Abstract

Subaperture testing provides an attractive alternative to large monolithic test optics for evaluation of large optical systems. We present a method for reducing subaperture testing data that requires no a priori knowledge of the relative piston and tilt of the subapertures. Results of applying this method to analyze subaperture testing interferograms are presented. In particular, the behavior of this method in the presence of data noise and for different subaperture configurations is studied.

© 1983 Optical Society of America

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References

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  1. C. Kim, J. Wyant, “Subaperture test of a large flat on a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981); J. Thunen, O. Kwon, “Full aperture testing with subaperture test optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Arizona, 1982).
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. IX.
  3. C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  4. GENZ is a computer code for generating data that simulate the output of fixed-fringe, phase-measuring, and lateral-sheer interferometers. It was written by W. Swantner, C. Barnard, W. Chow. The code and a user’s manual are available by writing to any of the above authors at the Institute for Modern Optics, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131.

1981 (1)

C. Kim, J. Wyant, “Subaperture test of a large flat on a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981); J. Thunen, O. Kwon, “Full aperture testing with subaperture test optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Arizona, 1982).

Barnard, C.

GENZ is a computer code for generating data that simulate the output of fixed-fringe, phase-measuring, and lateral-sheer interferometers. It was written by W. Swantner, C. Barnard, W. Chow. The code and a user’s manual are available by writing to any of the above authors at the Institute for Modern Optics, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. IX.

Chow, W.

GENZ is a computer code for generating data that simulate the output of fixed-fringe, phase-measuring, and lateral-sheer interferometers. It was written by W. Swantner, C. Barnard, W. Chow. The code and a user’s manual are available by writing to any of the above authors at the Institute for Modern Optics, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131.

Hanson, R.

C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Kim, C.

C. Kim, J. Wyant, “Subaperture test of a large flat on a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981); J. Thunen, O. Kwon, “Full aperture testing with subaperture test optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Arizona, 1982).

Lawson, C.

C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Swantner, W.

GENZ is a computer code for generating data that simulate the output of fixed-fringe, phase-measuring, and lateral-sheer interferometers. It was written by W. Swantner, C. Barnard, W. Chow. The code and a user’s manual are available by writing to any of the above authors at the Institute for Modern Optics, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. IX.

Wyant, J.

C. Kim, J. Wyant, “Subaperture test of a large flat on a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981); J. Thunen, O. Kwon, “Full aperture testing with subaperture test optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Arizona, 1982).

J. Opt. Soc. Am. (1)

C. Kim, J. Wyant, “Subaperture test of a large flat on a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981); J. Thunen, O. Kwon, “Full aperture testing with subaperture test optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 351, 1 (1982); C. Kim, “Polynomial fit of interferograms,” Ph.D. Dissertation (University of Arizona, Tucson, Arizona, 1982).

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. IX.

C. Lawson, R. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).

GENZ is a computer code for generating data that simulate the output of fixed-fringe, phase-measuring, and lateral-sheer interferometers. It was written by W. Swantner, C. Barnard, W. Chow. The code and a user’s manual are available by writing to any of the above authors at the Institute for Modern Optics, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131.

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Figures (3)

Fig. 1
Fig. 1

Subaperture testing experiment. Conventional testing techniques use a large reference optical flat instead of the array of smaller flats shown in the figure.

Fig. 2
Fig. 2

Different subaperture configurations. The behavior of these different configurations in the presence of data noise is summarized in Table 2.

Fig. 3
Fig. 3

Wave-front rms error versus percentage of noise in the data. Seven subapertures were used (Fig. 2f).

Tables (2)

Tables Icon

Table 1 Relationship between Zn Used in the Text and the Zernike Polynomialsa

Tables Icon

Table 2 Accuracy of Our Method for the Different Subaperture Configurations Shown in Fig. 2a

Equations (7)

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σ fit 2 = 1 N n = 1 N { W ( x n , y n ) D [ x n , y n ] } 2
W ( x , y ) = i = 1 N S [ P i Z 1 ( x , y ) + T x i Z 2 ( x , y ) + T y i Z 3 ( x , y ) ] χ ( x , y ; i ) + m = 4 L A m Z m ( x , y ) ,
α 1 k j P j + α 2 k j T x j + α 3 k j T y j + m = 4 L α m k j A m = β k j
j = 1 N S ( α 1 k j P j + α 2 k j T x j + α 3 k j T y j ) + m = 4 L γ k m A m = δ k
α i k j = n = N j 1 + 1 N j Z i ( x n , y n ) Z k ( x n , y n ) , β k j = n = N j 1 + 1 N j D [ x n , y n ] Z k ( x n , y n ) , γ k m = n = 1 N Z k ( x n , y n ) Z m ( x n , y n ) , δ k = n = 1 N D [ x n , y n ] Z k ( x n , y n ) ,
Δ 1 σ i n [ W ( x , y ) W i n ( x , y ) ] 2 1 / 2 ,
W ( x , y ) = m = 4 M A m Z m ( x , y )

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