Casting an optical table of concrete
Fabrication of the table
With several plans for optical experiments in mind, I started searching for an optical table. Small optical tables are made of stainless steel, usually they are expensive and relatively thin (so they are not ideally stiff). If one needs minimum manufacturing costs and high mechanical stiffness, why not try to make the table out of concrete?
On an usual optical table, a regular grid of threaded holes serves to attach the components. One can not machine threaded holes into a block of concrete, of course, but the situation is even simpler and requires no machining: The first step is to prepare a flat glass surface, on top of which are M5-sized flanged nuts, arranged into a regular 11x11 matrix with 25 mm spacing and glued by wax. The gluing is best done by melting a piece of a wax candle in a pan, and heating all nuts on the pan, all oriented flange-up. One disadvantage is that uninformed people ask about your cooking preferences with elevated eyebrow, another one is that plier is needed to handle the hot nuts. Anyway, this procedure ensures the wax reliably and easily attaches the nuts to the glass.
An important step, probably better done before the flanged nuts are put on the pan, is to stick a small (d=6 mm, l=15 mm) cylinder of styrofoam on top of the flanged-side of each nut. This ensures that concrete does not leak into the thread and also that, in future, longer screws can be used (without the risk of pulling out the nut when the screw tip reaches the concrete). On contrary, if the thread gets stuck with wax from the bottom side, it is of no harm.
The next step is ordinary concrete casting. One has to prepare a square (300x300 mm inner dimensions, 120 mm high) fence of wood and place it symmetrically around the nut matrix. First, prepare around 1 kg of finer concrete (0.5 kg of fine silica sand, 0.5 kg of Portland cement, ca. 0.25 liter of water) and pour it evenly to later form the surface of the table.
Let the concrete harden for about one day (it will still be soft, but it will already protect the nuts from displacement or from concrete leaking in). Next day, around 6 kg of concrete is prepared (i.e. 3 kg of sand, 2 kg of cement, ca. 0.5-1 liter water). Make the concrete much denser today, so that it does not flow too much. Pour and manually spread one third directly on the previous layer. Now take a 60 mm thick styrofoam and cut out four triangles that fill most of the space in the 300x300 mm square, put them in and fill the remaining space with concrete. About one third of concrete should remain to cover the styrofoam triangles by about a 15-20 mm layer. If the concrete is not too runny, the styrofoam triangles will not float.
The concrete hardens and cures for about four weeks. During this time, it may never get dry (or the curing process stops, leaving it soft and crumbling), so it is advisable to pack the whole project with polyethylene foil and dew it time to time. After few days, concrete is not susteptible to excess water.
After four weeks pass, everything can be carefully flipped and the glass plate can be detached by gently lifting it at edges. The result is documented on the following photo, already with a simple optical experiment that is described below.
Michelson interferometer and quadrature detection
Building a Michelson interferometer
I made several optical components, mostly from common aluminum L-profiles. I used a DVD laser diode (LD) as the optical source. (Here is a detailed photo; light is emitted from the front face of the 3 mm-long black AlGaInP bar. I removed the diode casing when I repaired a wire inside, but generally the casing should be left in place to protect the diode. Note that one has to be careful setting the diode current; plenty of useful information is on Sam's laser FAQ on diode lasers.) The diode beam was collimated with a lens from a scanner (L1) and directed by one adjustable mirror (M1) on a roughly 50% beamsplitter, also from a CD/DVD reader. Half of the beam energy passed through it and reflected back from M2, the second one likewise reflected back from M3. The beams met at the beamsplitter again, but with a time difference, defined by the position of the mirrors M2, M3 with regards to the beamsplitter.
Coherence of a DVD laser diode
The very basic experiment is to observe interference fringes, coming from a slight deviation of the beams impinging the beamsplitter. In fact, it is quite easy to obtain such an interference as I tried to document on the above figure. (The observed inter-fringe distance is the larger, the better both beams are collimated. It is appreciably harder to fine tune the mirror direction to produce an uniform bright/dark rectangle. When the BS-M2 distance is not equal to BS-M3, it is also important to adjust the beam collimation lens, otherwise circular interference fringes persist.)
The visibility of interference fringes gives important information about to what extent the source is coherent. When e.g. the BS-M2 distance is changed, one can deduce the coherence length of the diode. As a pleasant surprise, the interference could be observed also when I shifted M2 by over 10 cm! The coherence length of a laser diode is therefore much higher than is commonly though.
The downside of a laser diode is the low stability. The above is true when LD is stably operating in single mode. In fact, it is very sensitive to temperature changes. One can observe mode hopping, causing the interference to skip abruptly to a different position, or even random noisy opeation, causing the interference fringes to disappear. Single-mode operation can be held for about a minute when the diode is heated up and if air around it does not move.
Interferometers are extremely sensitive to the displacement of the mirrorn M2, M3 or of the beamsplitter BS. Shifting a mirror by a quarter of wavelength (i.e. 160 nm) makes the fringe maximum move to where a minimum was and vice versa.
The shift can be measured exactly with the quadrature detection scheme: Two ordinary photodiodes have to measure light intensity at different places in the interference pattern. When PD1 measures the maximum of a fringe, PD2 should be placed in half way between this maximum and an adjacent minimum. (In practice, the photodiodes tend to be too bulky, so I had to cut the output beam in half by another mirror M5 and glue two razor blades in front of each diode to make a narrow slit.)
When the output of both diodes is connected to an oscilloscope in X-Y mode, and one of the mirrors move, a point is shown that goes around a circular path of the oscilloscope screen. One turnabout corresponds to a shift by half of wavelength (i.e. 320 nm). If it is possible to see a change of one degree on the circle, one can measure a displacement of one nanometer, i.e. ca. 10 atomic distances.
This allows one to observe how the aluminum mirror mounts are elastic. Touching one of the mirrors with a little pressure (~ 1 N) makes the mirror move by ca. 1 μm. On the contrary, the optical table is really stiff and much higher force is needed to observe appreciable deformation.
If the photodiode output is preamplified by LM324 and connected to earphones, one can hear what is said near the optics. Especially the beamsplitter acts as a good microphone. This is the basic idea of spying conversation from outside the building using a laser microphone. (Also, when one taps the optical table with fingers, high-frequency mechanical oscillations of different components can be identified as disharmonic ringing around 1-3 kHz.)
In most lighters, a piezoelectric crystal is built in to produce a spark when hit by a little hammer. The piezoelectric effect is reciprocal; applied voltage must produce a proportional deformation. How much does the crystal change? Quadrature detection allows to easily determine such microscopic displacements. I clamped the piezoelectric crystal between the mirror (M3) and another aluminum profile.
The crystal was connected by thin copper wires that are perhaps not visible on the right photograph. Upon application of 30 V voltage, the X-Y trace systematically and reversibly rotated by ca. 10 degrees, so we may estimate that the piezocrystal deforms by 0.3 nm per volt. Obviously, piezoelectric actuators need to work with high voltage!