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 viewed (by optical sensors) spot 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. 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 both in industry and for robotics (and other research).
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').
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.
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!
A simple version of a Michelson interferometer is shown below:
_____ Mirror 1 (Moving)
^
|
| Beam
| Splitter
+-------+ | / |
| Laser |=========>/<---------->| Mirror 2 (Fixed)
+-------+ / | |
|
|
|
v Screen (or optical viewer,
------- magnifier, sensor, etc.)
(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.
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. Hewlett Packard (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" at the HP Test & Measurement Web Site Search Page.
(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.
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-Zender interferometer like the following
+-------+ 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.
(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:
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).
Now for different wavenumbers:
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.)
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.
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 player or CDROM 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 player may be useful even if you will be substituting a nice HeNe laser for the original laser diode in your experiments. Although 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!
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.
Also see the section: Basics of Interferometry and Interferometers.
The ring laser gyroscope, in principle, can replace these with a fully solid state system using counter-rotating laser beams, photodetectors, and digital electronics with no moving parts larger than photons and electrons.
In practice, it isn't so easy.
In its simplest form, the ring laser gyro (RLG) consists of a triangular block of glass drilled out for 3 helium-neon laser bores with mirrors at the 120 degree points - the corners. Counter-rotating laser beams - one clockwise (CW) and the other counter-clockwise (CCW) coexist in this resonator. At some point, a photosensor monitors the beams where they intersect. They will constructively or destructively interfere with one-another depending on the precise phase of each beam.
What is actually be measured is the integral of angular velocity or angle turned since the counting began. The angular velocity will be the derivative of the beat frequency. A dual (quadrature) detector can be used to derive the direction of rotation (analogous to how computer mice work!).
A complete 3-axis inertial platform would require 3 RLGs mounted at 90 degrees to each-other. The entire affair can be fabricated inside a solid glass block!
However, there are problems with this simplistic implementation. To provide a suitable phase reference, both laser beams must come from the same source or be locked to it. However, the sort of design described above had problems with slow rotation as the two beams would tend to lock to each-other and there would be no output! Some approaches for solving this problem added noise (dither) in an attempt to force the beams to be more independent. Others have attempted to keep the beams separate as much as possible except where they intersect at the photosensors.
For the most part, these difficulties have been overcome and modern aircraft and perhaps spacecraft as well are now using inertial platforms based on RLGs in place of mechanical gyroscopes.
So you want to build one?
(From: Douglas P. McNutt (dmcnutt@macnauchtan.com)).
The mechanical precision is the hard part and that's what makes it virtually impossible for an amateur to construct a ring laser gyro. The two opposite traveling waves have to have extremely high spectral purity which translates to high quality, high reflectance flats at the corners. Not a home job.
It might be easier to build a fiber gyro in which the light passes many times around an effective ring through a wound fiber.
(From: Christopher R. Carlen (crobc@epix.net)).
The mechanical part is horrendous. We have an open cavity HeNe at my school's lab, and it is a challenge to keep lasing on a heavy damped breadboard with the mirrors mounted on a thick dovetail rail, bolted to the breadboard.
Then you complicate that by going from a straight, two-mirror cavity to a three or four mirror cavity ring configuration, and then spin it real fast. Can you say "centrifugal force?"
A fiber loop isn't quite the same as a ring laser, because the ring laser actually has the laser gain medium in the ring. As opposed to having the beam directed into a ring. The gain medium in the ring cavity ensures a standing wave is set up in the cavity, which would not be so for the fiber loop.
Of interest for the future of laser gyros are the new photorefractive polymer devices that exhibit the property of two-beam coupling. This device allows coherent transfer of energy from one beam to another, when the beams are intersected in the material. This can be used to assemble a ring resonant cavity, pumped from the outside by a laser. This can be done with a small diode laser resulting in an assembly much smaller and easier to keep still while spinning than a gas laser ring cavity.
Photorefractive oscillators using inorganic PR crystals have been studied for some time. The first announcement of a resonant cavity using a PR polymer has just occurred in the past few weeks (March, 1998).
(From: Douglas Dwyer (ddwyer@ddwyer.demon.co.uk)).
If you are trying to make a laser gyro as a home project you've got a lifetime project.
I think the ring laser is often carved out of a solid block for stability , a major problem with both ring lasers and fibre gyros is locking of the two phases ie when rotated the phase relationship between the two paths sticks until a certain rotation rate is reached at which point the two paths unlock and it starts to work properly The solution to this could be to deliberately modulate the phase of the light with pseudo random noise and demodulate at the phase detector. Also as stated the fibre gyro is less attractive because of the inherent greater spectral width of the laser.
I wonder if one could bake a Mossbau gyro. I once saw turntable rotation detected by the relativistic effects on the gamma radiation and absorption. That could be easier.
Some applications for the Fourier transforms include:
The usual modern way of performing the Fourier transformer operation is to digitize the data and use a special optimized computer algorithm called the 'Fast Fourier Transformer' or FFT. However, even the most efficient variation of this approach is highly computationally intensive - especially when large multidimensional arrays like high resolution images are involved. To achieve adequate performance, digital signal processing accelerator cards, multiprocessors, or even supercomputers may be needed!
Enter Fourier optics.
It turns out that under certain conditions, a simple convex lens will perform the Fourier transform operation on a two dimensional (2D) image totally in *real time*. The theoretical implications of this statement are profound since real-time here means literally at the speed of light. In practice, it takes great effort and expense to make it work well. Many factors can degrade the contrast, resolution, and signal-to-noise ratio. Extremely high quality and expensive optics, precision positioning, and immaculate cleanliness are generally essential to produce a useful system. However, to demonstrate the basic principles of Fourier optics, all that is required is a common HeNe laser and some relatively simple low cost optics.
+-------+ Spatial Filter Input Fourier Transform Output
| Laser |===>()===---:---===()::():::><:::():::><:::():::><:::():::><:::()
+-------+ FL PH CL TR TL TP ITL OP
|<-f1->|<-f2->| |<-- f -->|<-- f -->|<-- f -->|<-- f -->|
A laser with a long coherence length is required. A diode laser will probably
not work well. Therefore, this is likely to be a HeNe type. A medium
power laser (i.e., 10 mW) will make for a brighter display but a 1 mW should
work just fine. CAUTION: Take appropriate precautions especially with a
higher power laser. However, once the beam has been collimated to a large
diameter, the hazards are reduced.
Ideally, you have a nice optical bench to mount all these components. Otherwise, you will have to improvise. The first three items (the spatial filter components) really do need to be accurately and stably positioned. See the section: Laser Beam Cleanup - the Spatial Filter.
Laboratory quality lenses for Fourier optics research cost thousands of dollars each. However, you can demonstrate the basic principles and do some very interesting experiments with inexpensive optics.
The ratio of F1/F2 should be roughly the same as the ratio of the diameters of the useful aperture of CL (desired diameter of the field of view) to the HeNe beam.
For example, with a laser producing a 1 mm diameter beam and a useful field of view diameter of 1 inch, the following will work:
Hint: have a book with examples of Fourier Transform pairs handy.)
I just finished a class in this, using "Linear Systems, Fourier Transforms, and Optics", by Gaskill (Wiley).
A coherent source yields a Fourier transform of the electric field, including the phase factors. An incoherent source will perform essentially the same effects on the radiance, rather than the field. A coherent source is used to develop the concepts, and so most of the books show the experimental verifications of spatial imaging with coherent sources.
A negative lens will give a virtual image. If you want to perform spatial filtering, I think you're forced to use a positive lens. You also perform the inverse transform with another positive lens. You should therefore be able to confirm basic spatial filtering concepts with a hobbyists' telescope.
Gaskill talks about a few special configurations, but the easiest to get to is to locate a laser to one side of the lens, place the transparency at the front focal plane, and find the Fourier transform plane at the point where the point source (a laser) comes to focus. To make things really simple, put the laser twice the focal distance away from the lens, the image at the focal distance, and find the FT at twice the focal distance on the far side of the lens. An alternative is to take a laser, collimate the light to obtain plane wave illumination, place the image anywhere between the source and the lens, and find the FT plane at the focal distance on the other side of the lens. It is the focal point of the light source that determines the position of the FT plane.
Like I say, I just took the class, am still shell-shocked, and haven't had a chance to absorb or experiment with these techniques, so I could be misunderstanding the text. (From: Norman Axelrod (naxelrod@ix.netcom.com)). Yes, you need a laser. HeNe works, but not a diode (the laser needs to have good coherence). Focus the laser through a pinhole (focusing lens and pinhole combination is called a spatial filter). then re-collimate the light with a lens. Place the image or aperture 1 focal length from the collimating lens, then you can either use a bare screen placed at distance away, or a second collimating lens. This is necessary to get the far-field pattern.
(From: Brian Rich (science@west.net)).
A really cool book about this that I have a copy of but may be out of print is "Laser Art and Optical Transforms" by T. Kallard. Look for it at a good university library.
(From: Norman Axelrod (naxelrod@ix.netcom.com)).
There is another way to phrase what is happening that might make it more intuitive for folks with more of an optics background.
First, the light used should be parallel and coherent.
The light transmitted through the transparency (or light reflected from a 2-dimensional image) is diffracted by the transmission and phase changes provided by the image. As is done in elementary physics, a lens (here, a high quality lens) is used to take the light that is diffracted at different angles and focus them at a distance of one focal length from the lens (just like a burning lens, except you use parallel coherent light coming into the initial transparency and you have more than one beam at the burning distance).
The key physical point is that the Fraunhofer diffraction pattern of an object is the Fourier transform of that object. This is true in the sense that the amplitude and the phase of the radiation at any point in the diffraction pattern are the amplitude and phase at the corresponding point in the Fourier transform.
For simple examples:
(From: Tom Sutherland (tom.sutherland@msfc.nasa.gov)).
Please allow me to recommend Professor Goodman's excellent and recently updated text "Fourier Optics". If I had my (last edition) copy in front of me I'd give you a better answer, however I do recall that the exact fourier transform of a pattern illuminated by a coherent plane wave is produced at the back focal plane of a lens if the pattern is located at the front focal plane of the lens. The intensity (but not the phase) of the fourier transform is produced if the pattern is located anywhere else in front of the lens (but of course there are some questions of scaling). (From: Robert Alcock (robert@fs4.ph.man.ac.uk)). Have a look at the book "Introduction to Fourier Optics" by J.W. Goodman. McGraw-Hill Book Company 1968. The first few chapters set the theoretical framework for the book by explaining 1D and 2D fourier transforms and scalar diffraction theory. I think that the chapters that you may find particularly interesting are:
(From: Herman de Jong (h.m.m.dejong@phys.tue.nl)).
Let me explain the optical Fourier Transform by lenses with an example: Suppose for simplification we essentially look at a two dimensional system: we use cylinder lenses and slit object.
When you use a broad laser beam and eliminate a slit (a pulse function), it will have a near field and a far-field pattern that is not exactly the same. The far-field pattern is a utopia but you get very close to the utopia the further away you put your screen. The intensity pattern is a squared sinc function (the sinc function is the FT of the pulse function) that scales with distance. We conclude the infinity pattern to be the squared of the FT of the slit and the associated E-field is actually the FT. If you use a cylindrical lens to image the slit on a screen you also get an FT provided you collect all relevant light from the slit onto your lens and the lens is perfect. It scales with the ratio of object an image distances It so happens that the FT of the FT the original but for a scaling factor and a minus sign in the inverse FT. I'm not sure how but in otical intensity FT's it makes no difference probably because of the squared of E-field that eliminates the minus sign.
It gets much more difficult to grasp with 3D and rotationally symmetrical optics, objects and images. You wouldn't want to know and I wouldn't be able to answer many questions.
(From: James A. Carter III (carter@photon-sys.com)).
It is possible to form the Fourier transform by placing the transparency in a convergent-cone optical field formed by a single laser. This technique is used when one wishes to scale the transform to be optimally sampled by a detector with fixed spatial sampling. Changing the location of the transparency with respect to the focus of the cone (i.e., changing the quadratic phase of the optical filed) will change the scale of the transforms as it maps spatial frequency (sometimes called the "plane wave spectrum") to spatial coordinates. Actually, no lens is required at all if you have a large enough lab and can invoke the "far field" condition. The "Fraunhofer" condition uses the quadratic phase of the lens to negate the second order term in the scalar diffraction integral using denoted as "Fresnel" diffraction. The far field condition puts the observation plane far enough away from the transparency plane to make it essentially a constant term in the integral and again you have a 2-D Fourier transform.
The lens can be thought of as a way to image the far field (ideally at infinity) to the back focal plane. If the transparency is not at the front focal plane, then the transform field (amplitude and phase) at the focal plane will have a quadratic phase term. The quadratic phase is irrelevant if the field is detected (with detector or film) because then all phase information is lost. If the field is recorded with a reference phase (i.e., a hologram), or is filtered for subsequently inversing the transform, then the quadratic phase should be corrected. The simplistic way to do this is to use a plane wave illumination (collimated source) and place the transparency at the front focal plane. Using your imagination and knowing the symmetry of the Fourier transform should justify this rational.
The field at the transform plane contains only the information that is collected and sampled by the lens. Thus, the ability to sample higher spatial frequencies depends on the collection angle (numerical aperture) of the lens. Some feel that the illumination beam must be spatially filtered to produce a uniform distribution. This is no more the case than saying that every Fast Fourier Transform should just be zero padded. Hamming, Hanning and other windowing algorithms are used to suppress the side-lobes produced by the finite sample extent. The Gaussian distribution of the laser can actually improve the fidelity of the transform and eliminate "ringing." The quality of the lens in terms of wavefront aberrations is important, but no more important than the wavefront quality of the beam. These phase aberrations may effect the point spread function of the system (seen when no transparency is present) and it is the point spread function that convolves with the transform and limits fidelity.
The text by Jack Gaskill and Joe Goodman are excellent for details. Another excellent source is the "(The New) Physical Optics Notebook: Tutorials in Fourier Optics" by Reynolds, DeVelis, Parrent, Thompson. This is available from Optical Engineering Press (SPIE). The "old" version of this was used in my training at the U. of Rochester when I took physical optics from one its early authors (Brian J. Thompson).
Many interesting things can be done with this simple engine. For more ideas, visit my (preliminary) Web site at http://www.photon-sys.com/
(From: Jeff Hunt (jhunt@ix.netcom.com)).
I'm a grad student at the Optical Sciences Center at the University of Arizona, and I think that Jack Gaskill's book on the subject is quite good. Just like Gaskill says, it covers what Goodman's text does, but it explains things in a way that is easier to understand (Goodman is the authority on the subject, from what I understand.)
(From: DeVon Griffin (devon@baggins.lerc.nasa.gov)).
Having done Gaskill ten years ago, I would say that the main drawback of the book is his notation. The m double-hat triple prime sort of thing makes trying to pick it back up after not having looked at it for awhile a daunting task.
(Portions from: Erik Huber (erik.p.huber@uibk.ac.at)).
I worked in a big disco as LJ - Did a lot of raves and such stuff. I also DJ a little just for fun. The laser power you need depends on the room you have. If you want to scan pictures you need more power. If you just use rays, you won't need so much.
WARNING: Be aware that the maximum laser power level for the human eye is about (2.5 mW)/(cm^2). Never look into the beam!
In the USA, laser shows in clubs/bars/parks are regulated by the CDRH (Center for Devices and Radiological Health, a division of the FDA). Audience scanning is NOT permitted in the USA while it is common in the rest of the world. A large scanned effect spreads the laser power over a wide area and usually has some motion to it (such as the sine waves used to make rippling sheets of light). This means that the energy density and the exposure times are low.
If the laser beams are not scanning directly on the audience [dancers] then the effects are probably safe. If the system uses scanned beam effects, then it is probably following the rules of it's jurisdiction and is probably safe.
(From: L. Michael Roberts (newsmail@LaserFX.com)).
To create visible beams in *total* darkness you can get away with as little as 100 mW. For beam effects in a club or other venue with some ambient lighting, 1 watt is about the minimum you need to make visible beam effects. Outdoors you will need 5-6 watts to make visible beams [again depending n ambient lighting conditions].
In all cases, a scattering medium (smoke or dust) is required to deflect the light towards the observer's eyes. In clean, clear air in winter, I have seen the beams from a 20 watt argon look lamer than the beams from a 1 watt indoors with a good haze.
(From: Steve Roberts (osteven@en.com)).
In a dark room with average dust levels and high humidity you can start to see the forward scattering of an HeNe beam at about 1 mW! 30 to 40 mW of argon makes an OK side view beam in a dim room, but its not exactly a Star Trek photon torpedo kind of glow. It helps if the argon is configured multiline and is doing more green then blue, as the eye peaks in the green. To see the beam in a well lit room requires smoke of some form.
Most laser light show types don't like the common aquafog, it irritates your lungs after constant exposure, so we use hazers indoors. A hazer works by making very tiny particles of medical grade oil. These are small enough to be flushed out of your lungs by normal breathing and if properly set up, are odorless and OSHA approved. Fog machines for the most part are crackers, they work by incomplete combustion of glycols (aquafog) or burning of oil in air. Hazers fragment the oil in CO2 and thus are almost odorless. Plans for a homemade hazer of sorts that uses air are at LaserFX on the "Backstage" pages. It has a slight odor but is not that bad to be around, and mind you I have asthma! I have done indoor shows for 1,200 people using 60 mW and a cracker. I have also done shows indoors for 100 people with a 5 mW hene, it depends on ambient lighting and air circulation/humidity.
It is a minimum of about 5 watts of argon light for a decent outdoor smokeless beam show, with 20 watts being more typical.
(From: Steve Quest (Squest@cris.com)).
Visible wavelength lasers are more visible in 'plain air' if the angle of incidence is low (you're close to the same angle of the beam) and if the power is greater than about 5 watts. I perform an outdoor laser show using a 30 to 57 (max) watt YAG (frequency doubled to 532 nm) which is plainly visible in mostly clear air (no need to smoke, or fog the air). When I want to do beam effects with a 5 watt argon/krypton white-light laser, I have to fog the air up.
Plain outdoor air has enough particulate matter to scatter a laser beam so long as it is above 25 or so watts, thus making the beam visible. Of course, the more power, the brighter the beam looks, but CDRH has limits, and that limit is .9725 mw/cm^2 at 750 feet, so the days of power beam shows going all the way to outer space and beyond is over :-(.
I use a Laserscope laser, which is FDA (Food and Drug Administration) approved, and am following CDRH (Center for Devices and Radiological Health) guidelines, receive FAA (Federal Aviation Administration) approval and air clearance before every show, and make sure that NOTAM (NOtice To AirMen) are issued to pilots flying in the area of my shows, giving exact details as to what is going on. Pilots love the shows, and air traffic routes planes WAY out of their flightpaths to fly near the beam shows to get the best seats in the house. :) However, I have to beam-off when they get too close, then they return to their flightpath, and I can resume the show.
I used to be able to sparkle off the new moon with my YAG at full power and full convergence. It takes some doing but you can see the sparkle from the Sea of Tranquillity with the naked eye off the corner cube reflector, aka: retroreflector left there in 1969 by the astronauts.
WARNING: Shooting a laser into the sky is irresponsible and highly illegal without prior approval from the proper agencies. Airline pilots do not appreciate being blinded! --- sam).
(From: James A. Carter III (jacarter3@earthlink.net)).
Just to let folks know where this Laser TV thing has been.
In the 1920's, a company in England, Scophony Labs (I think that's right) patented a method for using Bragg diffraction on tanks of water (that's right H20) to display TV signals using white light (thermal) sources. They had to use BIG beams because they didn't have lasers. BIG beams mean low modulation rates due to acoustic transit time. Their idea was to scan the spot so that the acoustic pulse was stationary on the screen. I believe that they didn't use galvonometric scanners for the horizontal scan, instead they put mirrors on motor shafts (similar to what some cinemagraphic projectors used at the time). The scan rate and magnification were selected so that the scan velocity vector was equal and opposite to the image of the acoustic velocity vector. This may have been an idea way ahead of its time.
Just ten years ago, I helped design the optics of a system that does display not only NTSC images but scan to HDTV as well. This is not a cheap system and is certainly is not suitable for avionics; although the Air Force (through TRW) did buy many systems. It used an air bearing motor to drive a many faceted polygonal mirror scanner for the horizontal scan and used a "galvo" scanner for the vertical. The AO modulators had enough band-width (at least 500 times what you get from PCAOMs) to project NTSC images in a flying spot mode. That is the scanner was going much to slow to give the Scophony condition. When we ramped the system (it was a closed loop continuous multiscan projector) to 1280 by 1024 sources, the scan was fast enough that we achieved the Scophony condition and realized over 35 MHz of video bandwidth per channel. This is somewhat inadequate for computer CAD graphics but was quite acceptable at the time. The display was dazzling, to say the least. Per laser color for each red, green and blue channel with red at a deep and rich 635 nm (dye laser pumped by the otherwise useless cyan lines), and the argon lines for green and blue. We used a 10 watt argon from Spectra-Physics to be the photon engine (SP was an investor here). One of these went to the NAB show and displayed our beloved President Ron.
Unfortunately, the lasers were not reliable enough, to expensive to repair and replace, and more light is always better. Further, the big guys (TRW and SP) started to bicker and the company went under. The last time I saw one of these systems was at SP Corporate in San Jose. I was there to install a 25 watt laser, but that's another story.
Current commercial work centers on dumping the high speed scanner and using an AO cell to modulate the whole line at one time. Bragg cell technology can give the Time-Bandwidth product (TBP) required which is certainly over 1000 and closer to 2000. Unfortunately, acoustic attenuation (Beer's law in time and space) and the non-uniformity of the laser source (typically Gaussian) require losses to make a nice uniform display. Even with HIGH power pulsed lasers (repping at the horizontal line rate or at a multiple), the display can lack luster.
As always, more photons... more photons...
(From: Tony Clynick (tony.clynick@btinternet.com)).
I am pleased to tell you that laser video projection is still very active in the UK. Based on the original laser video projector (LVP) made by Dwight-Cavendish in the early 1980's, the projector now made by the team at LCI (Laser Creations International in London) has been installed at several permanent sites in theme parks since 1994, mostly in East Asia, and has been used for dozens of temporary shows world-wide since 1987. Most applications are in exhibitions, outdoor shows and theme parks.
The LCI-LVP uses SP white-light lasers with special optics to provide good flesh-tones so the need for dye lasers is eliminated. A polygon scanner (GEC Marconi - thanks Alan) provides the line scanning, at rates of up to 36kHz. AO modulation and Scophony balance provides video bandwidth up to 30MHz, so HDTV (1250/50 and 1125/60), as well as PAL/NTSC/SECAM are available in the LCI-LVP. Output on screen of a peak-white modulated raster of over 15 watts has been achieved. The largest image projected so far was 50 metres wide. The collimated scanned beam provides an infinite depth-of-field, which was put to good use last year at the Singapore National Day on a giant 35m x 28m high-gain screen laid over the slanted stadium seating. The difference in projection distance between the top and bottom of the screen was nearly 100 metres, so the LVP was the only machine capable of a focussed image over the whole screen. All LVP's supplied so far by LCI are also capable of vector scanning using the waste AO beam.
(From: Chris Cebelenski). I know of one experimental project that uses an array of galvo's to project a raster image at 1/2 normal NTSC refresh rate (15 fps). The cost of this endevour so far has been, well, let's just say it's been expensive. :-)
Currently it's configured like this:
There are several problems with this:
(From: Steve Roberts (osteven@en.com)).
Two years ago I was at a Laser-FX conference in Canada, we had the chance to watch (I have it on tape) a Russian made scan system with no moving parts, all acousto-optic and almost totally analog driven, that produced sharp clean monochrome images without flicker the size of a billboard using a 6 watt 532 nm YAG . The marketing person explained that RGB existed in the lab and was not far away. I believe the company name was Lasys Technologies. Scan head and laser was about the size of a PC/AT case and sat on a tripod, and was easily handled with low weight. Ran off 220/3 phase, but I was told 220 single phase would not be a problem. Further details can be obtained from: L. Michael Roberts (lmichael@laser-fx.com) who was the organizer of the conference.