Abstract

A general analytical form of propagation errors in Fizeau interferometry is derived. The theory holds for any type of interferometry. The influence of the third-order aberrations is investigated as numerical examples. The experimental data agree with the theoretical prediction.

© 1993 Optical Society of America

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References

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  1. R. Jozwicki, “Influence of spherical aberration of an interferometric system on the measurement error in the case of a finite fringe,” Appl. Opt. 30, 3119–3125 (1991).
    [CrossRef]
  2. R. Jozwicki, “Influence of aberrations of Fizeau interferometer elements on measurement errors,” Appl. Opt. 30, 3126–3132 (1991).
    [CrossRef]
  3. J. M. Mehta, W. M. Worek, “Analysis of refraction errors for interferometric measurements in multicomponent systems,” Appl. Opt. 23, 928–933 (1984).
    [CrossRef] [PubMed]
  4. K. Kinnstaetter, A. W. Lohmann, J. Schwider, N. Streibl, “Accuracy of phase shifting interferometer,” Appl. Opt. 27, 5082–5089 (1988).
    [CrossRef] [PubMed]
  5. C. Evans, W. T. Estler, “Some observations on the performance of commercial phase measuring (Fizeau) interferometers used in surface figure metrology,” Proc. Am. Soc. Precision Eng. 4, 54–57 (1991).
  6. C. Huang, G. Lawrence, E. Levy, R. McMillan, “Performance analysis of the multichannel astrometric photometer,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.818, 408–418 (1987).
  7. C. Huang, “Design and analysis of the Astrometrical Telescope Facility,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1989).
  8. G. Lawrence, C. Huang, “High accuracy image centroiding with a Ronchi ruling,” Opt. Eng. 30, 598–606 (1991).
    [CrossRef]
  9. C. Huang, H. Jeong, B. Ruff, “Optimizing a DUV projection lens with a 442 nm laser interferometer,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 220–228 (1990).

1991

R. Jozwicki, “Influence of spherical aberration of an interferometric system on the measurement error in the case of a finite fringe,” Appl. Opt. 30, 3119–3125 (1991).
[CrossRef]

R. Jozwicki, “Influence of aberrations of Fizeau interferometer elements on measurement errors,” Appl. Opt. 30, 3126–3132 (1991).
[CrossRef]

C. Evans, W. T. Estler, “Some observations on the performance of commercial phase measuring (Fizeau) interferometers used in surface figure metrology,” Proc. Am. Soc. Precision Eng. 4, 54–57 (1991).

G. Lawrence, C. Huang, “High accuracy image centroiding with a Ronchi ruling,” Opt. Eng. 30, 598–606 (1991).
[CrossRef]

1988

1984

Estler, W. T.

C. Evans, W. T. Estler, “Some observations on the performance of commercial phase measuring (Fizeau) interferometers used in surface figure metrology,” Proc. Am. Soc. Precision Eng. 4, 54–57 (1991).

Evans, C.

C. Evans, W. T. Estler, “Some observations on the performance of commercial phase measuring (Fizeau) interferometers used in surface figure metrology,” Proc. Am. Soc. Precision Eng. 4, 54–57 (1991).

Huang, C.

G. Lawrence, C. Huang, “High accuracy image centroiding with a Ronchi ruling,” Opt. Eng. 30, 598–606 (1991).
[CrossRef]

C. Huang, H. Jeong, B. Ruff, “Optimizing a DUV projection lens with a 442 nm laser interferometer,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 220–228 (1990).

C. Huang, G. Lawrence, E. Levy, R. McMillan, “Performance analysis of the multichannel astrometric photometer,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.818, 408–418 (1987).

C. Huang, “Design and analysis of the Astrometrical Telescope Facility,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1989).

Jeong, H.

C. Huang, H. Jeong, B. Ruff, “Optimizing a DUV projection lens with a 442 nm laser interferometer,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 220–228 (1990).

Jozwicki, R.

Kinnstaetter, K.

Lawrence, G.

G. Lawrence, C. Huang, “High accuracy image centroiding with a Ronchi ruling,” Opt. Eng. 30, 598–606 (1991).
[CrossRef]

C. Huang, G. Lawrence, E. Levy, R. McMillan, “Performance analysis of the multichannel astrometric photometer,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.818, 408–418 (1987).

Levy, E.

C. Huang, G. Lawrence, E. Levy, R. McMillan, “Performance analysis of the multichannel astrometric photometer,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.818, 408–418 (1987).

Lohmann, A. W.

McMillan, R.

C. Huang, G. Lawrence, E. Levy, R. McMillan, “Performance analysis of the multichannel astrometric photometer,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.818, 408–418 (1987).

Mehta, J. M.

Ruff, B.

C. Huang, H. Jeong, B. Ruff, “Optimizing a DUV projection lens with a 442 nm laser interferometer,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 220–228 (1990).

Schwider, J.

Streibl, N.

Worek, W. M.

Appl. Opt.

Opt. Eng.

G. Lawrence, C. Huang, “High accuracy image centroiding with a Ronchi ruling,” Opt. Eng. 30, 598–606 (1991).
[CrossRef]

Proc. Am. Soc. Precision Eng.

C. Evans, W. T. Estler, “Some observations on the performance of commercial phase measuring (Fizeau) interferometers used in surface figure metrology,” Proc. Am. Soc. Precision Eng. 4, 54–57 (1991).

Other

C. Huang, G. Lawrence, E. Levy, R. McMillan, “Performance analysis of the multichannel astrometric photometer,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.818, 408–418 (1987).

C. Huang, “Design and analysis of the Astrometrical Telescope Facility,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1989).

C. Huang, H. Jeong, B. Ruff, “Optimizing a DUV projection lens with a 442 nm laser interferometer,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 220–228 (1990).

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Figures (3)

Fig. 1
Fig. 1

Simplified Fizeau system in which a marginal ray of the Fizeau objective is a chief ray of the viewing system.

Fig. 2
Fig. 2

Schematic diagram of an unfolded Fizeau viewing system, where the return rays from a Fizeau surface and from a test surface are heights r1 and r2 in the entrance pupil of the viewing system, respectively.

Fig. 3
Fig. 3

a, Contour and 3-D plots of the measured wave front with minimum tilt and defocus; b, contour and 3-D plots of the measured wave front with the same sphere but with 6λ of defocus introduced; c, contour and 3-D plots of the measured wave front with the same sphere but with 8.7λ of tilt introduced: fr, fringes; TIR, peak to valley.

Tables (1)

Tables Icon

Table 1 Summary of Propagation Error Resultsa

Equations (19)

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W = ( W r - W t ) + ( W r p - W t p ) .
ρ = H ,
W s ( ρ , θ ) = W r p - W t p = W v ( ρ , r 1 , θ ) - W v ( ρ , r 2 , θ ) .
r 1 = 1 NA r e W r r ( ρ , θ ) ρ ,
r 2 = 1 NA r e W t r ( ρ , θ ) ρ .
W ( H , r , θ ) = j , k , m W j k m H j r k cos m ( θ ) ,
W ( H , r , θ ) = W 111 H r cos ( θ ) + W 020 r 2 + W 040 r 4 + W 131 H r 3 cos ( θ ) + W 222 H 2 r 2 cos 2 ( θ ) + W 220 H 2 r 2 + W 311 H 3 r cos ( θ ) ,
W r r ( ρ ) = W 040 r ρ 4 .
W v ( r ) = W 040 v r 4 .
W t r ( ρ , θ ) = W 111 t ρ cos ( ϕ ) ,
W s ( ρ , ϕ ) = W 040 v ( 4 NA r e W 040 r ρ 3 ) 4 - W 040 v [ 1 NA r e W 111 t cos ( ϕ ) ] 4 .
W t r ( ρ ) = W 020 t ρ 2 ,
W s ( ρ ) = W 040 v ( 4 NA r e W 040 r ρ 3 ) 4 - W 040 v ( 2 NA r e W 020 t ρ ) 4 .
W t r ( ρ ) = W 040 t ρ 4 .
W s ( ρ ) = W 040 v ( 4 NA r e W 040 r ρ 3 ) 4 - W 040 v ( 4 NA r e W 040 t ρ 3 ) 4 .
W v ( H , r , θ ) = W 311 v H 3 r cos ( θ ) ,
W s ( ρ , ϕ ) = W 311 v ρ 3 ( 4 NA r e W 040 r ρ 3 ) - W 311 v ρ 3 ( 1 NA r e W 111 t ) cos ( ϕ ) .
W s ( ρ ) = W 311 v ρ 3 ( 4 NA r e W 040 r ρ 3 ) 4 - W 311 v ρ 3 ( 2 NA r e W 020 t ρ ) .
W s ( ρ ) = W 311 v ρ 3 ( 4 N A r e W 040 r ρ 3 ) 4 - W 311 v ρ 3 ( 4 N A r e W 040 t ρ 3 ) .

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