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[[File:Foucault-Test 1.png|thumb|right|500px|Foucault test setup to measure a mirror]]
The '''Foucault knife-edge test''' is an optical test to accurately measure the shape of concave [[curved mirror]]s. It is commonly used by amateur telescope makers for [[figuring]] [[primary mirror]]s in [[reflecting telescope]]s. It uses a relatively simple, inexpensive apparatus compared to other testing techniques.
==Overview==
The Foucault knife-edge test was described in 1858 by French physicist [[Léon Foucault]] as a way to measure conic shapes of optical mirrors.<ref>Texereau 1984 pp.68-70 section 2.25</ref> It measures mirror surface dimensions by reflecting light into a knife edge at or near the mirror's centre of curvature. In doing so, it only needs a tester which in its most basic 19th century form consists of a [[light bulb]], a piece of tinfoil with a pinhole in it, and a razor blade to create the knife edge. The testing device is adjustable along the X-axis (knife cut direction) across the Y-axis ([[optical axis]]), and is usually equipped with measurable adjustment to 0.001&nbsp;inch (25&nbsp;μm) or better along lines parallel to the optical axis.<ref name="Harbour39">Harbour 2008 p 39</ref> The test can measure errors in a mirror's curvature to fractions of [[wavelength]]s of light (or [[Angstroms]], millionths of an [[inch]], or [[nanometer]]s).<ref>Texereau 1984 p.70 section 2.26</ref><ref>{{Cite web| last = Sacek| first = Vladimir| title = 4.5.2. Foucault test| work = Notes on AMATEUR TELESCOPE OPTICS| publisher = Vladimir Sacek| date = 14 July 2006| url = http://www.telescope-optics.net/foucault_test.htm| access-date = 18 December 2010}}</ref>
==Foucault test basics==
[[File:Foucault-Test 2 rotated.jpg|thumb|left|150px| From top: Parabolic mirror showing Foucault shadow patterns made by knife edge inside radius of curvature R (red X), at R and outside R.]]
Foucault testing is commonly used by amateur telescope makers for [[figuring]] [[primary mirror]]s in [[reflecting telescope]]s.<ref>Texereau 1984 pp. 55-61 section 2.21</ref><ref>{{Cite web| last = Harbour| first = David A| title = Understanding Foucault: A Primer for Beginners (Second Edition)| publisher = The ATM's Workshop| date = July 2001| url = http://www.atm-workshop.com/foucault.html| access-date = 18 December 2010}}</ref> The mirror to be tested is placed vertically in a stand. The Foucault tester is set up at the distance of the mirror's radius of curvature (radius R is twice the focal length.) with the pinhole to one side of the centre of curvature (a short vertical slit parallel to the knife edge can be used instead of the pinhole). The tester is adjusted so that the returning beam from the pinhole light source is interrupted by the knife edge.
Viewing the mirror from behind the knife edge shows a pattern on the mirror surface. If the mirror surface is part of a perfect sphere, the mirror appears evenly lighted across the entire surface. If the mirror is spherical but with defects such as bumps or depressions, the defects appear greatly magnified in height.  If the surface is [[Parabola|paraboloidal]], the mirror usually looks like a doughnut or lozenge although the exact appearance depends on the exact position of the knife edge.
It is possible to calculate how closely the mirror surface resembles a perfect parabola by placing a [[André Couder|Couder]] mask,<ref>[http://w1.411.telia.com/~u41105032/couder/zcalc.htm Designing and calculating Couder screens for Foucault testing] {{Webarchive|url=https://web.archive.org/web/20210223193456/http://w1.411.telia.com/~u41105032/couder/zcalc.htm |date=2021-02-23 }} Ken Slater and Nils Olof Carlin</ref> Everest pin stick (after A. W. Everest)<ref>[http://stellafane.org/tm/atm/test/mask.html Stellafane ATM Build a Couder Mask; Build an Everest Pin Stick]</ref> or other zone marker<ref name="Harbour49-51">Harbour 2008 pp 49-51</ref> over the mirror. A series of measurements with the tester, finding the radii of curvature of the zones along the optical axis of the mirror (Y-axis). These data are then reduced and graphed against an ideal parabolic curve.
===Other testing techniques===
{{main|Ronchi test|Interferometry}}
A number of other tests are used which measure the mirror at the center of curvature. Some telescope makers use a variant of the Foucault test called a Ronchi test that replaces the knife edge with a grating (similar to a very coarse [[diffraction grating]]) comprising fine parallel wires, an etching on a glass plate, a photograph negative or computer printed transparency. Ronchi test patterns are matched to those of standard mirrors or generated by computer.
Other variants of the Foucault test include the Gaviola or [[Caustic test]] which can measure mirrors of fast [[F-number#Focal ratio in telescopes|f/ratio]] more accurately than the Foucault test which is limited to about (λ/8) [[wavelength]] accuracy on small and medium-sized mirrors. The Caustic test is capable of measuring larger mirrors and achieving a (λ/20) wave peak to valley accuracy by using a testing stage which is adjusted from side to side so as to measure each zone of each side of the mirror from the center of its curvature.<ref>{{Cite web| last = Baldwin| first = Jeff| title = The Caustic Test| work = Valley Skies| publisher = Stockton Astronomical Society| date = September 2000| url = http://stocktonastro.org/Newsletter/TTN_CausticTest.html| access-date = January 9, 2011| archive-url = https://web.archive.org/web/20110728061837/http://stocktonastro.org/Newsletter/TTN_CausticTest.html| archive-date = July 28, 2011| url-status = dead}}</ref>
The ''Dall null test'' uses a plano-convex lens placed a short distance in front of the pinhole.  With the correct positioning of the lens, a parabolic mirror appears flat under testing instead of doughnut-shaped so testing is much easier and zonal measurements are not needed.[http://www.atm-workshop.com/dall-null.html]
There are a number of [[Interferometry|interferometric]] tests which have been used including the [[Twyman–Green interferometer|Michelson-Twyman]] and the [[Michelson interferometer|Michelson]] method, both published in 1918, the Lenouvel method and the [[Fizeau interferometer|Fizeau]] method. Interferometric testing has been made more affordable in recent years by affordable lasers, digital cameras (such as webcams), and computers, but remains primarily an industrial methodology.
==See also==
* [[Schlieren photography]]
* [[Airy disk]]
* [[Amateur telescope making]]
* [[Angular resolution]] (see [[Angular resolution#Explanation]] for discussion of the Rayleigh criterion)
* [[Diffraction-limited system]]
* [[Huygens–Fresnel principle#Single slit diffraction]]
* [[Fabrication and testing of optical components]]
* [[Null corrector]]
* [[Strehl ratio]]
==References==
{{Reflist}}
*{{Cite book | last = Harbour | first = David A| title = Understanding Foucault: A primer for beginners|editor = William J Welker| publisher = Sapphire Publications | date = July 2013 | isbn = 978-1-62374-003-0| edition = 2nd}}
* {{Cite book| last = Texereau| first = Jean| title = How to Make a Telescope| publisher = Willman-Bell| date = 1984| location = Richmond, VA| isbn = 0-943396-04-2| edition = second English}}
*{{Cite book| last = Thompson| first = Allyn J| title = Making Your Own Telescope| publisher = Sky Publishing| date = 15 April 1947| location = Cambridge, MA| asin = B0007DK32U}}
==Further reading==
* L. Foucault, "Description des procedees employes pour reconnaitre la configuration des surfaces optiques," ''Comptes rendus hebdomadaires des séances de l'Académie des Sciences, Paris'', vol. 47, pages 958-959 (1858).
*L. Foucault, "Mémoire sur la construction des télescopes en verre argenté," ''Annales de l'Observatoire impériale de Paris'', vol. 5, pages 197-237 (1859).
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[[Category:Measuring instruments]]
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