July 2000 Newsletter

Stockton Astronomical Society

Valley Skies

Valley Skies - July 2000 Issue

The Telescope Nut
by Jeff Baldwin

Big Fringe Analysis

Light has a dual existence, that of a particle and that of a wave. We can use the wave nature of light to determine quite a bit about the optics of a system, and one way is fringe analysis. I use fringe analysis to determine if flat mirrors are truly flat, but fringe analysis can be used in a variety of situations.

Interference of waves can be constructive or destructive. If waves are phased with their crests aligned, they are said to have constructive interference, and if a wave's crest is aligned with another wave's trough, they are said to be destructively interfering. To see destructive interference and constructive interference at the same time, you can take two screen door screens and lay one over the other. When you look through a part where the material aligns you can see through the holes between the fabric of the screens. This would be constructive interference. If you shift one slightly with respect to the other, the holes on one screen align with the material of the other, and vice versa, and you can't see through the screen. This would be destructive interference. If you can see overlying patterns in the two screens lying together, where some places appear dark and some places allow light to pass through, then you are observing an interference pattern.

In fringe analysis you place a questionably flat optic over a known reference flat with an air space between them. If one is tilted slightly (incredibly slightly), then fringes will appear. Why? Because light passes through the glass, then out of the glass into the airspace between the glasses, then some of it reflects off the second glass back up towards the first glass, then through the first glass and out, eventually being seen by you. The light in the airspace on the way down can interfere with the light in the airspace coming up. This interference can be either constructive or destructive. If the space between the glasses is a multiple of 1/2 wave then the light had to go 1/2 wave down then 1/2 wave up for a total of 1 wave, which is constructive, or multiples of 1 wave which are constructive. If the thickness of the airspace is 1/4 wave less than a multiple of 1/2 wave, the total distance traveled will be some number of waves plus 1/2 wave, which will cause destructive interference. Since one glass is tilted slightly with respect to the other glass, the thickness of the airspace increases gradually from one side of the matching glasses to the other. This means that the airspace will gradually pass through thicknesses that are constructively interfering, then destructively interfering, and so on.

This causes lines or curves of interference patterns. If the lines are perfectly straight, then the glasses match and have the same shape. If the fringe patterns are curved, then they are not perfectly matched, and correction needs to be implemented.

Normal white light is insufficient for fringe analysis. The light source needs to be very monochromatic. Fluorescent lamps are not monochromatic, but have two very strong lines of energy, green and violet, that will allow the tester to see fringes. I use an uncoated mercury vapor lamp with a green filter which allows a wavelength of 536.4 nm of extremely monochromatic light to illuminate my fringe tester. Another lamp given to us by Eric Reichenbach is a low pressure sodium lamp producing 587 and 589 nm wavelengths. These very close wavelengths make fine fringes and the light is very bright. Some folks use red lasers in ping pong balls to make a bright monochromatic light source, but I have found this to be very difficult. LEDs don't work well--the band width is not narrow enough.

It is easy to judge if a fringe is straight to within a tenth of a fringe simply by drawing a straight line over the fringe and comparing. Since the fringes represent 1/2 wave in optical difference, a tenth of a fringe is a 20^th of a wave in surface error. This is pretty good. I photograph the fringes with a video camera, then upload the image onto my computer. I then draw straight lines on the image and count pixels to see what fraction of a fringe the errors are. I can also goof with the contrast of the fringes, which helps tremendously.

Some telescopes, such as a classical cassegrain, use convex hyperboloidal secondary mirrors. If the mirror were concave, the testing of the mirror would be easy, just finding centers of curvature using a Foucault test or a caustic test. I grind and polish two pieces of glass to the right RoC, then polish both. I test the concave mirror to be sure it is of the right RoC and is null on the knife-edge test, confirming that it is extremely spherical. Then I place the convex mirror on it with spacers and look at the fringes. At first the fringes are straight because both mirrors are spheres. I then figure the convex mirror until the fringe pattern matches the mathematically predicted pattern that the hyperboloid would exhibit against the sphere. The mirror is then done, but star testing to confirm is highly recommended.

The spacers took me a while to get right. I used to use Saran Wrap, which worked, but wasn't easy to use. A guy on the Internet suggested that I try the cellophane that comes on cigarette packs, CD packs, and other clear wrapped objects. I cut them into triangles, place them on the bottom glass, then lay the other glass on top. If the fringes are too numerous or too few, I move the appropriate triangle until the fringes are easier to see. When the glass sits on the thinner part of the triangle, it moves down slightly (really slightly). I can't increase height (it's like pushing a rope, you can only pull).

Secondary mirrors are tested when they are round disks. When the glass tests flat to the degree required, we saw it out with a drill press at a 45° angle. We pitch another glass disk against it to protect the optical surface, put it in a box at the correct angle, fill the box with plaster, then drill with a metal tube and grit. When we pop it apart we have an elliptical flat, and after beveling the sharp edges it is shipped to the coaters.

One more thing about secondary mirrors: they can be very flat but not perfectly smooth. Not only does the mirror need to be fringe tested, but also tested for smoothness. To do this you place the secondary mirror in front of a spherical mirror at a 45° angle and knife-edge test the spherical mirror via the flat. There will be a double reflection on the flat, increasing the illusion of roughness. If it looks smooth through this, it's smooth. If it shows dog biscuit or microripple, you're not done rubbing yet.

Here is the 4.00" secondary mirror that was in my 24" f/3.7 before I made a new flat for it. Notice that if a straight line were cast across the image there would be about 1 fringe deviation. This means that the mirror is 1/2 wave peak to valley from being a flat mirror, which stinks. Since this mirror is placed into the optical path at a 45° angle, the curvature across the minor axis appears differently to the spherical wave-front from the primary mirror than the curvature across the major axis. This caused terrible astigmatism, and the mirror was replaced. I still have this mirror somewhere if anybody wants to ruin their telescope.

Here is an image of a convex hyperboloidal secondary mirror for a classical cassegrain that I made two years ago. It is incomplete in that it is not smooth, but you can see that the sphere and the hyperboloid are different: the fringes are not straight. The crest of the fringe pattern is at the 71% zone, where the circle is. (X marks the center.) When finished, this crest was 0.965 waves from a sphere, which is almost two fringes.

One last note about interferometric testing. It doesn't lie at all. The Foucault test has ambiguities, errors, interpretation, and numerous other faults that can mislead the tester into thinking the mirror is right on. None of these exist with fringe testing and other interferometric testing. Waves don't lie. There are, however, a couple of ways to screw up.

One is that you must let the glass obtain ambient temperature with the air and the other glass. When the glass expands with heat, the size and shape change and the fringes show that.

The other is that the glass weighs something, and, when you lay it on another piece of glass, its weight presses onto the other glass, and they are suspended against each other at the spacer contact point. If the glass is heavy it will bend the other glass (or itself), and if the glass is thin the other glass will bend it. When that happens, the fringes change. You can actually figure a glass thinking it has an error, when in fact it might have been fine except that gravity bent it.

Straight Fringes!...Jeff Baldwin
For more information on Telescope Making jump to the ATM page.