Abstract

We proposed a general algorithm for phase-shifting shadow moiré by an iterative self-tuning algorithm. In our proposed system, the grating is translated in equal distance to introduce phase shifts across the field of view. The proposed algorithm produces accurate phase information with five interferograms and can calibrate the precise phase step during the process of the height demodulation. Compared with the traditional method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase-shift shadow moiré when reconstructing surfaces from fringe patterns. Numerical simulations and optical experiments show that the proposed method can eliminate the nonuniform phase-shift error and possesses a superior performance to existing typical phase-shifting algorithms.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef]
  2. M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express 17, 21867–21881 (2009).
    [CrossRef]
  3. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2505 (1987).
    [CrossRef]
  4. J. Schmit and K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase shifting interferometry,” Appl. Opt. 34, 3610–3619 (1995).
    [CrossRef]
  5. J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
    [CrossRef]
  6. H. Bi, Y. Zhang, K. V. Ling, and C. Wen, “Class of 4+1-Phase algorithms with error compensation,” Appl. Opt. 43, 4199–4207 (2004).
    [CrossRef]
  7. Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
    [CrossRef]
  8. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
    [CrossRef]
  9. K. G. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236–253 (2001).
    [CrossRef]
  10. Z. Y. Wang and B. T. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004).
    [CrossRef]
  11. J. C. Estrada, M. Servin, and J. A. Quiroga, “A self-tuning phase-shifting algorithm for interferometry,” Opt. Express 18, 2632–2638 (2010).
    [CrossRef]
  12. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
    [CrossRef]
  13. J. F. Mosiño, M. Servin, J. C. Estrada, and J. A. Quiroga, “Phasorial analysis of detuning error in temporal phaseshifting algorithms,” Opt. Express 17, 5618–5623 (2009).
    [CrossRef]
  14. J. A. Gómez-Pedrero and J. A. Quiroga, “Measurement of surface topography by RGB shadow-moiré with direct phase demodulation,” Opt. Lasers Eng. 44, 1297–1310(2006).
    [CrossRef]
  15. H. Guo and M. Chen, “Least-squares algorithm for phase-stepping interferometry with an unknown relative step,” Appl. Opt. 44, 4854–4858 (2005).
    [CrossRef]
  16. H. B. Du, H. Zhao, B. Li, and Z. W. Li, “Algorithm for phase shifting shadow Moiré with an unknown relative step,” J. Opt. 131–5 (2011).
  17. C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 1998).

2011 (1)

H. B. Du, H. Zhao, B. Li, and Z. W. Li, “Algorithm for phase shifting shadow Moiré with an unknown relative step,” J. Opt. 131–5 (2011).

2010 (1)

2009 (2)

2006 (1)

J. A. Gómez-Pedrero and J. A. Quiroga, “Measurement of surface topography by RGB shadow-moiré with direct phase demodulation,” Opt. Lasers Eng. 44, 1297–1310(2006).
[CrossRef]

2005 (1)

2004 (2)

2001 (1)

1996 (2)

1995 (1)

1993 (2)

J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
[CrossRef]

1987 (1)

1974 (1)

Bi, H.

Brangaccio, D. J.

Bruning, J. H.

Chen, M.

Creath, K.

Du, H. B.

H. B. Du, H. Zhao, B. Li, and Z. W. Li, “Algorithm for phase shifting shadow Moiré with an unknown relative step,” J. Opt. 131–5 (2011).

Eiju, T.

Estrada, J. C.

Falkenstorfer, O.

J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Gallagher, J. E.

Gómez-Pedrero, J. A.

J. A. Gómez-Pedrero and J. A. Quiroga, “Measurement of surface topography by RGB shadow-moiré with direct phase demodulation,” Opt. Lasers Eng. 44, 1297–1310(2006).
[CrossRef]

Guo, H.

Han, B. T.

Hariharan, P.

Herriott, D. R.

Larkin, K. G.

Li, B.

H. B. Du, H. Zhao, B. Li, and Z. W. Li, “Algorithm for phase shifting shadow Moiré with an unknown relative step,” J. Opt. 131–5 (2011).

Li, Z. W.

H. B. Du, H. Zhao, B. Li, and Z. W. Li, “Algorithm for phase shifting shadow Moiré with an unknown relative step,” J. Opt. 131–5 (2011).

Ling, K. V.

Manduchi, R.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 1998).

Mosiño, J. F.

Oreb, B. F.

Quiroga, J. A.

Rosenfeld, D. P.

Schmit, J.

Schreiber, H.

J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Schwider, J.

J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Servin, M.

Surrel, Y.

Tomasi, C.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 1998).

Wang, Z. Y.

Wen, C.

White, A. D.

Zhang, Y.

Zhao, H.

H. B. Du, H. Zhao, B. Li, and Z. W. Li, “Algorithm for phase shifting shadow Moiré with an unknown relative step,” J. Opt. 131–5 (2011).

Zoller, A.

J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Appl. Opt. (8)

J. Opt. (1)

H. B. Du, H. Zhao, B. Li, and Z. W. Li, “Algorithm for phase shifting shadow Moiré with an unknown relative step,” J. Opt. 131–5 (2011).

Opt. Eng. (1)

J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993).
[CrossRef]

Opt. Express (4)

Opt. Lasers Eng. (1)

J. A. Gómez-Pedrero and J. A. Quiroga, “Measurement of surface topography by RGB shadow-moiré with direct phase demodulation,” Opt. Lasers Eng. 44, 1297–1310(2006).
[CrossRef]

Opt. Lett. (1)

Other (1)

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Optical arrangement of shadow moiré.

Fig. 2.
Fig. 2.

Flowchart of phase retrieval algorithm proposed.

Fig. 3.
Fig. 3.

Residual errors in the presence of nonuniform phase-shifting error.

Fig. 4.
Fig. 4.

Residual errors in the presence of nonuniform phase-shifting error and noise: (a) the proposed PSA, (b) Guo’s PSA.

Fig. 5.
Fig. 5.

STD of height error in the presence of nonuniform phase-shifting error and noise.

Fig. 6.
Fig. 6.

Measurement result obtained by use of the proposed PSA: (a) the reconstructed surface, (b) the nonuniform phase step.

Fig. 7.
Fig. 7.

STD of measurement height error of several algorithms.

Equations (10)

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

In(x,y)=A(x,y)+B(x,y)cos[ϕ(x,y)+nδ(x,y)],(n=2,1,0,1,2),
δ(x,y)=2πdΔh/[p(h+z(x,y))],
δs=2πdΔh/ph>δ.
ϕ=atan(I2I42I3I1I5sin(δe)).
z^=phϕ2πdpϕ.
Δhc=p(h+z^)δe/2πd.
δu=2πdΔhc/p(h+z^).
max(|zqzq1|)<ε,
p=0.05mm,d=100mm,h=160mm.
h1h2=Δh,

Metrics