August 2001 Newsletter

Stockton Astronomical Society

Valley Skies

Valley Skies - August 2001 Issue

The Telescope Nut
by Jeff Baldwin

Fringes II

I discussed fringe-testing flats once before, but since I am about to make a secondary mirror for the 40" scope, I thought I'd hit it again.

The larger the telescope, the flatter the secondary needs to be. The faster the telescope, the flatter the secondary needs to be. The larger the ratio between the distance from the eyepiece to the secondary compared to the distance from the secondary to the primary--the flatter the secondary needs to be. Unfortunately, I fit into all three categories with this project.

I have one more category, and that is the absolute massive size of the secondary mirror. My secondary has to have a minor axis of 7"; that's a huge secondary as far as I'm concerned. Buying a secondary mirror for this project is cost prohibitive. I can get one for about $1000, but it would not be of high enough quality. To have a very, very flat secondary mirror of this size and not spend $4000, I have to make it myself. It will most likely be as challenging to produce as the primary. It will be equally important, since every photon that hits the primary also hits the secondary.

If the secondary mirror had a slight curve to it, imagine what would happen when it was mounted at a 45° angle. The eyepiece would see a mirror that had different radii of curvatures from its point of view, and this would translate into astigmatism. If the mirror were set very close to the eyepiece, most likely it would be an insignificantly small error, so a sloppy secondary would work. However, Big Dude is a 40" f/3.6, and the secondary mirror is 20.75" away, so it needs to be non-spherical--it needs to be very flat.

The mirror also needs to be smooth. Fringe testing will let us see how flat it is, but it isn't very good in determining how smooth it is, unless you thoroughly analyze the shapes of the fringes. Two tests need to be done: one is the fringe test, the other is a knife-edge test on a known sphere. The light between the sphere and the test apparatus is reflected twice off the secondary flat, once on the way to the mirror, and again on the way back. If the sphere still looks smooth, then the secondary is also smooth.

What is a fringe? Remember that light exists in a duality. It is a particle, and it is a wave. Fringe testing uses the wave nature of light.

Let's place two glasses together, one above the other, so that they are slightly tilted with respect to each other.

Light is passing through the air above the top glass. It strikes the glass, and three things happen: part of the light is reflected back up, part of the light is absorbed into the material, and part of the light passes through the material. The light that passes through the material hits the interface between the bottom of that glass and the airspace. Three things happen again. Part of the light reflects back up, part is absorbed into the material, and part passes through into the airspace. This light continues to the bottom glass where, again, part of the light reflects back up, part is absorbed, and part passes through the bottom glass. The light that is reflected upward from the bottom glass hits the bottom of the top glass, and the same three things happen, passage, reflection, and absorption.

What I want to talk about is the interaction between the light that is passing out of the top glass downward into the airspace, and the light that is reflecting upward off the top of the bottom glass. These light waves interact with each other as waves, producing what is called interference.

When waves interfere with each other, they can produce constructive or destructive interference. Constructive interference is when the troughs and crests align (in-phase) and the amplitude of the wave increases. Destructive interference is when the troughs of one wave align with the crests of the other, and vice versa (out-of-phase). This neutralizes the energy of the waves, and the amplitude decreases. Now examine the above image of the two glasses together. Notice how the airspace between them varies from thin to thick. This means that in-phase and out-of-phase conditions alternate. The result is that we see alternating bands of destructive and constructive interference. The illusion, if the glasses are both very smooth and flat, is that there are bars of light and dark across the faces of these glasses.

If the two glasses mate perfectly, the bars will be straight lines. However, if the glasses mate imperfectly, the bars will bend, due to the fact that the distances between the areas on the glasses where they mate at ½ wave intervals varies irregularly. If the glasses are smooth, but not mating, hopefully it will be due to the glasses being spherical, which is easy to correct. Here is a fringe test sample of errors.

If the distance between the glasses is ½ wave, then the difference between the phases of the light is 1 wave, since there was a ½ wave trip down and a ½ wave trip back. This means that the bars represent differences of ½ wave on the glasses. Now, it could be 3547 waves plus this half wave, but at least it is easily seen what the difference in the shapes are. We usually string a straight line across the glass. We look to see how many bars the straight line compares to on the fringes. In the above left image, there is about ½ bar difference, which is ½ of ½ wave, or¼ wave. Same with the next image, only the other way. If the bars are seen as perfectly straight lines all the way across the glass, then they are most likely 1/10 of a fringe from flat or better. 1/10 of a fringe is 1/10 of ½ wave, or 1/20 wave. Keep in mind that if you have two glasses that are 1/10 wave apart, then it is possible that each is 1/20 wave in error, since 1/20 wave on one and 1/20 wave on the other add up to a difference of 1/10 wave. When you are making the flats, you have to do some arithmetic to see which way and how far the flats are from being flat.

When making your first flat and a reference flat, you have three glasses, A, B and C. You grind A with B, then B with C, then C with A. You cut-throat these together throughout the project. Three will fight each other to flat, where only two will make a natural curve. After you have finished your project and have a reference flat, then you can work only one at a time judging it against the reference.

The light has to be very monochromatic. I use a mercury bulb, uncoated, and a green filter. This produces light of 546.1 nm wavelength. My fringe box for this setup could only take up to 10" glass. Since my secondary mirror will have a 7" minor axis, that means it will have a 10" major axis. It will need to be cut from 12" glass. Since my existing fringe box was too small, I had to build a larger one. Eric Reichenbach had a low-pressure sodium bulb, which produces light of 589 nm and 589.6 nm wavelengths, so close that they will work out as monochromatic. I built a fringe box that will take up to 20" glasses. I don't see us exceeding that too soon. Here is a side-view of the fringe box I recently built.

The Na vapor light at the top produces a nearly monochromatic light (589 nm and 589,6 nm). The light shines downward through a diffuser, which acts like a lamp-shade, shining the light from a region rather than a point. This light progresses downward through the diagonal plate glass and to the two glasses. Between the two glasses, a fringe pattern is produced. The optician looks into the diagonal glass, which acts as a 45° mirror, and he sees the glasses with the fringe pattern.

Once the glass is flat, an oval secondary mirror has to be cut out of it. Sawing through the glass at a 45° angle will do the trick. Don Taylor has 7" pipe for me to saw this out.

This is the side view of the drill press assembly. The good glass and a dummy glass are fused together with blocking pitch. They are set into a box at a 45° angle, and the box is filled with plaster. A hole saw of the correct minor axis diameter is drilled downward through the glasses. When it is all disassembled, the secondary mirror is oval shaped and ready to be cleaned and aluminized.

If you are interested in seeing fringes, stop by the ATM workshop and I'll show them to you. Enjoy!

Clear Skies...Jeff Baldwin
For more information on Telescope Making jump to the ATM page.

bald@gotnet.net
http://members.gotnet.net/bald/atm/atm.htm

Related Telescope Nut articles:
Aug. '99 issue: Optical Flats for Secondary Mirrors
Nov. '99 issue: Secondary Mirror Size & Offset
July 2000 issue: Fringe Analysis

(Telescope Nut articles are archived on the SAS website)