Abstract

We propose an even-/odd-synthesis method for the elimination of additional aberration caused by misalignment or environmental vibration during the calibration of a Fizeau interferometer reference surface (RS). The odd and even parts of an RS can be obtained, because surface errors could be divided into rotationally symmetric and nonrotationally symmetric terms. We then propose a least-squares algorithm with a dual-objective optimization function for calibration of the measurement results at the confocal position. Finally, a complete RS can be eventually obtained by synthesizing the odd and even parts of the RS. It has been verified through experiments that the measurement repeatability of the PV value is better than 0.003λ, and the root-mean-square value is better than 0.0003λ.

© 2011 Optical Society of America

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References

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  1. C. J. Evans and R. E. Parks, “Absolute testing of spherical optics,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 185–187.
  2. Chris J. Evans and Robert N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015–1021 (1996).
    [CrossRef] [PubMed]
  3. P. Murphy, J. Fleig, and G. Forbes, “Novel method for computing reference wave error in optical surface metrology,” Proc. SPIE TD02, 138–140 (2003).
    [CrossRef]
  4. A. E. Jensen, “Absolute calibration method for Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).
  5. B. E. Truax, “Absolute interferometric testing of spherical surfaces,” Proc. SPIE 1400, 61–68 (1990).
    [CrossRef]
  6. K. Creath and J. C. Wyant, “Testing spherical surfaces: a fast, quasi-absolute technique,” Appl. Opt. 31, 4350–4354(1992).
    [CrossRef] [PubMed]
  7. D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).
    [CrossRef]
  8. K.-E. Elssner, R. Burrow, J. Grzanna, and R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661(1989).
    [CrossRef] [PubMed]
  9. L. A. Selberg, “Absolute testing of spherical surfaces,” in Optical Fabrication and TestingOSA 1994 Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 181–184.
  10. R. Schreiner, J. Schwider, N. Lindlein, and K. Mantel, “Absolute testing of the reference surface of a Fizeau interferometer through even/odd decompositions,” Appl. Opt. 47, 6134–6141(2008).
    [CrossRef] [PubMed]
  11. S. O’Donohue, G. Devries, and P. Murphy, “New methods for calibrating systematic errors in interferometric measurements,” Proc. SPIE 5869, 58690T (2005).
    [CrossRef]

2008 (1)

2007 (1)

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).
[CrossRef]

2005 (1)

S. O’Donohue, G. Devries, and P. Murphy, “New methods for calibrating systematic errors in interferometric measurements,” Proc. SPIE 5869, 58690T (2005).
[CrossRef]

2003 (1)

P. Murphy, J. Fleig, and G. Forbes, “Novel method for computing reference wave error in optical surface metrology,” Proc. SPIE TD02, 138–140 (2003).
[CrossRef]

1996 (1)

1994 (2)

C. J. Evans and R. E. Parks, “Absolute testing of spherical optics,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 185–187.

L. A. Selberg, “Absolute testing of spherical surfaces,” in Optical Fabrication and TestingOSA 1994 Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 181–184.

1992 (1)

1990 (1)

B. E. Truax, “Absolute interferometric testing of spherical surfaces,” Proc. SPIE 1400, 61–68 (1990).
[CrossRef]

1989 (1)

1973 (1)

A. E. Jensen, “Absolute calibration method for Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

Burrow, R.

Creath, K.

Devries, G.

S. O’Donohue, G. Devries, and P. Murphy, “New methods for calibrating systematic errors in interferometric measurements,” Proc. SPIE 5869, 58690T (2005).
[CrossRef]

Elssner, K.-E.

Evans, C. J.

C. J. Evans and R. E. Parks, “Absolute testing of spherical optics,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 185–187.

Evans, Chris J.

Fleig, J.

P. Murphy, J. Fleig, and G. Forbes, “Novel method for computing reference wave error in optical surface metrology,” Proc. SPIE TD02, 138–140 (2003).
[CrossRef]

Forbes, G.

P. Murphy, J. Fleig, and G. Forbes, “Novel method for computing reference wave error in optical surface metrology,” Proc. SPIE TD02, 138–140 (2003).
[CrossRef]

Grzanna, J.

Jensen, A. E.

A. E. Jensen, “Absolute calibration method for Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

Kestner, Robert N.

Lindlein, N.

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).
[CrossRef]

Mantel, K.

Murphy, P.

S. O’Donohue, G. Devries, and P. Murphy, “New methods for calibrating systematic errors in interferometric measurements,” Proc. SPIE 5869, 58690T (2005).
[CrossRef]

P. Murphy, J. Fleig, and G. Forbes, “Novel method for computing reference wave error in optical surface metrology,” Proc. SPIE TD02, 138–140 (2003).
[CrossRef]

O’Donohue, S.

S. O’Donohue, G. Devries, and P. Murphy, “New methods for calibrating systematic errors in interferometric measurements,” Proc. SPIE 5869, 58690T (2005).
[CrossRef]

Parks, R. E.

C. J. Evans and R. E. Parks, “Absolute testing of spherical optics,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 185–187.

Schreiner, R.

Schwider, J.

Selberg, L. A.

L. A. Selberg, “Absolute testing of spherical surfaces,” in Optical Fabrication and TestingOSA 1994 Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 181–184.

Spolaczyk, R.

Truax, B. E.

B. E. Truax, “Absolute interferometric testing of spherical surfaces,” Proc. SPIE 1400, 61–68 (1990).
[CrossRef]

Wyant, J. C.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

A. E. Jensen, “Absolute calibration method for Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

Proc. SPIE (3)

B. E. Truax, “Absolute interferometric testing of spherical surfaces,” Proc. SPIE 1400, 61–68 (1990).
[CrossRef]

P. Murphy, J. Fleig, and G. Forbes, “Novel method for computing reference wave error in optical surface metrology,” Proc. SPIE TD02, 138–140 (2003).
[CrossRef]

S. O’Donohue, G. Devries, and P. Murphy, “New methods for calibrating systematic errors in interferometric measurements,” Proc. SPIE 5869, 58690T (2005).
[CrossRef]

Other (3)

C. J. Evans and R. E. Parks, “Absolute testing of spherical optics,” Optical Fabrication and Testing Workshop, OSA Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 185–187.

L. A. Selberg, “Absolute testing of spherical surfaces,” in Optical Fabrication and TestingOSA 1994 Technical Digest Series, Vol.  13 (Optical Society of America, 1994), pp. 181–184.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Optical path of the Fizeau interferometer.

Fig. 2
Fig. 2

Results obtained at the 0 ° position.

Fig. 3
Fig. 3

Results obtained at the 180 ° position.

Fig. 4
Fig. 4

OPD of W 1 ( r , θ ) W 2 ( r , θ + π ) .

Fig. 5
Fig. 5

Odd deviations of the RS.

Fig. 6
Fig. 6

Zernike coefficients of odd deviations before and after calibration.

Fig. 7
Fig. 7

Results at cat’s-eye position.

Fig. 8
Fig. 8

Even deviations of the RS.

Fig. 9
Fig. 9

Results of synthesis.

Fig. 10
Fig. 10

Calibration results obtained by TPM.

Fig. 11
Fig. 11

PV value of calibration.

Fig. 12
Fig. 12

RMS value of calibration.

Equations (17)

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W 1 = W A W T ,
W 2 = W A W T ,
W 3 = W A W F ,
W A ( r , θ ) = 2 W L ( r , θ ) + 2 n W R ( r , θ ) ,
W T ( r , θ ) = 2 W L ( r , θ ) + 2 ( n 1 ) W R ( r , θ ) + 2 W S ( r , θ ) ,
W T ( r , θ ) = 2 W L ( r , θ ) + 2 ( n 1 ) W R ( r , θ ) + 2 W S ( r , θ + π ) ,
W F ( r , θ ) = W L ( r , θ ) + ( n 1 ) W R ( r , θ ) + ( n 1 ) W R ( r , θ + π ) + W L ( r , θ + π ) ,
W 1 ( r , θ ) W 2 ( r , θ + π ) = 2 W R ( r , θ ) 2 W R ( r , θ + π ) ,
W 3 ( r , θ ) + W 3 ( r , θ + π ) = 2 W R ( r , θ ) + 2 W R ( r , θ + π ) .
W ( r , θ ) = k , l R l k ( r ) ( α l k cos k θ + α l k sin k θ ) ,
W ( r , θ + π ) = { W ( r , θ ) m     is even W ( r , θ ) m     is odd .
W 1 ( r , θ ) W 2 ( r , θ + π ) = 2 W R ( r , θ ) 2 W R ( r , θ + π ) = 4 W R ( r , θ ) odd ,
W 3 ( r , θ ) + W 3 ( r , θ + π ) = 2 W R ( r , θ ) + 2 W R ( r , θ + π ) = 4 W R ( r , θ ) even .
Δ W ( r , θ ) = W 1 ( r , θ ) W 2 ( r , θ + π ) = [ 2 W R ( r , θ ) 2 W S ( r , θ ) ] [ 2 W R ( r , θ + π ) 2 W S ( r , θ + 2 π ) + Δ w ] = 4 W R ( r , θ ) odd Δ w ,
[ Δ W ( r , θ ) even Δ w even ] 2 0.
Δ W ( r , θ ) = W 1 ( r , θ ) W 2 ( r , θ ) = [ 2 W R ( r , θ ) 2 W S ( r , θ ) ] [ 2 W R ( r , θ ) 2 W S ( r , θ + π ) + Δ w ] = 2 W S ( r , θ + π ) 2 W S ( r , θ ) Δ w = 4 W S ( r , θ ) odd Δ w ,
V = α 1 [ Δ W ( r , θ ) Δ w ] 2 + α 2 [ Δ W ( r , θ ) even Δ w even ] 2 min ,

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