Abstract

A new algorithm for measuring the profile of an aspheric cylindrical surface is developed in which directions of the surface normal and slopes at various locations are found with the aid of a retroreflected beam. The locations of retroreflection can be found with the simple algorithm developed in this paper, and the surface profile is integrated from the slope. The accuracy of the new algorithm is determined mostly by the algorithm’s ability to find the true range of the surface being integrated. In the measurement of the surface sagitta over the range of 5000 μm, the accumulated error from the integration is less than 30 μm.

© 1991 Optical Society of America

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References

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  1. A. D. Schnurr, A. Mann, “Optical figure characterization for cylindrical mirrors and lenses,” Opt. Eng. 20, 412–416 (1981).
  2. J. M. Geary, “Data analysis in fiber optic testing of cylindrical optics,” Opt. Eng. 28, 212–216 (1989).
  3. D. Malacara, C. Menchaca, “Imaging of the wavefront under test in interferometry,” in Southwest Conference on Optics ’85, S. C. Stotlar, ed., Proc. Soc. Photo-Opt. Instrum. Eng.540, 34–40 (1985).

1989 (1)

J. M. Geary, “Data analysis in fiber optic testing of cylindrical optics,” Opt. Eng. 28, 212–216 (1989).

1981 (1)

A. D. Schnurr, A. Mann, “Optical figure characterization for cylindrical mirrors and lenses,” Opt. Eng. 20, 412–416 (1981).

Geary, J. M.

J. M. Geary, “Data analysis in fiber optic testing of cylindrical optics,” Opt. Eng. 28, 212–216 (1989).

Malacara, D.

D. Malacara, C. Menchaca, “Imaging of the wavefront under test in interferometry,” in Southwest Conference on Optics ’85, S. C. Stotlar, ed., Proc. Soc. Photo-Opt. Instrum. Eng.540, 34–40 (1985).

Mann, A.

A. D. Schnurr, A. Mann, “Optical figure characterization for cylindrical mirrors and lenses,” Opt. Eng. 20, 412–416 (1981).

Menchaca, C.

D. Malacara, C. Menchaca, “Imaging of the wavefront under test in interferometry,” in Southwest Conference on Optics ’85, S. C. Stotlar, ed., Proc. Soc. Photo-Opt. Instrum. Eng.540, 34–40 (1985).

Schnurr, A. D.

A. D. Schnurr, A. Mann, “Optical figure characterization for cylindrical mirrors and lenses,” Opt. Eng. 20, 412–416 (1981).

Opt. Eng. (2)

A. D. Schnurr, A. Mann, “Optical figure characterization for cylindrical mirrors and lenses,” Opt. Eng. 20, 412–416 (1981).

J. M. Geary, “Data analysis in fiber optic testing of cylindrical optics,” Opt. Eng. 28, 212–216 (1989).

Other (1)

D. Malacara, C. Menchaca, “Imaging of the wavefront under test in interferometry,” in Southwest Conference on Optics ’85, S. C. Stotlar, ed., Proc. Soc. Photo-Opt. Instrum. Eng.540, 34–40 (1985).

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the retroreflection test.

Fig. 2
Fig. 2

Interferograms of the measured surface when the reflection mirror is rotated by 1° with respect to each interferogram.

Fig. 3
Fig. 3

Demonstration of the unshifted position of the optical path minimum (at pixel number 38) with two interferograms phase shifted by an arbitrary quantity.

Fig. 4
Fig. 4

Setup of the retroreflection test. B.S., beam splitter.

Fig. 5
Fig. 5

Photograph of the setup, where M, A, and R represent the reflection mirror, tested surface, and reference plate, respectively.

Fig. 6
Fig. 6

Locations of the optical path minima corresponding to measured angles.

Fig. 7
Fig. 7

Derivatives of the tested surface (crosses represent measurement positions).

Fig. 8
Fig. 8

Sagitta measured from a plane parallel to the facet ab shown in Fig. 1.

Fig. 9
Fig. 9

Discrepancy of profiles as the result of a change of 0.0001 in the unit transfer factor.

Fig. 10
Fig. 10

Discrepancy of profiles simulated by a random change of the azimuth angle of the reflection mirror within the range of 30 arcsec.

Fig. 11
Fig. 11

Interferogram of part of the measured surface: slightly zigzag fringes show defects from polishing.

Equations (6)

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N ^ = f x i ^ + f y j ^ - k ^ [ 1 + ( f x ) 2 + ( f y ) 2 ] 1 / 2 ,
f / x = tan ( ϕ 1 ) ,
I = a + b cos θ ( x ) ,
I x = - b sin θ θ x .
ϕ 1 = ½ ( 90 ° - ϕ 2 ) .
f x d x ,

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