Abstract

We describe the interferometric testing of a slow (f/16 at the center of curvature) off-axis parabola, intended for use in an x-ray spectrometer, that uses a spherical wave front matched to the mean radius of the asphere. We find the figure error in the off-axis mirror by removing the theoretical difference between the off-axis segment and the spherical reference from the measured wave-front error. This center of curvature test is easy to perform because the spherical reference wave front has no axis and thus alignment is trivial. We confirm that the test results are the same as the double-pass null test for a parabola that uses a plane autocollimating mirror. We also determine that the off-axis section apparently warped as the result of being cut from the symmetric parent part.

© 1995 Optical Society of America

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References

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  1. R. E. Parks, “Alignment of off-axis conic mirrors,” in Optical Fabrication and Testing, 1980 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1980).
  2. R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology I, N. Balasubramanian, J. C. Wyant, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 153, 56–63 (1978).

Parks, R. E.

R. E. Parks, “Alignment of off-axis conic mirrors,” in Optical Fabrication and Testing, 1980 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1980).

R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology I, N. Balasubramanian, J. C. Wyant, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 153, 56–63 (1978).

Other (2)

R. E. Parks, “Alignment of off-axis conic mirrors,” in Optical Fabrication and Testing, 1980 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1980).

R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology I, N. Balasubramanian, J. C. Wyant, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 153, 56–63 (1978).

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Figures (7)

Fig. 1
Fig. 1

Measured surface error over full 127-mm-diameter aperture of the off-axis parabola referenced to a sphere. Contour interval is 316 nm.

Fig. 2
Fig. 2

Measured surface error over full aperture after data are rotated 15° clockwise. Contour interval is 316 nm.

Fig. 3
Fig. 3

Measured surface error after theoretical departure is subtracted between the reference sphere and the off-axis parabola. Contour interval is now 32 nm.

Fig. 4
Fig. 4

Measured surface error of the off-axis parabola over the full aperture as null tested against a flat. Contour is 32 nm.

Fig. 5
Fig. 5

Data in Fig. 4, rotated clockwise by 11°. Contour is 32 nm.

Fig. 6
Fig. 6

Data in Fig. 4, reduced to 80% of full aperture. Contour is 32 nm.

Fig. 7
Fig. 7

Parameters of the off-axis segment relative to the symmetric asphere.

Tables (2)

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Table 1 Zernike Coefficients of the Off-Axis Test

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Table 2 Definition of the Zernike Polynomials

Equations (7)

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a n m = a n m cos ( m θ ) + a n - m sin ( m θ ) ,
a n - m = a n - m cos ( m θ ) - a n m sin ( m θ ) ,
x = x + h ,             y = y .
x = b x ,             y = b y ,
Δ z = ( k / 8 R v 3 ) [ ( b x + h ) 2 + ( b y ) 2 ] 2 + [ k ( k + 2 ) / 16 R v 5 ] [ ( b x + h ) 2 + ( b y ) 2 ] 3 .
Δ z = a 4 0 U 4 0 + a 3 1 U 3 1 + a 2 2 U 2 2 + a 2 0 U 2 0 + a 1 1 U 1 1 + a 0 0 U 0 0 + higher order terms ,
Δ R = k ( 4 h 2 + b 4 ) / 4 R v .

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