Phase-shifting digital holography is a digital measurement technology of a complex optical field profile that uses focal plane array detectors without the loss of bandwidth. It has been known that the accuracy of phase-shifting digital holography is limited mainly by the phase tolerance of reference. In this Letter, it is revealed that the uncertainty in an expected signal is highly dependent on the phase of the signal itself, as well as the phase tolerance of the reference. Based on the uncertainty analysis, we propose a novel scheme of phase-shifting digital holography that exploits an uncertainty property to enhance the measurement accuracy even under significant reference phase tolerance.

© 2012 Optical Society of America

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2009 (1)

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2006 (1)

2004 (1)

2000 (1)

1997 (1)

1995 (1)

1991 (1)

Cai, L. Z.

Chen, X.

Cho, S. W.

Creath, K.

Dong, G. Y.

Fienup, J. R.

S. T. Thurman and J. R. Fienup, Signal Recovery and Synthesis, OSA Technical Digest (2007) paper SMC1.

Gramaglia, M.

Hahn, J.

Kim, H.

Lai, G.

Lee, B.

Liu, J. P.

Liu, Q.

Meng, X. F.

Poon, T. C.

Schmit, J.

Shen, X. X.

Thurman, S. T.

S. T. Thurman and J. R. Fienup, Signal Recovery and Synthesis, OSA Technical Digest (2007) paper SMC1.

Wang, Y. R.

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yatagai, T.

Yeazell, J. A.

Zhang, T.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Geometric interpretation of phase-shifting digital holography and (b) its expression in the transformed coordinate system.

Fig. 2.
Fig. 2.

(a) Necessary condition of twin image noise elimination and (b) uncertainty region of the estimated signal which is represented as the red-colored intersection area of two blue circular-shaped bands.

Fig. 3.
Fig. 3.

Uncertainties as a function of the phase of the expected signal for (a) phase and (b) amplitude of two-step holography, and (c) phase and (b) amplitude of three-step holography.

Fig. 4.
Fig. 4.

Minimum achievable uncertainties for (a) amplitude and (b) phase of signal in proposed method where tolerances of the reference phases are set to 10°.

Equations (7)

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