Interference is a wave phenomenon that reinforces (constructive) and diminishes (destructive) two wavefronts, audio, water, or in this case, optical. While not evident in everyday life, these effects can be seen on a macro-scale, for example, with two rocks dropped in a pond. In this example, the circular waves produced individually simply travel out from the source point, but when they meet at the same point, the peaks of one wave are diminished by the troughs of the other, and when the peaks / valleys coincide, they are reinforced, increasing the amplitude.
An optical device that measures this is called an interferometer, with an example shown below, in the form of a Twyman-Green interferometer, which is using a laser source. Coincidentally, it is a green laser, not to be confused with the name Twyman-Green.
The wavelength of this light is 532 nm (0.532 microns, 5.32 E-7 meters), which, in reflection as is done here, implies a "fringe" spacing of 0.532 microns / 2, or 0.266 microns = 266 nanometers (nm) between adjacent bright or dark fringes.
It is possible, of course, to do interferometry on a microscopic scale. Often, this is done to measure the surface texture, or micro-roughness, of a polished glass optical surface. In the past, this involved taking your part to an interference micrcoscope, or if it was too large, to make a surface replica and then measure that. There is now at least a couple of models of portable units that can be placed on a surface and measure it directly. One such is the NanoCam Sq, from 4D Technology and another is the "Point Source Microscope", from Optical Perspectives Group, an autostigmatic microscope fitted with an interference objective and a phase-shifter, which when connected to a computer can measure the local texture of the glass surface.
The source for interference microscopy can be a laser, LED, or white light. Nikon and others make very nice instruments, such as these white light microscopes.
Peter de Groot, from Zygo, has written a very nice overview of interference microscopy.
Shown here is the PSM, configured as a "Micro Finish Topographer (MFT)", on the surface of the 8.4 meter (27.5 foot) diameter GMT1 mirror, with Paul, Buddy and Leslie taking data.
Typical data (from another mirror) might look like the below figures, with about 550 nm of tilt across the aperture (using a 10x Mirau objective).
If we (numerically) remove the tilt, the data now looks like this:
In this example, which is fairly typical, the rms error is about 20 Angstroms (1 Å = 1 E-10 meters, or 0.1 nm), or 2 nm rms. It is an average of 500 individual data sets, with a peak-to-valley error of about 0.25 microns. Much of this, however, is pixel noise which isn't random. While it is possible that there are pits in the surface, it is highly unlikely they are that small, and furthermore, it is even more unlikely that a polished surface would have spikes sticking up! All of the observed spikes are noise. Random errors get reduced by 1/√N, so for N=500, there is about 22.4 times as much random noise in a single measurement as in this average. The scale on the final 2-D plot is ± 5 nm! Normal microscopic techniques, even "fancy" ones like DIC, simply give an image, perhaps similar in character to the interference fringes on the left. Interference microscopy, with phase-shifting and computer analysis, gives actual surface heights, so 3D maps, as shown in the rightmost figures, can be produced.
Interference requires two beams (more about two-beam interferometry can be found on Nikon's Microscopy U), so a beamsplitter is needed somewhere in the path, in this case, inside the objective. Special objectives, of several types are available. Here, we used a Mirau, described below (the figure, featuring a metallurgical Nikon Optiphot, is taken from a Venezuelan research paper* by Jesús González-Laprea, José Cappelletto & Rafael Escalona. In a Mirau, the beamsplitter is the final element, which reflects part of the light back up to a reference mirror inside, which when re-combined in the image plane, creates an interference pattern.
Other objective types include the Michelson, which has a standard beam splitter and separate reference mirror (much like the Twyman-Green above), and Multi-beam interference (described in detail on Nikon's Microscopy U), which while I haven't yet used yet, it seems much like a Fabry-Perot, with high finesse fringes.
Using the 10x M Plan DI, the following images were obtained on the Optiphot with an epi-illuminator. This is simply a microscope slide with some gunk on it. There are about six fringes of tilt, so there is three waves at about 550 nm, or 1.65 microns of tilt across the field. The green ones are with a GIF filter in the illumination path, making the information easier to obtain. The colored ones are white-light interference fringes, with the various wavelengths smearing together the farther from the zero order (white fringe with black surrounding it) one gets.
The second set of images is with the focus changed, intentionally getting away from the zero order, so the colors are a little strange.
While I haven't made much progress, I am working on a dedicated bench-top system of my own, using finite conjugate (210/0) objectives of the Mirau (10x and 20x) and multi-beam (40x) variety, with a PZT phase-shifter, from Physik-Instrumente. Also called a piezo-electric transducer, PZT is short for lead zirconate titanate (Pb[ZrxTi1-x]O3), which expands with an applied voltage, or creates a voltage in response to mechanical length changes. While I haven't looked lately, manufacturers of this type of unit included Zygo and Wyko / Veeco / Bruker. In fact, I think the tilt stage is out of an old Zygo unit.
What is shown here is a granite base with a vertical stage, with 6 inches (150 mm) of travel, with a 5-axis translation, tilt, rotation stage to hold the sample. Unlike almost all other forms of microscopy, the tilt of the sample is critical, not just an annoyance if misaligned, so a fancy tilt stage is required. Below is shown a 10x Mirau objective (Nikon 210/0 M Plan DI) focused on the internal reference mirror from the sample side and the back side.
The PZT, a PhysikInstrumente (PI) piezo unit with M25 thread (with an RMS adapter) is shown below.
Let's have a look inside an old Zygo interference microscope!
* While I have access to virtually every paper ever written, through my being a part of The University of Arizona, many of you don't - so this is one case where the paper is freely available on the web. While it is not really an overview article, it is available, and I like to reference the places that I "lift" figures from. You may also notice that almost all of the inteferometer companies are from Tucson, being spin-offs from the UofA Optical Sciences Center (now the College of Optical Sciences).
for navigation!