Abstract

A closed loop phase control system using an all-fiber optical configuration has been developed for use in phase stepping interferometry. This system drives the relative phase of two interfering beams through a sequence of π/2 rad increments so that the initial relative phase of these beams can be determined. This phase stepping system uses optical fibers to provide spatially uniform phase steps from a flexible, easily aligned optical configuration. In addition, this system uses phase feed back to eliminate phase modulator errors and to compensate for phase drifts caused by environmental disturbances.

© 1991 Optical Society of America

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References

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  1. G. O. Rosvold, “Fast Measurements of Phase Using a PC-Based Frame Grabber and Phase Stepping Technique,” Appl. Opt. 29, 237–241 (1990).
    [CrossRef] [PubMed]
  2. K. Creath, “Holographic Contour and Deformation Measurement Using a 1.4 Million Element Detector Array,” Appl. Opt. 28, 2170–2175 (1989).
    [CrossRef] [PubMed]
  3. D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
    [CrossRef]
  4. S. Nakadate, H. Saito, “Fringe Scanning Speckle-Pattern Interferometry,” Appl. Opt. 24, 2172–2180 (1985).
    [CrossRef] [PubMed]
  5. K. Creath, “Phase-Shifting Speckle Interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  6. M. Chang, C.-P. Hu, P. Lam, J. C. Wyant, “High Precision Deformation Measurement by Digital Phase Shifting Holographic Interferometry,” Appl. Opt. 24, 3780–3783 (1985).
    [CrossRef] [PubMed]
  7. P. Hariharan, B. F. Oreb, N. Brown, “Real-Time Holographic Interferometry: A Microcomputer System for the Measurement of Vector Displacements,” Appl. Opt. 22, 876–880 (1983).
    [CrossRef] [PubMed]
  8. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  9. J. Schwider, “Phase Shifting Interferometry: Reference Phase Error Reduction,” Appl. Opt. 28, 3889–3892 (1989).
    [CrossRef] [PubMed]
  10. C. Ai, J. C. Wyant, “Effect of Piezoelectric Transducer Nonlinearity on Phase Shift Interferometry,” Appl. Opt. 26, 1112–1116 (1987).
    [CrossRef] [PubMed]
  11. P. Carre, “Installation et Utilisation du Compateur Photoelectrique et Interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
    [CrossRef]
  12. 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]
  13. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983), p. 186.
  14. R. Dandliker, R. Thalmann, “Heterodyne and Quasi-Heterodyne Holographic Interferometry,” Opt. Eng. 24, 824–831 (1985).
  15. V. Srinivasan, H. C. Liu, M. Halioua, “Automated Phase-Measuring Profilometry of 3-D Diffuse Objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef] [PubMed]
  16. D. R. MacQuigg, “Hologram Fringe Stabilization Method,” Appl. Opt. 16, 291–292 (1977).
    [CrossRef] [PubMed]
  17. M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All Single-Mode Fibre Optic Holographic System with Active Fringe Stabilization,” J. Phys. E. 18, 185–186 (1985).
    [CrossRef]
  18. J. C. Wyant, “Use of an AC Heterodyne Lateral Shear Interferometer with Real-Time Wavefront Correction Systems,” Appl. Opt. 14, 2622–2626 (1975).
    [CrossRef] [PubMed]
  19. C. R. Mercer, G. Beheim, “Active Phase Compensation System for Fiber Optic Holography,” NASA Tech. Memo. TM-101295 (1988).
  20. C. R. Wylie, Advanced Engineering Mathmetics (McGraw-Hill, New York, 1975), p. 416.
  21. N. Lagakos, J. A. Bucaro, J. Jarzynski, “Temperature-Induced Optical Phase Shifts in Fibers,” Appl. Opt. 20, 2305–2308 (1981).
    [CrossRef] [PubMed]

1990 (1)

1989 (2)

1987 (2)

1986 (1)

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

1985 (5)

S. Nakadate, H. Saito, “Fringe Scanning Speckle-Pattern Interferometry,” Appl. Opt. 24, 2172–2180 (1985).
[CrossRef] [PubMed]

K. Creath, “Phase-Shifting Speckle Interferometry,” Appl. Opt. 24, 3053–3058 (1985).
[CrossRef] [PubMed]

M. Chang, C.-P. Hu, P. Lam, J. C. Wyant, “High Precision Deformation Measurement by Digital Phase Shifting Holographic Interferometry,” Appl. Opt. 24, 3780–3783 (1985).
[CrossRef] [PubMed]

R. Dandliker, R. Thalmann, “Heterodyne and Quasi-Heterodyne Holographic Interferometry,” Opt. Eng. 24, 824–831 (1985).

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All Single-Mode Fibre Optic Holographic System with Active Fringe Stabilization,” J. Phys. E. 18, 185–186 (1985).
[CrossRef]

1984 (1)

1983 (1)

1981 (1)

1977 (1)

1975 (1)

1974 (1)

1966 (1)

P. Carre, “Installation et Utilisation du Compateur Photoelectrique et Interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Ai, C.

Beheim, G.

C. R. Mercer, G. Beheim, “Active Phase Compensation System for Fiber Optic Holography,” NASA Tech. Memo. TM-101295 (1988).

Brangaccio, D. J.

Brown, N.

Bruning, J. H.

Bucaro, J. A.

Carre, P.

P. Carre, “Installation et Utilisation du Compateur Photoelectrique et Interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Chang, M.

Corke, M.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All Single-Mode Fibre Optic Holographic System with Active Fringe Stabilization,” J. Phys. E. 18, 185–186 (1985).
[CrossRef]

Creath, K.

Dandliker, R.

R. Dandliker, R. Thalmann, “Heterodyne and Quasi-Heterodyne Holographic Interferometry,” Opt. Eng. 24, 824–831 (1985).

Eiju, T.

Gallagher, J. E.

Halioua, M.

Hariharan, P.

Herriott, D. R.

Hu, C.-P.

Jackson, D. A.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All Single-Mode Fibre Optic Holographic System with Active Fringe Stabilization,” J. Phys. E. 18, 185–186 (1985).
[CrossRef]

Jarzynski, J.

Jones, J. D. C.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All Single-Mode Fibre Optic Holographic System with Active Fringe Stabilization,” J. Phys. E. 18, 185–186 (1985).
[CrossRef]

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983), p. 186.

Kersey, A. D.

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All Single-Mode Fibre Optic Holographic System with Active Fringe Stabilization,” J. Phys. E. 18, 185–186 (1985).
[CrossRef]

Lagakos, N.

Lam, P.

Liu, H. C.

MacQuigg, D. R.

Mercer, C. R.

C. R. Mercer, G. Beheim, “Active Phase Compensation System for Fiber Optic Holography,” NASA Tech. Memo. TM-101295 (1988).

Nakadate, S.

Oreb, B. F.

Robinson, D. W.

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Rosenfeld, D. P.

Rosvold, G. O.

Saito, H.

Schwider, J.

Srinivasan, V.

Thalmann, R.

R. Dandliker, R. Thalmann, “Heterodyne and Quasi-Heterodyne Holographic Interferometry,” Opt. Eng. 24, 824–831 (1985).

White, A. D.

Williams, D. C.

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Wyant, J. C.

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983), p. 186.

Wylie, C. R.

C. R. Wylie, Advanced Engineering Mathmetics (McGraw-Hill, New York, 1975), p. 416.

Appl. Opt. (14)

S. Nakadate, H. Saito, “Fringe Scanning Speckle-Pattern Interferometry,” Appl. Opt. 24, 2172–2180 (1985).
[CrossRef] [PubMed]

K. Creath, “Phase-Shifting Speckle Interferometry,” Appl. Opt. 24, 3053–3058 (1985).
[CrossRef] [PubMed]

M. Chang, C.-P. Hu, P. Lam, J. C. Wyant, “High Precision Deformation Measurement by Digital Phase Shifting Holographic Interferometry,” Appl. Opt. 24, 3780–3783 (1985).
[CrossRef] [PubMed]

P. Hariharan, B. F. Oreb, N. Brown, “Real-Time Holographic Interferometry: A Microcomputer System for the Measurement of Vector Displacements,” Appl. Opt. 22, 876–880 (1983).
[CrossRef] [PubMed]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef] [PubMed]

J. Schwider, “Phase Shifting Interferometry: Reference Phase Error Reduction,” Appl. Opt. 28, 3889–3892 (1989).
[CrossRef] [PubMed]

C. Ai, J. C. Wyant, “Effect of Piezoelectric Transducer Nonlinearity on Phase Shift Interferometry,” Appl. Opt. 26, 1112–1116 (1987).
[CrossRef] [PubMed]

G. O. Rosvold, “Fast Measurements of Phase Using a PC-Based Frame Grabber and Phase Stepping Technique,” Appl. Opt. 29, 237–241 (1990).
[CrossRef] [PubMed]

K. Creath, “Holographic Contour and Deformation Measurement Using a 1.4 Million Element Detector Array,” Appl. Opt. 28, 2170–2175 (1989).
[CrossRef] [PubMed]

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]

V. Srinivasan, H. C. Liu, M. Halioua, “Automated Phase-Measuring Profilometry of 3-D Diffuse Objects,” Appl. Opt. 23, 3105–3108 (1984).
[CrossRef] [PubMed]

D. R. MacQuigg, “Hologram Fringe Stabilization Method,” Appl. Opt. 16, 291–292 (1977).
[CrossRef] [PubMed]

J. C. Wyant, “Use of an AC Heterodyne Lateral Shear Interferometer with Real-Time Wavefront Correction Systems,” Appl. Opt. 14, 2622–2626 (1975).
[CrossRef] [PubMed]

N. Lagakos, J. A. Bucaro, J. Jarzynski, “Temperature-Induced Optical Phase Shifts in Fibers,” Appl. Opt. 20, 2305–2308 (1981).
[CrossRef] [PubMed]

J. Phys. E. (1)

M. Corke, J. D. C. Jones, A. D. Kersey, D. A. Jackson, “All Single-Mode Fibre Optic Holographic System with Active Fringe Stabilization,” J. Phys. E. 18, 185–186 (1985).
[CrossRef]

Metrologia (1)

P. Carre, “Installation et Utilisation du Compateur Photoelectrique et Interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Opt. Commun. (1)

D. W. Robinson, D. C. Williams, “Digital Phase Stepping Speckle Interferometry,” Opt. Commun. 57, 26–30 (1986).
[CrossRef]

Opt. Eng. (1)

R. Dandliker, R. Thalmann, “Heterodyne and Quasi-Heterodyne Holographic Interferometry,” Opt. Eng. 24, 824–831 (1985).

Other (3)

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983), p. 186.

C. R. Mercer, G. Beheim, “Active Phase Compensation System for Fiber Optic Holography,” NASA Tech. Memo. TM-101295 (1988).

C. R. Wylie, Advanced Engineering Mathmetics (McGraw-Hill, New York, 1975), p. 416.

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Figures (7)

Fig. 1
Fig. 1

Phase control system used in a phase stepping speckle interferometer.

Fig. 2
Fig. 2

Phase control circuit, showing the oscillator (OSC), the integrator (INT), and the high voltage amplifier (HV AMP).

Fig. 3
Fig. 3

Effect of phase stabilization on VPD1.

Fig. 4
Fig. 4

Phase error θERR as a function of time.

Fig. 5
Fig. 5

Displacement measurement interferometer.

Fig. 6
Fig. 6

Photodiode outputs VPD1 and VPD2 during four consecutive phase steps.

Fig. 7
Fig. 7

Change in φ as a function of VPZT3.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

V PD 1 ( t ) = K PD 1 I 1 { 1 + η 1 cos [ 2 θ 2 β sin ( ω t ) ] } ,
V PD 1 ( t ) = K PD 1 I 1 + η 1 K PD 1 I 1 cos ( 2 θ ) × { J 0 ( 2 β ) + n even [ 2 J n ( 2 β ) cos ( n ω t ) ] } + η 1 K PD 1 I 1 sin ( 2 θ ) { n odd [ 2 J n ( 2 β ) sin ( n ω t ) ] } ,
E 1 = C 1 sin ( 2 θ ) ,
θ ERR = E 1 / ( 2 C 1 ) ,
V n = K PD 2 I 2 [ 1 + η 2 J 0 ( β ) cos ( θ n + φ ) ] .
φ = tan 1 [ ( V 4 V 2 ) / ( V 1 V 3 ) ] ,

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