Foucault knife-edge test
Simple optical test for measuring concave mirror shapes.
The Foucault knife-edge test measures the precise shape of concave mirrors. Amateur telescope makers often use it to figure the primary mirrors in reflecting telescopes, as the setup is simpler and cheaper than other methods.
French physicist Léon Foucault described the test in 1858 for measuring the conic shapes of optical mirrors. It works by reflecting light from a pinhole source into a knife edge placed near the mirror’s center of curvature. The basic 19th-century tester needed only a light bulb, tinfoil with a pinhole, and a razor blade for the knife edge. The tester moves along the X-axis (the knife cut direction) and the Y-axis (the optical axis), with adjustments as fine as 0.001 inch (25 μm) or better along lines parallel to the optical axis. The test can detect errors in mirror curvature down to fractions of a wavelength of light—angstroms, millionths of an inch, or nanometers.
In practice, the mirror sits vertically in a stand. The tester is placed at the mirror’s radius of curvature (twice the focal length), with the pinhole to one side of the center of curvature (a short vertical slit parallel to the knife edge can replace the pinhole). The tester is adjusted so the returning beam from the pinhole is cut by the knife edge. Looking at the mirror from behind the knife edge reveals a pattern. A perfect spherical mirror appears evenly lit across its surface. A spherical mirror with bumps or depressions shows them greatly magnified in height. A paraboloidal surface usually looks like a doughnut or lozenge, depending on the knife edge’s exact position.
To measure how close the mirror is to a perfect parabola, a Couder mask, Everest pin stick, or other zone marker is placed over the mirror. A series of measurements finds the radii of curvature of zones along the optical axis. These data are then reduced and graphed against an ideal parabolic curve.
Other tests also measure mirrors at the center of curvature. The Ronchi test replaces the knife edge with a grating of fine parallel wires, an etching, a photographic negative, or a computer-printed transparency. Its patterns are matched to standard mirrors or computer-generated ones. The Gaviola or Caustic test measures fast f/ratio mirrors more accurately than the Foucault test, which is limited to about λ/8 wavelength accuracy on small and medium mirrors.
- Described by
- Léon Foucault
- Year described
- 1858
- Basic components
- light bulb, tinfoil with pinhole, razor blade
- Adjustment precision
- 0.001 inch (25 μm) or better
- Measurement accuracy
- fractions of wavelengths of light (Angstroms, millionths of an inch, or nanometers)
Lore & Background
The Foucault knife-edge test was described in 1858 by French physicist Léon Foucault as a way to measure conic shapes of optical mirrors. It measures mirror surface dimensions by reflecting light into a knife edge at or near the mirror's centre of curvature. In its most basic 19th century form, the tester consists of a light bulb, a piece of tinfoil with a pinhole, 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. The test can measure errors in a mirror's curvature to fractions of wavelengths of light.
Foucault testing is commonly used by amateur telescope makers for figuring primary mirrors in reflecting telescopes. The mirror to be tested is placed vertically in a stand, and the tester is set up at the distance of the mirror's radius of curvature. Viewing the mirror from behind the knife edge shows a pattern: if the mirror surface is part of a perfect sphere, it appears evenly lighted; if spherical with defects, the defects appear greatly magnified; if paraboloidal, the mirror usually looks like a doughnut or lozenge. It is possible to calculate how closely the mirror surface resembles a perfect parabola by placing a Couder mask, Everest pin stick, or other zone marker over the mirror and taking a series of measurements.
Reader's Guide
The Foucault knife-edge test remains significant as a foundational technique for amateur telescope makers, offering a relatively simple and inexpensive apparatus compared to other testing methods. The article notes that other testing techniques exist, such as the Ronchi test which replaces the knife edge with a grating, and 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 λ/20 wave peak to valley accuracy. The Dall null test uses a plano-convex lens to make a parabolic mirror appear flat under testing, simplifying the process. Interferometric tests, including the Michelson-Twyman and Fizeau methods, have been made more affordable in recent years by affordable lasers, digital cameras, and computers, but remain primarily an industrial methodology. The Foucault test's legacy is its role as a practical, accessible method for mirror figuring, despite the existence of more advanced techniques.
Did You Know?
- The test can measure mirror errors to fractions of wavelengths of light.
- A perfect spherical mirror appears evenly lighted across the entire surface under the test.
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