Foucault knife-edge test
Encyclopedia
Léon Foucault
Jean Bernard Léon Foucault was a French physicist best known for the invention of the Foucault pendulum, a device demonstrating the effect of the Earth's rotation...
to measure conic shapes of optical mirrors, with error margins measurable in fractions of wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s of light (or Angstroms, millionths of an inch
Inch
An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot...
, or nanometers). It is commonly used by amateur telescope makers for figuring
Figuring
Figuring is the process of final polishing of an optical surface to remove imperfections or modify the surface curvature to achieve the shape required for a given application.-Types of figuring:...
small astronomical mirrors
Primary mirror
A primary mirror is the principal light-gathering surface of a reflecting telescope.-Description:The primary mirror of a reflecting telescope is a spherical or parabolic shaped disks of polished reflective metal , or in later telescopes, glass or other material coated with a reflective layer...
. Its relatively simple, inexpensive apparatus can produce measurements more cost effectively than most other testing techniques.
It measures mirror surface dimensions by reflecting light into a knife edge at or near the center radius (R) of mirror 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 razorblade to create the knife edge. The testing device is adjustable along the X-axis cutting the knife edge across the optical axis
Optical axis
An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens or microscope.The optical axis is an imaginary line that defines the path along which light propagates through the system...
and must have measurable adjustment to 0.001 inch (25 µm) or better along the Y-axis parallel to the optical axis. According to Texereau it amplifies mirror surface defects by a factor of one million, making them easily accessible to study and remediation.
Foucault test basics
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 paraboloidal
Parabola
In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...
, 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 Couder
André Couder
André Couder was a French optician and astronomer. From 1925, he worked in the optics laboratory of the Paris Observatory. Between 1952 and 1958 he was vice-president of the International Astronomical Union....
mask, Everest pin stick (after A. W. Everest) or other zone marker 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). This data is then reduced and graphed against an ideal parabolic curve.
Other testing techniques
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 gratingDiffraction grating
In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as...
) 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/ratio more accurately than the Foucault test which is limited to about (λ/8) wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
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.
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 very much easier and zonal measurements are not needed.http://www.atm-workshop.com/dall-null.html
There are a number of interferometric
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...
tests which have been used including the Michelson-Twyman and the Michelson
Michelson interferometer
The Michelson interferometer is the most common configuration for optical interferometry and was invented by Albert Abraham Michelson. An interference pattern is produced by splitting a beam of light into two paths, bouncing the beams back and recombining them...
method, both published in 1918, the Lenouvel method and the Fizeau
Fizeau interferometer
A Fizeau interferometer is similar to a Fabry–Pérot interferometer in that they both consist of two reflecting surfaces. In a Fizeau interferometer, however, the two surfaces are usually much less than totally reflecting , so that secondary reflections don't contribute greatly to the fringe...
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
- Airy disk
- Amateur telescope makingAmateur telescope makingAmateur telescope making is the activity of building telescopes as a hobby, as opposed to being a paid professional. Amateur telescope makers build their instruments for personal enjoyment of a technical challenge, as a way to obtain an inexpensive or personally customized telescope, or as a...
- Angular resolutionAngular resolutionAngular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object...
(see Angular resolution#Explanation for discussion of the Rayleigh criterion) - Diffraction-limited system
- Huygens–Fresnel principle#Single slit diffraction
- Knife-edge effectKnife-edge effectIn electromagnetic wave propagation, the knife-edge effect or edge diffraction is a redirection by diffraction of a portion of the incident radiation that strikes a well-defined obstacle such as a mountain range or the edge of a building....
- Fabrication and testing of optical components
- Null correctorNull correctorA null corrector is an optical device used in the testing of large aspheric mirrors. A spherical mirror of any size can be tested relatively easily using standard optical components such as laser, mirrors, beamsplitters, and converging lenses. One method of doing this using a Shack cube is shown...
- Strehl ratioStrehl ratioThe Strehl ratio, named after the German physicist and mathematician Karl Strehl , is a measure for the optical quality of telescopes and other imaging instruments...
Further reading
- L. Foucault, "Description des procedees employes pour reconnaitre la configuration des surfaces optiques," Comptes rendus hebdomadaires des séances de l'Academie 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).