Abstract

The relationships between figure errors on an optical flat and wave-front aberrations when the flat is tested in the Ritchey-Common configuration are examined by the real ray-tracing lens analysis program polycon. A new data reduction method for the test is demonstrated. The test is simulated, and rays are traced using polycon. Unit magnitude Zernike term surface errors are added, one by one, to the flat under simulated test, and the effect on the wave front is derived by real ray tracing. This results in a table of influence functions for the particular test geometry. The simulation is repeated for one or more different field angles or azimuthal rotations of the flat to obtain other sets of influence functions. By using these influence functions it is possible to deduce what surface errors on the flat are responsible for any arbitrary test wave-front errors measured up to the order of the influence functions derived. The effectiveness of this method is compared with other existing methods by computer simulations.

© 1983 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  2. W. Primak, Appl. Opt. 6, 1917 (1967).
    [CrossRef] [PubMed]
  3. A. A. Common, R. Astron. Soc. Mon. Note 48, 105 (1888).
  4. G. W. Ritchey, Smithson. Contrib. Knowl. 34, 3 (1904).
  5. J. Texereau, How to Make a Telescope (Interscience, New York, 1957).
  6. A. G. Ingalls, Ed., Amateur Telescope Making Book I (Scientific American, New York, 1972).
  7. B. Tatian, “An Analysis of the Ritchey-Common Test for Large Plane Mirrors,” Itek Corp. Internal Report, Lexington, Mass. (1967).
  8. J. B. Houston, Opt. Eng. 14, S88 (1975).
  9. H. D. Polster, Appl. Opt. 9, 840 (1970).
    [CrossRef] [PubMed]
  10. T. A. Fritz, “Interferometric Evaluation for a Ritchey-Common Test Configuration,” M.S. Thesis, U. Arizona, Tucson (1980).
  11. L. J. Golden, “The Ritchey-Common Test Applied to a Large Vertically Hung Quartz Mirror and the Impact of Results Obtained on the KPNO Stressed Mirror Polishiong Experiment,” Kit Peak National Observatory, The NNTT Technology Development Program Report1 (1981).
  12. K. L. Shu, “Analysis of Alignment and Surface Figure Errors in Optical Systems,” Ph.D. Dissertation, U. Arizona, Tucson (1982).

1975 (1)

J. B. Houston, Opt. Eng. 14, S88 (1975).

1970 (1)

1967 (1)

1904 (1)

G. W. Ritchey, Smithson. Contrib. Knowl. 34, 3 (1904).

1888 (1)

A. A. Common, R. Astron. Soc. Mon. Note 48, 105 (1888).

Common, A. A.

A. A. Common, R. Astron. Soc. Mon. Note 48, 105 (1888).

Fritz, T. A.

T. A. Fritz, “Interferometric Evaluation for a Ritchey-Common Test Configuration,” M.S. Thesis, U. Arizona, Tucson (1980).

Golden, L. J.

L. J. Golden, “The Ritchey-Common Test Applied to a Large Vertically Hung Quartz Mirror and the Impact of Results Obtained on the KPNO Stressed Mirror Polishiong Experiment,” Kit Peak National Observatory, The NNTT Technology Development Program Report1 (1981).

Houston, J. B.

J. B. Houston, Opt. Eng. 14, S88 (1975).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Polster, H. D.

Primak, W.

Ritchey, G. W.

G. W. Ritchey, Smithson. Contrib. Knowl. 34, 3 (1904).

Shu, K. L.

K. L. Shu, “Analysis of Alignment and Surface Figure Errors in Optical Systems,” Ph.D. Dissertation, U. Arizona, Tucson (1982).

Tatian, B.

B. Tatian, “An Analysis of the Ritchey-Common Test for Large Plane Mirrors,” Itek Corp. Internal Report, Lexington, Mass. (1967).

Texereau, J.

J. Texereau, How to Make a Telescope (Interscience, New York, 1957).

Appl. Opt. (2)

Opt. Eng. (1)

J. B. Houston, Opt. Eng. 14, S88 (1975).

R. Astron. Soc. Mon. Note (1)

A. A. Common, R. Astron. Soc. Mon. Note 48, 105 (1888).

Smithson. Contrib. Knowl. (1)

G. W. Ritchey, Smithson. Contrib. Knowl. 34, 3 (1904).

Other (7)

J. Texereau, How to Make a Telescope (Interscience, New York, 1957).

A. G. Ingalls, Ed., Amateur Telescope Making Book I (Scientific American, New York, 1972).

B. Tatian, “An Analysis of the Ritchey-Common Test for Large Plane Mirrors,” Itek Corp. Internal Report, Lexington, Mass. (1967).

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

T. A. Fritz, “Interferometric Evaluation for a Ritchey-Common Test Configuration,” M.S. Thesis, U. Arizona, Tucson (1980).

L. J. Golden, “The Ritchey-Common Test Applied to a Large Vertically Hung Quartz Mirror and the Impact of Results Obtained on the KPNO Stressed Mirror Polishiong Experiment,” Kit Peak National Observatory, The NNTT Technology Development Program Report1 (1981).

K. L. Shu, “Analysis of Alignment and Surface Figure Errors in Optical Systems,” Ph.D. Dissertation, U. Arizona, Tucson (1982).

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Figures (8)

Fig. 1
Fig. 1

Ritchey-Common test configuration.

Fig. 2
Fig. 2

Pupil mapping in Ritchey-Common test configuration. The dotted circle on the right is the circular aperture of the flat as viewed in normal incidence. The shape of the solid curve is the apparent pupil as viewed from O [see Eq. (2)].

Fig. 3
Fig. 3

Oblique beam incidence effect on optical path difference [see Eq. (3)].

Fig. 4
Fig. 4

Ritchey-Common test example.

Fig. 5
Fig. 5

Contour map of the surface errors of sampe flat A. The contour interval is 0.25 wave [see Eq. (22)].

Fig. 6
Fig. 6

Ritchey test wave-front errors of flat A when viewed at several Ritchey angles. The contour interval is 0.5 wave.

Fig. 7
Fig. 7

Contours of figure error on flat A retrieved by each method. Contour step is 0.25 wave.

Fig. 8
Fig. 8

Surface with figure errors up to sixth order is tested and retrieved with fourth-order figure design. (a) true surfaces figure (contour step 0.2 wave); (b) retrieved figure by fourth-order design (contour step is 0.2 wave); and (c) residual errors with contour step changed (contour step is 0.05 wave).

Tables (9)

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Table I Single-Pass Ritchey Wave Front of the Flat

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Table II Relative Weight of Each Surface Term to the Wave Front W2,2 Term as a Function of Ritchey Angle

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Table III Double-Pass Wave Front Error Coefficients from polycon for Test of Flat A at Various Ritchey Angles

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Table IV Influences of Surface Error Terms to the Wave Front Errors In Ritchey-Common Test Example

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Table V Accuracy of the Figure Retrieved by Each Method In Test of Flat A

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Table VI Accuracy of the Figure Retrieved by Each Method in Test of Flat B

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Table VII Results of Figure Design Method for 50 Experiments with Random Wave Front Errors of δWn,m ⩽ ±0.025

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Table VIII Results of Figure Design Method for 50 Experiments with Random Wave Front Errors of δWn,m ⩽ ±0.025 and Errors of 0.1, 0.2° in the Ritchey Angles

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Table IX Sixth-Order Surface Retrieved with Fourth-Order Figure Design

Equations (28)

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Δ s ( X s , Y s ) = n , m S n , m Z n , m ( X x , Y s ) ,
X s X p / cos θ 1 ± X p tan θ 2 F / # ,             Y s Y p .
OPD 2 Δ s cos I = 2 Δ s | sin [ θ ± tan - 1 ( 2 F / # X p ) ] | .
OPD ( X p , Y p ) 2 | sin [ θ ± tan - 1 ( 2 F / # X p ) ] | Δ s ( X p / cos θ 1 ± X p tan θ 2 F / # , Y p ) .
OPD ( X p , X p ) 2 cos θ Δ s ( X p cos θ , Y p ) = W n , m Z n , m ( X p , Y p ) .
W 2 , 0 = S 2 , 0 ( 1 + cos 2 θ ) cos θ + S 2 , 2 sin 2 θ 2 cos θ + 3 S 4 , 0 cos θ 4 × ( 3 cos 4 θ - 2 cos 2 θ - 1 ) ,
W 2 , 2 = 2 S 2 , 0 sin 2 θ ) cos θ + S 2 , 2 ( 1 + cos 2 θ ) cos θ + 3 S 4 , 0 cos θ 2 × ( 3 cos 3 θ - 4 cos 2 θ + 1 ) ,
W 2 , - 2 = 2 S 2 , - 2 ,
W 3 , 1 = S 3 , 1 2 ( 3 cos 2 θ + 1 ) ,
W 3 , - 1 = S 3 , - 1 cos θ 2 ( 1 cos 2 θ + 3 ) ,
W 4 , 0 = S 4 , 0 cos θ 4 ( 3 cos 4 θ + 2 cos 2 θ + 3 ) ,
W 3 , 3 = 3 S 3 , 1 2 ( 1 cos 2 θ - 1 ) ,
W 3 , - 3 = 3 S 3 , - 1 2 ( 1 cos 2 θ - 1 ) ,
W 4 , 2 = 3 S 4 , 0 cos θ 2 ( 1 cos 4 θ - 1 ) ,
W 4 , 4 = 3 S 4 , 0 cos θ 2 ( 1 cos 2 θ - 1 ) 2 .
Δ s = - 0.3420 Z 2 , 1 - 0.1460 Z 2 , 2 - 0.2421 Z 2 , - 2 + 0.0262 Z 3 , 1 - 0.0378 Z 3 , - 1 + 0.0473 Z 4 , 0 .
W 2 , 0 = S 2 , 0 ( 1 + cos 2 θ ) cos θ + S 2 , 2 sin 2 θ 2 cos θ ,
W 2 , 2 = 2 S 2 , 0 sin 2 θ cos θ + S 2 , 2 ( 1 + cos 2 θ ) cos θ ,
W 2 , - 2 = 2 S 2 , - 2 .
Δ s ( X s , Y s ) = 2 cos [ θ ± tan - 1 ( 2 F / # X p ) ] OPD ( X x / cos θ 1 X s sin θ 2 F / # , Y s ) .
Δ s = 0.5 Z 2 , 0 + 0.1 Z 2 , 2 + 0.1 Z 2 , - 2 + 0.1 Z 3 , 1 + 0.1 Z 3 , - 1 + 0.1 Z 4 , 0 ,
[ 1.3639 4.0392 0 0.8209 0 1.69993 0 0 3.9832 0 0.5874 0 0.3427 0.0271 0 4.9030 0 1.4779 0 0 0.0169 0 3.5661 0 0.0286 - 0.0103 0.0013 0.1124 0.0014 4.2413 3.2546 4.1693 0 0.3543 0 2.5893 0 0 3.9135 0 0.3989 0 0.4568 - 0.1115 0 4.6352 0 0.7278 0 0 - 0.0253 0 2.5901 0 0.0205 - 0.0080 0.0013 0.0390 0.0014 3.0817 ] [ S 2 , 0 S 2 , 2 S 2 , - 2 S 3 , 1 S 3 , - 1 S 4 , 0 ] = [ 1.3379 0.4571 0.8122 0.3583 0.4489 2.3384 0.4313 0.7535 0.2565 0.3212 ] .
Δ s = 0.4999 Z 2 , 0 + 0.1000 Z 2 , 2 + 0.1000 Z 2 , - 2 + 0.1000 Z 3 , 1 + 0.1000 Z 3 , - 1 + 0.0999 Z 4 , 0 .
[ S 2 , 0 S 2 , 2 S 2 , - 2 S 3 , 1 S 3 , - 1 S 4 , 0 ] = [ R ] [ S 2 , 0 S 2 , 2 S 2 , - 2 S 3 , 1 S 3 , - 1 S 4 , 0 ] ,
[ R ] = [ 1 0 0 0 0 cos 2 α sin 2 α 0 0 - sin 2 α cos 2 α 0 0 0 0 cos α sin α 0 0 0 - sin α cos α 0 0 0 0 0 1 ] .
[ W n , m ( ϕ = α ) s i , j ] [ s i , j ] = [ W n , m ( ϕ = 0 ) s i , j ] [ R ] [ S i , j ] = [ W n , m ( θ = α ) ] ,
[ W n , m ( ϕ = α ) s i , j ] [ s i , j ] = [ W n , m ( ϕ , α ) ] ,
[ W n , m ( ϕ = α ) S i , j ] = [ W n , m ( ϕ = 0 ) S i , j ] [ R ] .

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