Abstract

Focus retrocollimated interferometry is described for measuring long radius of curvature (⩾1 m), and achievable accuracy is discussed. It is shown that this method can be applied to both concave and convex spherical surfaces and can provide measurement to accuracy of 0.01–0.1%.

© 2001 Optical Society of America

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References

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  1. J. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 428–430.
  2. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
    [CrossRef]
  3. M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
    [CrossRef]
  4. Y. W. Lee, H. M. Cho, I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35, 480–483 (1996).
    [CrossRef]
  5. H. H. Hopkins, Wave Theory of Aberration (Oxford University, Oxford, UK, 1950), p. 14.

1996

Y. W. Lee, H. M. Cho, I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35, 480–483 (1996).
[CrossRef]

1992

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

1980

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

Bruning, J.

J. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 428–430.

Cho, H. M.

Y. W. Lee, H. M. Cho, I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35, 480–483 (1996).
[CrossRef]

Gerchman, M. C.

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberration (Oxford University, Oxford, UK, 1950), p. 14.

Hunter, G. C.

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

Lee, I. W.

Y. W. Lee, H. M. Cho, I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35, 480–483 (1996).
[CrossRef]

Lee, Y. W.

Y. W. Lee, H. M. Cho, I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35, 480–483 (1996).
[CrossRef]

Selberg, L. A.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

Opt. Eng.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1966 (1992).
[CrossRef]

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

Y. W. Lee, H. M. Cho, I. W. Lee, “Measurement of a long radius of curvature using a half-aperture bidirectional shearing interferometer,” Opt. Eng. 35, 480–483 (1996).
[CrossRef]

Other

H. H. Hopkins, Wave Theory of Aberration (Oxford University, Oxford, UK, 1950), p. 14.

J. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 428–430.

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Figures (4)

Fig. 1
Fig. 1

FRCI principle for measuring the long radius of curvature.

Fig. 2
Fig. 2

Measurement configuration and procedures for long radius of curvature. BS, beam splitter.

Fig. 3
Fig. 3

Variation of ΔR/ R with R for R from 1–9 m. Square, Δf/ f = ∼0.04%; circle, Δf/ f = ∼0.01%; triangle, Δf/ f = ∼0.005%.

Fig. 4
Fig. 4

Variation of ΔR/ R with R for R from 10–90 m. Square, Δf/ f = ∼0.04%; circle, Δf/ f = ∼0.01%; triangle, Δf/ f = ∼0.005%.

Tables (3)

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Table 1 Relations between ΔW and Wave Aberration for Different Judgment Methods

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Table 2 Effect of Interferometry Sensitivity on Null-Position Error

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Table 3 Experiment of a Long-Radius-of-Curvature Measurement

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

R=ff/x.
f=f
R=f2/x.
δRR=2 Δff-Δxx+ΔtR,
ΔxΔt=8f/D2ΔW,
ΔtR10 μm4 μmR10-710-6.
δRR=2 Δff-Δxx.
ΔRR=4Δff2+Δxx21/2=4Δff2+Rf22Δx21/2.

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