Abstract

I describe and demonstrate a rapid and simple technique for calibrating spherical reference surfaces in Fizeau interferometry. A flat mirror at the focus of the test wavefront and a partial occlusion of the test beam enable a double-pass measurement of one half of the surface against the other, which gives an error map for half the aperture. Subsequent rotations of the beam stop and stitching together of several measurements yields the full-aperture calibration file. The method always produces point-symmetrical surface maps and is therefore not exact. However, most actual reference surfaces are approximately point symmetric and therefore the trade-off of accuracy for expediency is reasonable in practice.

© 2008 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, 1992).
  2. G. Schulz and J. Schwider, in Progress in Optics XIII, (North Holland, 1976), p. 101.
  3. U. Griesmann, Q. Wang, J. Soons, and R. Carakos, Proc. SPIE 5869, 189 (2005).
  4. J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
    [CrossRef]
  5. K.-E. Elssner, R. Burow, J. Grzanna, and R. Spolaczyk, Appl. Opt. 28, 4649 (1989).
    [CrossRef] [PubMed]
  6. A. Jensen, J. Opt. Soc. Am. 63, 1313 (1973).
  7. K. Creath and J. Wyant, Appl. Opt. 31, 4350 (1992).
    [CrossRef] [PubMed]
  8. M. Sjödahl and B. Oreb, Opt. Eng. 41, 403 (2002).
    [CrossRef]
  9. R. Parks, C. Evans, and L. Shao, in Optical Fabrication and Testing Workshop, Vol. 12OSA Technical Digest Series (Optical Society of America, 1998), p. 80.

2008

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

2005

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, Proc. SPIE 5869, 189 (2005).

2002

M. Sjödahl and B. Oreb, Opt. Eng. 41, 403 (2002).
[CrossRef]

1992

1989

1973

A. Jensen, J. Opt. Soc. Am. 63, 1313 (1973).

Burke, J.

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

Burow, R.

Carakos, R.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, Proc. SPIE 5869, 189 (2005).

Creath, K.

Elssner, K.-E.

Evans, C.

R. Parks, C. Evans, and L. Shao, in Optical Fabrication and Testing Workshop, Vol. 12OSA Technical Digest Series (Optical Society of America, 1998), p. 80.

Green, K.

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

Griesmann, U.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, Proc. SPIE 5869, 189 (2005).

Grzanna, J.

Jensen, A.

A. Jensen, J. Opt. Soc. Am. 63, 1313 (1973).

Leistner, A.

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, 1992).

Oreb, B.

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

M. Sjödahl and B. Oreb, Opt. Eng. 41, 403 (2002).
[CrossRef]

Parks, R.

R. Parks, C. Evans, and L. Shao, in Optical Fabrication and Testing Workshop, Vol. 12OSA Technical Digest Series (Optical Society of America, 1998), p. 80.

Puhanic, E.

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

Schulz, G.

G. Schulz and J. Schwider, in Progress in Optics XIII, (North Holland, 1976), p. 101.

Schwider, J.

G. Schulz and J. Schwider, in Progress in Optics XIII, (North Holland, 1976), p. 101.

Shao, L.

R. Parks, C. Evans, and L. Shao, in Optical Fabrication and Testing Workshop, Vol. 12OSA Technical Digest Series (Optical Society of America, 1998), p. 80.

Sjödahl, M.

M. Sjödahl and B. Oreb, Opt. Eng. 41, 403 (2002).
[CrossRef]

Soons, J.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, Proc. SPIE 5869, 189 (2005).

Spolaczyk, R.

Stuart, W.

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

Wang, Q.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, Proc. SPIE 5869, 189 (2005).

Wyant, J.

Appl. Opt.

J. Opt. Soc. Am.

A. Jensen, J. Opt. Soc. Am. 63, 1313 (1973).

Opt. Eng.

M. Sjödahl and B. Oreb, Opt. Eng. 41, 403 (2002).
[CrossRef]

Proc. SPIE

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, Proc. SPIE 5869, 189 (2005).

J. Burke, K. Green, W. Stuart, E. Puhanic, A. Leistner, and B. Oreb, Proc. SPIE 7064, 70640E (2008).
[CrossRef]

Other

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, 1992).

G. Schulz and J. Schwider, in Progress in Optics XIII, (North Holland, 1976), p. 101.

R. Parks, C. Evans, and L. Shao, in Optical Fabrication and Testing Workshop, Vol. 12OSA Technical Digest Series (Optical Society of America, 1998), p. 80.

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Figures (5)

Fig. 1
Fig. 1

(a) Principle sketch of transmission sphere calibration setup. TS, transmission sphere assembly (several lenses); BS, beam stop; RS, reference surface; M, mirror; double-pointed arrow, focus control; rays drawn as solid lines, directly reflected reference wavefront S r , sampling right part of reference surface; rays drawn as dashed lines, transmitted object wavefront S l , sampling left part of reference surface. S l is reflected three times ( mirror reference surface mirror ) . (b) Interferogram of double-pass measurement with coordinate system.

Fig. 2
Fig. 2

Complete set of transmission sphere subaperture measurements in double-pass geometry for synthesizing a reference file. The gray scale is 10 nm (black) to + 10 nm (white) in all images.

Fig. 3
Fig. 3

(a) Stitched calibration file from eight subaperture measurements; (b) calibration file from random ball averaging test. The gray scale is 10 nm (black) to + 10 nm (white) in both images.

Fig. 4
Fig. 4

(a) Error map between Figs. 3b, 3a with overlaid horizontal and vertical line-plot cursors; (b) same error map with overlaid ± 45 ° line cursors. The gray scale is 5 nm (black) to + 5 nm (white). (c) Line plots for (a); (d) line plots for (d). Vertical scales are ± 10 nm .

Fig. 5
Fig. 5

Phase maps of high-precision spherical mirror: (a) uncalibrated, (b) calibrated by the ball-averaging method, (c) calibrated by the double-pass method. The gray scale is 15 nm (black) to + 15 nm (white).

Equations (4)

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Δ L ( x 0 , y 0 ) = 4 R 2 Δ h ( x 0 , y 0 ) 2 Δ h ( x 0 , y 0 ) ,
Δ L ( x 0 , y 0 ) = 4 R 2 Δ h ( x 0 , y 0 ) 2 Δ h ( x 0 , y 0 ) = Δ L ( x 0 , y 0 ) ,
Δ h pas ( x 0 , y 0 ) = Δ h pas ( x 0 , y 0 ) Δ L ( x 0 , y 0 ) = Δ L ( x 0 , y 0 ) 0 ,
Δ h ( x , y ) = λ 8 π Δ φ ( x , y ) .

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