One of the more useful items for an ATM to own is an ‘optical flat’, a disk that has a surface flat to some accurately known fraction of a wavelength of light. Considering that one wavelength of light is about two millionths of an inch, making a flat of any appreciable size is quite an accomplishment. Often, flats are made to tolerances of less than 1/10th of a wavelength of light.
This raises the question of how to test such a surface. A good dial indicator can read directly to .0001", and one can estimate between graduations to about 1/5th of that. Thus, with careful application, a good dial indicator can measure to .00005, or 50 millionths of an inch. That sounds impressive, until you realize that one wavelength of red light is about ten times smaller yet! So, to measure to a tenth of a wave, our dial indicator is about 100 times too crude.
Luckily, there is an elegant solution to this problem. We can use light itself to test the flatness of a surface, as long as we have a flat of know quality to compare against.
Visible light is just one very small part of the electromagnetic spectrum, which encompasses everything from radio waves with wavelengths measured in the tens of meters, to X-rays with wavelengths of xxxx. In a manner similar to water waves, two waves of light can add peak-to-peak, and result in twice the intensity, or add peak-to-valley, and cancel each other out. In practice, two flat pieces of glass are arranged face-to-face with a small tilt and air gap in between, and illuminated. Where the distance between the faces is an even multiple of xxxx, the light will destructively interfere, and a dark "fringe" will be visible as a gap in the light reflected from the face of the flat being tested.
[tilt diagram here]
While white light will show beautiful colored fringes, often called "Newton’s rings", a monochromatic (single wavelength) source is required to get clean fringes with good contrast.
[Newton’s rings photo here]
There are any number of ways to make a monochromatic source, but lately this has become very simple indeed, thanks to a recommendation from Peter Smith. Compact fluorescent lamps (or CFL’s) have recently appeared on the market, as a premium priced replacement for incandescent bulbs. Unlike an ordinary incandescent bulb, which radiates across all wavelengths of the visible spectrum, CFL’s emit light in a few, very distinct wavelengths.
[pair of photos here]
These photos were taken with an inexpensive spectrometer from The Learning Tree, but you can see this effect for yourself with a prism or even a CD. Cut a small slit (an inch or so long, and about 0.1" wide) in a piece of black paper, and cover the back side of the slit with some white paper to act as a diffuser. Place the black paper in front of a CFL, and look either through a prism or look at the reflection from a compact disk (the side with the groove, not the label!). You should see a set of lines, something like the above photo. Repeat the test with an incandescent lamp, and you’ll see a broad, continuous spectrum.
By choosing the appropriate filter, you can isolate just one of the spectral lines. For example, using a red filter will eliminate the yellow, green , blue and violet lines, leaving a monochromatic red light source. The filter material need not be anything expensive. Red acetate, about $3 for a 24"x24" sheet from an art supply store works very well. I’ve found that in some cases, you’ll need a double layer of acetate to get complete elimination of the remaining lines.
For small flats of 2" or 3" in size and quick tests, one can
simply place the flat on the surface to be tested, and illuminate the pair with
a filtered CFL. For larger flats, or more definitive tests, a viewing box makes
testing much easier. When testing flats, viewing at an angle will introduce a
bit of distortion to the fringes.
Therefore, the preferred way to test is on the axis of the flat, and from a
distance of five to ten times the element diameter.
The classic fringe viewer has the light source at the top of a tall box, and a half silvered mirror for viewing. Some years ago, I was fortunate enough to purchase a 16" flat at a very low price, so I built a box big enough to accommodate this flat in its case, about 18" square.
The light source is just two CFL’s wired in parallel. Below them is a set of slats to hold a 20x23" sheet of Plexiglas, which supports the acetate filters and the sheet of gift wrapping tissue used as a diffuser. For the half-silvered mirror, I ordered a 23x30 sheet of ¼" glass from a local window glass supplier. He also coated it with a layer of "Solar Cool" a bronze-tinted reflective window film. Auto parts stores sell similar products for car windows, but take note that most window film adhesives will dissolve plexiglas as they dry, so either use the static cling variety of film, or glass for the angled reflector. I decided to use ¼" glass to minimize the flex and reduce the danger of accidental breakage.
The box was built with a 2"x2" wood frame and ¼" plywood. The base, made from ¾" plywood is a bit more substantial, as it was meant to carry the large flat without distortion. The inside of the light box portion was painted gloss white, and the rest of the inside was painted flat black to reduce stray reflections and improve contrast. A small faceplate covers the front of the light box portion, and the entire exterior was painted ‘Shoptask Yellow", to match my grinding machine, sine table, and Shoptask lathe/mill.
The basic idea is to place the element to be tested on the reference flat, and observe the fringes. If the surface under test is fairly flat, you’ll get either a ‘bulls-eye’ ring pattern, or a series of arcs, depending on whether the air gap is perfectly parallel (rings) or slightly wedge shaped (arcs). If the surface is perfectly flat, you’ll get perfectly straight fringes with a wedge air gap.
In practice, placing two flats together is a bit tricky. The tendency is to clack them together at the edges (referred to as "playing castanets" ), and this of course runs the risk of chipping or scratching. Much easier is to place a sheet of very clean, lint free paper on top of the reference flat, and then place the other disk on the paper. You can then draw the paper out sideways, and the fringes will appear as the paper clears the edge. (Thanks yet again to Peter Smith for this handy technique.)
By placing a lightweight straightedge across the fringes, you can count how many fringes the straightedge intersects. Every two fringes represent a difference of one wavelength. (Remember to only count one intersection per fringe for rings patterns, even though the straightedge may cross a fringe twice).