors actually being what's
measured). The Gas Cell Compensator, above, can also be used for
this purpose if a way is devised to fill it with the test gas, for
example by adding a second hose barb so there are entry and exit ports.
Inexpensive glass cuvettes with polished parallel sides would make suitable
containers to introduce liquids, or with an improvised cover, gases, without
the need for additional plumbing.
Cuvettes are typically 1 cm wide but may be up to 5 cm or more in length.
1 cm is not enough width for both beams in an arm to fit and the length
is desirable to maximize the sensitivity. So, two cuvettes side-by-side
may be needed. Or a custom cuvette could be constructed from pieces of
microscope slides sealed with RTV Silicone.
As a simple test, start with the cuvette(s) being empty and allow the
interferometer to come to thermal equilibrium. Then carefully add some alcohol
(at the same temperature and filled to below the level of the beam)
and watch the fringe signal as vapors come off the liquid.
Mounting the cuvette(s) on the power resistor heater could allow the effects
of temperature to be explored either with a liquid or gas. But interpreting
the results may be more complex than it appears at first.
More on this is left as an exercise for the student's imagination. ;-)
If you have successfully constructed any of the interferometers, it will have
been obvious that avoiding generating a varying fringe signal due to vibrations
is a challenge even if the entire setup is on a stone countertop. :)
But what about actually enhancing this effect? The mirror on the loudspeaker
does that to some extent. However, by mounting one of the reflectors (cube
corner or mirror) remotely, it will be possible to easily detect someone
walking across the room or a truck going down the street a block away.
Or an earthquake.
For these experiments where one of the arms is of considerable length,
the beam expander will need to be mounted on the laser. Without it, the
beam would expand too much to be useful. Also, for the unstabilized
HeNe laser, rather than making the
PLD zero, it will need to be a multiple of the laser tube cavity length,
around 137.6 mm or 5.417 inches for the JDSU 1107/P or 1108/P. But don't
get carried away putting the reflector 25 meters away. Remote alignment
will be a large challenge at the very least. And with every additional
increment of the tube cavity length, the signal will degrade.
(Measuring this may in itself be an interesting exercise.)
Start with perhaps 0.5 meter
plus or minus whatever is needed for the PLD to be 0 mod(137.6 mm).
The optimal distance may best be found by maximizing the fringe amplitude.
The remote reflector should preferably be mounted on a separate structure,
not the same table as the rest of the setup. Another table or wall,
for example. Or even suspended by springs or wires.
Either arm can be extended but using Arm 2 with the
linear stage may be simpler for mounting to a slab of wood or aluminum.
A displacement measuring system would be ideal. Using µMD0, it
would be possible to record data and (with some simple formatting in
Excel) then display it like a seismograph. But just watching the
fringe signal on the scope should provide some valuable insight into
what's going on. Not only vibrations, but temperature changes and
even air convection should be detectable.
Variations on the basic interferometers can be used to sense tilt (angle),
lateral movement (straightness), deviation from right angle (squareness),
and others. See Optics for
Interferometers Using Two-Frequency Lasers. The same optics
can be used with single frequency lasers.
There are some other variations on the Michelson interferometer that may
be put together using parts in this kit, starting with the original form
of the Michelson Interferometer.
This is identical to the original except that it uses the polarized laser
and PBS cube as the beam-splitter. But note that the PBS passes and reflects
the X (parallel to the baseplate) and Y (orthogonal to the baseplate)
polarized components and they retrace their steps on the return
journey. Thus a Non-Polarizing Beam-Splitter (NPBS) must be inserted to pick
off both of them before passing through the linear polarizer at 45 degrees
to combine them for the detector.
The NPBS can be the variable Attenuator Plate (AP) that is part of the
quadrature decoder, but mounting it and determination of the optimal
attenuation is left as an exercise for the student.
Without the cube corners and/or QWPs to separate the outgoing and return
beams, everything will be jumbled together and there will be back-reflections
directly to the laser. This won't cause damage but there could be serious
instability in the resulting behavior. However, with a polarized HeNe, the
effects may not be detectable either visually or even in the fringe signal.
But for a random polarized laser, the result would be mode polarization
switching, which could reak havoc with the signal.
The NRRPMI minimizes the required
size of the optical components but with no retro-reflector,
will require very precise in
alignment during setup to maintain a usable signal with any significant
movement. It is most similar to the original Michelson interferometer but
the addition of the QWPs avoids (most) back-reflections to the laser.
The PMI is probably the most common of the interferometers that use a planar
mirror.
However, it is asymmetric in terms of the beam paths. The reference (Arm 1)
is single pass while the measurement (Arm 2) is double pass. To achieve a
PLD close to 0 - required for the non-single mode laser - the positions of
the two reflectors must differ significantly.
Note how close the mirror on the stage is to the PBSC in the diagram - and
that may not even be close enough for the paths to be equal!
For this reason, while the PMI is widely used, the HSPMI is recommended as the
one to be built after the LI.
This is commonly used where space is tight since it doesn't require two
offset beams. Normally, much smaller PBSC and CCs could and would be used.
As with the NRRPMI, above, the use of the QWPs avoids most back-reflections
to the laser.
The MLI adds a pair of QWPs to direct the beam to the detector out the side
of the PBSC and is achitecturally similar to the SBI but with offset beam
paths that have two additional advantages: (1) retro-reflections back to
the laser are reduced further and (2) the beams don't hit the apex or
edges of the cube corner trihedral prisms. However, only under very
specific cercumstances would the additional cost of the QWPs likely
be justified.
The remote reflector is a cube corner which is better for long distances
yet it has double the resolution of the normal LI, the same as the PMI.
The signal level may be even lower than with the PMI since the CCs are
slightly lossier than planar mirrors. A single pass
through the silver coated CCs is ~86% resulting in a
net transmission of ~74% since there are two passes.
For the planar mirrors these values are closer to 90% and 81%, respectively.
The CCs also mess slightly with the polarization. With linearly polarized
light, the plane of polarization is rotated by ~±10 degrees depending
on which set of internal surfaces are involved. What the effect is on
the circularly polarized light is not known.
What would be the effect if only one of the QWPs were present in Arm 1 or
Arm 2? Try it!
This doubles the resolution over the PMI or HSPMI. The HRPMI is also
high stability because the two beam paths have the same length through
the optics, and a PLD of 0 if the distance in Arm 1 and Arm 2 are the
matched. This will be much more complext to align and may require
additional parts and determination. ;-)
The HRPMI is essentially an HSPMI in which instead of the return beam
going to the detector, it is reflected back into the interferometer, but
offset in position by an additional cube corner, so it traverses all of
the optics a second time. So instead of 2 passes, it becomes 4 passes.
In principle, this could be extended to 6 or more passes using a similar
approach, but as you will undoubtedly see if you're crazy enough to attempt
to implement the HRPMI, that will be tough enough to align.
Drawing the detailed beam paths for the HRPMI showing how the photons
are routed would be more work than it's worth. But since it is
equivalent to the HP/Agilent/Keysight 10716A, a Web search will
find information, but no need to bother Google, get it at
HP/Agilent/Keysight
10716A High Resolution Plane Mirror Interferometer.
However, the 10716A is normally used with a two
frequency laser for heterodyne interferometry. So, wherever it refers to
"ΔF", replace that with "ΔΦ" since we are changing the
phase rather than the frequency.
The HRPMI setup requires some additional optics (another turning mirror
and adjustable mount for an unmounted cube corner). The only way to
really test it without a measurement display would be with one of the
methods of fine tuning path length - loudspeaker, PZT, air pressure,
tmperature, etc. The micrometer stage will simply not have fine enough
control to reliably detect a difference between X1 or X4. Thus the
setup is shown with the loudspeaker.
Although drawn with all the beam paths in a plane, it is possible to
implement it in 3-D as a 2x2 array within the PBSC by carefully
offsetting the cube corners (as is done in the actual 10716A).
Consider everything about the HRPMI to be a challenge. :-)
This question inevitably comes up with interferometers where visible fringes
are produced. Where does the light go that would be in the dark spaces?
In principle, with perfect alignment, a visible display could be totally
bright or totally dark. It is possible to demonstrate this here
by viewing the fringe display directly on a screen behind a linear polarizer
oriented at 45 degrees. And by rotating the LP between +45 degrees and -45
degrees, it would go between light and dark.
The analog with the signal is that it can be high
or low. But since the laser is still lasing and with no polarizer in front
of the detector, the detected signal is more or less constant. So when the
signal is low (or the spot is dark),
where is the missing power? I'll save you some of your brain
cycles and state that with the LP film, it's lost in the plastic
and actually increases its temperature a miniscule amount.
But what about a Polarizing Beam-Splitter (PBS) like the large one that is
the heart of this setup? They have negligible losses and
it would be simple in principle to use one
in place of the LP film. To do that, either the PBSC would need to be
rotated 45 degrees or the polarization of the beam would need to be
rotated 45 degrees so that the PBS can generate the two polarized outputs.
Rotating the polarization of the beam
can be done with a Half WavePlate, but there is none in the kit, believe
it or not. ;-) However,
it can be simulated using two pieces of LP film and the Attenuator Plate
(AP) as a Non-Polarizing Beam-Splitter (NPBS). This isn't quite identical
because there will still be losses in the LPs, but if oriented at ±45
degrees, the effect will be the same.
Dual Polarization Detector using LPs at ±45
Degrees
This uses the same CP as the quad decoder but for these experiments,
the QWP portion is totally irrelevant and the QWP (sticky) side goes toward
the photodiodes for both.
It should be pretty obvious what is going to happen, but seeing it is not
quite the same as theory. ;-)
The basic detector using a single photodiode like the DET110 can generate a
signal corresponding to light and dark fringes, but cannot provide direction
information, essential for using an interferometer in metrology applications.
The Quad-Sin-Cos decoder provides a pair of outputs that are 90 degrees offset
from each-other in position, similar to the outputs of a rotary or linear
encoder:
This show a rotary optical encoder which uses a pair of LEDs and
photodiodes physically offset by 90 degrees to generate Quad-Sin-Cos analog
signals which are then thresholded to yield Quad-A-B digital signals.
The specific type of sequence is called a "Gray" code (not based on color
but attibutable to someone named Frank Gray) and has the property that any
possible allowable change in value is a change in only a single bit.
This eliminates the ambiguity with sensors using the normal binary order
where two bits can change at not quite the same time.
(The animated encoder graphic seems to be all over the Web. If anyone knows
who the original copyright holder is, I will acknowledge them.)
Many other types of encoders produce similar signals. They may use
optical, mechanical, or magnetic sensing, among others.
An interferometer with angled paths for the two interfering beams produces
fringes similar to the pattern of an optical encoder so a quad detector
could be built with offset photodiodes. However, more commonly, the
90 degree phase shift is done optically using a single combined beam
as shown below. If thresholded and converted to digital form, the
result would be a Quad-A-B format.
This shows variations on one
of several common implementations for a Quad-Sin-Cos decoder
that provides Sine and Cosine outputs for use in a displacement measuring
system. This is among the simplest. In most instances, the photodiodes
would be reverse biased to provide a linear response. It may be possible to
get away without that for initial testing but it will probably be needed if
doing anything useful with the outputs. In addition, a third "Intensity"
channel is almost always included to accommodate variations in detected power
due to the laser aging, changes in alignment, and contamination over time. The
Intensity channel can be implemented electronically or optically with a
non-polarizing beam-splitter at the input and additional photodiode.
The output signals from these will be close to sinusoidal with a relative
phase close to plus or minus 90 degrees depending on the.
direction of motion of the remote reflector or ring laser gyro.
The purpose of the angled arrangement is to minimize the difference between
the amplitudes of the two polarizations. Otherwise, with 45 degrees being
close to the Brewster angle (around 57 degrees), one will be much larger
than the other. Even so-called 50:50 beam-splitters may be subject to this,
so using the angled arrangement for either one may be beneficial. The
parts for the version using the Attenuator Plate (AP)
are what are in the kit, which simplifies
construction. Using the AP also permits the relative amplitudes of the
Channel A and B signals to be balanced without electronic adjustments.
Some resourcefulness will be required to mount the parts in this kit to
put together a Quad-Sin-Cos decoder. A variable attenuator plate is
included that may be used as the NPBS. Pieces of CP will be satisfactory
for both the combination of the LP+QWP (since that's exactly what the
CP is), as well as the LP (flipped) since the output polarization doesn't
affect PD behavior. See the information on polarization, below.
This would be a great excuse to finally make good use of
that 3-D printer sitting idle. ;-) A simple
frame could be designed to mount the AP via its spring and screw so its
position, and thus reflection and transmission,
would be adjustable in the beam. Slots and/or faces
would be used to attach the pieces of CP and the PDs. Be creative!
This is probably overkill though.
Quadrature Detector using Variable Attenuator Plate
and Circular Polarizer Sheets. Optical Layout, Parts), Constructed on Solderless Breadboard, Protoboard, and PCB Assembly
These photos show a diagram for the preferred implementation of the
Quad decoder itself, the typical parts, and 3 perfectly workable
construction options, the first of which uses a
small solderless breadboard and doesn't require any soldering. For that one,
the AP and pieces of CP sheet could be glued to wires that would be stuck in
holes. Or U-shaped pieces of wire could simply be stuck in holes to keep
the CPs and AP in place. ;-)
Before constructing the prototype or PCB versions, it was dedirable to
to conclusively prove that the simple Type 3 scheme with CPs for the
polarization optics actually worked as advertised, so
a prototype version was installed on the Michelson Interferometer test-bed:
In the interest of expediency, it cheats and used an NPBS rather than a
plate beam-splitter or variable attenuator, two Thorlabs DET110s rather
than bare photodiodes, but the QWP+LP for Channel B
is a piece of CP (as in the diagram on the right, above) stuck to
a microscope cover slip that is glued to a platter clamping ring
from an ancient defunct harddrive. Got that? :)
The ugly scope screen shots below were taken using this setup:
Displacement Positive (Left) and Negative (Right)
Capturing a decent photo while twiddling the micrometer screw is quite
challenging. ;-) But the conclusions are clear: This simple Quad decoder
does its job well with a phase shift of ±90 degrees. If the Arm 2
mirror or retro-reflector were on an electronically controlled positioner
like a loudspeaker voice coil or linear motor driven with a ramp, the waveforms
would be textbook quality. ;-) But with only a small stretch of the
imagination, it can be seen that the screenshots agree with the expected
behavior based on the diagrams, above.
The prototype on a prototyping board was then constructed and tested to
confirm similar behavior, and then the simple PCB was made so that mounting
of the photodiodes and other electrical components would be simplified. There
is nothing to really secure the AP/BS but that could be done with
double-sided tape.
Constructing the Quad-Sin-Cos Detector
The mounting scheme doesn't need to be fancy or pretty but should hold the
pieces securely while maintaining alignment. This can use bits of tape and
Epoxy or other adhesive. The CPs, QWPs, and NPBS plate are expendible so
feel free to chop them up if necessary for them to fit. :)
The photos above show various possibilities not involving a 3-D printer :),
including a simple PCB (which is available), but some soldering is required
for that. The simplest approach is to use the same Solderless Breadboard (SB)
as the Single Channel Detector, attached to the post using the Detector
Adapter Plate as in this closeup:
Set up the HeNe laser so that there is a linearly polarized beam.
Orient the polarization to be at 45 degrees or preferably, the
output of the interferometer as well.
Mount the AP at an angle as close to normal to the incident beam
as is convenient to still be able to locate the Channel B CP and PD
in the reflected beam. The rational for this is to minimize the
effect of the angled plate on the polarization of the reflected and
transmitted beams. Why? If you're into fancy 3-D-printed mounts,
it can be arranged to use the screw/spring
combination to adjust it's position, and thus attenuation (or
transmission and reflection). But that certainly is not required and
the screw and spring can be relegated to your junk drawer. ;-)
Mount one PD to intercept the transmitted beam. (This will be
designated Channel A or 1.)
Trim the leads if necessary so that in conjunction with adjusting the
height of the platform, the beam can be approximately centered
vertically in the AP.
Adjust the position of the AP
so that the transmitted and reflected beam intensities are
approximately equal. This will be near or at the higher-density end
of the AP. If perfect balance is not possible, the remaining
adjustment will need to be done with the Gain trim-pots (substituting
for the fixed resistors, or later when the interface circuit is built).
Install the second PD (Channel B or 2)
to intercept the reflected beam. Note that
the AP glass is slightly tilted so it may be necessary to trim the PD's
leads or bend them over so its height will be correct.
The PDs should be reverse biased with
5 to 15 VDC (+ to cathode, the right leg facing front).
A load resistor of approximately 100K ohms
should result in a decent signal amplitude for a ~1 mW laser. If too high
or too low using only the laser, no need to change until using the actual
interferometer output. To accomodate lower power lasers and/or losses
in the interferometer optics, 1M ohm trim-pots are included in the kits for
this purpose. The typical wiring is shown below.
R-Protect PD1 Yellow
+-----/\/\----+--|<|---<<-----------------------+----------o Scope Channel 1
| | |
| | PD2 Blue |
| +--|<|---<<---------------------------+------o Scope Channel 2
| | |
| / /
| R-Load1 \ \ R-Load2
| / /
| DC Power \ \
| Red +| |- Black | |
+-----------------------<<---------||||---------+---+-------o Scope Ground
| |
|<--- SBB or QDx PCB --->|<----- Scope / Power Wiring ------>
PD Pins: Facing Front of PD with Legs Down: Anode on left, Cathode on right.
In the photo, above, one piece of CP sheet is stuck directly to the channel 1.
PD. The other piece of CP sheet is simply propped in front of the channel 2
PD with the sticky side facing out. Long term, that side should be protected
with some 5 Minute Epoxy or a microscope cover slip.
The AP is just sitting on the SB. Dabs of 5 Minute Epoxy, wire loops,
or other means can be used to secure them more permanently. If using wire
loops, take care not to short out anything that shouldn't be connected. ;)
The following must be done using the output of the interferometer that has
been properly aligned so that interference can be seen on a white screen
if a linear polarizer is placed in the output beam at 45 degrees.
Make sure you hands are clean or use a pair of latex surgical gloves when
handling the pieces of CP.
Cut a pair of 0.5x0.5cm or larger pieces of the CP sheet aligned with the
original edges.
Carefully remove the protective film from both sides of the cut pieces.
One side is simply bare plastic; the other side has a sticky adhesive.
The adhesive-side of the CP is the QWP with its optical axis at 0/90
degrees (aligned) with the edges; the other side is the LP with its
axis at 45 degrees. This can be confirmed by testing with a
linearly polarized laser or a
random polarized laser with a separate linear polarizer in front of it:
When the CP's LP-side faces the laser, rotating it will result in
the transmitted intensity going very close to 0.
With the CP-side facing the laser, there will be little or no change
in intensity.
Channel A: Attach the adhesive side of one of the pieces of CP
directly to the front of the Channel A PD making sure to keep it aligned
with the horizontal and vertical axes. This will result in its LP-side
facing the AP oriented so the polarization axis is at 45 degrees
(edges aligned with the X and Y axes). The result should be a
strong signal as the micrometer stage is moved or whatever is
convenient to change the PLD.
Channel B: Attach the other piece of CP in the reflected beam
so that its QWP-side faces the AP and is oriented at 0/90 degrees (edges
also aligned with the X and Y axes). This is best done by using a drop
of 5 Minute Epoxy to stick it directly to the Channel B PD, but if large
enough, it can just be placed in front of the PD with a wire loop or
something similar to stabilize it. Just make sure that the wire loop
doesn't short out something important. ;)
The result should be a strong signal as the micrometer stage
is moved or whatever is convenient to change the PLD. Once correct
behavior is confirmed, coat the adhesive-side with a thin layer
of 5 Minute Epoxy to prevent it from attracting contamination like
dirt and dust, or stick it to a microscope cover slip.
Fine tune interferometer alignment to maximize signal amplitude
and adjust the values of the PD load resistors so that the signal amplitudes
are between 3 and 5 V p-p.
Observe the Channel A and B signals on the oscillscope. They should
be in quadrature (or very close). This means the phase shift between them
should flip from +90 to -90 degrees depending on the direction of motion
as in the photos, above.
Note: Even if the peak-peak amplitudes are made equal, it may not
be possible to avoid an offset on one channel. In that case, the
scope vertical position can be set to superimpose them on the screen,
and later, the Threshold trim-pots can be set appropriately.
More on all this below in the section on displacement measurement.
By replacing the common HeNe laser head with a stabilized single frequency
laser, PLDs of up to 10s to 100s of meters would be supported with
essentially no other changes. They would
become very boring. :) But that's exactly what is needed for most metrology
applications. (Strictly speaking, no laser is truly single
frequency but rather Single Longitudinal Mode or SLM, which is pretty
darn close to SF for all practical purposes. But whatever it's called,
HeNes are close to ideal in this respect.)
With an SF laser and the Quadrature Detector, the signal output from
any of these interferometer configurations will provide complete
displacement information that can be used with a measurement display or
for closed-loop control. Systems using SF lasers are called homodyne
interferometers.
SF HeNe lasers are available for order of $5,000 from a few laser
companies (though this number has been dwindling). But fortunately,
it is possible to construct one from readily available parts for less than
1/20th as much. The laser tube can be identical to the one used in
the JDSU 1107 or 1108 random polarized HeNe laser head that comes with some of
these interferometer kits. Adding a heater to control cavity length
along with a simple controller using discrete analog components or an
Arduino turns it into an SLM laser with performance similar to that of
the high priced ones. If interested, a kit of parts
along with detailed assembly instructions is available. For the manuals,
go to Sam's
Electronics and Laser Kit Information and Manuals.
Another approach to displacement measurement uses
heterodyne interferometers, which are based on lasers producing a
beam with two orthogonally components at slightly different optical
frequencies (typically between 1 MHz and 20 MHz).
Rather than measuring the amplitudes of sin and cos
signals from a Quad detector, these systems measure the phase difference
between a "REF" signal direct from the laser and a "MEAS" signal that
is the Dopplar-shifted return from the "Tool" - the part that
moves. The vast majority of systems in use in the Universe
today are heterodyne. This has been confirmed by at least one totally
non-scientific study counting the number of surplus SF and TF lasers that show
up on eBay. ;-) The heterodyne approach has several advantages including
signal processing being in the AC domain, superior immunity
to noise, and not as sensitive to misalignment or contamination of optics
Most of the interferometer optics for homodyne and heterodyne systems
are identical and in fact, the PBSC, housed CCs, and QWPs in this kit
are actually intended for heterodyne systems.
Where a random polarized laser tubes meets certain requirements (which
turn out to be present in many of the HeNe laser tubes that
used to be used in 100s of thousands of supermarket checkout
barcode scanners), applying an axial magnetic field will result
in the normal single longitudinal mode splitting into two components
that are left and right circular polarized, which are converted to
orthogonal linear polarization
with a QWP. Stabilization is then similar to that of SF laser, above, and
a kit is also available. Since the SF and TF lasers are very similar,
it may be possible to use the same tube and controller.
However, the detector also needs to change and it becomes more complex.
Rather than a pair of photodiodes as in the Quad
detector, two optical receivers must be used. These convert the difference
frequency to an electrical signal. There is one for the difference
frequency direct from the laser called "REF" and another for the return
beam through the interferometer call "MEAS". The difference in their
phase is what the measurement electronics utilizes to complete displacement.
The optical receiver for REF can be relatively simple since it monitors
the output of the laser directly which doesn't vary much. But the one ofr
MEAS is usually more elaborate with automatic gain control built-in so
that it can accomodate changes in signal amplitude and be able to
deal with the output of the laser being split n-ways for multiple axes.
Finally, the output from an interferometer using a single frequency
or two frequency
laser may be processed to yield displacement information in digital
form.
In their simplest form, the measurement electronics for a homodyne
system is just a quadrature decoder circuit driving an
up-down counter; for the heterodyne system it is a pair
of accumulators and a subtractor. In practice, they are considerably
more complex, in part to provide sub-wavelength interpolation and extend
the range down to nm resolution. And yes, kits are available for these
as well.
However, a basic implementation for demonstration purposes
can be done with a $3 microprocessor board and a few inexpensive
parts as shown below:
Typical Homodyne Interferometer Measurement Setup using µMD0
Where the path length difference is limited to be less than a few cm, a
multi-longitudinal mode (not strictly single frequency) laser like the
one in these kits may be used.
The trim-pots on the left are the load resistors for the
quadrature detector. The 100K value should be satisfactory to resultin
a signal of a few volts p-p using a laser with an output power of
around 1 mW and no beam expander. (The expanded beam may slightly
exceeds the dimensions of the photodiodes so the sensitivity will be
reduced.) For a lower power laser or a laser
with a beam expander, larger values may be required. Or for finer control,
fixed resistors can be added in series with the trim-pots. The trim-pots
on the right adjust the comparator threshold for the Sin and Cos signals from
the Quad decoder, with the feedback resistors providing some hysteresis.
The Atmega 328P Nano 3.0 board runs firmware that is compatible with
the µMD GUI. Of course, no high tech system would be complete without
indicator lights :), so LEDs can be added to monitor the A and B inputs.
The minimal implementation is shown below along with a shot of the laptop
screen while twiddling the linear stage micrometer:
µMD0 and Interface (left), µMD GUI Display while changing Displacemet (right)
Simple PCBs for the quad detector and interface
will be available, but should not be required for a student project. ;-)
And the complete Michelson interferometer setup interfaced to µMD0 below:
Overall Setup showing Interferometer, Scope, µMD0 with
Interface, and µMD GUI Display
While the bandwidth of the photodiode + resistor combination is quite
limited, probably a few thousand counts/second, if that. But
it is sufficient to track the movement of the micrometer stage,
though not if it's pushed back and forth by hand without the
micrometer. That would require a
proper transimpedance pre-amp circuit. µMD0 has a maximum slew
rate believed to be above 125,000 counts/second, or around 1 cm/s
with the Linear Interferometer.
(Going forward, one of these will be standard, so the title is historical.)
This modifies Arm 2 so that the optic can be easily moved over a large
distance to cover the range of PLDs of interest for the HeNe
laser being used. It's more a matter of convenience than a
requirement since the other setups can do this, but it requires
physically remounting the linear stage assembly and/or adjusting the
micrometer. However, adding this option is not just a matter of
adding the rail as it impacts the height, and thus other components.
Here is a diagram of the version for the LI:
The others would be similar.
V1.5 uses a Thorlabs rail and carrier with the
Parker linear stage shown in the lower right. The only other change
(which is independent of this) is to add a pedestal to the Wood Block
which eliminate the HP mount for the PBS cube since it served no purpose
and added cost.
Future versions of this kit will probably include a rail as the default,
though the exact details may differ.
The Alternative Rail Project:
Using the Thorlabs RLA rail with RC carrier is dirt simple since it is
designed for use with optical components and that is what V2.0 will use
initially. But One issue with these is that the carrier and rail are both
aluminum and with metal-metal contact, it doesn't really move silky smooth.
A low tech solution of some was might improve the situation, but
as an alternative, a ball bearing linear rail is being considered.
It will use an MGN15C carriage block with either a 150 or 300 mm rail.
The Far East versions of these should have adequate precision for what
is required here. A prototype using a 300 mm rail is shown below:
Prototype of Arm 2 using MGN15C Ball Bearing Linear Rail:
Front View (left), Back View (center), Closeup of Locking Bracket
(Right)
It has a Newport U100A adjustable mount with a planar mirror and Thorlabs
knobs :) on a generic micrometer stage. The end holes of the 300 mm
rail line up nearly perfectly with breadboard holes. Those in the 150 mm
rail do not align, so a 6-32 tapped hole must be added to the breadboard
for one end. Screws in the end holes poking up will serve as the
end-stops as a default. Adding a stop to the ends of the rail or
on the breadboard would achieve almost an additional inch of travel though.
They could just be a small plate glued there.
The locking bracket can be installed at either end of the carriage which
may be convenient depending on whether the micrometer is end or side
adjusted. The thumbscrew can be set for any level of
resistance, always with silky-smooth movement. ;-) A
steel machinists' scale glued to the breadboard will work at least
as well as the graduations on the Thorlabs rail.
The hand-rubbed urethaned oak plank is not included. ;-) Stay tuned.
For either the Thorlabs or MGN15C, all but the very slowest movement will
overwhelm the simple quad-A-B interface to µMD0 and it will lose count.
So they are intended for
convenience in coarsely locating the Arm 2 reflector. But if a proper
transimpedance preamp is added, tracking should be maintained over the
full range with careful enough alignment.
Modified laser head cylinders may be available made of transparent aluminum
(a.k.a., acrylic or Plexiglas). While there isn't a huge amount of action
that would be visible, it would add a cheery glow to the setup. And at the
same time (and more importantly), a thin-film heater can be added to the
laser tube to control cavity length. The photo on the left is a closeup
of the laser while the one on the right is the rail setup with
Thermal Expandsion experiment using the glowing laser.
HeNe Laser Tube in Transparent Acrylic Cylinder with Heater
(left), Scope Display of Fringe Signal while Heating Glass Block in
Arm 1 (right)
(Click on images for high resolution versions.)
Something like this would be used to house the single frequency or two
frequency lasers described above. The heater would also be useful to
accelerate mode sweep for experiments dealing with the interferometer
response particularly for random polarized lasers.
Three types of optics that affect the polarization are used
in various parts of the interferometer:
Linear Polarizer (LP):
A linear polarizer only passes light that is aligned with its polarization
axis. More precisely, it obeys Malus's law whereby the optical power of the
light passed is equal to:
Io = I * cos2(Θi)
where:
Io is the output power.
I is the input power.
Θi is the angle between the input and polarizer's
axis.
Where the input light has multiple polarized components with differing
polarization orientations, the result is the sum of Malus's law applied
to each one.
One use of an LP in this interferometer is to combine the two orthogonally
polarized components from the PBSC at 45 degrees so they line up and
can interfere at the detector.
Quarter WavePlate (QWP):
A QWP is a part of the Circular Polarizer (CP) and are used in the
quadrature-sin-cos detector. The effect of a QWP is summarized below.
For the following, "θ" is the angle with respect to the fast
axis of the waveplate.
Input Output
------------------------------------------------
Linear, θ = +45° Right circular
Linear, θ = -45° Left circular
Right circular Linear, θ = -45°
Left circular Linear, θ = +45°
Linear, θ not +/-45° Elliptical
Elliptical, θ = 0 or 90° Linear at angle
"Elliptical, θ = 0 or 90°" means its major and minor axes are
aligned with the waveplate optic axes. This case can be easily decomposed
into the vector sum of a linear component (which is unchanged) and a circular
component which gets transformed into a linear component at 45°.
QWPs are used in several of the interferometers. Their optical axes are
always at ±45 degrees. (The handedness of the circular polarization
will be swapped but that doesn't matter here - they are unmarked
and can be mounted either way.) Thus when light polarized at 0 or 90
degrees passes through the QWP, it is converted to circular polarization.
When that is reflected from a CC or plane mirror, the handedness
flips and when it passes back through the QWP,
the polarization axis is rotated 90 degrees. This allows the PBSC to
redirect it resulting in the various beam paths required by the
interferometers.
Circular Polarizer (CP): The CP is a combination of an LP and QWP:
For the detectors, the CP would be used like an LP since the output
polarization doesn't matter to a photodiode.
However, if placed in front of a linearly polarized laser, or used to modify
the polarization of a random polarized laser, the circular polarized output
makes a subtle difference in how the interferometer behaves. That will be
something to analyze.
And as a point of interest CPs are used in front of LCD displays to increase
their contrast under ambient illumination: With the LP side toward the viewer,
ambient light will pass through it and the QWP, and be reflected by the
display itself. But when CP light is reflected, the "handedness" flips
and the result is linear polarization at 90 degrees to what it was originally,
and thus blocked by the LP. That is part of the reason your smart
phone screen looks dark when nothing is displayed on it.
However, while
circular polarizers intended for use with cameras are constructed as shown
above, the "polarizing films" sold for smart phones and the like may or
may not be true CPs. Some are just linear polarizers or linear polarizers
coated with a weak neutral density filter. And it's not clear how one can
select the proper type since the sellers are typically clueless. The only
actual CPs consistent with the above diagram I've found so far were listed as
something like: "New Backlit Screen Modify Part Polarizing film For GBA GBC
GBA SP N_ES". Those listed as "LCD Polarizer Film Polarization film Polarized
Light Film For ip.ccHHH" may also be CPs but with (1) the adhesive and
non-adhesive sides swapped and
(2) the axes of the LP and QWP rotated 45 degrees. They may also have a weak
ND filter. Sometime a faint colored line can be seen which is at the
orientation of theh LP or 90 degrees from it. But that doesn't help with
whether there is a QWP, though sometimes there are also a series of small
circles, presumably to indicate CP, though they tend to be on the
opposite side from the QWP. Those listed specifically
for iPhones were of the simple LP type (usually with a faint line at
90 degrees to the LP axis parallel to the short
side). Interestingly though, the protective
film that normally gets discarded is birefringent and may even be a QWP.
Which of course makes little sense. :( :) Confused yet? I sure am. :( :)
This same scheme is also used in what is sometimes called a "poor man's
optical isolator", whose purpose is to minimize back-reflections from an
optical setup into the laser, which may destabilize it or worse. The
combination of a linear polarizer (or PBSC) and QWP acts as a "diode"
for polarized light. It's called "poor man's" because it is much less
expensive than a Faraday isolator, and adequate for many purposes. But
for it to work well, any reflective surfaces in the optical setup must
not mess with the polarizaton.
The piece of CP provided in these kits is intended for such an application.
It can be cut into smaller pieces since they only need to be
slightly larger than the beam, which even if expanded is only ~4 mm.
As noted shown in the diagram above, the optical axes of the QWP are
at 0 degrees with respect to the edges of the CP and the axis of the LP
is at 45 degrees.
The CP comes with protective film on both sides which MUST be removed because
it acts like some type of waveplate and messes with the polarization. The side
of the CP with the QWP is sticky since that was intended to go against the
screen. To prevent it from collecting dirt and fingerprints, the smaller
pieces to be actually used in the detector(s) should be stuck to
microscope cover slips (included) or glass windows. CAUTION: Microscope
cover slips are thin and fragile - don't press too hard.
There are two basic types of HeNe lasers with respect to polarization of
the output beam: Random polarized and linearly polarized. With just a
pair of mirrors and HeNe gas, the result will usually random polarized.
To construct a linearly polarized HeNe laser, a Brewster-angle plate is
added inside the laser cavity. (Search for: "Brewster Angle".)
This introduces an orientation dependent loss with respect to polarization
and virtually 100 percent of the photons will then be linearly polarized
with the orientation with minimal loss. The Brewster plate on the types
of HeNe laser tubes used here are buried within one of the mirror mount
stems and are thus not readily visible.
Although the experiments are
described with a linear polarized HeNe laser, it is possible to
use a random polarized laser instead if one is more readily available.
However, its output will need to be converted to linear polarization
in a very specific way with a linear polarizer to behave the same.
But a random polarized laser can also demonstrate some interesting
interferometer behavior not available with a linear polarized laser.
Most random polarized lasers do not actually have polarization varying, well,
at random. :) The term "random polarized" with respect to to HeNe
laser simply means that nothing special is done to control the
polarization. (I.e., no Brewster plate.)
In the case of many red (633 nm) HeNe lasers, that means:
There are two polarization axes instead of one.
They are orthogonal to each-other.
Their orientation cannot be predicted without testing
but remains fixed for the life of the tube.
Adjacent longitudinal modes have orthogonal polarization.
And note that this only applies to red HeNes, not even other color HeNes,
let alone most other lasers. Murphy must have taken a day off when the
HeNe laser was invented because these attributes end up being quite
useful - in fact fundamentally important - for many applications.
A laser tube with these characteristics would be considered "well behaved".
if the longitudinal modes move smoothly through the neon gain curve
without abrupt changes in amplitude and not all are like this. :( :)
A "flipper" will have
"polarization switching" whereby at some point or points during mode
sweep, the two sets of longitudinal modes will swap their polarization
axes, usually instantly.
For some truly nasty tubes, this will happen continuously, somewhat
well, at random. Flippers are often not suitable for an interferometer
because in the region of the flip, there may be excessive optical noise,
possibly due to even the smallest amount of back-reflection,
which will show up as large oscillations in the fringe signal.
(While that in itself may be interesting, it will also be confusing.)
The simplest way to test for a well behaved random polarized laser is to
put the output through a linear polarizer and monitor it on a graphing
laser power meter or photodiode and data acquisition system. Adjust
the orientation of the polarizer for the maximum amplitude of the mode
sweep variation. That aligns it with one of the polarization axes.
Then inspect the plot over a couple minutes (from a cold start to
get the fastest mode sweep) for abrup changes in amplitude. There
should be none.
The following animation shows the mode sweep of a random polarized HeNe
laser similar to the JDSU 1107 or 1108. The red and blue lines represent
the amplitudes of the orthogonal polarized outputs. To actually view these
live with a similar display
requires an instrument called a Scanning Fabry-Perot Interferometer
(SFPI) with a dual polarization detector. While commercial SFPIs cost
several thousand dollars, an SFPI with these capabilities can be built
as a nice student project at modest cost. It's all done with mirrors. ;-)
Mode Sweep of Short Random Polarized HeNe Laser
A linearly polarized HeNe laser of similar length would have both modes be the
same polarization and same color. :)
The rate at which the modes pass through the neon gain curve will depend
on how fast the tube is expanding from heating of the gas discharge, so it will
slow down as it reaches thermal equilibrium from a cold start.
Plots of the two polarized modes for a well behaved tube (non-flipper) would
look something like:
Mode Amplitude Plots of Well Behaved Short Random Polarized HeNe Laser
The plots cover the time range from a cold start to close to thermal
equilibrium. Note how both the red and blue plots are continuous.
A full mode sweep cycle at the start is a few seconds
while at the end it is a few minutes. After that it would be
irregular as just ambient air moving around will have a significant
effect.
(For a linearly polarized tube with similar physical characteristics,
the amplitude of the output would be the sum of the red and blue plots.)
The plots of a typical flipper might look like the following (zoomed
in to a few mode sweep cycles to show details):
Mode Amplitude of Short Random Polarized "Flipper" HeNe Laser
(The shape of the curves differ due to the tube not being the same model.)
The vertical green line is the instant of the flip, which occurs quite close
to the same location during each mode sweep cycle.
However, experience shows that in the interferometer, there may be
nasty stuff going on around that region and it won't be confined to an
instantaneous event. The detected signal may be very noisy.
For an academic challenge, a random polarized flipper
is probably the most interesting type of tube to study.
But a good understanding of what's going on is necessary to
not to go insane attempting to decipher the behavior.
The next most interesting tube would be one that is random polarized and
well behaved. One or two of the kits put together to date
includes that type of laser. A random polarized flipper can
be provided in place of or in addition to the linear polarized
or random polarized well behaved tube if interested. :-)
The Generic or Parker linear stages should move silky-smooth both with the
micrometer and if simply pushed up and back. But if there
is any roughness - or if the fit appears to be loose, the bearings may be
fine tuned without disassembly via recessed setscrews on the side of the
moving part of the stage.
Generic stage: There are 4 setscrews located on the side
of the stage. Depending on the version, these may be on either side.
It may also be necessary to loosen screws on the top which secure the
inner track(s). If there is a locking knob, some may be concealed
under the lock-plate.
Parker stage: There are 3 setscrews located on the side opposite
the lock knob (if present) which may be concealed by a sticker.
A 1/16" hex driver may be used to tighten or loosen them the smallest amount
which should not be more than 1/10th of a turn.
The micrometer can be lubricated with light grease if it seems rough or tight.
The ball bearings for the state itself should not need lubrication unless
serious dust or other contamination has gotten into the tracks.
So you took great pains to attach the turning mirror but then realized it's
centered on the bracket instead of being closer to the rear. (It may work OK
where it is especially if the laser has no beam expander) so don't panic
just yet!).
Where the adhesive is accessible, a single-edge razor blade can often be
used to slice it or get underneath and peel it off. But that may not be
possible if the turning mirror were attached in the wrong location with
bits of Epoxy underneath it. Or reusing the mirror stuck to the PZT.
Attempting to pry the thin mirrors off would likely result in bits of glass.
The easiest method where the parts can withstand it is to use a common
heat gun. The exact temperature at which the typical Devcon 5 Minute Epoxy
decomposes is not known. The datasheet only states that the "Operating
Temperature" range is -40 °F to +200 °F but not what happens at
+201 °F. ;-) It may exceed +500 °F. However, from
experience, a sufficient temperature
can be reached in a couple minutes to soften the Epoxy
without damaging parts made of glass or metal. However, some plastics
might melt. ;( As the critical temperature is reached, the Epoxy will
soften, so work over a non-flammable surface that won't damage the part
to be removed and gently prod it with a popsicle stick or something
similar until it falls off. After cooling, the residue can be removed
by scraping or with isopropyl alcohol. Since the Epoxy at least partially
decomposes, this method should not be used for repositioning, only removal.
Clean the two surfaces and then start fresh. ;)
CAUTION: Don't try this with the gas cell or loudspeaker, they would likely
get damaged.
Here is assorted information on V2.0, which will be what is
intended to be available for sale, directly from me or through eBay.
There are three versions, though customization is possible.
They will use standard size breadboards so they are easier to obtain and
are more professional looking, being black anodized.
The Basic version uses a 6x18" breadboard and will be able to do the
linear interferometer using cube corners, the pressure and temperature
sensors, and displacement measurement using uMD0. The smaller width
breadboard compared to V1.0 and V1.5 only affects the mounting of the
Arm 1 post holder.
The Deluxe version also uses a 6x18" breadboard and in addition to
everything in the Basic version, it will be able to do
the interferometers using planar mirrors, actuators using
planar mirrors, and more on laser coherence and effect of mode sweep.
The Deluxe+ version uses an 8x24" breadboard to facilite more
experiments on coherence length and mode sweeep, as well as being
able to add other optics in Arm 2.
The Basic version really has enough for an introduction to interferometry
and can be upgraded to the Deluxe version by adding the appropriate parts.
Other changes compared to V1.0 and V1.5 include:
V2.0 uses an aluminum plate on Thorlab posts rather than a wood block for
the PBS and turning mirror mount. Both are very stable, but the plate
affair is more in keeping with optical setups and doesn't contribute to the
demise of trees. ;-)
A custom detector made from discrete parts replaces the Thorlabs DET110.
The performance for the purposes of these kits is identical. And it
facilitates adding a second channel for the quad-sin-cos decoder or X/Y
detector and also simplifies the wiring with a terminal block and/or
jumper wires instead of requiring BNC cables and clip leads. Both a
solderless breadboard and assembled PCB version will be included.
The adjustable mounts will be either Thorlabs KM100s or Newport U100s.
For the purposes of these kits, they are functionally equivalent and the
Thorlabs are smaller and sleeker. ;-) The U100s are more precise (and a
lot pricier if bought new!), though these versions lack knobs, requiring
the use of a 5/64" ball driver, which may be less convenient. But never
fear, appropriate Thorlabs knobs will be included in the kit.
The QWPS and mounted CC in the Deluxe and Deluxe+ versions
may be custom parts rather than from HP/Agilent.
They will be functionally equivalent without issues of availability.
The generic stage will be used, though the Parker 3902 may be an option.
The generic stage is equally good for positioning here, possibly even more
stable due to its wider track spacing.
Both will have either a Thorlabs or MGN15 rail.
The only things here now are more comprehensive
mounting height diagrams, and photos of the two versions.
The first is the Basic version with the 6x18" the breadboard, new
interferometer mount with Linear Interferometer, linear stage on
6 inch rail, and quad detector PCB attached to the SG-µMD0 PCB:
The next one is the Deluxe version configured for the High Stability
Plane Mirror Interferometer.
The next is the Deluxe+ "Stretch" version on the 8x24" breadboard
with linear stage on 12 inch rail. The laser includes a beam
expander but it is otherwise configured the same way.
These are the parts for each setup except as noted.
Replicating it should be straightforward but might as well go for
V2.0. It requires no machining for the
linear stage except 1 or 2 tapped holes and includes the rail so it is
more flexible for exploring the modes and coherence length/period of
the HeNe laser. The original setup was designed based on the
availability of certain parts.
The 8x18" optical breadboard for V1.0 and V1.5 is custom with the dimensions
selected to be convenient for the projects while being able to easily ship
Worldwide. If machining it, fewer than half the
standard holes are enough based on all reasonable mounting locations, but
that's only worth it if you're paying by the hole. ;-) Several sizes of
commercial breadboards would also be suitable, though no supplier found
so far has the 8x18" size now used.
Most other standard opto-mechanical parts are from Thorlabs. The major
difference between V1.0/1.5 and V2.0-A/B is in the length of some of the posts.
The JDSU 1107P and 1108P, or similar laser heads from Melles Griot/Pacific
Lasertec like the 05-LHR/P-211 are ideal for these experiments. The criteria
include being linearly polarized, eye-safe output power, and physical size.
Optics companies like Edmunds, Newport, and Thorlabs have suitable lasers
(though most are made by JDSU and PLT), but eBay is often a good source
at a fraction of the cost. The laser could also be a bare tube safely
enclosed, though the preferred linearly polarized variety is not that
common at the low power of 0.5 to 1 mW. Random polarized heads and tubes
can be used (and actually add some interesting areas to study) if
certain criteria are met, primarily that they are not
"flippers". See section: Linear Polarized versus
Random Polarized HeNe Laser.
Parts List for V1.0 and V1.5
Quantity Description
------------------------------------------------------------------------------
Baseplate/Optical breadboard:
1x Aluminum plate 18x8x1/2" tapped 1/4-20 144 places on 1" centers.
Laser Assembly:
1x Laser consisting of 0.5-1 mW JDSU 1107/P or 1108/P laser head
and power supply. Some kits have a JDSU 1205 lab-style
power supply but this only runs on 115 VAC. Others will have
a Laser Drive 103-23 brick and universal wall adapter
which may be used Worldwide.
1x ~1x1" piece of circular polarizer. Consists of linear polarizer
(+/-45 degrees) with QWP (0/90 degrees). Cut up as needed.
This is only required for random polarized lasers.
1x Beam Expander (optional) consisting of:
1x Beam Expander Adapter Plate. The front bezel of the laser has
had 3 tapped holes added for this.
1x HP/Agilent 6 mm beam expander, modified, must be glued or
press-fit into Beam Expander Adapter Plate.
1x 3 M2.5 x 5 mm cap-head screws.
2x Small Ring Mount each with four 8-32 x 1.5" or 1.25" thumbscrews
1x 8-32 x 1/2" caphead screw to secure the ring mounts and optional
#8 plastic washer to provide compliance if the mounting hole in the
rings is threaded (some are) so the orientation can be set correctly.
An 8-32 x 1/2" setscrew can substitute for the caphead screw so
as not to impinge on the available space for the laser head.
2x Thorlabs TR2 post with 1/2" 1/4-20 setscrew to attach to baseplate
Interferometer Assembly:
1x HP/Agilent 10702A or 10706A PBS. This is either on an adjustable
base (V1.0) or only a frame (V1.5).
1x HP/Agilent 10703A Cube Corner with 2x 4-40 x 3/8" caphead screw.
2x HP/Agilent 10722A Quarter WavePlate or custom equivalent with
2x 4-40 x 3/8" capheads screw. (Included in V1.0, option for V1.5.)
1x PBS Mounting Block with 3/4" 1/4-20 cap screw to attach to baseplate.
V1.0 is for use with HP 10711A PBS mount while V1.5 uses 4x #4 x 2"
wood screws to attach PBS assembly directly to block.
1x Turning mirror (Approximately 1/2" x 1").
1x Turning mirror bracket. (V1.0 and V1.5 height differ.)
1x #5x3/4" round head wood screw for turning mirror bracket.
2x #5x3/4" round head wood screws (only for V1.0 PBS mount).
Arm 1:
1x Thorlabs KM100 or Newport U100 mirror mount with 3/8" 8-32 cap
screw to secure it to post.
1x 1 inch bare Cube Corner.
1x 1 inch diameter planar mirror. (Installed or to be installed in
mirror mount.)
1x Thorlabs TR1 or TR1.5 post.
1x Thorlabs PH2 post holder with 1/2" 1/4-20 setscrew.
Arm 2:
1x Thorlabs KM100 or Newport U100 mirror mount with 3/8" 8-32 cap
screw to secure it to post.
1x 1 inch Cube Corner.
1x 1 inch diameter planar mirror. (Installed or to be installed in
mirror mount.)
1x Thorlabs PH1 post holder.
Linear Stage Assembly (V1.0 only):
1x Linear Stage Top Adapter Plate.
2x M3 x 8 mm cap-head screws.
1x 40 x 40 mm generic linear stage. The micrometer is Metric.
1x Linear Stage Bottom Adapter Plate with 1/2" 1/4-20 setscrew.
4x 4-40 x 1/4" Philips head screws.
4x 1/4-20 1/2" cap screws.
Rail Option for studying the effects of limited coherence length (replaces
linear stage assembly, above, and will be standard going forward).
1x Parker 3902 or 3902M micrometer linear stage (modified).
1x 4-40 Philips head screw to secure post holder to stage.
1x 4-40 3/8" screw, washer, and nut to secure RC1 to stage.
1x Thorlabs RC1 dovetail rail carrier.
1x Thorlabs RLA0600 dovetail 6" optical rail.
2x #10 washer and 8-32 3/8" cap head screw for end-stops.
Custom Single Channel Detector and Quadrature Decoder:
1x Variable attenuator plate to be used as NPBS.
2x 1/2" piece of sheet (may be used as CP or LP), cut to size.
2x Silicon photodiodes.
1x 1K ohm resistor (PD protection).
1x Jumper wires, etc.
1x Solderless breadboard with adhesive back, 170 tie points.
1x Detector adapter plate.
1x 8-32 x 1/2" setscrew.
2X Load resistors, 100K to 1M typical, or 1M trim-pot
Deluxe Single Channel Detector (original version):
1x Thorlabs DET110 biased photodiode with SM1 threaded ring.
1x BNC cable with banana jack/screw terminals (M-M cable,
BNC FMF "T", BNC M-to-terminals).
Common to All detectors:
1x Thorlabs PH2 post holder with 1/2" 1/4-20 setscrew.
1x Thorlabs TR1 or TR1.5 post with 1/2" 8-32 setscrew for DET110
and 8-32 3/8" cap head screw for prototyping or PCB.
1x Thorlabs BA1S with 1/4-20 3/8" caphead screw to attach to PH2 and
1/4-20 5/8" caphead sscrew to attach to base.
1x Set of assorted resistors for termination 1K-1M and/or trim-pots.
Micro Measurement Display 0 (µMD0):
1x Atmega 328 Nano 3.0 microcomputer board with pins soldered.
1x Homodyne firmware for Nano (may be preloaded or download from
µMD0 Manual).
1x µMD Graphics User Interface (download from
µMD0 Manual).
1x Solderless breadboard 3-1/4" x 2-1/4", 25 columns.
1x LM393P dual voltage comparator.
1x 3 mm Red LED and 1K ohm resistor.
1x 3 mm green LED and 47K ohm resistor.
2x 100K to 1M ohm resistors or 1M ohm trim-pot.
2x 10K ohm trim-pots.
2x 100K ohm resistor.
2x 470K ohm resistors.
Voice Coil Actuator:
1x 1-1/2" to 2" loudspeaker.
1x 1" D x 1/4" T aluminum or Acrylic Speaker mounting Disk.
1x Speaker mirror (Approximately 1/2"x 1", same as turning mirror).
Piezo Transducer:
1x 27 mm PZT beeper element with spacer.
1x #2 washer to use as spacer.
1x PZT mirror (Approximately 1/2"x 1", similar to turning mirror).
Gas Cell Compensator (Air Pressure and Temperature):
1x 1" OD, 7/8" ID, 2" L Acrylic tube.
2x 1-1/8" D glass or Acrylic window.
1x 10-32 to hose barb adapter.
1x 8-32 3/8" or 1/2" set-screw.
1x Blood pressure bulb with valve.
1x Blood pressure gauge.
1x 3-3.5 mm (or 1/8") ID Rubbor tubing to connect.
1x Hose barb "T" for 4 mm tubing.
1x Thorlabs PH2 post holder.
1x Thorlabs TR1 or TR1.5 post.
1x Thorlabs BA1S with 1/4-20 3/8" caphead screw to attach to PH and
1/4-20 5/8" caphead sscrew to attach to base.
Thermal Expansion:
1x ~1x1x2 cm compensator plate or other block with polished sides.
1x Power resistor(s) - 2x10 ohm or 1x25 ohm, 10 W.
1x Screw terminal to 5.5/2.1 female barrel connector adapter.
1x Wood or Delrin "chip" with 8-32 Nylon set-screw (1x2x3/16" typical).
Test Equipment / Tools / Supplies:
1x Scope (USB or stand-alone) with two 1X/10X probes.
1x DMM.
1x 10K ohm potentiometer wired with 10K ohm current limiting resistor.
1x 12 VDC 1 A power pack (PD bias, voice coil, PZT, thermal expansion).
1x Screw terminal to 5.5/2.1 female barrel connector adapter.
1x Screwdriver set (medium flat and Philips).
1x Jewelers' screwdriver set.
1x Hex wrench set (ball-end preferred).
1x Two part Epoxy (separate tubes preferred).
- Hookup wire and jumper wires.
10x Wire nuts just in case. ;-)
Here is a separate parts list covering only the fasteners (screws, washers,
etc.) for V1.0 and V1.5 with the rail option. This should be redundant.
Laser Assembly:
8x 8-32 1-1/4" to 1-1/2" Nylon thumbscrews for rings.
2x 8-32 1/2" caphead screws, join posts to rings.
2x 1/4-20 1/2", set screw; join posts to breadboard.
PBS Assembly:
1x #5, 1/2" or 3/4" round head wood screws; join mirror bracket to wood
block.
4x #4, 2" round head wood screws; join PBS to wood block (version
without HP mount).
1x 1/4-20 1" caphead screw; join wood block to breadboard.
6x 4-40 3/8" caphead screw, optics to PBS cube (should already be
attached to PBS cube).
Mirror Mounts:
2x 8-32 3/8" caphead screw; join mirror mount to post (Thorlabs KM100
or Newport U100).
1x 1/4-20 1/2" setscrew; join Arm 1 post holder to breadboard.
Detector and Sensor:
2x 1/4-20 3/8", caphead screw; BA to PH.
2x 1/4-20 1/2", caphead screw; BA to breadboard.
1x 8-32 3/8" caphead screw; detector board to post (if using detector
board).
1x 8-32 1/2" setscrew; DET110 to post (if using DET110).
1x 8-32 1/2" setscrew; pressure sensor acrylic cylinder to post.
1x 8-32 nut; spacer/strengthener for setscrew above.
1x 8-32 1/2" Nylon setscrew, temperature sensor wood "chip" to post.
Parker Stage and Rail Assembly
1x 4-40 1/2" caphead screw, Parker stage to RC1 carrier.
1x 4-40 nut; Parker stage to RC1 carrier.
1x #4 washer (3/8" diameter preferred if available); Parker stage to
RC1 carrier.
1x 4-40 3/8" Philips or flat head; 1" post holder to Parker stage. The
length is critical to not extend too far into Parker stage - confirm
before tightening. The head diameter must be larger than the ID of the
1/4-20 threaded hole in the post holder. Else a washer will be needed.
2x 1/4-20 3/8" caphead screw; attach rail to breadboard.
2x 8-32, 3/8" or 1/4"; caphead screw; stops on rail.
2x Large #10 washers for stops on rail.
