Abstract

A wavelength-tuned Fizeau interferometer is applied to the problem of flatness testing of transparent plates. When the plate is positioned at a specific distance from the reference surface and an integer-math 13-frame phase-shifting algorithm is applied, the system directly filters out unwanted interference arising from backsurface reflections. The resulting front-surface profile exhibits less than 2 nm of residual error attributable to spurious reflections from within the plate.

© 2000 Optical Society of America

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References

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  1. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wave front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
    [CrossRef]
  2. K. Freischlad, “Large flat panel profiler,” in Flatness, Roughness, and Discrete Defect Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE2862, 163–171 (1996).
    [CrossRef]
  3. P. G. Dewa, A. W. Kulawiec, “Grazing incidence interferometry for measuring transparent plane-parallel plates,” U.S. patent5,923,425 (13July1999).
  4. P. de Groot, “Grating interferometer for metrology of transparent flats,” in Optical Fabrication and Testing, Vol. 6 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 28–30.
  5. C. Ai, “Multimode-laser interferometric apparatus for elimination background interference fringes from thin-plate measurements,” U.S. patent5,452,088 (19September1995).
  6. P. de Groot, “Metrology of transparent flats,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 160–168.
  7. K. Okada, J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” in Laser Interferometry: Quantitative Analysis of Interferograms, R. J. Pryputniewicz, ed., Proc. SPIE1162, 395–401 (1989).
  8. K. Okada, H. Sakuta, T. Ose, J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
    [CrossRef] [PubMed]
  9. G. E. Sommargren, “Interferometric wavefront measurement,” U.S. patent4,594,003 (10June1986).
  10. P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, “300-mm aperture phase shifting Fizeau interferometer,” Opt. Eng. 38, 1371–1380 (1999).
    [CrossRef]
  11. K. G. Larkin, B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740–1748 (1992).
    [CrossRef]
  12. K. Freischlad, C. L. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7, 542–551 (1990).
    [CrossRef]
  13. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]
  14. P. de Groot, “Phase shifting interferometer and method for surface topography measurement,” U.S. patent5,473,434 (5December1995).
  15. The high-resolution phase-shifting mode in the Zygo Corporation MetroPro PSI software employs the 13-frame algorithm given by Eqs. (22) and (23).
  16. L. L. Deck, “Phase-shifting via wavelength tuning in very large aperture interferometers,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 432–442 (1999).
    [CrossRef]
  17. P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
    [CrossRef]
  18. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
    [CrossRef] [PubMed]

1999 (1)

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, “300-mm aperture phase shifting Fizeau interferometer,” Opt. Eng. 38, 1371–1380 (1999).
[CrossRef]

1996 (1)

1995 (1)

1992 (1)

1990 (2)

1987 (1)

1983 (1)

Ai, C.

C. Ai, “Multimode-laser interferometric apparatus for elimination background interference fringes from thin-plate measurements,” U.S. patent5,452,088 (19September1995).

Burow, R.

de Groot, P.

P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
[CrossRef]

P. de Groot, “Metrology of transparent flats,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 160–168.

P. de Groot, “Grating interferometer for metrology of transparent flats,” in Optical Fabrication and Testing, Vol. 6 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 28–30.

P. de Groot, “Phase shifting interferometer and method for surface topography measurement,” U.S. patent5,473,434 (5December1995).

Deck, L. L.

L. L. Deck, “Phase-shifting via wavelength tuning in very large aperture interferometers,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 432–442 (1999).
[CrossRef]

Dewa, P. G.

P. G. Dewa, A. W. Kulawiec, “Grazing incidence interferometry for measuring transparent plane-parallel plates,” U.S. patent5,923,425 (13July1999).

Eiju, T.

Elssner, K.-E.

Fairman, P. S.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, “300-mm aperture phase shifting Fizeau interferometer,” Opt. Eng. 38, 1371–1380 (1999).
[CrossRef]

Farrant, D. I.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, “300-mm aperture phase shifting Fizeau interferometer,” Opt. Eng. 38, 1371–1380 (1999).
[CrossRef]

Freischlad, K.

K. Freischlad, C. L. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7, 542–551 (1990).
[CrossRef]

K. Freischlad, “Large flat panel profiler,” in Flatness, Roughness, and Discrete Defect Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE2862, 163–171 (1996).
[CrossRef]

Grzanna, J.

Hariharan, P.

Koliopoulos, C. L.

Kulawiec, A. W.

P. G. Dewa, A. W. Kulawiec, “Grazing incidence interferometry for measuring transparent plane-parallel plates,” U.S. patent5,923,425 (13July1999).

Larkin, K. G.

Merkel, K.

Okada, K.

K. Okada, H. Sakuta, T. Ose, J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
[CrossRef] [PubMed]

K. Okada, J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” in Laser Interferometry: Quantitative Analysis of Interferograms, R. J. Pryputniewicz, ed., Proc. SPIE1162, 395–401 (1989).

Oreb, B. F.

Ose, T.

Sakuta, H.

Schwider, J.

Sommargren, G. E.

G. E. Sommargren, “Interferometric wavefront measurement,” U.S. patent4,594,003 (10June1986).

Spolaczyk, R.

Surrel, Y.

Tsujiuchi, J.

K. Okada, H. Sakuta, T. Ose, J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280–3285 (1990).
[CrossRef] [PubMed]

K. Okada, J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” in Laser Interferometry: Quantitative Analysis of Interferograms, R. J. Pryputniewicz, ed., Proc. SPIE1162, 395–401 (1989).

Ward, B. K.

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, “300-mm aperture phase shifting Fizeau interferometer,” Opt. Eng. 38, 1371–1380 (1999).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

P. S. Fairman, B. K. Ward, B. F. Oreb, D. I. Farrant, “300-mm aperture phase shifting Fizeau interferometer,” Opt. Eng. 38, 1371–1380 (1999).
[CrossRef]

Other (10)

P. de Groot, “Phase shifting interferometer and method for surface topography measurement,” U.S. patent5,473,434 (5December1995).

The high-resolution phase-shifting mode in the Zygo Corporation MetroPro PSI software employs the 13-frame algorithm given by Eqs. (22) and (23).

L. L. Deck, “Phase-shifting via wavelength tuning in very large aperture interferometers,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 432–442 (1999).
[CrossRef]

K. Freischlad, “Large flat panel profiler,” in Flatness, Roughness, and Discrete Defect Characterization for Computer Disks, Wafers, and Flat Panel Displays, J. C. Stover, ed., Proc. SPIE2862, 163–171 (1996).
[CrossRef]

P. G. Dewa, A. W. Kulawiec, “Grazing incidence interferometry for measuring transparent plane-parallel plates,” U.S. patent5,923,425 (13July1999).

P. de Groot, “Grating interferometer for metrology of transparent flats,” in Optical Fabrication and Testing, Vol. 6 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 28–30.

C. Ai, “Multimode-laser interferometric apparatus for elimination background interference fringes from thin-plate measurements,” U.S. patent5,452,088 (19September1995).

P. de Groot, “Metrology of transparent flats,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 160–168.

K. Okada, J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” in Laser Interferometry: Quantitative Analysis of Interferograms, R. J. Pryputniewicz, ed., Proc. SPIE1162, 395–401 (1989).

G. E. Sommargren, “Interferometric wavefront measurement,” U.S. patent4,594,003 (10June1986).

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Figures (10)

Fig. 1
Fig. 1

Fringe pattern in a Fizeau interferometer when viewing a transparent plate. The complicated interference effects, including backsurface reflections, defeat conventional PSI with mechanical phase shifting.

Fig. 2
Fig. 2

Laser-based Fizeau interferometer viewing a transparent plate. LD, laser diode.

Fig. 3
Fig. 3

Single-pixel intensity modulation in a Fizeau interferometer during a continuous shift in source wavelength. The solid curve represents the expected signal from a single object surface. The dotted curve represents the signal when viewing a transparent plate object, including unwanted distortions resulting from spurious backsurface reflections.

Fig. 4
Fig. 4

Frequency content of the dotted-curve signal shown in Fig. 3. The desired fundamental frequency ν 1, here normalized to 1, is accompanied by several parasitic modulations as noted in Table 1.

Fig. 5
Fig. 5

Theoretical frequency response of the five-frame, Δα = π/2 PSI algorithm, including the averaging or integrating bucket effect of the phase change during the data-acquisition time interval Δt. Unfortunately this algorithm is sensitive to the unwanted harmonics shown in Fig. 4.

Fig. 6
Fig. 6

Theoretical cyclic error as a function of the fundamental phase θ for a five-frame PSI algorithm in the presence of reflections.

Fig. 7
Fig. 7

Theoretical frequency response of the 13-frame, Δα = π/4 PSI algorithm. This algorithm suppresses the high-frequency modulations shown in Figs. 3 and 5.

Fig. 8
Fig. 8

Theoretical frequency response of the 15-frame, Δα = π/2 PSI algorithm. This algorithm is effective at suppressing spurious modulations for the case in which Γ = 0.5 (see Table 1). Note the change in horizontal scale with respect to Figs. 6 and 7.

Fig. 9
Fig. 9

Experimental data processed with the five-frame, Δα = π/2 PSI algorithm showing the predicted 40-nm peak-to-valley profile distortion resulting from backsurface reflections from a transparent plate.

Fig. 10
Fig. 10

Experimental data showing the suppression of profile distortions when wavelength-tuned interferometry is used with the 13-frame, Δα = π/4 PSI algorithm described in the text. The transparent plate object is identical to the one profiled in Fig. 9.

Tables (1)

Tables Icon

Table 1 Modulation Frequencies Resulting from Wavelength Tuning a Fizeau Interferometer with a Transparent Plate Objecta

Equations (25)

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θ=2kh1-h0+2kL,
ϕ=2knh2-h1+2knT,
g=|u|2,
u=r0+r expiθ1+rr0 expiθ,
r=r1+r2 expiϕ1+r1r2 expiϕ.
r0=-R,  r1=R,  r2=-R.
g=2R32-cosθ-cosϕ+cosθ+ϕ+OR2.
gt=2R32-cosθ+ν1t-cosϕ+ν2t+cosθ+ϕ+ν3t+OR2,
ν1=2Ldk/dt,
ν2=Γν1,
ν3=Γ+1ν1,
Γ=nT/L.
θ=tan-1m=0M-1 smgmm=0M-1 cmgm+const,
Δα=ν1Δt,
Sν=m=0M-1 sm exp-imΔαν/ν1,
Cν=m=0M-1 cm exp-imΔαν/ν1.
Iν=|Sν|2+|Cν|21/2.
s=0 2 0 -2 0,
c=-1 0 2 0 -1.
Sν=i sinπν/2ν1,
Cν=sin2πν/2ν1.
s=-3 -4 0 12 21 16 0 -16 -21 -12 0 4 3,
c=0 -4 -12 -12 0 16 24 16 0-12 -12 -4 0.
s=-1 0 9 0 -21 0 29 0-29 0 21 0 -9 0 1,
c=0 -4 0 15 0 -26 0 30 0-26 0 15 0 -4 0.

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