For an example of one such system using a tiny Nd:YAG laser rod pumped by the electronic flash unit from a disposable (single use) 35 mm pocket camera, see the paper: Micro-Laser Range Finder Development: Using the Monolithic Approach.
(difference frequency) * c
Distance = ----------------------------
2 * (chirp rate)
Where c is the velocity of light.
Dynamic implementation in the form of a laser scanner can actually be used to implement a 3-D profile measurement system. If a laser beam is scanned across a 3-D object, and the spot is viewed (by optical sensors) from two different locations, it is possible to determine the instantaneous distance to the spot (on the object). This can be down digitally (using a pair of CCD cameras - slow) or analog using a pair of 4-quadrant photodiodes. With a more constrained system (see below), only a single sensor is needed. This isn't a simple project either but at least doesn't depend on precision on the order of the wavelength of light! Such scanners exist and are used in conjunction with robotics (and other research), in industrial CAD/CAM for construction of computer models from real-world objects, and many other applications.
(From: Steve Roberts (osteven@akrobiz.com).)
One approach is to use a frame grabber, a translation stage, and a simple laser with a simple line generating optic. You put the piece to be scanned on the translation stage, shoot the line onto it from above and look at it with the camera. The line creates a cross-section of one small part of the object and the camera records it. Then you process out the laser light from the background, advance the translation stage one more linewidth, and take the next slice and so on - sort of a crude from of computed tomography.
(From: Paul Mathews (optoeng@whidbey.com).)
You might want to look at some modules designed for this purpose. The Sharp's Distance Measuring Sensors are compact and sensitive. They include the emitter LED, detector photodiodes, and signal processing circuitry in a compact integrated module.
There are also some nice application notes available from Hamamatsu for use with their Position Sensing Diodes and related ICs.
Manufactures/suppliers of devices used in laser rangefinders include: E-O Devices and Analog Modules.
To distant scene.
^ ^
| |
| C/------/D
|A |
\--------\ (B is partially silvered or a half mirror to
adjust B| permit viewing of both sides from the scene.)
angle ^
view here
| |
|<- baseline -->|
The further apart the mirrors are (size of baseline), the greater the useful
range. Adjust the angle of mirror A or D until the images are
superimposed. Calibrate the angular setting to distance.
The distance from A to the scene is then: tan(angle A) * baseline.
For long distances, C and D can be eliminated - they compensate for the difference in path lengths of the two views - else the sizes would not be the same. (Even this doesn't work perfectly in any case. Can you figure out why?)
You can add telescopes and other optics if you like - this is just the basics.
Look Ma, no electronics. :-)
Note that SLR cameras do NOT use this approach as they are entirely optical (meaning that adjusting the focus only controls the lens - nothing else!). With SLRs, a pair of shallow prisms oriented in opposite directions (or many in the case of a 'microscreen' type) are cemented onto a clear area of the ground glass. When the image is precisely focused onto the ground glass, the prisms have no effect. However, when the image is in front or behind, they divert the rays such that the two halves of the image move apart (or the image breaks up in the case of the 'microscreen').
There were some "Amateur Scientist" articles in Scientific American a few decades ago on constructing several types of optical range finders. These were included in the book, "Light and Its Uses". See the section: A HREF="laserclt.htm#cltsi">Scientific American Articles on Lasers and Related Topics.
My students construct a simple laser rangefinder using a few basic parts:
Equipment:
Basic procedure:
Rough diagram of rangefinder setup:
To wall To wall
^ ^
| \
distance | first reflected beam \ second reflected beam
| \
| angle \
Laser --3"---/------------------------------------/
Beam splitter Rotary table with mirror
|<------------- 6 feet ------------->|
Of course, you can make the non-laser version of this type of rangefinder (but
this is a laser FAQ! --- sam). My students also make that one as well. Both
are pretty neat and demonstrate the power of trig to determine distances!
I am just finishing the development of a range finder based on the TOF (pulse-Time-Of-Flight) measurement method. There are also different methods like phase-shift method which compares the phase shift between outgoing modulated beam and reflected light.
The Pulse TOF method has some advantages which make it very useful: you can use relatively high pulse power and still be in the Class I safety range.
While building such a range finder there are two crucial components which have influence on its accuracy: the time measurement circuits and the receiver. Our aim was to build a laser scanner with the resolution of 1 cm which means that you have to be able to measure the time with the resolution of 67 ps. The range of the scanner should be approx. 30m. We are not ready yet but there are some results.
For the first prototype we used a 1.25 GHz oscillator and special microstrip design to get the resolution of 70 ps. In the current prototype we use a special prototype IC which should deliver 50 ps resolution.
The problems are on the receiver side, a relatively large jitter (which I'm fighting now) destroys my high time measurement precision. The jitter on the input results in the distance differences of approximately 10 cm). This can be filtered out by averaging of a number of measurements and that is what we are doing now. Our measurement frequency is at present 100 kHz, but we will probably perform the averaging over 10 measurements so that effective measurement rate will be 10 kHz.
(From: jfd (jezebel@snet.net).)
The problem is getting simultaneous long standoff range and extremely accurate range. You can phase detect with accuracies in the sub-inch range using direct detected RF modulated LIDARS or you can use an interferometric technique with a reference to get sub-micron distances.
(From: Robert (romapa@earthlink.net).)
For much better resolution than would be possible with simple sampling while still maintaining low cost, digital TOF rangefinders can combine a precision analog temporal interpolator with say a CMOS system running at 100 MHz. The analog circuitry to accomplish this is in many production units (for different applications) - but 5 ps resolution has been achieved with low-cost components and in production for 15 years from at least one manufacturer. The idea is interpolate between the digital count periods with a precision time-to-voltage converter which is then sampled by microcontroller and combined with the digital counter results.
(From: Bill Sloman (bill_sloman@my-deja.com).)
You may be able to achieve this at low unit cost, but getting a precision analog temporal interpolator to work well next to CMOS running at 100 MHz isn't something I'd describe as easy.
We developed a system of this sort at Cambridge Instruments between 1988 and 1991 using a mixture of 100K ECL and GigaBit Logic's GaAs for the digital logic. Any digital signal going to or from the analog temporal interpolator was routed as a balanced pair on adjacent tracks, and we were very careful about the layout, but we still had to work at getting the noise on the interpolator output down to the 60 picosecond jitter on our 800 MHz master clock (getting a better master clock was the next priority).
Current-steering logic (like ECL and GaAs) is a lot quieter than voltage-steering logic (like TTL and CMOS), which is why very fast DACs and ADCs use ECL interfaces. Precision analog interpolators are no less sensitive.
Do you know who has actually achieved that 5 ps resolution and for what application? Tektronix and time domain reflectometers come to mind, though Tektronix isn't exactly cheap. IIRR Triquint was originally their in-house analog foundry and I think Tektronix has been using GaAs ASICs in their faster gear for quite some time now.
The hybrid approach certainly isn't new, but getting it to work is a fair test of one's analog skills.
Of course, using phase-shift not only makes for easier circuit design, but also lets you run your LED at a 50% duty cycle, giving you a lot more reflected photons to work with than the 0.01% you get with TOF.
(From: Lou Boyd (boyd@fairborn.dakotacom.net).)
The Texas Instruments book "Optoelectronics: Theory and Practice" published by McGraw-Hill had a chapter (23) on the design of an LED/Si Diode rangefinder with schematics of the transmitter, receiver, and timing section. This was a phase modulated design but obsolete by todays standards. Low cost modern rangefinders like those by Leica or even Bushnell are far more advanced in the detection circuit than that in the TI book. Most eye-safe commercial rangefinders use phase modulated techniques. This gives good accuracy but limited range, usually less than 1 kilometer with measurement times typically 1/10 second.
Most military rangefinders use a much higher power transmitter with a time of flight method. A time of flight rangefinder just sends a single pulse and receives it. Some use multiple pulses for improved resolution and range but that typically isn't necessary. A counter is started on the rising edge of the transmitted pulse and stopped when the rising edge of the receive pulse is detected. If the counter is measuring a 150 MHz (approx) clock the range will be displayed in meters. Unfortunately that fast of counter requires at least a few high speed chips beyond the capability of standard CMOS or TTL logic. Since the round trip takes only 6.667 microseconds per kilometer you don't even need blanking on the displays. They can be attached directly to the counters or just read by a computer. A four or five digit counter suffices for most purposes. There is a little added complexity on sophisticated units for making the sensitivity of the receiver increase with time after the pulse is transmitted. This is sometimes done by charging a capacitor attached to a gain control which increases the gain with the square of time out to the maximum the unit is capable of. These rangefinders tend to be expensive because of the technology but the electronics is simple in concept. Ranges are limited only by the transmit power which can be extremely high using solid state Q switched lasers.
Surplus lasers and the associated electronics from military rangefinders have been showing up on the surplus market in the $300 range. Unfortunately the receivers have not.
For some insight on the level of complexity involved look at the boards sold by E-O Devices These are time of flight pulsed laser rangefinder components designed for use primarily with LED's or diode lasers. Also check Analog Modules for examples of state of the art variable gain rangefinder receivers. If you want one of their modules plan on spending between $1,000 and $2,000. :-(
Phase shift methods allow achieving high precision in distance resolution with lower power and lower speed circuitry. That equates to lower cost and higher precision. Which type is best depends on what properties are needed.
Parameter Single Pulse Phase Shift ------------------------------------------------------------------- Range 100 m to 100 km 1 m to 10 km Resolution 1 m any target 1 mm corner cube to 1 m any Cost $5000 and up $100 and up Power level 10 w to 1 MW 1 mW to 1 W Time to read sub-ms 0.01 to 10 seconds Applications artillery, navigation surveying, hunting
Single pulse rangefinders typically use YAG or erbium lasers while most of the phase shift type use diode lasers.
(From: Don Stauffer
Which type to use depends a bit on what range resolution you are looking
for. If you want high resolution, you will be working with a high
modulation frequency. Then you may find many circuits designed for
receiving audio modulation may not provide enough bandwidth.
Also, there is the range ambiguity problem. If you go high enough in
frequency, you may find some range ambiguity.
You will also likely be needing very accurate phase measurement circuits
if you are using moderate modulation frequency, so study carefully high
accuracy phase detectors. These are not trivial circuits. In order for
them to work well, you need a pretty good SNR.
(From: A. E. Siegman (siegman@stanford.edu).)
Adding to what others have said, hand-held laser rangefinders using
low-power RF-modulated CW lasers (a.k.a. diode lasers) together with
phase-detection techniques are simpler, cheaper, smaller, *much* more
battery efficient, and much safer; and are more or less replacing the
pulsed hand-held versions of yore.
These techniques are also moderately old. Coherent (maybe Spectra also) were
making widely used laser surveying instruments ("Geodolite"?) that
worked this way a couple decades or more ago (and there may have
been incoherent light source versions even further back).
I suppose that compared to TOF, one disadvantage is that it takes longer to
integrate up the signal to get a range finding, and if you're in a tank
battle and want to get off the first shot before alerting the enemy that
you're illuminating him and giving him a chance to duck, the pulsed type may
still be better.
Do some web searching: You can buy binoculars with a built-in diode
laser rangefinder from Amazon, and use it to measure the distance to the
pin on your next golf outing.
(From: Louis Boyd (boyd@apt0.sao.arizona.edu).)
Prior to laser diodes (1960's) there were optical geodimeters which
used a tungsten lamp, a Kerr shutter (which modulates light at
multi-megahertz rates using polarizers and high voltage rf driven
nitrobenzene), and photomultiplier receivers. These could measure
distances to a few centimeters at ranges of several kilometers. They
were large, expensive, and a bi*ch to calibrate. They used phase shift
techniques similar to modern diode rangefinders, but without the aid of
microprocessors. They switched modulation frequencies to resolve phase
ambiguities.
Modern rangefinders often use pseudorandom modulation and
cross-correlation computation to give the round-trip delay which is
proportional to distance. Distance resolution can be much finer than
the length of the shortest pulse.
With modern geodimeters the distance accuracy is primarily limited by
uncertainty of light propagation velocity in the air since it's not
practical to measure the pressure and humidity at all points along the
path, but can be accurate to better than 1 part in 10^6 with care. Tape
and chain is difficult to get better than 1 part in 10^3 which is the
typical accuracy of $200 pocket laser rangefinders.
(From: Mike Poulton (mpoulton@mtptech.com).)
Using pulses is not very practicable - if you want to achieve a resolution of
a few mm over a distance of 100 m or so, you find that you'd need extremely
short pulses (recall that 1 ns corresponds to 30 cm or 12 inches,
approximately, so you's need pulses of a few ps); you could do this with
a W-switched SS laser, but those little hand-held devices, who do
have a resolution in this order of magnitude, cannot work in this
way. They use a RF-modulated CW signal from a laser diode, say
with 100 MHz, and measure the phase shift of the 100 MHz signal between
outgoing and incoming beams. This phase shift can be very accurately
measured by first converting the 100 MHz down to a few 100 kHz (like
a superheterodyne receiver).
Some while ago I had been interested in such a circuit myself (for
measuring optical path lengths) but didn't find anything useful on the web.
(From: Repeating Rifle (SalmonEgg@sbcglobal.net).)
Equipment of this ilk is called *distance measuring equipment* or DME and
has all but replaced the use of chains in surveying practice. Various
implementations have been used. Some use high frequencies to obtain
precision and lower frequencies for range ambiguity resolution. Others use
inconmensurate frequencies that are not all that different from one another.
I you match the filtering to the transmission, you pretty much get the same
signal to noise ration for all kinds of devices. The broad-band pulses
mentioned above use short pulses. The CW devices use narrow band filters.
The first items of this nature used RF directly without light.
Trade names that come to mind quickly are tellurometer and geodimeter.
For the military rangefinders that use high power pulses, signal processing
is less than optimum. An error of 5 meters will usually not be a big deal.
For surveying, that kind of error will usually be unacceptable. In both
cases extended (in range) targets will introduce error.
Almost all of the inexpensive hand-held rangefinders on the market use a
simplified form of phase detection with relatively low modulation rates.
Phase sensing rangefinders uses a variable pulse width modulated laser diode.
It would use use thousands of on/off transitions in determining each distance
measurement by comparing the modulation pattern to the returned signal using
cross-correlation techniques. Resolution is a function of measurement
time, speed and size of the registers, and instrument stability. Single
pulse TOF rangefinders on the other hand are generally used for very
long ranges (several km and up) with very high pulse power (kilowatts to
megawatts peak) and range resolution rarely better than a meter. Low
power single pulse rangefinders are rare as the expense of the detection
circuits isn't justified for the low resolution.
The accuracy of quality surveying distance meters is limited primarily
by the uncertainty of the velocity of propagation of light through the
atmosphere. That varies of with air pressure and humidity which can't
easily be determined over the entire path. Still, they're orders of
magnitude better than a tape or chain.
(From: Phil Hobbs (pcdh@us.ibm.com).)
Modulated CW measurements also allow you to use very narrow measurement
bandwidths very easily (e.g. with a PLL), which helps the SNR very much. In
shorter range units, sinusoidal modulation can also be used to prevent
back-reflections from causing mode hopping. You choose delta-f so that the
phase modulation of the back-reflection (in radians) is at a null of the
zero-order Bessel function J0. This can make a huge difference (3 orders of
magnitude) in the back-reflection sensitivity.
A Q-switched solid state laser will give you short pulses with minimal fuss.
A unit like the small surplus Nd:YAG laser (SSY1) described in chapter:
Solid State Lasers was originally part of the M-1
tank rangefinders and thus should be ideal. It is quite trivial to build a
suitable power supply these laser heads since a passive Q-switch is used and
this doesn't require any electrical control.
A few mJ should be sufficient. (SSY1 is probably in the 10 to 30 mJ range
using the recommended pulse forming network.) With a Q-switched laser, the
required short pulse if created automagically eliminating much of the
complexity of the laser itself.
Diode laser assemblies from the Chieftain tank rangefinder are also available
on the surplus market but you probably would have to build a pulsed driver for
them which would be more work.
For the detector, a PIN photodiode or avalanche photodiode (APD) would be
suitable. The preamp is the critical component to get the required ns
response time. You need to sample both the pulse going out and the return
since the delay from firing the flashlamp (if you are using a solid state
laser) to its output pulse is not known or constant.
15 cm resolution requires a time resolution of about 1 ns (twice what you
might think because the pulse goes out and back). GHz class counters are no
big deal these days.
However, approaches that are partially analog (ramp and A/D) which don't
require such high speed counters are also possible. In fact, if your digital
design skills aren't so great, this is probably the easiest way to get decent
resolution, if possibly not the greatest accuracy/consistency. All you need
is a constant current source and an A/D (Analog to Digital converter). This
can be as simple as a FF driving a transistor buffer to turn the voltage to
charge the capacitor on and off with a transistor set up with emitter feedback
for as a constant current source. Or, it can just be an exponential charge
with non-linear correction done in software. The A/D doesn't need to be fast
as long as its output word has enough bits for your desired resolution. For
a typical exponential charging waveform, add 1 bit to the required A/D word
size. For example, determining distance over 100 meters to to 5 cm resolution
would require that the full voltage ramp be about 700 ns in duration (a bit
over maximum round trip time, cut off sooner if there is a return pulse) and
then sampled with a 12 bit A/D.
Another even simpler way of doing this is to charge the capacitor as above
but then discharge it with a much longer time constant and determine how long
it takes to reach a fixed voltage. By making the discharge time constant
sufficiently large, any vanilla flavored microprocessor could be used for
control and timing.
All in all, these are non-trivial but doable projects.
See the previous sections on laser rangefinders for more info.
Here is a Web site that appears to go into some detail on the design of
TOF laser rangefinders:
This was seen as a project in a Dutch book: "Lasers in Theorie en Praktijk:
Experimenten - Meten - Holografie", by Dirk R. Baur, Uitgeverij
Elektuur/Segment B.V., Postbus 75, 6190 AB, Beek (L) The Netherlands.
I'm not convinced that the circuit as presented works - there is at least
one part value (C4, 100 uF) which would appear to be much larger than
desired inside the feedback loop. The principle appears valid though.
In order for this to be implemented with a normal CCD camera, either direct
control of the electronic shutter is needed, bypassing any synchronous logic,
or a "sync" output from the camera must be available. Also note that the
charge integration times involved - 10s or 100s of ns - are orders of
magnitude smaller than those normally used on all but very specialized CCD
cameras, even with a fast shutter. So, sensitivity is going to be very low.
A high power pulsed laser may be needed to generate adequate photons and even
then, the CCD may not be able to supply enough charge.
However, there are CCD image sensors that have been designed specifically
for this application. They include logic on each pixel to enable the arrival
time to be determined and stored. This permits an entire depth map to be
captured with a single TOF pulse. See, for example:
CSEM Optical
Time-Of-Flight Imaging - A Technology for Multiple Applications.
If the surface is smooth and flat over a scale of 5 to 10 um, this could work
as a way of determining distance to the pickup. In other words, the dominant
return from the surface has to be a specular reflection back to the source in
order for the focus servo to lock properly. (The width and depth of the
pits/lands of the CD or DVD disc is small compared to the beam so they are
mostly ignored by the focus servo.) I don't know how much angular deviation
could be tolerated.
The output would be an analog voltage roughly proportional to focus error
which could be mapped to lens height (assuming the device is in a fixed
orientation with respect to gravity - more complex if you want to do this
while on a roller coaster or in microgravity!). The total range would be 1 to
2 mm with an accuracy of a few um.
Also see the section: Can I Use the Pickup from
a CD/DVD Player or CD/DVDROM Drive for Interferometry?, which would be
even more precise but more complex. The practical issues of using the guts of
these devices are also discussed there.
Since the 'stylus' of a CD player has an effective size of around 1 um (DVD
would be even less), it could in principle be used to implement a very high
resolution optical encoder for use in linear, rotary, or other sensing
application. The stand-off distance (from objective lens to focal point) can
be a couple of mm which may be an advantage as well. While this is probably
somewhat less difficult than turning a CD player into an interferometer (see
below), it still is far from trivial. You will have to create an encoder disc
or strip with a suitable reflective pattern with microscopic dimensions.
Without access to something like a CD/DVD mastering unit or semiconductor
wafer fab, this may be next to impossible. Your servo systems will need to
maintain focus (at least, possibly some sort of tracking as well) to the
precision of the pattern's feature size. To obtain direction information,
the 'track' would need to have a gray code pattern similar to that of a normal
optical encoder - but laid down with um accuracy in such a way that the
photodiode array output would pick it up. (Implementing an absolute encoding
scheme would probably require so many changes to the pickup as to make it
extremely unlikely to be worth the effort.) Of course, you also need laser
diode driver circuitry and the front-end electronics to extract the data
signal. Not to mention the need for a suitable enclosure to prevent
contamination (like lathe turnings) from gumming up the works. And, with your
device in operation, any sort of vibration or mechanical shock could cause a
momentarily or longer term loss of focus and thus loss of your position or
angle reference.
If you are still interested, see the section:
Can I Use the Pickup from a CD/DVD Player or
CD/DVDROM Drive for Interferometry? since some of the practical issues of
using the guts of these devices are discussed there.
For example, if the outgoing laser beam is modulated at 1 GHz and the
reflected beam is combined with this same reference 1 GHz in the sensor
photodiode or a mixer, for relative speeds small compared to c (the velocity
of light), the difference frequency will be approximately 1 Hz per 0.5
foot/second.
A simple version of a Michelson interferometer is shown below:
In a perfectly symmetric Michelson interferometer, the fringe pattern should
uniformly vary between bright and dark (rather than stripes or concentric
circles of light) depending on the phase difference between the two beams
that return from the two arms. A circular pattern is expected if the two
curvatures of the wavefront are not identical due to a difference in
arm-lengths or differently curved optics. Stripes (straight or curved) in
any direction) would be an indication of a misalignment of some part of the
interferometer (i.e. the beams do not perfectly overlap or one is tilted
with respect to the other).
(Yes, about 50 percent of the light gets reflected back toward the laser and
is wasted with this particular configuration. This light may also destabilize
laser action if it enters the resonator. Both of these problems can be easily
dealt with using slightly different optics than what are shown.)
A long coherence length laser producing a TEM00 beam is generally used for
this application. HeNe lasers have excellent beam characteristics especially
when frequency stabilized to operate in a single longitudinal mode. However,
some types of diode lasers (which are normally not thought of as having
respectable coherence lengths or stability) may also work. See the section:
Interferometers Using Inexpensive Laser
Diodes. Even conventional light sources (e.g., gas discharge lamps
producing distinct emission lines with narrow band optical filters) have
acceptable performance for some types of interferometry.
Such a setup is exceedingly sensitive to EVERYTHING since positional shifts
of a small fraction of a wavelength of the laser light (10s of nm - that's
nanometers!) will result in a noticeable change in the fringe pattern. This
can be used to advantage in making extremely precise position or speed
measurements. However, it also means that setting up such an instrument in a
stable manner requires great care and isolated mountings. Walking across the
room or a bus going by down the street will show up as a fringe shift!
Interferometry techniques can be used to measure vibrational modes of solid
bodies, the quality (shape, flattness, etc.) of optical surfaces, shifts in
ground position or tilt which may signal the precursor to an earthquake, long
term continental drift, shift in position of large suspended masses in the
search for gravitational waves, and much much more. Very long base-line
interferometry can even be applied at cosmic distances (with radio telescopes
a continent or even an earth orbit diameter apart, and using radio emitting
stars or galaxies instead of lasers). And, holography is just a variation on
this technique where the interference pattern (the hologram) stores complex
3-D information.
NASA has some information on interferometry oriented toward cosmic
measurements at the: NASA
Interferometry Page. And you can try your hands at aligning a Michelson
interferometer at the
NASA Interactive
Interferometer Page.
This isn't something that can be explained in a couple of paragraphs. You
need to find a good book on optics or lasers. Gordon McComb's: "The Laser
Cookbook [1} and the Scientific American collection: "Light and its Uses [5]"
include various type of interferometers which can be built with (relatively)
readily available parts. Agilent
(among others) manufacture 'Laser Interferometry Measurement Systems' based on
these techniques. Information and application notes are available by searching
for the key words: "Laser" or "Dimensional Measurement". For Agilent in
particular, searching for "5501" or "5517" will find information on their
specific systems.
Also see the Amateur
Interferometry Group (AIG) Web site. The AIG is an informal gathering of
people interested in designing, building, and operating various types of laser
interferometers. Much of the information relates directly to the testing
of optical components for astronomical telescopes but there should be much of
general interest as well.
If you've used a CD or DVD or a harddrive, in all likelihood, the
equipment that defined their track position and spacing was controlled
by a dimensional measurement system using a two frequency
interferometer. Additional applications include semiconductor steppers,
multiaxis precision machine tools, and others where very accurate non-contact
measurements or submicron positioning are required.
In two frequency interferometers such as those manufactured by Hewlett-Packard
(now Agilent), a special stabilized HeNe laser is used that produces two
slightly different frequencies (wavelengths) of light simultaneously
based on Zeeman splitting. By locking the difference frequency to
a highly stable reference oscillator, the accuracy and stability of the
measurements can be much more precise even compared to a normal frequency
stabilized HeNe laser system. In addition, since the comparison between
the reference beam and measurement beam is based on this difference
frequency as well, the system is more immune to noise.
A diagram of the general approach is shown in
Interferometer Using Two Frequency HeNe Laser.
The two frequency laser consists of a HeNe laser tube surrounded by
permanent magnets which produce a constant axial magnetic field.
The laser tube is short enough that only a single longitudinal mode will
normally oscillate if it is near the center of the gain curve. (Those on
either side will not see enough gain.) The axial magnetic field results
in the Zeeman effect splitting the beam into two slightly different
frequencies which are circularly polarized in opposite directions. Thus,
instead of the laser output being a single line (wavelength), it becomes
a pair of lines at slightly different wavelengths which correspond to slightly
different frequencies. The difference between the two frequencies is
typically in the 1.5 to 4 MHz range which makes it extremely easy to
process electronically. The actual difference frequency is determined
by the strength of the magnetic field (and other physical details) as
well as how far away the (split) lasing mode is from the center of the
doppler broadened HeNe gain curve. The beat frequency is lowest when
the lasing mode is centered on the gain curve and increases the further
away from the center it is. At some point, the sub-mode furthest from the
center will cease to oscillate at all due to insufficient gain and the beat
will disappear. (If the tube is too long, more than one Zeeman split mode
may be present simultaneously resulting in a superposition of beat frequencies
which are not generally terribly useful.)
There is a piezo element and/or heater inside the laser tube to precisely
adjust cavity length. A feedback control system typically consisting
of a phase locked loop using a temperature stabilized quartz
oscillator as a reference is used to adjust the cavity length to
maintain the beat frequency at a specific point near the center of the
gain curve. The exact center would be optimum but might be difficult
to guarantee so it's probably slightly on one side. (Lower or upper
will depend on which one provides negative feedback stability.) For a
given tube/magnet combination, this sets the actual laser wavelengths
- and thus the measurement increment - to a very precise and constant
value which remains essentially unchanged for the life of the
instrument. For example, with the doppler broadened gain curve for
the HeNe laser being about 1.5 GHz FWHM (1 part in about 300,000 with
respect to the 474 THz optical frequency at 633 nm) and a 1 percent
accuracy within the gain curve, the absolute wavelength accuracy will
then be better than 1 part in 30 million! Not too shabby for what
is basically a very simple system. :)
Since the output of the laser is a beam consisting of a pair of
circularly polarized components, a wave plate is used to separate
these into two orthogonal linearly polarized waves, called F1 and F2.
The beam consisting of F1 and F2 is split into two parts: One part
goes through a polarizer at 45 degrees to F1 and F2 (to recover a
signal with both F1 and F2 linearly polarized in the same direction)
to a photodiode to generate a local copy of the reference frequency
for the laser stabilization feedback as well as the measurement
electronics; the second is the measurement beam which exits the laser.
The purpose of the remainder of the interferometer is essentially to
measure the path length change between two points. In a typical
installation, the beam consisting of F1 and F2 is sent through a
polarizing beam splitter. F1 goes to a corner (retro) reflector on
the object whose position is being measured and F2 goes to a corner
reflector fixed with respect to the beam splitter. However,
differential measurements could be made as well using F2 in some other
manner. Various "widgets" are available for making measurements of
rotary position, monitoring multi-axis machine tools, etc.
The return from the object corner reflector is F1+dF1 (delta-F1) which
is recombined with F2 and sent to a "receiver" module - a photodiode
and preamp which generates a new difference frequency, F1+dF1-F2.
This is mixed with the original F1-F2 reference to produce an output
which is then simply dF1. A change in the position of the object by
316 nm (1/2 the laser wavelength) results in dF1 going through a whole
cycle. By keeping track of the number of complete cycles of dF1 as
well as its phase, this provides measurements of object position down
to a resolution of a few nm with an accuracy of 0.02 ppm!
More information on the two frequency HeNe laser can be found in the
sections: Hewlett-Packard HeNe Lasers and
Two Frequency HeNe Lasers Based on Zeeman
Splitting. Searching on the Agilent Web site will yield some
more product specific information and application notes on two frequency
interferometers.
Your initial response might be: "Well, no system is ideal and the beams won't
really be perfectly planar so, perhaps the energy will appear around the
edges or this situation simply cannot exist - period". Sorry, this would be
incorrect. The behavior will still be true for the ideal case of perfect
non-diverging plane wave beams with perfect optics.
Perhaps, it is easier to think of this in terms of an RF or microwave, acoustic, or other source:
OK, I know the anticipation is unbearable at this point. The answer is that
the light is reflected back to the source (the laser) and the entire optical
path of the interferometer acts like a high-Q resonator in which the energy
can build up as a standing wave. Light energy is being pumped into the
resonator and has nowhere to go. In practice, unavoidable imperfections of
the entire system aside, the reflected light can result in laser instability
and possibly even damage to the laser itself. So, there is at least a chance
that such an experiment could lead to smoke!
(From: Art Kotz (alkotz@mmm.com).)
We don't have to to think all that hard to figure out where all the energy
is dissipated in a Michelson interferometer. Nor do we have to refer to
imperfect components either. The thought experiment of perfect non-absorbing
components still renders a physically correct solution.
To summarize a (correct) previous statement, in a Michelson interferometer
with flat surfaces, you can get a uniform dark transmissive exit beam. The
power is not dissipated as heat. There is an alternate path that light can
follow, and in this case, it exits the way it came in (reflected back out to
the light source).
In fact, with a good flat Fabry-Perot interferometer, you can actually
observe this (transmission and reflection from the interferometer alternate
as you scan mirror spacing).
In the electrical case, imagine a transmitter with the antenna improperly
sized so that most of the energy is not emitted. It is reflected back to the
output stage of the transmitter. If the transmitter can't handle dissipating
all that energy, then it will go up in smoke. Any Ham radio operators out
there should be familiar with this.
(From: Don Stauffer (stauffer@htc.honeywell.com).)
Many of the devices mentioned have been at least in part optical resonators.
It may be instructive to look at what happens in an acoustic resonator like an
organ pipe or a Helmholtz resonator.
Let's start with a source of sound inside a perfect, infinite Q resonator.
The energy density begins to build up with a value directly proportional to
time. So we can store, theoretically, an infinite amount of acoustic energy
within the resonator.
Of course, it is impossible to build an infinite Q resonator, but bear with me
a little longer. It is hard to get an audio sound source inside the resonator
without hurting the Q of the resonator. So lets cut a little hole in the
resonator so we can beam acoustic energy in. Guess what, even theoretically,
this hole prevents the resonator from being perfect. It WILL resonate.
No optical resonator can be perfect. Just like in nature there IS no
perfectly reflecting surface (FTIR is about the closest thing we have). Every
time an EM wave impinges on any real surface, energy is lost to heat. With
any source of light beamed at any surface, light will be turned into heat. In
fact, MOST of the energy is immediately turned to heat. By the laws of
thermodynamics, even that that is not converted instantaneously into heat, but
goes into some other form of energy, will eventually turn up as heat. You pay
now, or you pay later, but you always pay the entropy tax.
(From: Bill Vareka (billv@srsys.com).)
And, something else to ponder:
If you combine light in a beam splitter there is a unavoidable phase relation
between the light leaving one port and the light leaving the other.
So, if you have a perfect Mach-Zhender interferometer like the following
(From: A. Nowatzyk (agn@acm.org).)
A beam-splitter (say a half silvered mirror) is fundamentally a 4 port device.
Say you direct the laser at a 45 degree angle at an ideal, 50% transparent
mirror. Half of the light passes through straight, the rest is reflected at a
90 degree angle. However, the same would happen if you beam the light from
the other side, which is the other input port here. If you reverse the
direction of light (as long as you stay within the bounds of linear optics,
the direction of light can always be reversed), you will see that light
entering either output branch will come out 50/50 on the two input ports. An
optical beam-splitter is the same as a directional coupler in the RF or
microwave realm. Upon close inspection, you will find that the two beams of a
beam-splitter are actually 90deg. out of phase, just like in an 1:1
directional RF coupler.
In an experiment where you split a laser beam in two with one splitter and
then combine the two beams with another splitter, all light will either come
out from one of the two ports of the second splitter, depending on the
phase. It is called a Mach-Zehnder interferometer.
Ideal beam-splitters do not absorb any energy, whatever light enters will come
out one of the two output ports.
There will be interference but you won't see any visible patterns unless the
two sources are phase locked to each-other since even the tiny differences in
wavelength between supposedly identical lasers (HeNe, for example) translate
into beat frequencies of MHz or GHz!
(From: Charles Bloom (cbloom@caltech.edu).)
The short answer is yes.
Let's just do the math. For a wave-number k (2pi over wavelength), ordinary
interference from two point-like apertures goes like:
Now for different wavenumbers:
The L dependence is the usual phenomenon of "beats" which is also a type of
interference, but not the nice "fringes" we get with equal wavelengths (the L
dependence is like a Michelson-Morely experiment to compare wavelengths of
light, by varying L (the distance between the screen and the sources) I can
count the frequency of light and dark flashes to determine k-K.
So you would like to add a precision measurement system to that CNC machining
center you picked up at a garage sale or rewrite the servo tracks on all your
dead hard drives. :) If you have looked at Agilent's products - megabucks
(well 10s of K dollars at least), it isn't surprising that doing this may be
a bit of a challenge. As noted in the section:
Basics
of Interferometry and Interferometers, a high quality (and expensive)
frequency stabilized single mode HeNe laser is often used. For home use
without one of these, a short HeNe laser with a short random polarized tube
(e.g., 5 or 6 inches) will probably be better than a high power long one
because it's possible only 2 longitudinal modes will be active and they will
be orthogonally polarized with stable orientation fixed by the slight
birefringence in the mirror coatings. As the tube heats up, the polarization
will go back and forth between the two orientations but should remain constant
for a fair amount of time after the tube warms up and stabilizes. Also see
the section: Inexpensive Home-Built Frequency
or Intensity Stabilized HeNe Laser.
The problem with cheap laser diodes is that most have a coherence length that
is in the few mm range - not the several cm or meters needed for many
applications (but see the section: Can I Use
the Pickup from a CD Player or CDROM Drive for Interferometry?). There
may be exceptions (see the section:
Interferometers Using Inexpensive
Laser Diodes) and apparently the newer shorter wavelength (e.g., 640 to
650 nm) laser pointers are much better than the older ones but I don't know
that you can count on finding inexpensive long coherence length laser diodes.
Even if you find that a common laser diode has adequate beam quality when you
test it, the required stability with changes in temperature and use isn't
likely to be there.
The detectors, front-end electronics, and processing, needed for an
interferometer based measurement system are non-trivial but aren't likely to
be the major stumbling block both technically and with respect to cost. But
the laser, optics, and mounts could easily drive your cost way up. And,
while it may be possible to use that $10 HeNe laser tube, by the time you
get done stabilizing it, the effort and expense may be considerable.
Note that bits and pieces of commercial interferometric measurings systems
like those from HP do show up on eBay and other auction sites from time to
time as well as from laser surplus dealers. The average selling prices are
far below original list but complete guaranteed functional systems or rare.
(From: Randy Johnson (randyj@nwlink.com).)
I'm an amateur telescope maker and optician and interferometry is a technique
and method that can be used to quantify error in the quality of a wavefront.
The methods used vary but essentially the task becomes one of reflecting a
monochromatic light source, (one that is supplied from narrow spectral band
source i.e., laser light) off of, or transmitting the light through a reference
element, having the reference wavefront meet the wavefront from the test
element and then observing the interference pattern (fringes) that are formed.
Nice straight, unwavering fringe patterns indicate a matched surface quality,
curved patterns indicate a variation from the reference element. By plotting
the variation and feeding the plot into wavefront analysis software (i.e., E-Z
Fringe by Peter Ceravolo and Doug George), one can assign a wavefront rating
to the optic under test.
The simplest interference test would involve two similar optical surfaces in
contact with each other, shining a monocromatic light source off the two and
observing the faint fringe pattern that forms. This is known as a Newton
contact interferometer and the fringe pattern that forms is known as Newton's
rings or Newton's fringes, named for its discoverer, you guessed it, Sir Issac
Newton. If you would like to demonstrate the principle for yourself, try a
couple of pieces of ordinary plate glass in contact with each other, placed
under a fluorescent light. Though not perfectly monochromatic, if you observe
carefully you should be able to observe a fringe pattern.
Non-contact interferometry is much tougher as it involves the need to get a
concentrated amount of monochromatic light through or reflected off of the
reference, positioning it so it can be reflected off of the test piece, and
then positioning the eye or imaging device so that the fringe pattern can be
observed, all this while remaining perfectly still, for the slightest
vibration will render the fringe pattern useless.
(From: Bill Sloman (sloman@sci.kun.nl).)
An interferometer is a high precision and expensive beast ($50,000?). You use
a carefully stabilized mono-mode laser to launch a beam of light into a cavity
defined by a fixed beam splitter and a moving mirror. As the length of the
cavity changes, the round-trip length changes from an integral number of
wavelengths of light - giving you constructive interference and plenty of
light - to a half integral number of wavelengths - giving you destructive
interference and no light.
This fluctuation in your light output is the measured signal. Practical
systems produce two frequency-modulated outputs in quadrature, and let you
resolve the length of a cavity to about 10 nm while the length is changing at
a couple of meters per second. The precision is high enough that you have to
correct for the changes in speed of light in air caused by the changes
temperature and pressure in an air-conditioned laboratory.
Hewlett-Packard invented the modern interferometer. When I was last involved
with interferometers, Zygo was busy trying to grab a chunk of the market from
them with what looked liked a technically superior product. Both manufacturers
offered good applications literature.
(From: Mark Kinsler (kinsler@froggy.frognet.net).)
You can get interferometer kits from several scientific supply houses. They
are not theoretically difficult to build since they consist mostly of about
five mirrors and a lens or two. But it's not so easy to get them to work
right since they measure distances in terms of wavelengths of light, and
that's *real* sensitive. You can't just build one on a table and have it work
right. One possible source is: Central Scientific Company.
(From: Bill Wainwright (billmw@isomedia.com).)
Yes, you can build one on a table top. I have done it. I was told it could
not be done but tried it anyway. The info I read said you should have an
isolation table to get rid of vibrations I did not, and even used modeling
clay to hold the mirrors. The main problem I had was that the image was very
dark and I think I will use a beam splitter in place of one of the mirrors
next time. The setup I had was so sensitive that lightly placing your finger
on the table top would make the fringes just fly. To be accurate you need to
take into account barometric presure and humidity.
While I don't know how to select a laser diode to guarantee an adequate
coherence length, it certainly must be a single spatial (transverse) mode
type which is usually the case for lower power diodes but those above 50
to 100 mW are generally multimode. So, forget about trying to using a 1 W
laser diode of any wavelength for interferometry or holography. However,
single spatial mode doesn't guarantee that the diode operates with a single
longitudinal mode or has the needed stability for these applications. And,
any particular diode may operate with the desired mode structure only over
a range of current/output power and/or when maintained within a particular
temperature range.
(From: Steve Rogers (scrogers@pacbell.net).)
I have been involved with laser diodes for the last 15 years or so. My first
was a pulsed (only ones available at that time) monster that peaked 35 watts
at 2 kHz with 40 A pulses! It was a happy day when they could operate CW and
visible to say the least. Anyway, in the course of my working travels, I have
built numerous Twymann-Green double pass interferometers for the wave front
distortion analysis of laser rods, i.e., Nd:Yag, Ruby, Alexandrite, etc. The
standard reference light source for this instrument has always been the 632.8
nm HeNe laser. Good coherence length and relatively stable frequency was its
strong suit.
When visible diode lasers came out I often wondered aloud about their
suitability as a replacement for the HeNe. I despise HeNe lasers. They are
bulky and I have been shocked too many times from their power supplies.
I assumed that since CD player laser diodes at 780 nm could have coherence
lengths on the order of tens of centimeters or into the meters (!!, see, for
example: Katherine Creath, "Interferometric Investigation of a Diode Laser
Source", Applied Optics (24 1-May-1985) pp. 1291-1293), Visible Laser Diodes
(VLDs) could make excellent replacements. As it turned out, VLDs tend to have
coherence lengths which are considerably shorter according to the latest
technical literature and I held off on experimenting with them. Last week, I
went through my shop and found enough mirrors, beam splitter, assorted optics
to throw together my own double-pass interferometer for home use. This
coincided with my acquisition of a 635 nm 5 mw diode module - a good one from
Laserex.
To make a longer story shorter, I assembled said equipment with the VLD and
WOW! excellent fringe contrast (a test cavity of four inches using a .250" x
4.0" Nd:Yag rod as the test sample.) When a HeNe laser was substituted for
the VLD, virtually no difference in the manual calculation of wave front
distortion (WFD) and fringe curvature/fringe spacing. The only drawback with
the VLD is that it produces a rectangular output beam. When collimated you
have a LARGE rectangular beam rather than a nice round HeNe style beam. My
interferometer now occupies a space of 10" x 10" and is fully self contained.
It probably could even be made smaller. Not only that, but it runs on less
than 3 V!!!
I am just as surprised as you are with the results that I achieved. This is
one reason why it took me so long to attempt this experiment (something like
4 to 5 years). I have always assumed that a HeNe laser would be FAR superior
in this configuration than a VLD would be. Perhaps others may know more about
the physics than I do. One thing is certain, these are "single mode" index
guided laser diodes and typically exhibit the classic gaussian intensity
distribution which is not so evident with the "gain guided" diodes. This in
turn implies a predominant lasing mode which in turn would imply a (somewhat)
stable frequency output. Purists would note that this VLD has a nominal
wavelength of 635 nm +/- 10 nm while the HeNe laser is pretty much fixed at
632.8 nm. This variable could account for extremely minor WFD differences.
(From: W. Letendre (wjlservo@my-dejanews.com).)
There's an outfit in Israel selling a diode based laser interferometer enough
cheaper than Zeeman split HeNe units to suggest that they are using a laser
diode in the 'CD player' class, or perhaps a little better. They are able to
measure, 'single pass' (retro rather than plane mirror) over lengths of up to
about 0.5 m, suggesting that as an upper limit for coherence length.
People sometimes ask about using the focused laser beam for for scanning or
interferometry. This requires among other things convincing the logic in
the CD/DVD player or CD/DVDROM drive to turn the laser on and leave it on
despite the possible inability to focus, track, or read data. The alternative
is to remove the optical pickup entirely and drive it externally.
If you keep the pickup installed in the CD player (or other equipment),
what you want to do isn't going to be easy since the microcontroller will
probably abort operation and turn off the laser based on a failure of the
focus as well as inability to return valid data after some period of time.
However, you may be able to cheat:
CAUTION: Take care around the lens since the laser will be on even when there
is no disc in place and its beam is essentially invisible. See the section:
Diode Laser Safety before attempting to
power a naked CD player or simlar device.
It may be easier to just remove the pickup entirely and drive it directly. Of
course you need to provide a proper laser diode power supply to avoid damaging
it. See the chapter: Diode Laser Power
Supplies for details. You will then have to provide the focus and/or
tracking servo front-end electronics (if you need to process their signals or
drive their actuators) but these should not be that complex.
Some people have used intact CD player, CDROM, and other optical disc/k drive
pickup assemblies to construct short range interferometers. While they have
had some success, the 'instruments' constructed in this manner have proven
to be noisy and finicky. I suspect this is due more to the construction of
the optical block which doesn't usually take great care in suppressing stray
and unwanted reflections (which may not matter that much for the original
optical pickup application but can be very significant for interferometry)
rather than a fundamental limitation with the coherence length or other
properties of the diode laser light source itself as is generally assumed.
In any case, some of the components from the optical block of that dead CD/DVD
player may be useful even if you will be substituting a nice HeNe laser for
the original laser diode in your experiments. Although CD optics are optimized
for the IR wavelength (generally 780 nm), parts like lenses, diffraction
grating (if present and should you need it), and the photodiode array, will
work fine for visible light. However, the mirrors and beam splitter (if
present) may not be much better than pieces of clear glass! (DVDs lasers are
635 to 650 nm red, so the optics will be fine in any case.)
Unfortunately, everything in a modern pickup is quite small and may be a bit
a challenge to extract from the optical block should this be required since
they are usually glued in place.
If what you want is basic distance measurements, see the section:
Using a CD or DVD Optical Pickup for Distance
Measurements which discusses the use of the existing focusing mechanism
for this purpose - which could be a considerably simpler approach.
Also see the section: Basics of Interferometry
and Interferometers.
The longitudinal mode structure of a laser is one of those concepts
that is often explained but not so often demonstrated. There are
a number of indirect ways of showing that it exists including
monitoring the beat frequencies between modes and looking at
the fringe patterns in a Michelson or other conventional
interferometer. One of the clever ways of actually being able
to display the modes as they would appear in a textbook is to
use an instrument called a Scanning Fabry-Perot Interferometer
(SFPI). While conceptually simple, even a basic SFPI can
resolve detail in the longitudinal mode structure of a laser
that represents better than 1 part in 10,000,000 compared
to the frequency of oscillation of the laser.
An SFPI consists of a pair of mirrors with relatively high
reflectivity (90% to 99.9% or more is typical) mounted
in a rigid frame. In most SFPIs, the laser under test (LUT) is
aimed into one end and a photosensor is mounted beyond the other end.
The coarse spacing and alignment of the mirrors can be adjusted by
micrometer screws. The axial position of one of the mirrors can also
be varied very slightly (order of a few half-wavelengths of the LUT)
by a linear PieZo Transducer (PZT). By driving the PZT
with a ramp waveform and watching the response of the photosensor
on an oscilloscope, the longitudinal modes of the LUT can be displayed
in real time. In essence, the comb response of the SFPI is used
as a tunable filter (by the PZT) to analyze the fine detail of the
optical spectrum of the LUT. As long as the FSR (c/2*L except under
certain conditions, described below) of the SFPI is larger than the
extent of the lasing mode structure of the LUT, the mode display
will be unambiguous. Where this condition isn't satisfied, the mode
display will wrap around and may be very confusing. For example,
the common helium-neon (HeNe) laser has a gain bandwidth of about 1.5 GHz
and longer HeNe laser tubes will generally operate with multiple
longitudinal modes covering much of this range. Thus the
FSR of an SFPI to be used with such a laser must
be greater than 1.5 GHz, corresponding to an SFPI cavity length of
less than about 100 mm (assuming c/2*L). For Nd:YAG, the gain bandwidth
is about 150 GHz, which results in a required SFPI cavity length of
less than 1 mm! However, in practice, lasers don't necessarily lase
over their entire gain bandwidth, especially if specific steps have
been taken to assure single or dual mode operation (also called single
or dual frequency operation). For those - which include many useful
lasers - the requirement can be relaxed such that the FSR of the SFPI
only needs to be larger than the width of the expected mode structure.
And for a single mode laser, this would be only the width of the lasing
line itself. Therefore, in these cases, a long cavity low FSR SFPI will
result in the highest resolution.
Commercial scanning Fabry-Perot interferometers usually cost thousands
of dollars - or more! But it's possible to construct an SFPI that
demonstrates the basic principles - and can be even quite useful -
for next to nothing, and one that rivals commercial instruments for
less than $100.
The resolution ("resolvence") of a Fabry-Perot interferometer is determined
by the wavelength, mirror reflectance, mirror spacing, and incidence angle
of the input beam. For the following, we assume normal incidence (which
will be satisfied in most practical situations).
Consider an SFPI with a mirror spacing (d) of 80 mm and reflectance (R) of
99 percent at a wavelength (Lambda) of 632.8 nm (red HeNe laser):
Another measure of the performance of an interferometer or laser cavity
is the "finesse". This dimensionless quantity is the ratio of the
FSR to the resolution. In essence, for the SFPI, finesse determines the
how much fine detail is possible within one FSR. The reflectance finesse
is equal to pi*sqrt(R)/(1-R) where R is the reflectance of each mirror (which
are assumed to be equal). For R near 1 as would be the
case in a useful SFPI, this reduces to pi/(1-R). While other factors
will affect the finesse, this equation will be reasonably accurate for
a properly designed spherical mirror cavity. So, with a reflectivity of
99 percent for both mirrors, the finesse will be roughly 300. If the
FSR is 1.875 GHz as in the example above, the resolution will be
approximately 6 MHz, which is in agreement with that calculation.
Other factors will conspire to reduce the useful resolution of a practical
SFPI. At modestly high mirror reflectivity (e.g., R=99%), these include
alignment, input beam diameter, and input beam collimation. As R is pushed
closer to 100%, the quality of the mirrors, their cleanliness, and internal
losses become increasingly important. But for the example above, even if
the actual finesse is worse by an order of magnitude compared to the theory,
it will still be possible to easily resolve the individual modes of any
common HeNe laser and probably even the nearly 2 meter long Spectra-Physics
model 125 (177 cm resonator, mode spacing of 85 MHz). This is a factor of
better than 1 part in 10,000,000 comparing resolution to optical frequency!
However, note that while textbooks will tell you that the peaks should get
through with little attenuation, this is probably not going to be true with
practical high finesse SFPIs. (At least not those you're likely to see!)
The amplitude of the peaks will depend critically on the quality of the
mirrors and of course, on the alignment. For "laser quality" dielectric
mirrors, I've gotten as high as 5 to 10 percent peak transmission for a
high finesse SFPI using mirrors with a reflectivity of 99.8%. I'm sure
this can be improved upon but even so, for a 1 mW laser, there is still
more than enough optical power at the output of the SFPI to produce a
nice display on most scopes using a 1:1 probe without a preamp.
(From: A. E. Siegman (siegman@stanford.edu).)
In evaluating the effect of losses in Fabry-Perot mirrors you really
have to distinguish between internal losses (or loss-equivalent effects,
like scattering) that are physically located "inside" the mirrors (i.e.,
inside the effective reflection plane of each end mirror), and external
losses that are physically located "outside" the effective reflection
plane, but still within the physical layer of the mirror.
Losses that are outside the mirrors are effectively just additional
external transfer losses in the system, i.e. they have the same effect
as if they were separate from the FP, so that they don't affect the FP
itself but just weaken the light before or after the FP.
Losses inside the mirrors (aka "internal" losses) are more serious
because they are exposed to the higher-intensity resonant fields inside
the FP and therefore can significantly affect the finesse and peak
transmission of the FP.
Just measuring the net reflectivity and net transmission of the mirror
itself won't clearly distinguish between these internal and external
losses. Also, how you'd describe a situation where the losses are
distributed through a moderately thick mirror layer is something I've
never thought through; doing this would require a slightly more
sophisticated wave calculation of forward and backwave wave propagation
inside the finite-thickness partially absorbing mirror layer itself.
(Too bad I'm no longer actively teaching laser courses; this
calculation would make a nice homework problem to torment -- sorry,
educate -- students.)
One way to eliminate the transverse mode problem is to use a cavity
configuration called a Mode Degenerate Interferometer (MDI) in which the
higher order transverse modes have the same frequency/wavelength as some
of the TEM00 (longitudinal) modes and thus simply fall on top of them
in the display. Even though each peak in the display representing a
longitudinal mode of the input laser may actually be
built up of contributions from multiple transverse modes excited in
the resonator of the interferometer, the characteristics
of the individual longitudinal mode components in each of these
transverse mode are the same so the accuracy of the resulting display
isn't affected. (This should not be confused with the very different
situation of a laser having multiple transverse modes in
its output where the frequencies, phases, amplitudes, and
polarizations of the corresponding longitudinal modes in each
transverse mode may differ.)
Two practical arrangements that satisfy this condition are the (1)
spherical cavity (d=2*r) and (2) confocal cavity (d=r). The confocal
cavity has the larger finesse and is thus usually employed in SFPIs
since the finesse is a measure of Q-factor with respect to the FSR
or mode spacing, and thus higher finesse results in better resolution.
A planar cavity (r is infinity) doesn't support higher order modes at all
but is generally a less desirable configuration (see below).
Note that the term "confocal" actually refers to any cavity where the
focal points of the two mirrors are coincident. However, only the case
where d=r is stable and thus useful for the MDI SFPI.
The frequencies of the transverse modes of a symmetric cavity
Fabry-Perot resonator are given by the following equation:
where:
The interferometer will be mode degenerate when there are TEM00 modes that
have the same frequency as some of the transverse modes. The
requirement for this to be satisfied is for the inverse cosine term
in the equation above to be equal to pi divided by an integer, l. Then
there will be "l" types of modes with one type - where (1+m+n) is equal to
1, modulo(l) - having the same frequencies as some TEM00 modes.
When (1+m+n) is not equal to 1, modulo(l), that mode will fall
in between the TEM00 modes in locations depending on (m+n)/l, modulo(l):
While the confocal and spherical MDI configurations are the best known
and most widely used, it's possible to make use of cavities having values
of l other than 1 or 2 and they may be useful for certain applications.
See: Variable
Free Spectral Range Spherical Mirror Fabry-Perot Interferometer. Though
that's for the advanced course, here are a couple of examples:
Further investigation of these special cases is left as an exercise
for the reader. :)
For the confocal cavity, half of the transverse modes are not
mode degenerate when an on-axis input beam is used as
there are two types of modes depending on whether the quantity
(1+m+n) is even or odd:
This seems a bit strange that the TEM00 modes (m+n=0) have non-integer mode
numbers but the equation has been confirmed from at least two different
sources.
As noted, with two sets of peaks, the FSR is effectively cut
in half to c/(4*d). Rearranging the equation above with the new FSR of c/(4*d)
out in front, one sees that the various transverse modes (those that
differ in m+n) result in a frequency difference of c/(4*d). However,
integer differences in q corresponding to the longitudinal modes, still
have an FSR of c/(2*d). Where a paraxial beam (one parallel to the
optical axis) enters the confocal cavity off-center, the beam path repeats
itself after two traversals of the cavity (in a zigzag pattern) and the
FSR is easily seen to be c/(4*d) rather than c/(2*d). However, if the
beam is very well aligned and centered, the FSR will be c/(2*d) since only
some symmetric modes will be excited.
Note that when adjusting the mirror distance to be confocal, there will be
many positions where the SFPI may appear to work but which aren't quite
confocal. Depending on the specific distance, non-degenerate higher order
modes will result in ghost peaks and/or a variation in the amplitude of
the lasing modes depending on their position on the voltage ramp drive
signal. The amplitude will also be lower overall. However, when the
correct distance is approached, all of these ghosts will collapse into
the desired high amplitude display. Don't be fooled! Thus it's best to
know or determine the exact RoC for the mirrors before installing them in
the SFPI so the initial distance can be set reasonably precisely.
Planar mirrors may also be used since a true flat-flat cavity does not
support stable higher order modes, degenerate or otherwise, but it is
the most difficult to align and
the realizable finesse is lower than for the confocal arrrangement. The
"effective fineese" is also much more dependant on the alignment than
with the MDI or with other non-planar configurations. Also, with optimal
alignment, the incident beam is reflected directly back into the laser
which may result in instability for some types of lasers. However, where
the distance between the mirrors of the SFPI is adjustable (as in some
general purpose instruments like the TecOptics FPI-25), there is no
choice. (Intracavity etalons also usually use planar mirrors but the
finesse of these does not generally need to be very high.)
My challenge was to prove that I could construct an SFPI that would
at least demonstrate the basic principles and possibly even be useful.
The results are described in this and the following sections.
All of mine cost me absolutely nothing (except time) but
that wouldn't sound as credible as $1.00 or $2.00 or $3.00. :)
The heart of the SFPI is its two mirrors. For longer visible
wavelengths (i.e., 600 to 700 nm), the mirrors can be the OCs salvaged from a
pair of dead red (632.8 nm) HeNe laser tubes. For other wavelength ranges,
mirrors from green (532 nm) DPSS lasers, green or blue ion lasers, HeCd, and
other lasers may be useful. While some of these mirrors may have a relatively
broad band reflectance, this cannot be counted on. More often than not,
the reflectance falls off dramatically beyond 10 or 20 nm from the spec'd
wavelength. And, obtaining proper single mode performance
of the SFPI without great pain may require that mirrors with specific
reflectances and RoCs not normally found in common lasers be used.
Of course (gasp!), suitable mirrors can be also be purchased.
For common wavelengths, they may be available from companies like CASIX at
very reasonable prices. But in general, obtaining the optimum mirror might
require ordering a set of custom mirrors. It's not the ground and polished
mirror glass itself that will cost a lot of money. They can often be
standard concave lenses with suitable curvature available from places
like Edmund Industrial Optics or Melles Griot. It's the custom coating,
which can easily exceed $1,000, and it doesn't matter that much whether
the lot is 2 mirrors or 200 mirrors as what counts is the coating machine
time. So, find 99 friends who want to build the same SFPI and the
per-mirror cost could still be quite low. :)
As far as attempting to coat your own mirrors - in two words: Forget it. :)
Unless you have access to a dielectric mirror coating machine and know how
to use it (and are permitted to use it!), there is no way to produce coatings
that will do anything more than provide a hint of what's possible. Metal
(aluminum, silver, gold) coated mirrors do not work well since their maximum
reflection coefficient is around 94 to 97 percent and they have high
absorption losses. Thus finesse will be poor and the photodetector
signal will be very small. And except for gold, the coatings degrade
(tarnish, oxidize) in air without a protective layer, with silver being
the worst. For good quality dielectric mirrors, absorption losses only
become a major concern for very high reflectivities (perhaps above 99.9%)
and modern coatings do not degrade significantly under normal conditions
as long as they are not subject to physical abuse or improper cleaning
techniques.
When specifying the mirror RoC (r) for a particular application, it
usually makes sense to base it on the maximum frequency range over
which there will be action, not simply on the gain bandwidth of the
laser(s) being observed. Not only will this result in the best
resolution, but doing otherwise may simply not be practical.
For common gas lasers like the HeNe and argon ion which
have longitudinal modes filling most of their gain bandwidth,
(1.5 GHz and 5 GHz, respectively) there's no choice if the
display is to be unambiguous. But where the modes have already
been limited by an etalon or some other means, only the range
of the modes that are present need to fit into the SFPI's FSR.
For example:
The other major components of the SFPI include the PieZo Transducer (PZT) to
move one of the mirrors a micron or so, and a photodiode to monitor the
output beam.
High quality PZTs can be purchased at exorbitant cost. But the beeper from
a digital watch or similar device will work nearly as well and has the
advantage that it runs on much lower voltage than some other types. You
never did like that alarm anyhow. :) But no need to discombobulate your
watch as these piezo elements can be purchased from electronics distributors
or surplus places for about $1.00. :) While they aren't quite as linear or
have as good a frequency response as the high priced units, these deficiencies
don't really matter much for an SFPI. And since they will move several microns
on only 50 V, a high voltage amplifier isn't needed as with many commercial
SFPIs. The 20 or 30 V p-p output of a typical function generator is quite
adequate.
.
The photodiode can be almost anything since it needs neither a large area or
high frequency response. I typically use a photodiode from a barcode
scanner with a 10K ohm resistor load and 10:1 or 1:1 scope probe. Where
more sensitivity is needed as with very high-R mirrors or low power lasers,
a transimpedance amplifier with very high gain using can be added since
frequency response isn't critical. Any garbage op-amp will suffice.
Everything else is hardware. The structure and mirror mounts are easily
home-built. However, one area where it may be hard to compete with
commercial SFPIs is in minimizing the effects of temperature. They typically
construct the main support as a cylinder or set of rods made from Invar,
a low coefficient of thermal expansion alloy. Some designs further
compensate for residual effects by balancing them against those
of the PZT resulting a near zero net change in FSR with respect
to temperature and/or may include a heater in a closed-loop temperature
stablization system. Invar stock is available or can be salvaged from
various dead lasers. Some people build SFPIs by mounting the back mirror
and PZT in an Invar tube, positioning the front mirror using a 5-axis
lab stage, and then gluing it in place permanently when the optimal
mirror spacing and alignment has been determined. But glue tends to be
too permanent for my taste. :) Constructing the SFPI using Invar rods
is nearly as good. But simply enclosing a non-Invar based SFPI in an
insulating box will go a long way in reducing temperature effects.
A triangle (or sawtooth) wave source (it can be a simple circuit constructed
for this purpose or a general purpose function generator) and oscilloscope
(preferably dual trace and/or with an X-Y display mode) will be required to
view the scan but needn't be dedicated to the SFPI, so they don't count
toward the cost!
The next few sections include general descriptions and photos of several
home-built SFPIs. Schematics for both a photodiode preamp and simple
function generator are provided later in this chapter.
The basic design is shown in Home-Built Scanning
Fabry-Perot Interferometer 1. My prototype uses the OC mirrors from
a couple of dead Aerotech 1 mW HeNe laser tubes. The PZT is the beeper
from some sort of musical greeting card with a 4 mm hole drilled in the
center. The photodiode is from a barcode scanner.
The frame and mounts are a bit different than those shown in the
diagram, above. They were made from the platter clamping plates from some
ancient 5-1/4" harddrives, hex spacers, and miscellaneous scrap metal.
The circular plates are nice because they have predrilled holes with
6-fold symmetry thus simplifying construction. See
Photo of Sam's $1.00 Scanning Fabry-Perot
Interferometer. Here is a summary:
The front mirror is removable so other reflectances or RoCs can be tried. The
rear mirror is glued to the PZT. The hole was made by placing the PZT
on a hard surface (e.g., an aluminum plate) and drilling through it slowly
with modest pressure using a normal metal bit in a drill press. The piezo
material is more of a compressed powder than a true ceramic so it's possible
to grind it away (using the metal drill) with minimal chipping. Thin flexible
wires were already attached but if they aren't, solder the top lead near the
edge to leave room for the mirror and to minimize any change in elasticity of
the top surface. Once soldered, Secure the wires mechanically with a drop of
adhesive. Also note that the metallization tends to disappear with even
modest heat or stress so solder quickly. Conductive paint or silver Epoxy
can be used to touch up bare spots if needed but use as thin a layer as
possible as it may increase stiffness and reduce response sensitivity in
that area. For this reason, DO NOT coat the entire surface with adhesive
of any type!
To perform initial alignment, I used a yellow-orange HeNe laser thinking it
would be easier since the mirrors are less reflective away from the
632.8 nm design wavelength. The scatter off of the mirror surfaces was used
as the initial means of setting alignment, by minimizing the size of the line
or blob formed by the multiple reflections. With a pair of concave mirrors,
not only do they have to be aligned with respect to the input beam, they also
have to be aligned with respect to each other. In other words, their optical
axes must coincide which requires walking them until the scatter pattern is
minimized. When misaligned, it will be a line or circle and no amount of
adjustment of only one mirror may improve it. Once the initial alignment
was done, the PZT could be driven and the output of the photodiode used to
fine tune it. In retrospect, using the funny color HeNe laser wasn't
necessary as enough red light gets through to be easily seen for alignment
purposes. And the display of the modes of that multi-wavelength and
multi-transverse mode laser was definitely strange.
The preliminary results using a Melles Griot 05-LHR-911 HeNe laser were
also confusing. This is a 2 mW laser using a tube with about 165 mm between
mirrors, corresponding to a mode spacing of 883 MHz. The scope trace in
Sam's SFPI Display of Melles Griot 05-LHR-911 HeNe
Laser - Initial Attempt shows a jumbled mess due to many transverse modes
being excited in the SFPI. The trace on the left should cover a span of
approximately three FSRs of the SFPI - about 19.5 GHz. Three clumps that look
about the same are clearly visible but the complexity isn't real. The trace
on the right is an expanded region of the one on the left. A hint of the
modes of the laser can be seen but only a hint. The 05-LHR-911 should have
2 or 3 longitudinal modes at most but the short cavity of the SFPI using
long radius mirrors is resonating with multiple transverse modes.
There is also some hysteresis in the PZT response. It's barely visible
on the display as the pattern differs slightly on the positive and negative
slopes of the triangle driving function. Using X-Y mode on the scope would
show up the hysteresis more clearly. Reducing the sweep speed slightly
virtually eliminates the hysteresis. (A 20 trace/second display has
minimal hysteresis and is still quite usable. Of course, this wouldn't
be an issue with a digital scope
The overall linearity of the PZT is around 5 to 10 percent over a range of
+/-20 V, corresponding to 5 or 6 FSRs of the SFPI. I've actually tested
several PZTs (another one was from a digital clock for which the alarm was more
of a nuisance than useful!). The response of one is compressed more toward
the upper end of the voltage range; the other is slightly compressed at both
ends. Within a single FSR, the linearity is probably better than 2 percent
and a range of a single FSR provides all the information usually needed.
For a system of this type where qualitative information is most important,
perfect linearity, especially over multiple FSRs, really isn't a major issue
in any case as long as it is known and doesn't change over time. A third
PZT was quite linear but had a range of only around 1 FSR of the SFPI -
probably due to the excessively thick layer of silver Epoxy I used to cover
some bald spots on the piezo disk.
To confirm that transverse modes were the cause of the complex display and to
partially remedy the situation, I aligned the SFPI more carefully by adjusting
the front mirror so that the 05-LHR-911 beam bounced directly back to the
source with dancing interference patterns, then aligned the rear mirror
for maximum amplitude of the displayed signal, and added an aperture about
0.3 mm in diameter (a pin hole in a piece of aluminum foil) inside the SFPI
cavity. The aperture was mounted on a micropositioner but could be installed
permanently so that doesn't blow my budget. :) The results are shown
in Sam's SFPI Display of Melles Griot 05-LHR-911 HeNe
Laser. The sequence of the six traces
show the modes of the 05-LHR-911 cycling over time as they
move under the HeNe gain curve. The horizontal scale is the same as
in the jumbled mess trace, above, but the transverse modes have been
almost entirely eliminated. The distance between similar peaks (2.2 boxes
on the screen) is the FSR of the SFPI - about 6.5 GHz. The distance
between longitudinal modes (0.3 boxes) is the 883 MHz FSR of the 05-LHR-911.
The math even works. :) So, this represents success of sorts
but alignment of everything is super critical and any vibrations - even
the audio from a radio - create havoc with the display. There is also
a quasi-periodic fluctuation in amplitude of all the displayed modes with
no corresponding power fluctuations in the laser. I suspect this to be
due to residual mode competition in the SFPI as the frequency of the modes
changes relative to the SFPI cavity, possibly a side effect of the aperture.
Sam's SFPI Display of a Melles Griot 05-LHR-151 HeNe
Laser shows the result using the same setup for a longer laser with more
closely spaced modes - 436 MHz compared to 833 MHz for the 05-LHR-911. With
this higher power laser, there are still some non-TEM00 modes just visible in
the display but they are fairly low level.
Sam's SFPI Display of Vertically Polarized Modes
of Melles Griot 05-LHR-151 HeNe Laser shows the effect of inserting
a polarizing filter into the beam. Since adjacent modes tend to be
of orthogonal polarization in randomly polarized HeNe lasers, every other
mode on the display has disappeared.
Finally, I tried a Spectra-Physics model 117A HeNe laser head, which when
used with its mating controller is a frequency or intensity stabilized
(single longitudinal mode) laser. I'm running it on an SP-248 so it's
not stabilized but the modes are a bit interesting. The mode spacing is
around 600 MHz which is consistent with a 2 to 3 mW HeNe laser. However,
as the modes cycle, there isn't a smooth progression through the gain
curve. It almost seems as though having exactly 2 modes is enhanced somehow
and that it's very unlikely to see 1 or 3 modes. When 1 or 3 modes would be
expected to pop up, they might appear very briefly, or be skipped
entirely in favor of the 2 modes one of which is on the opposite
side of the gain curve. The polarizations of the modes also appear to
be of the "flipper" variety, changing suddenly rather than staying with
a particular mode. I don't know if this behavior is by design. However,
since orthogonally polarized modes are sensed by a pair of photodiodes
in the laser head and used for stabilization, strong mode pairs could be
beneficial.
After determining experimentally that an aperture helped but didn't
totally eliminate the transverse mode problem, a Post Doc in our lab wrote
a simple Matlab program to calculate Hermite Gaussian transverse mode
profiles given the mirror RoCs and the distance between mirrors. Plugging
in the long radius SFPI cavity configuration revealed that the TEM00 and
TEM10/01/11 modes have a high degree of overlap regardless of axial position.
So, any aperture that suppresses them very effectively would also result in
unacceptable attenuation of the TEM00 mode. So, on to plan B. :)
I hope to have a compiled version of this program available in the near
future as it appears to be quite useful for visualizing cavity modes in
general.
Here is a summary of the configurations I've tried so far on the $1.00
SFPI:
Of these, the first is probably the best choice unless super high resolution
is needed. All except the flat-flat required an aperture inside the SFPI
cavity to suppress non-TEM00 (transverse) modes.
The mirrors were actually Melles Griot plano concave lenses custom
coated (along with a batch of microchip laser crystals) for 1,540 nm.
Now, it's perhaps a not so well known fact that a dielectric mirror
coated for a wavelength of X nm will also perform reasonably
well at a wavelength around X/3 nm (think of a stack of 3/4 lambda layers
instead of 1/4 lambda layers). The actual reflectance function will depend
on the design of the original mirror (number of layers, uniformity of
layer thickness, etc.) and will likely be slightly lower in maximum
reflectance, but possibly not by much. So, these mirrors should work
in a wavelength range centered around 513 nm (1,540/3).
I had two types available: Those that were supposed to be 98 percent
as OC mirrors and those that were supposed to be HR mirrors, both at 1,540 nm.
Here are how they performed at the two green wavelengths of interest:
For 532 nm, neither is really ideal. The "OC" is a bit low - I would have
preferred around 99% to achieve a higher finesse. However, 97.8% is still
decent. ThBuilding a Time-of-Flight Laser Rangefinder
The following is what I would suggest for a relatively low cost approach
achieving 15 to 50 cm resolution and 100 meter or more range. However, also
see the next section for a much simpler approach that may be adequate.
Resonant Time-of-Flight Laser Rangefinder
This is a slightly modified approach and may be made to work with relatively
simple inexpensive circuitry. The idea is to use a normal IR or visible
laser diode (e.g., such as from a CD or DVD player) in conjunction with a
common photodiode to form an oscillator whose frequency will depend on the path
delay between them - i.e., the distance to the "target". Basically, the
laser diode is turned on which sends out a leading edge of a light pulse.
The light hits the target and is reflected back into the photodiode, which
turns the laser diode off. The loss of signal then turns the laser diode
on and the cycle repeats continuously. The oscillating frequency is
then equal to 1 over (4 times the distance to the target plus 2 times
the internal circuit delay). A simple frequency to voltage converter
drives an analog meter. No really high speed components are needed.
Time-of-Flight Laser Rangefinder using CCD
Camera
Each pixel of a CCD-based image sensor accumulates charge proportional to the
light intensity and shutter open or "gate time". For normal video, the
electronic shutter is open for a duration which is a large fraction of a video
frame to maximize sensitivity and minimize aliasing in moving images. For stop
motion photography, much shorter shutter open times are used. If it were
possible to synchronize the electronic shutter with the generation of a light
pulse illuminating the scene, then the amount of charge in each CCD cell would
also depend on how long it takes for the light to reach the CCD (since the
shutter would close before the light from more distant points returned). One
problem, of course, is that this is possible only under very special
conditions. A way to get around this would be to do the measurement in two
steps:
Using a CD or DVD Optical Pickup for Distance
Measurements
The simplist way of doing this may be to use the existing focusing mechanism of
the pickup. Focus in a CD or DVD device depends on a reflection from a
relatively flat smooth surface (the metalized information layer of the disc/k)
to produce an elliptical spot back at the photodiode array. The major axis of
the ellipse lies on a diagonal (45 or 135 degrees) and depends on the distance
above or below optimal focus - at that point, it is a perfect circle. A four
quadrant photodetector takes the difference of the amplitude of the return
signals from the two pairs of diagonally opposed quadrants to determine the
focus error. See the document:
Notes on the
Troubleshooting and Repair of Compact Disc Players and CDROM Drives for
more on how optical pickups actually work.
Using a CD or DVD Optical Pickup in a Precision Position
or Angle Encoder
Conventional optical encoders - whether they are the dirt-cheap variety inside
your computer mouse or the precision type found in industrial robots and other
machine tools - consist of a light source or sources, some means of
interrupting or varying the light intensity based on linear position or
rotation angle, and photodetectors to convert the light to an electrical
signals. By using various patterns on film or glass strips or discs, relative
(2 bits) or absolute (many bits) measurements can be made with a computer or
dedicated logic calculating position or angle, speed or rotation rate,
acceleration, and so forth from this data. Through clever design and
careful manufacturing, extremely high resolution is possible using conventional
LEDs or incandescent lamps for the light source(s). However, lasers can be
used as well with some potential advantages - even higher precision and
stand-off (some distance between the moving parts) operation.
Measuring Speed with a Laser
Speed is just the rate of change of position so any of the approaches that
measure position can be adapted for speed measurements by simply taking
a pair of readings and computing their difference with respect to time.
More direct methods using CW lasers depend on using some form of the doppler
shift of the reflected beam, usually of a subcarrier imposed on the the
laser beam by amplitude modulation.
General Interferometers
Basics of Interferometry and Interferometers
The dictionary definition goes something like:
"INTERFEROMETER: An instrument designed to produce optical interference
fringes for measuring wavelengths, testing flat surfaces, measuring small
distances, etc."
As an example of an interferometer for making precise physical measurements,
split a beam of monochromatic coherent light from a laser into two parts,
bounce the beams around a bit and then recombine them at a screen, optical
viewer, or sensor array. The beams will constructively or destructively
interfere with each-other on a point-by-point basis depending on the net
path-length difference between them. This will result in a pattern of light
and dark fringes. If one of the beams is reflected from a mirror or corner
reflector mounted on something whose position you need to monitor extremely
precisely (like a multi-axis machine tool), then as it moves, the pattern will
change. Counting the passage of the fringes can provide measurements accurate
to a few nanometers!
_____ Mirror 1 (Moving)
^
|
| Beam
| Splitter
+-------+ | / |
| Laser |=========>/<---------->| Mirror 2 (Fixed)
+-------+ / | |
|
|
|
v Screen (or optical viewer,
------- magnifier, sensor, etc.)
Interferometers Using Two Frequency Lasers
The interferometers described in the previous section and found in physics
labs (assuming such topics are even taught with hands-on experience!) all
use CW lasers and look at the fringe shifts as the relative path lengths of
the two arms is changed. While this works in principle and has been used
widely, modern commercial measurement systems based on interferometry often
use more sophisticated techniques to reduce susceptibility to noise and
improve measurement accuracy and stability.
Where Does All the Energy Go?
Suppose we have a Michelson interferometer (see the section:
Basics of Interferometry and
Interferometers) set up with a perfectly collimated (plane wave source)
and perfectly plane mirrors adjusted so that they are perfectly perpendicular
to the optical axis (for each mirror) and the beam splitter is also of perfect
construction and oriented perfectly. In this case, there won't be multiple
fringes but just a broad area whose intensity will be determined by the
path-length difference between the two beams. Where this is exactly 1/2
wavelength (180 degrees), the result will be nothing at all and the screen
will be absolutely dark! So, where is all the energy going? No, it doesn't
simply vanish into thin air or the ether, vacuum, the local dump, or anywhere
else. :-)
Hint: From the perspective of either of the two signals, how is this different
(if at all) than imposing a node (fixed point) on a transmission line? Or at
the screen of the interferometer? After all, a nodal point is just an
enforced location where the intensity of the signal MUST be 0 but here it is
already exactly 0. For the organ pipe, such a nodal point is a closed end;
for the string, just an eye-hook or a pair of fingers!
+-------+ BS M
| Laser |=====>[\]---------\
+-------+ | | M = Mirror
| | BS = Beam Splitter
| BS |
M \---------[\]---->A
|
|
V
B
If you set it up so that there is total cancellation out of, say, port A, then
Port B will have constructive interference and the intensity coming out port B
will equal the combined intensity coming in the two input ports of that final
beam splitter. This is due to the phase relation between the light which is
reflected at the beam splitter. That which is reflected and goes out port A
will be 180 degrees out of phase with that which is reflected and goes out
port B. The transmitted part of port A and port B are the same. Hence the
strict phase relationship between the light from the two output ports. This
is an unavoidable result of the time-reversal symmetry of the propagation of
light.
Interference between E/M Radiation of Different
Wavelengths
We all know that light from a single coherent source can create interference
patterns and such. What about arbitrary uncorrelated sources?
Psi = (e^(ik(L+a).) + e^(ik(L-a).))/2
= e^(ikL) * cos(ka)
I = Psi^* Psi = cos^2(ka)
(a is actually like (x-d)^2/L where 2d is the slit separation, and x is the
position along the screen; L is the distance from the center of the slits to
our point on the screen).
Psi = ( e^(ik(L+a).)+ e^(iK(L-a).))/2
I = Psi^* Psi = 1/2 [ 1 + Re{ e^(i ( k(L+a) - K(L-a) ).)} ]
= 1/2 [ 1 + cos( L(k-K) + a(k+K) ) ]
= cos^2[ 1/2( L(k-K) + a(k+K) ) ]
This is almost a nice interference pattern as we vary 'a', but we've got some
nasty L dependence, and in the regime L >> a where our approximations are
valid, the L dependence will dominate the a dependence (unless (k-K) is very
small; in particular, we'll get interference roughly when a(k+K) ~ 10 and
L(k-K) ~ 1 , and L >> a , which implies |k-K| << |k+K| , nearly equal
wavelengths.)
What about Hobbyist Interferometry?
Building something that demonstrates the principles of interferometry may not
be all *that* difficult (see the comments below). However, constructing a
useful interferometer based measurement system is likely to be another matter.
Interferometers Using Inexpensive Laser Diodes
The party line has tended to be that the coherence length of diode lasers is
too short for interferometry or holography. (See the sections beginning with:
General Interferometers.) While I was aware
of CD laser optics being used with varying degrees of success for relatively
short range interferometry (a few mm or cm - see the section:
Can I Use the Pickup from a CD Player or CDROM
Drive for Interferometry?), the comments below are the first I have seen
to suggest that performance using some common laser diodes may be at least on
par with that of a system based on a typical HeNe laser (though not a high
quality and expensive frequency stabilized single mode HeNe laser).
Can I Use the Optical Pickup from a CD/DVD Player or
CD/DVDROM for Interferometry?
With the nice precision optics, electromechanical actuators, laser diode, and
photodiode array present in the mass produced pickup of a CD/DVD player,
CD/DVDROM drive, or other optical disc/k drive, one would think that
alternative uses could be found for this assembly after it has served for many
years performing its intended functions - or perhaps, much earlier, depending
on your relative priorities. :-) (Also see the section:
Using a CD or DVD Optical Pickup in a Precision
Position or Angle Encoder.
Where such a feature is not provided:
Scanning Fabry-Perot Interferometers
Introduction
While the interferometers described in the previous sections have
many applications in diverse areas, the Scanning Fabry-Perot
Interferometer (SFPI) is specifically designed to make measurements
of the longitudinal (axial) mode structure of CW lasers.
It rates it's own set of sections both due to its importance and
because it is possible to construct a practical SFPI at low cost
without the need for a granite slab or optical table for stability.
Principles of Operation
An SFPI uses the optical transmission characteristics of a
specially designed Fabry-Perot (F-P) resonator as a very
selective filter to scan across the optical spectrum of
the laser. Any F-P resonator will have a transmission
behavior that has peaks and valleys based on optical
frequency (or wavelength). The peaks will be located
where the distance between mirrors is an integer multiple
of one half the laser wavelength. As the reflectivity of the
mirrors approaches 100 percent, the peaks become increasingly
narrow and the valleys increasingly flat and close to zero
transmission. This characteristic looks like that of a "comb"
filter which is very selective.
(Lambda)2 * (1-R) 4*10-13 * 0.01
Delta-Lambda = ------------------- = --------------------- =
2*d*pi*sqrt(R) 0.16 * 3.14 * 0.995
~8*10-15 m = 0.000008 nm or about 6 MHz. (633 nm corresponds to 474 THz.)
Mode Degenerate Fabry-Perot Interferometer
A major disadvantage of the general spherical F-P cavity is that super precise
alignment and control of the input beam size and collimation, along with
an intracavity aperture, may be needed to suppress higher order transverse
modes in the SFPI resonator. Even though not present in a TEM00 laser,
higher order modes are almost unavoidable in the SFPI cavity and
may in fact dominate the display and render it completely useless.
Even if such time consuming steps are taken, there will always be
uncertainty as to what is actually being seen. The flat-flat cavity
doesn't have this problem but suffers from disadvantages of its own,
mainly in the need for a well collimated input and very precise mirror
alignment to achieve high finesse and as a result, reflection of the
input back directly back into the laser, which may be destabilizing in
some cases.
c 1 d
fmn = ------ [q + ---- (1 + m + n) * cos-1(1 - ---)]
2 * d pi r
More Information on SFPI Theory and Practice
In addition to what is present in the sections below, check out the following
links:
Constructing Inexpensive Scanning Fabry-Perot Interferometers
I have used commercial Scanning Fabry-Perot Interferometers (SFPIs).
For example, the TecOptics FPI-25 is an example of a very solidly constructed
precision instruments with adjustments for just about everything.
However, being so general, in some sense it is not optimal for anything!
There are somewhat less flexible but easier to use SFPIs from companies
like Thorlabs and
Toptica
Photonics. These have the advantage of being quite robust and mostly
insensitive to temperature variations (with some being temperature
stabilized), and are available with mirrors coated for relatively broadband
reflectivity. They also have a price tag to match - those from Thorlabs
start at around $3,000 not including the driver box. You don't want to
ask about what the very flexible SFPIs cost. :)
Sam's $1.00 Scanning Fabry-Perot Interferometer
This is the first of three (so far) SFPIs I've constructed, differing
mostly in the mirrors and their spacing. It is non-mode-degenerate,
having been built before I knew about such things. :)
Sam's $2.00 Scanning Fabry-Perot Interferometer
Well, it wasn't actually $2.00. :) I found some small radius mirrors
originally intended for a research project that is now in limbo.
These should work well in a confocal configuraion in the green region
of the spectrum free of those annoying transverse modes!
Reflectivity at Reflectivity at
Mirror Type 532 nm (Green DPSS) 543.5 nm (Green HeNe)
-----------------------------------------------------------------
OC (98%@1,540nm) 97.8% 88%
HR (HR@1,540nm) 99.8% 99%
