Abstract

Multiple wavelength interferometry is combined with a heterodyne array sensing technique to provide an approach for measuring highly aberrated optical surfaces. Interferometric measurements created with long effective wavelengths are obtained by digitally combining complex exposures collected at different optical wavelengths. The heterodyne array sensing method is straightforward to implement and holds promise for rapid wavefront measurements with high spatial and phase resolution. Measurements of a tilted, flat surface are presented and analyzed.

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References

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  1. D. K. Marker and C. H. Jenkins, Surface precision of optical membranes with curvature, Opt. Express 1, 324-331 (1997).
    http://epubs.osa.org/oearchive/source/2668.htm
    [CrossRef] [PubMed]
  2. Holographic Interferometry, P.K. Rastogi, ed., Springer Ser. Opt. Sci. 68, (Springer, Berlin, 1994).
  3. P. Hariharan, Quasi-heterodyne hologram interferometry, Opt. Eng. 24, 632-638 (1985).
  4. Y. Ishii, J. Chen, and K. Murata, Digital phase-measuring interferometry with a tunable laser diode, Opt. Lett. 12, 233-235 (1987).
    [CrossRef] [PubMed]
  5. I. Yamaguchi, J. Liu, and J. Kato, Active phase-shifting interferometers for shape and deformation measurements, Opt. Eng. 35, 2930-2937 (1996).
    [CrossRef]
  6. D. G. Voelz, L. McMackin, J. K. Boger, and M. P. Fetrow, Double-exposure heterodyne imaging for observing line-of-sight deformation, Opt. Lett. 22, 1027-1029 (1997).
    [CrossRef] [PubMed]
  7. J. C. Wyant, "Testing aspherics using two-wavelength holography," Appl. Opt. 10, 2113-2118 (1971).
    [CrossRef] [PubMed]
  8. K. Creath, "Step height measurement using two-wavelength phase-shifting interferometry," Appl. Opt. 26, 2810-2816 (1987).
    [CrossRef] [PubMed]
  9. R. Dandliker, R. Thalmann and D. Prongue, "Two-wavelength laser interferometry using superheterodyne detection," Opt. Lett. 13, 339-341 (1988).
    [CrossRef] [PubMed]
  10. E. Gelmini, U. Minoni, and F. Docchio, "Tunable, double wavelength heterodyne detection interferometer for absolute distance measurements," Opt. Lett. 19, 213-215 (1994).
    [CrossRef] [PubMed]

Other (10)

D. K. Marker and C. H. Jenkins, Surface precision of optical membranes with curvature, Opt. Express 1, 324-331 (1997).
http://epubs.osa.org/oearchive/source/2668.htm
[CrossRef] [PubMed]

Holographic Interferometry, P.K. Rastogi, ed., Springer Ser. Opt. Sci. 68, (Springer, Berlin, 1994).

P. Hariharan, Quasi-heterodyne hologram interferometry, Opt. Eng. 24, 632-638 (1985).

Y. Ishii, J. Chen, and K. Murata, Digital phase-measuring interferometry with a tunable laser diode, Opt. Lett. 12, 233-235 (1987).
[CrossRef] [PubMed]

I. Yamaguchi, J. Liu, and J. Kato, Active phase-shifting interferometers for shape and deformation measurements, Opt. Eng. 35, 2930-2937 (1996).
[CrossRef]

D. G. Voelz, L. McMackin, J. K. Boger, and M. P. Fetrow, Double-exposure heterodyne imaging for observing line-of-sight deformation, Opt. Lett. 22, 1027-1029 (1997).
[CrossRef] [PubMed]

J. C. Wyant, "Testing aspherics using two-wavelength holography," Appl. Opt. 10, 2113-2118 (1971).
[CrossRef] [PubMed]

K. Creath, "Step height measurement using two-wavelength phase-shifting interferometry," Appl. Opt. 26, 2810-2816 (1987).
[CrossRef] [PubMed]

R. Dandliker, R. Thalmann and D. Prongue, "Two-wavelength laser interferometry using superheterodyne detection," Opt. Lett. 13, 339-341 (1988).
[CrossRef] [PubMed]

E. Gelmini, U. Minoni, and F. Docchio, "Tunable, double wavelength heterodyne detection interferometer for absolute distance measurements," Opt. Lett. 19, 213-215 (1994).
[CrossRef] [PubMed]

Supplementary Material (3)

» Media 1: MOV (903 KB)     
» Media 2: MOV (1260 KB)     
» Media 3: MOV (1612 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Diagram of heterodyne array profilometer.

Fig. 2.
Fig. 2.

Phase maps of a tilted surface for the equivalent wavelengths in Table 1. [Media 1]

Fig. 3.
Fig. 3.

Unwrapped phase profile plots of a tilted surface for the equivalent wavelengths in Table 1. [Media 2]

Fig. 4.
Fig. 4.

Optical path profiles of a tilted surface for the equivalent wavelengths in Table 1. [Media 3]

Tables (1)

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Table 1. Complex exposure wavelengths and resulting equivalent wavelengths

Equations (5)

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E a ( r m , λ a ) = A a ( r m , λ a ) exp { j ( ϕ a ( r m , λ a ) + ϕ refa ) } ,
E b ( r m , λ b ) = A b ( r m , λ b ) exp { j ( ϕ b ( r m , λ b ) + ϕ refb ) } .
arg { E a ( r m , λ a ) E b ( r m , λ b ) * } = ϕ a ( r m , λ a ) ϕ b ( r m , λ b ) + ϕ refa ϕ refb .
ϕ eq r m λ a = ϕ a ( r m , λ a ) ϕ b ( r m , λ b ) = 2 πOPD ( r m ) λ eq ,
λ eq = λ a λ b λ a λ b .

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