Abstract

An advanced interferometer was built for surface metrology in environments with severe vibration. This instrument uses active control to compensate for effects of vibration to allow surface measurement with high-resolution phase-shifting interferometry. A digital signal processor and high-speed phase control from an electro-optic modulator allows phase measurements at 4000 Hz. These measurements are fed back into a real-time servo in the digital signal processor that provides a vibration-corrected phase ramp for the surface measurements taken at video rates. Unlike fringe locking, which compensates vibration to keep the phase constant, we show a true phase servo that allows the phase to be stabilized while it is ramped, enabling surface measurements using phase-shifting interferometry that requires multiple images with controlled phase shifts.

© 2001 Optical Society of America

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References

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  1. D. L. Modisett, “Phase-shifting interferometry at high frame rates,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).
  2. C. L. Koliopoulos, “Simultaneous phase shift interferometer,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 119–127 (1991).
    [CrossRef]
  3. I. Yamaguchi, J. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 10, 2930–2937 (1996).
    [CrossRef]
  4. L. Deck, “Vibration-resistant phase-shifting interferometry,” Appl. Opt. 35, 6655–6662 (1996).
    [CrossRef] [PubMed]
  5. G. C. Cole, “Vibration compensation for a phase shifting interferometer,” M.S. thesis (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1997).
  6. G. C. Cole, J. H. Burge, L. Dettmann, “Vibration stabilization of a phase shifting interferometer for large optics,” in Optical Manufacturing and Testing II, H. Stahl, ed., Proc. SPIE3134, 438–446 (1997).
    [CrossRef]
  7. M. A. Karim, Electro-Optical Devices and Systems, PWS-Kent Series in Electrical Engineering (PWS-Kent, Boston, Mass., 1990), Chap. 7.
  8. J. M. Palmer, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication, 1998).
  9. J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

1996 (2)

I. Yamaguchi, J. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 10, 2930–2937 (1996).
[CrossRef]

L. Deck, “Vibration-resistant phase-shifting interferometry,” Appl. Opt. 35, 6655–6662 (1996).
[CrossRef] [PubMed]

Bruning, J. H.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Burge, J. H.

G. C. Cole, J. H. Burge, L. Dettmann, “Vibration stabilization of a phase shifting interferometer for large optics,” in Optical Manufacturing and Testing II, H. Stahl, ed., Proc. SPIE3134, 438–446 (1997).
[CrossRef]

Cole, G. C.

G. C. Cole, J. H. Burge, L. Dettmann, “Vibration stabilization of a phase shifting interferometer for large optics,” in Optical Manufacturing and Testing II, H. Stahl, ed., Proc. SPIE3134, 438–446 (1997).
[CrossRef]

G. C. Cole, “Vibration compensation for a phase shifting interferometer,” M.S. thesis (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1997).

Deck, L.

Dettmann, L.

G. C. Cole, J. H. Burge, L. Dettmann, “Vibration stabilization of a phase shifting interferometer for large optics,” in Optical Manufacturing and Testing II, H. Stahl, ed., Proc. SPIE3134, 438–446 (1997).
[CrossRef]

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Karim, M. A.

M. A. Karim, Electro-Optical Devices and Systems, PWS-Kent Series in Electrical Engineering (PWS-Kent, Boston, Mass., 1990), Chap. 7.

Kato, J.

I. Yamaguchi, J. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 10, 2930–2937 (1996).
[CrossRef]

Koliopoulos, C. L.

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 119–127 (1991).
[CrossRef]

Liu, J.

I. Yamaguchi, J. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 10, 2930–2937 (1996).
[CrossRef]

Modisett, D. L.

D. L. Modisett, “Phase-shifting interferometry at high frame rates,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).

Palmer, J. M.

J. M. Palmer, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication, 1998).

Yamaguchi, I.

I. Yamaguchi, J. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 10, 2930–2937 (1996).
[CrossRef]

Appl. Opt. (1)

Opt. Eng. (1)

I. Yamaguchi, J. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 10, 2930–2937 (1996).
[CrossRef]

Other (7)

G. C. Cole, “Vibration compensation for a phase shifting interferometer,” M.S. thesis (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1997).

G. C. Cole, J. H. Burge, L. Dettmann, “Vibration stabilization of a phase shifting interferometer for large optics,” in Optical Manufacturing and Testing II, H. Stahl, ed., Proc. SPIE3134, 438–446 (1997).
[CrossRef]

M. A. Karim, Electro-Optical Devices and Systems, PWS-Kent Series in Electrical Engineering (PWS-Kent, Boston, Mass., 1990), Chap. 7.

J. M. Palmer, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication, 1998).

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

D. L. Modisett, “Phase-shifting interferometry at high frame rates,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 119–127 (1991).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Illustration of basic vibration servo. The active element, EOM, makes a correction in response to external inputs (from the surface-measurement computer and vibration) to the system.

Fig. 2
Fig. 2

Traces of the phase-shifter control signal and the signal on the photodiode for the vibration-compensation servo.

Fig. 3
Fig. 3

Basic phase command structure for the vibration-compensation method. The photodiode intensities are used to calculate phase errors at 4000 Hz. During a surface measurement, a ramp is initiated and an integrating bucket technique is used to calculate a phase map (this picture is taken from Cole’s thesis5).

Fig. 4
Fig. 4

Layout of the interferometer.

Fig. 5
Fig. 5

EOM is the phase shifter of the interferometer.

Fig. 6
Fig. 6

Plot of the contrast of the photodiode signal for square detector versus the amount of tilt in the interferogram. We have shown system performance with no degradation with a contrast of 0.05.

Fig. 7
Fig. 7

Comparison of the theoretical and the measured vibration-rejection percentages for 4-kHz system operation (measured vibration rejection data is taken from Cole’s thesis5).

Fig. 8
Fig. 8

Illustration of how PBS separates and then recombines the two polarizing beams. Polarization leakage is shown. α, phase-shift angle; ϕ, phase difference between the test and reference beams; m 2, intensity extinction ratio of the PBS. Dots and short bars indicate the polarizations.

Fig. 9
Fig. 9

Surface map made with phase-shifting interferometry for three cases: (a) in the presence of severe vibration with the servo turned off, (b) in the same severe environment with the servo operational, and (c) the same surface, measured with standard phase-shifting interferometry in a quiet environment.

Tables (2)

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Table 1 Typical Values of the Parameters in Calculating the Residual Phase-Step Error of Surface Measurement

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Table 2 System Specifications

Equations (22)

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nx=no-12 no3p63VW,
nz=ne.
Δϕ=ϕz-ϕx=2πλ12 no3p63dW V.
Ax, y=A1x, y+A2x, ycosϕx, y+α,
I= Ax, ydxdy= A1x, ydxdy+cos α  A2x, ycosϕx, ydxdy-sin α  A2x, ysinϕx, ydxdy=I1+I2 cosγ+α,
I1= A1x, ydxdy,
I2= A2x, ycosϕx, ydxdy2+ A2x, ysinϕx, ydxdy21/2,
tanγ= A2x, ysinϕx, ydxdy A2x, ycosϕx, ydxdy.
I2I1=sinαπαπ.
ϕ1=A sin2πft,
ϕ2=A sin2πft-Δt,
Δϕ=ϕ1-ϕ2=2A sinπfΔtcos2πft-Δt2,
Rejection=1001-2 sinπfΔt.
I=I11+γ cos ϕ.
I=αI1+1-αI11+γ cos ϕ=I11+1-αγ cos ϕ).
γ=1-αγ,
I=|E|2=α11+1m2expiϕ+α2×expiαexpiϕ+1m22,
Iα1 expi sin ϕm2+α2×expiα+ϕ-sin ϕm22=|α1|2+|α2|2+2α1α2 cosα+ϕ-2 sin ϕm2.
Δϕϕ=-2 sin ϕm2rad.
SNR=CIN=CINEPB,
σp=151SNR.
r=ΔtΔT1/2σp,

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