The Foucault knife-edge test is an optical test to accurately measure the shape of concave curved mirrors. It is commonly used by amateur telescope makers for figuring primary mirrors in reflecting telescopes. It uses a relatively simple, inexpensive apparatus compared to other testing techniques.
The Foucault knife-edge test was described in 1858 by French physicist Léon Foucault as a way to measure conic shapes of optical mirrors. [1] 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 inch (25 µm) or better along lines parallel to the optical axis. [2] The test can measure errors in a mirror's curvature to fractions of wavelengths of light (or Angstroms, millionths of an inch, or nanometers). [3] [4]
Foucault testing is commonly used by amateur telescope makers for figuring primary mirrors in reflecting telescopes. [5] [6] 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, 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 mask, [7] Everest pin stick (after A. W. Everest) [8] or other zone marker [9] 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.
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/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. [10]
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.
There are a number of interferometric tests which have been used including the Michelson-Twyman and the Michelson method, both published in 1918, the Lenouvel method and the 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.
Amateur 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 research tool in the field of astronomy. Amateur telescope makers are usually a sub-group in the field of amateur astronomy.
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Jean Bernard Léon Foucault was a French physicist best known for his demonstration of the Foucault pendulum, a device demonstrating the effect of Earth's rotation. He also made an early measurement of the speed of light, discovered eddy currents, and is credited with naming the gyroscope.
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A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Many variant forms are in use and some employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a catoptric telescope.
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.
The Newtonian telescope, also called the Newtonian reflector or just a Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton, using a concave primary mirror and a flat diagonal secondary mirror. Newton's first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope. The Newtonian telescope's simple design has made it very popular with amateur telescope makers.
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In physics, the wavefront of a time-varying wave field is the set (locus) of all points having the same phase. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal frequency.
A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, headlamps, early lighthouse focusing systems, optical telescopes, microscopes, and telephoto lenses. Other optical systems that use lenses and mirrors are also referred to as "catadioptric", such as surveillance catadioptric sensors.
The Maksutov is a catadioptric telescope design that combines a spherical mirror with a weakly negative meniscus lens in a design that takes advantage of all the surfaces being nearly "spherically symmetrical". The negative lens is usually full diameter and placed at the entrance pupil of the telescope. The design corrects the problems of off-axis aberrations such as coma found in reflecting telescopes while also correcting chromatic aberration. It was patented in 1941 by Soviet optician Dmitri Dmitrievich Maksutov. Maksutov based his design on the idea behind the Schmidt camera of using the spherical errors of a negative lens to correct the opposite errors in a spherical primary mirror. The design is most commonly seen in a Cassegrain variation, with an integrated secondary, that can use all-spherical elements, thereby simplifying fabrication. Maksutov telescopes have been sold on the amateur market since the 1950s.
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In optical testing a Ronchi test is a method of determining the surface shape (figure) of a mirror used in telescopes and other optical devices.
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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.
The Klevtsov–Cassegrain telescope is a type of catadioptric Cassegrain telescope that uses a spherical primary mirror and a sub-aperture secondary corrector group composed of a small lens and a Mangin mirror.
A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.
