Abstract

The caustic or Gaviola test, used for testing aspheric mirrors, has been studied with reference to the research of Schroader [ “The caustic test,” in Amateur Telescope Making III, A. G. Ingalls, ed. (Kingsport Press, Kingsport, Tenn., 1953), pp. 429–456]. It is shown that the two central formulas, which are used to determine the mirror quality, give significant errors for the large-diameter, short-focal-length mirrors commonly used in astronomical optics. We derive analytically two alternative equations, which are more exact, and show that they lead to significant improvement.

© 1998 Optical Society of America

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References

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  1. R. Platzeck, E. Gaviola, “On the errors of testing and a new method for surveying optical surfaces and systems,” J. Opt. Soc. Am. 29, 484–500 (1939).
    [CrossRef]
  2. I. H. Schroader, “The caustic test,” in Amateur Telescope Making III, A. G. Ingalls, ed. (Kingsport Press, Kingsport, Tenn., 1953), pp. 429–456.
  3. A. Mackintosh, “Testers and testing,” in Advanced Telescope Making Techniques, A. Mackintosh, ed. (Willmann-Bell, Richmond, Va., 1977), pp. 33–38.
  4. J. Ojeda-Castaneda, “Foucault, wire and phase modulation tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 260–264.
  5. R. D. Sigler, “Testers and testing,” in Advanced Telescope Making Techniques, A. Mackintosh, ed. (Willmann-Bell, Richmond, Va., 1977), pp. 44–45.

1939 (1)

Gaviola, E.

Mackintosh, A.

A. Mackintosh, “Testers and testing,” in Advanced Telescope Making Techniques, A. Mackintosh, ed. (Willmann-Bell, Richmond, Va., 1977), pp. 33–38.

Ojeda-Castaneda, J.

J. Ojeda-Castaneda, “Foucault, wire and phase modulation tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 260–264.

Platzeck, R.

Schroader, I. H.

I. H. Schroader, “The caustic test,” in Amateur Telescope Making III, A. G. Ingalls, ed. (Kingsport Press, Kingsport, Tenn., 1953), pp. 429–456.

Sigler, R. D.

R. D. Sigler, “Testers and testing,” in Advanced Telescope Making Techniques, A. Mackintosh, ed. (Willmann-Bell, Richmond, Va., 1977), pp. 44–45.

J. Opt. Soc. Am. (1)

Other (4)

I. H. Schroader, “The caustic test,” in Amateur Telescope Making III, A. G. Ingalls, ed. (Kingsport Press, Kingsport, Tenn., 1953), pp. 429–456.

A. Mackintosh, “Testers and testing,” in Advanced Telescope Making Techniques, A. Mackintosh, ed. (Willmann-Bell, Richmond, Va., 1977), pp. 33–38.

J. Ojeda-Castaneda, “Foucault, wire and phase modulation tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 260–264.

R. D. Sigler, “Testers and testing,” in Advanced Telescope Making Techniques, A. Mackintosh, ed. (Willmann-Bell, Richmond, Va., 1977), pp. 44–45.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram (not to scale) of a parabolic mirror with its pole at the origin of coordinate system A. The center of curvature of the mirror is at C. For a light source kept at C, the image of an off-axis element IJ (at depth -r) is formed along the caustic curve at H. GI and GJ are the normals (schematic) to the mirror at I and J.

Fig. 2
Fig. 2

Graphic representation of the deviations at the mirror surface for different zone heights r (see Section 3). The deviation has been shown in millimeters and also in fractions of wavelength (λ = 5000 Å).

Equations (20)

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X = 3 r 2 R ,
Y = 2 r 3 R 2 .
y 2 = 2 Rx .
x 1 ,   y 1 = - r + ξ 2 2 R - r + ξ ,
x 2 ,   y 2 = r + ξ 2 2 R - r - ξ .
y - y 1 / x - x 1 = - y 1 / R .
tan θ = r - ξ / R - x 1 ,   tan θ - ϕ = r - ξ / R .
m 1 = 2   tan θ - ϕ + tan θ tan 2 θ - ϕ - tan θ 1 + 2   tan θ tan θ - ϕ - tan 2 θ - ϕ .
tan θ = r + ξ / R - x 2 ,   tan θ - ϕ = r + ξ / R .
x c = y 2 - y 1 + m 1 x 1 - m 2 x 2 m 1 - m 2 ,
y c = m 1 m 2 x 1 - x 2 - m 2 y 1 + m 1 y 2 m 1 - m 2 .
m 1 | ξ 0 = m 2 | ξ 0 = 2 rR 3 2 R 4 + R 2 r 2 + r 4 ,   m 1 | ξ 0 = - m 2 | ξ 0 = 2 R 3 - 2 R 4 + r 2 R 2 + 3 r 4 2 R 4 + R 2 r 2 + r 4 2 ,   x 1 | ξ 0 = x 2 | ξ 0 = r 2 2 R ,   x 1 | ξ 0 = - x 2 | ξ 0 = - r R .
X N = x c - R
= 3 r 2 R 1 + r 2 / R 2 + r 4 / 12 R 4 + r 6 / 12 R 6 1 - r 2 / 2 R 2 - 3 r 4 / 2 R 4 ,
Y N = y c
= 2 r 3 R 2 1 + r 2 / R 2 1 - r 2 / 2 R 2 - 3 r 4 / 2 R 4 .
Error = Y obs - Y
= Y N - Y - X N - X tan δ ,
tan δ = Y N + r / X N + R - r 2 / 2 R .
deviation = k × error ,

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