Abstract

The phase retrieval algorithm has been used in this paper for whole reconstruction of the optical wave fields. The quantitative information of the phase distribution as well as the intensity distribution of the reconstruction field at different locations along the propagation direction has been achieved from double or multi in-line holograms. Numerical reconstructions of the wave fields from experimentally recorded in-line holograms are presented. This technique can be potentially applied for aberrated wave front analyzing and 3D imaging.

© 2003 Optical Society of America

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References

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Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

G. Pedrini, P. Froning, H. Tiziani, F. Santoyo, �??Shape measurement of microscopic structures using digital holograms,�?? Opt. Commun. 164 257-268 (1999).
[CrossRef]

S. Lai, B. Kemper, G. v. Bally, �??Off-axis reconstructions of in-line holograms for twin-image elimination,�?? Opt. Commun. 169 37-43 (1999).
[CrossRef]

K. A. Nugent, �??Twin-image elimination in Gabor holography,�?? Opt. Commun. 78 293-299 (1990).
[CrossRef]

J. B. Tiller, A. Barty, D. Paganin, K. A. Nugent, �??The holographic twin image problem: a deterministic phase solution,�?? Opt. Commun. 183 7-14 (2000).
[CrossRef]

Opt. Eng.

L. Onural and P. D. Scott, �??Digital decoding of in-line holograms,�?? Opt. Eng. 26, 1124-1132 (1987).

C. Wagner, W. Osten, S. Seebacher, �??Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,�?? Opt. Eng. 39 79-85 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Optics & Laser Technology

S. Murata, N. Yasuda, �??Potential of digital holography in particle measurement,�?? Optics & Laser Technology 32 567-574 (2000).
[CrossRef]

Optik (Stuttgart)

R. W. Gerchberg and W. O. Saxton, �??A practical algorithm for the determination of phase from image and diffraction plane pictures,�?? Optik (Stuttgart) 35 237-246 (1978).

Other

J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, San Francisco, Calif., 1968) Cap. 5.

Supplementary Material (6)

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup for in-line holography.

Fig. 2.
Fig. 2.

Pure phase object used in experiment.

Fig. 3.
Fig. 3.

Holograms recorded at different distance. (a) d=7.40cm (b) d=8.15cm and (c) d=8.90cm.

Fig. 4.
Fig. 4.

Video presentation of reconstructed wave field at different distance from the hologram plane along the z axis direction, d′=8.90cm to d′=2.00cm with step of Δd′=1.0mm. (a) Intensity (1.85MB) and (b) phase (1.83MB) distributions. Constructed by using a single hologram.

Fig. 5.
Fig. 5.

Video presentation of reconstructed wave field at different distance from the hologram plane along the z axis direction, d′=8.90cm to d′=2.00cm with step of Δd′=1.0mm. (a) Intensity (2.43MB) and (b) phase (2.47MB) distributions. Constructed by using double holograms.

Fig. 6.
Fig. 6.

Schematic diagram of the iterative method of phase retrieval for whole wave field reconstruction.

Fig. 7.
Fig. 7.

Video presentation of reconstructed wave field at different distance from the hologram plane along the z axis direction, d′=8.90cm to d′=2.00cm with step of Δd′=1.0mm. (a) Intensity (2.38MB) and (b) phase (2.28MB) distributions. Constructed by using three holograms.

Equations (11)

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U 2 ( x 2 , y 2 ) = U 1 ( x 1 , y 1 ) h ( x 1 , y 1 , d )
h ( x 1 , y 1 , d ) = exp ( i 2 π d λ ) i λ d exp [ i π λ d ( x 1 2 + y 1 2 ) ] .
I ( x 2 , y 2 ) = U 2 ( x 2 , y 2 ) 2
= 1 a ( x 1 , y 1 ) h ( x 1 , y 1 , d ) 2
= 1 a * ( x 1 , y 1 ) h * ( x 1 , y 1 , d ) a ( x 1 , y 1 ) h ( x 1 , y 1 , d )
+ a ( x 1 , y 1 ) h ( x 1 , y 1 , d ) 2 .
U r ( x r , y r , d ' ) = I ( x 2 , y 2 ) h ( x 2 , y 2 , d ' ) ,
U r ( x r , y r , d ' ) = 1 a ( x 1 , y 1 ) a * ( x 1 , y 1 ) h ( x 1 , y 1 , 2 d )
+ a ( x 1 , y 1 ) h ( x 1 , y 1 , d ) 2 h ( x 1 , y 1 , d ) ,
U r ( x r , y r , d ' ) = F 1 { F { I ( x 2 , y 2 ) } H ( ξ , η , d ' ) } ,
H ( ξ , η , d ' ) = exp ( i 2 π d ' λ ) exp [ i π λ d ' ( ξ 2 + η 2 ) ] .

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