Abstract

This paper describes a method to enhance the capability of two-wavelength phase-shifting interferometry. By introducing the phase data of a third wavelength, one can measure the phase of a very steep wave front. Experiments have been performed using a linear detector array to measure surface height of an off-axis parabola. For the wave front being measured the optical path difference between adjacent detector pixels was as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 25-Å rms (λ = 6328 Å).

© 1985 Optical Society of America

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References

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  1. J. H. Bruning, “Fringe Scanning Interferometers,” in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978).
  2. C. Koliopoulos, “Interferometric Optical Phase Measurement Techniques,” Ph.D. Dissertation, Optical Sciences Center, U. Arizona (1981).
  3. 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 (1983).
    [Crossref] [PubMed]
  4. J. C. Wyant, “Testing Aspherics Using Two-Wavelength Holography,” Appl. Opt. 10, 2113 (1971).
    [Crossref] [PubMed]
  5. C. Polhemus, “Two-Wavelength Interferometry,” Appl. Opt. 12, 2071 (1973).
    [Crossref] [PubMed]
  6. Y.-Y. Cheng, J. C. Wyant, “Two-Wavelength Phase Shifting Interferometry, Appl. Opt. 23, 4539 (1984).
    [Crossref] [PubMed]

1984 (1)

1983 (1)

1973 (1)

1971 (1)

Bruning, J. H.

J. H. Bruning, “Fringe Scanning Interferometers,” in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978).

Burow, R.

Cheng, Y.-Y.

Elssner, K.-E.

Grzanna, J.

Koliopoulos, C.

C. Koliopoulos, “Interferometric Optical Phase Measurement Techniques,” Ph.D. Dissertation, Optical Sciences Center, U. Arizona (1981).

Merkel, K.

Polhemus, C.

Schwider, J.

Spolaczyk, R.

Wyant, J. C.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for the MWLPSI.

Fig. 2
Fig. 2

(a) Two-wavelength surface height plot for λeql, where λeql = 6.45 μm. (b) Some data as in Fig. 2(a) but with both tilt and focus removed. (c) Two-wavelength surface height plot for λeqs, where λeqs = 1.93 μm. (d) Single wavelength surface height plot for λ = 6328 Å obtained by single-wavelength PSI.

Fig. 3
Fig. 3

(a) 2π ambiguity corrected surface height plot for λeqs. (b) Same data as in Fig. 3(a) but with both tilt and focus removed.

Fig. 4
Fig. 4

(a) 2π ambiguity corrected single-wavelength surface height plot for λ = 6328 Å. (b) Same data as in Fig. 4(a) but with both tilt and focus removed. (c) Repeatability of the surface height measurement by the MWLPSI.

Equations (1)

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Δ OPD n + 1 = { 1 2 π [ Δ ϕ ( n + 1 ) b Δ ϕ ( n + 1 ) a ] λ eq if λ a > λ b , 1 2 π [ Δ ϕ ( n + 1 ) a Δ ϕ ( n + 1 ) b ] λ eq if λ b > λ a .

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