Abstract

The amount of displacement of a diffused object can be measured using phase-shifting digital holography with a polarization imaging camera. Four digital holograms in quadrature are extracted from the polarization imaging camera and used to calculate the phase hologram. Two Fourier transforms of the phase holograms are calculated before and after the displacement of the object. A phase slope is subsequently obtained from the phase distribution of division between the two Fourier transforms. The slope of the phase distribution is proportional to the lateral displacement of the object. The sensitivity is less than one pixel size in the lateral direction of the movement. The longitudinal component of the displacement can be also measured separately from the intercept on the phase axis along the phase distribution of the division between two Fourier transforms of the phase holograms.

© 2011 Optical Society of America

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References

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  1. H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–666.
  2. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett.22, 1268–1270 (1997).0146-9592
    [CrossRef]
  3. M. Kuechel and W. Wiedmann, “In-process metrology for large astronomical mirrors,” Proc. SPIE1333, 280–294 (1990).0277-786X
  4. A. J. P. van Haasteren and H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt.33, 4137–4142 (1994).0003-6935
    [CrossRef]
  5. A. Hettwer, J. Kranz, and J. Schwider, “Three channel phaseshifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39, 960–966 (2000).0091-3286
    [CrossRef]
  6. T. Kiire, S. Nakadate, and M. Shibuya, “Phase-shifting interferometer based on changing the direction of linear polarization orthogonally,” Appl. Opt.47, 3784–3788 (2008).0003-6935
    [CrossRef]
  7. T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt.47, 4787–4792 (2008).0003-6935
    [CrossRef]
  8. M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.
  9. M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.
  10. J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X
  11. Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phaseshifting digital holography,” Appl. Phys. Lett.85, 1069–1071 (2004).0003-6951
    [CrossRef]
  12. M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X
  13. T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camer,” Opt. Rev.17, 210–213 (2010).1340-6000
    [CrossRef]
  14. T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt.50, B31–B37 (2011).0003-6935
    [CrossRef]
  15. T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt.48, H244–H250 (2009).0003-6935
    [CrossRef]
  16. T. Kakue, Y. Moritani, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Image quality improvement of parallel four-step phase-shifting digital holography by using the algorithm of parallel two-step phase-shifting digital holography,” Opt. Express18, 9555–9560 (2010).1094-4087
    [CrossRef]
  17. H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev.17, 176–180(2010).1340-6000
    [CrossRef]
  18. T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express18, 18975–18980 (2010).1094-4087
    [CrossRef]
  19. I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta28, 1359–1376 (1981).0030-3909
    [CrossRef]
  20. W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental mechanics,” Opt. Eng.21, 427–431 (1982).0091-3286
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    [CrossRef]
  22. C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng.37, 1290–1298 (1998).0091-3286
    [CrossRef]
  23. B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech.41, 29–39 (2001).0014-4851
    [CrossRef]
  24. P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng.40, 1613–1620 (2001).0091-3286
    [CrossRef]

2011

2010

2009

2008

2005

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X

2004

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phaseshifting digital holography,” Appl. Phys. Lett.85, 1069–1071 (2004).0003-6951
[CrossRef]

2001

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech.41, 29–39 (2001).0014-4851
[CrossRef]

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng.40, 1613–1620 (2001).0091-3286
[CrossRef]

2000

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phaseshifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39, 960–966 (2000).0091-3286
[CrossRef]

1998

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng.37, 1290–1298 (1998).0091-3286
[CrossRef]

1997

1994

1993

1990

M. Kuechel and W. Wiedmann, “In-process metrology for large astronomical mirrors,” Proc. SPIE1333, 280–294 (1990).0277-786X

1982

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental mechanics,” Opt. Eng.21, 427–431 (1982).0091-3286

1981

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta28, 1359–1376 (1981).0030-3909
[CrossRef]

Awatsuji, Y.

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt.50, B31–B37 (2011).0003-6935
[CrossRef]

T. Kakue, Y. Moritani, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Image quality improvement of parallel four-step phase-shifting digital holography by using the algorithm of parallel two-step phase-shifting digital holography,” Opt. Express18, 9555–9560 (2010).1094-4087
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express18, 18975–18980 (2010).1094-4087
[CrossRef]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt.48, H244–H250 (2009).0003-6935
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phaseshifting digital holography,” Appl. Phys. Lett.85, 1069–1071 (2004).0003-6951
[CrossRef]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

Brock, N.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

Bruning, J. H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–666.

Chen, D. J.

Chiang, F. P.

Chrysochoos, A.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech.41, 29–39 (2001).0014-4851
[CrossRef]

Davis, C. Q.

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng.37, 1290–1298 (1998).0091-3286
[CrossRef]

Don, H. S.

Frankena, H. J.

Freeman, D. M.

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng.37, 1290–1298 (1998).0091-3286
[CrossRef]

Fujii, A.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Fujii, M.

Goodson, K. E.

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng.40, 1613–1620 (2001).0091-3286
[CrossRef]

Hayes, J.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

Hettwer, A.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phaseshifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39, 960–966 (2000).0091-3286
[CrossRef]

Ito, K.

Kakue, T.

Kiire, T.

Kranz, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phaseshifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39, 960–966 (2000).0091-3286
[CrossRef]

Kubota, T.

T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography,” Appl. Opt.50, B31–B37 (2011).0003-6935
[CrossRef]

T. Kakue, Y. Moritani, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Image quality improvement of parallel four-step phase-shifting digital holography by using the algorithm of parallel two-step phase-shifting digital holography,” Opt. Express18, 9555–9560 (2010).1094-4087
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Experimental demonstration of parallel two-step phase-shifting digital holography,” Opt. Express18, 18975–18980 (2010).1094-4087
[CrossRef]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt.48, H244–H250 (2009).0003-6935
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phaseshifting digital holography,” Appl. Phys. Lett.85, 1069–1071 (2004).0003-6951
[CrossRef]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

Kuechel, M.

M. Kuechel and W. Wiedmann, “In-process metrology for large astronomical mirrors,” Proc. SPIE1333, 280–294 (1990).0277-786X

Matoba, O.

Millerd, J.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

Moritani, Y.

Morris, M. N.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X

Muracciole, J. M.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech.41, 29–39 (2001).0014-4851
[CrossRef]

Nakadate, S.

Némoz-Gaillard, M.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech.41, 29–39 (2001).0014-4851
[CrossRef]

Nishio, K.

Nitanai, E.

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev.17, 176–180(2010).1340-6000
[CrossRef]

Nomura, T.

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev.17, 176–180(2010).1340-6000
[CrossRef]

North-Morris, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

Novak, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

Numata, T.

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev.17, 176–180(2010).1340-6000
[CrossRef]

Peters, W. H.

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental mechanics,” Opt. Eng.21, 427–431 (1982).0091-3286

Ranson, W. F.

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental mechanics,” Opt. Eng.21, 427–431 (1982).0091-3286

Saif, B.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phaseshifting digital holography,” Appl. Phys. Lett.85, 1069–1071 (2004).0003-6951
[CrossRef]

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–666.

Schwider, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phaseshifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39, 960–966 (2000).0091-3286
[CrossRef]

Shibuya, M.

Shimozato, Y.

Suzuki, H.

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev.17, 176–180(2010).1340-6000
[CrossRef]

Tahara, T.

Tan, Y. S.

Ura, S.

van Haasteren, A. J. P.

Wattrisse, B.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech.41, 29–39 (2001).0014-4851
[CrossRef]

Wiedmann, W.

M. Kuechel and W. Wiedmann, “In-process metrology for large astronomical mirrors,” Proc. SPIE1333, 280–294 (1990).0277-786X

Wyant, J. C.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

Yamaguchi, I.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett.22, 1268–1270 (1997).0146-9592
[CrossRef]

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta28, 1359–1376 (1981).0030-3909
[CrossRef]

Yatagai, T.

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camer,” Opt. Rev.17, 210–213 (2010).1340-6000
[CrossRef]

Zhang, T.

Zhou, P.

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng.40, 1613–1620 (2001).0091-3286
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phaseshifting digital holography,” Appl. Phys. Lett.85, 1069–1071 (2004).0003-6951
[CrossRef]

Exp. Mech.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech.41, 29–39 (2001).0014-4851
[CrossRef]

Opt. Acta

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta28, 1359–1376 (1981).0030-3909
[CrossRef]

Opt. Eng.

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental mechanics,” Opt. Eng.21, 427–431 (1982).0091-3286

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng.40, 1613–1620 (2001).0091-3286
[CrossRef]

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng.37, 1290–1298 (1998).0091-3286
[CrossRef]

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phaseshifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39, 960–966 (2000).0091-3286
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

H. Suzuki, T. Nomura, E. Nitanai, and T. Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev.17, 176–180(2010).1340-6000
[CrossRef]

T. Kiire, T. Yatagai, S. Nakadate, and M. Shibuya, “Quadrature phase-shifting interferometer with a polarization imaging camer,” Opt. Rev.17, 210–213 (2010).1340-6000
[CrossRef]

Proc. SPIE

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE5869, 58691B (2005).0277-786X

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE5531, 304–314 (2004).0277-786X

M. Kuechel and W. Wiedmann, “In-process metrology for large astronomical mirrors,” Proc. SPIE1333, 280–294 (1990).0277-786X

Other

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 547–666.

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Figures (10)

Fig. 1.
Fig. 1.

Imaging devices. (a) Polarization imaging camera (PIC) composed of polarized array and imaging device, in which a polarizer on each pixel has a different polarization axis and the four different axes are arranged into a unit cell. (b) Conventional imaging camera, in which to acquire data for four different polarization angles, it is necessary to rotate the polarizer placed in front of the detector array.

Fig. 2.
Fig. 2.

Configuration of polarizer array in the polarization imaging camera. The values such as 0, 90, 180, and 270 degrees represent the amount of the phase shift at each pixel. Holograms in quadrature phase-shift are extracted from the pixels having the same phase-shift value in the original image.

Fig. 3.
Fig. 3.

Measurement configuration for phase hologram displacement according to lateral displacement of object scattered. The characteristic of the Fourier transform for translation can be applied to the lateral displacement measurement of the phase hologram.

Fig. 4.
Fig. 4.

Experimental setup of polarization interferometer with the polarization imaging camera.

Fig. 5.
Fig. 5.

Original holograms and calculated phase holograms. (a) and (b) are raw images directly captured by the PIC before and after 6.0 μm displacement of the object, respectively. (c) and (d) are quadrature phase-shifted holograms extracted from the images (a) and (b), respectively. (e) and (f) are phase holograms resulting from the phase calculation with the phase-shifted holograms (c) and (d), respectively.

Fig. 6.
Fig. 6.

Phase distribution images of the complex numbers resulting from the division of the digital Fourier transforms of the phase holograms shown in Figs. 5(e) and (f). (a) and (b) are with and without through the low-pass filtering to the complex number, respectively. The slope of the phase change from black to white expresses the lateral displacement in the moving direction.

Fig. 7.
Fig. 7.

Plot data of the phase distribution shown in Fig. 6(b) in the middle horizontal direction, and straight line fitted by its linearly approximation. The amount of the displacement is 6.19 μm due to the slope of the function of the line approximated linearly.

Fig. 8.
Fig. 8.

Plot data for slopes of lines fitting to phase distributions in experimental results for only lateral displacement, and linear solid line for its theoretical value.

Fig. 9.
Fig. 9.

Plot of slopes of lines fitted to phase distributions in experimental results for displacement in the diagonal direction. Straight line for its theoretical value. This graph shows that the stage angle is 43.0 degrees with respect to the imaging plane.

Fig. 10.
Fig. 10.

Plot of intercept value of linearly approximated lines of experimental phase distributions for displacement in the diagonal direction.

Equations (7)

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UO(x,y,θ)=AO(x,y)exp{i[φO(x,y)+θ(j,k)]},
UR(θ)=ARexp{i[φRθ(j,k)]},
I(x,y,θ)=|UO(x,y,θ)+UR(θ)|2=AO2(x,y)+AR2+2AO(x,y)ARcos[Δφ(x,y)+2θ(j,k)],
Δφ=tan1[I(x,y,3π/4)I(x,y,π/4)I(x,y,0)I(x,y,π/2)].
F(ω)=f(x)exp(iωx)dx,
F(ω)exp(iωΔx)=f(xΔx)exp(iωx)dx=f(x)exp[iω(x+Δx)]dx,
exp(iωΔx)=F(ω)exp(iωΔx)F(ω).

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