Understanding Foucault by Habour David

Author:Habour, David [Habour, David]
Language: eng
Format: azw3
Tags: Science & Technical
ISBN: 9781623740122
Publisher: Sapphire Publications
Published: 2013-07-20T16:00:00+00:00

Figure 22.

The distance between the light source (which, remember, is at the C of C), and the point where the edge-rays focus is labeled “d”. The greatest radius of the mirror is identified as “r”. We find that the distance d is determined by the equation r2/R.

This tells us that the knife edge must be capable of traveling at least this distance “d” along the mirror’s optical axis, and it is this distance which must be accurately measured. How accurate? Playing with some numbers for r and R for various mirror diameters and focal ratios, one can easily see that “d” is on the order of 0.09” ( for a small diameter, short focus mirror) to 0.6” (large diameter, short focus). (Short focus mirrors always have a greater “d”.) Thus the reason the Foucault tester must be capable of accurately measuring around 0.001”. We don’t need to measure optical tolerances in "millionths of an inch" because the physical measure is in relatively large fractions of an inch! Even when the range of “d” is no greater than 0.09” a repeatable measure no finer than 0.001” will provide quite satisfactory results. You needn’t be able to measure the Y-axis more accurately.

Now it is important to reiterate that in the design of a modern Foucault Tester, the point source of light is not fixed in position as it was in the originally invented Foucault test. Rather, the light source and the knife edge move together, and hence, the distance “d” in Figure 22 is halved! The equation for ‘d’ becomes d = r2/2R, which is the equation we used earlier in this text, see Figure 10. (Why this is true is left as an exercise for the reader.)

This brings us to the other part of the answer as to how we can get by with measurements along the OA which are so large compared to the wavelength of light. It is this: The appearance of the shadows on the mirror in the eye (or camera) reveals features which are fractional wavelengths in depth! When the shadows on the mirror’s surface appear smooth, they are! When the surface looks like a lemon peel, or ripple, it is! These optical defects can’t be (easily) measured, but they can be seen! And these defects don’t need to be measured, rather, by learning what these defects look like, and how to deal with them during figuring and polishing, the Foucault test reveals the progress toward a suitable mirror surface without the need to measure defects which are, in fact, millionths of an inch in span!

Look back now at Figure 21. While the broad dark and light areas important to the test are clearly visible, fine detail is also visible in the photograph which reveals rings and artifacts from polishing which are far smaller than the wavelength of light which can’t be measured. But information from both characteristics (the broad light and dark shadows, and the finer artifacts) provide crucial information to the mirror-maker on how the work is proceeding.

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