Abstract

We discuss quantization effects of hologram recording on the quality of reconstructed images in phase-shifting digital holography. We vary bit depths of phase-shifted holograms in both numerical simulation and experiments and then derived the complex amplitude, which is subjected to Fresnel transformation for the image reconstruction. The influence of bit-depth limitation in quantization has been demonstrated in a numerical simulation for spot-array patterns with linearly varying intensities and a continuous intensity object. The objects are provided with uniform and random phase modulation. In experiments, digital holograms are originally recorded at 8 bits and the bit depths are changed to deliver holograms at bit depths of 1 to 8 bits for the image reconstruction. The quality of the reconstructed images has been evaluated for the different quantization levels.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. L. P. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer Academic, Dordrecht, The Netherlands, 2004), pp. 40–44 and pp. 541–573.
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    [CrossRef] [PubMed]

2004

2003

2001

1998

T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1211–1213 (1998).
[CrossRef]

1997

1996

1994

1990

1972

M. A. Kronrod, N. S. Merzlyakov, L. Yaroslavsky, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

1967

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 22, 77–79 (1967).
[CrossRef]

Brophy, C. P.

Burton, D. R.

Goodman, J. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 22, 77–79 (1967).
[CrossRef]

Jüptner, W.

Kato, J.-I.

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, L. Yaroslavsky, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Lalor, M. J.

Lawrence, R. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 22, 77–79 (1967).
[CrossRef]

Lilley, F.

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, L. Yaroslavsky, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Mizuno, J.

Ohta, S.

Schnars, U.

Skydan, O. A.

Surrel, Y.

Yamaguchi, I.

Yaroslavsky, L.

M. A. Kronrod, N. S. Merzlyakov, L. Yaroslavsky, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Yaroslavsky, L. P.

F. Zhang, I. Yamaguchi, L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668–1670 (2004).
[CrossRef] [PubMed]

L. P. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer Academic, Dordrecht, The Netherlands, 2004), pp. 40–44 and pp. 541–573.

Zhang, F.

Zhang, T.

T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1211–1213 (1998).
[CrossRef]

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

Zhao, B.

Appl. Opt.

Appl. Phys. Lett.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 22, 77–79 (1967).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Sov. Phys. Tech. Phys.

M. A. Kronrod, N. S. Merzlyakov, L. Yaroslavsky, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Other

L. P. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer Academic, Dordrecht, The Netherlands, 2004), pp. 40–44 and pp. 541–573.

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Figures (17)

Fig. 1
Fig. 1

Configuration for hologram recording and reconstruction by use of phase-shifting digital holography. BS, beam splitter; PZT, piezoelectric transducer; ADC, analog-to-digital converter.

Fig. 2
Fig. 2

Simulated objects with 8-bit resolution and 512 × 512 pixels: (a) 16 × 16 spot-array patterns with each spot having 9 × 9 pixels and stepwise intensity and (b) continuous intensity object.

Fig. 3
Fig. 3

Simulated hologram for 16 × 16 spot-array patterns with (a) uniform phase and (b) random phase.

Fig. 4
Fig. 4

Intensity histogram at the CCD plane for the spot-array patterns with uniform phase and random phase: (a) histogram of object and reference beam intensities and (b) histogram of interference patterns at the CCD.

Fig. 5
Fig. 5

Reconstructed images for spot-array patterns with random phase distribution: (a) image at 4-bit quantization and (b) averaged image intensity of spots against the object intensity.

Fig. 6
Fig. 6

Simulated hologram for the continuous object with (a) uniform phase and (b) random phase.

Fig. 7
Fig. 7

Intensity histogram at the CCD plane for the continuous object with uniform and random phase modulations: (a) histogram of object and reference beam intensities and (b) histogram of interference patterns at the CCD.

Fig. 8
Fig. 8

Reconstructed images for uniform phase-modulated objects at (a) 2-, (b) 4-, and (c) 6-bit quantization levels.

Fig. 9
Fig. 9

Reconstructed images for random phase-modulated objects at (a) 2-, (b) 4-, and (c) 6-bit quantization levels.

Fig. 10
Fig. 10

Intensity relation between the object and the reconstructed images at 4-, 6-, and 8-bit quantization for the continuous object.

Fig. 11
Fig. 11

Experimental setup for in-line phase-shifting digital hologram recording. BS, beam splitter; PZT, piezoelectric transducer with a half-mirror; LD, laser diode.

Fig. 12
Fig. 12

Hologram recording at a moderate reference beam intensity: (a) hologram recorded at 8 bits and (b) intensity histogram.

Fig. 13
Fig. 13

Hologram recording at a relatively high reference beam intensity: (a) hologram recorded at 8 bits and (b) intensity histogram.

Fig. 14
Fig. 14

Block diagram for bit-depth adjustments of optically recorded holograms. ADC, analog-to-digital converter; RMSE, root-mean-square error.

Fig. 15
Fig. 15

Reconstructed images from various quantization levels of holograms at (a) 8, (b) 4, and (c) 2 bits at a moderate reference beam intensity.

Fig. 16
Fig. 16

Reconstructed images from various quantization levels of holograms at (a) 8, (b) 4, and (c) 2 bits at a relatively high reference beam intensity.

Fig. 17
Fig. 17

Normalized rms of the reconstructed image error as a function of quantization bit depth for real objects and simulated ones with random phase modulation.

Equations (11)

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U O ( x , y ) = n = 0 N - 1 m = 0 M - 1 I O ( x , y ) exp [ i ϕ O ( x , y ) ] × δ ( x - n Δ x , y - m Δ y ) ,
U ( x , y ) = - - U O ( x , y ) exp { i k 2 z O [ ( x - x ) 2 + ( y - y ) 2 ] } d x d y ,
I H ( x , y ; δ ) = U R ( x , y ; δ ) + U ( x , y ) 2 = U R 2 + U 2 + 2 R [ U R U * exp ( i δ ) ] .
U ( x , y ) = 1 4 I R { [ I H ( x , y ; 0 ) - I H ( x , y ; π ) ] + i [ I H ( x , y ; π / 2 ) - I H ( x , y ; 3 π / 2 ) ] } ,
U ( x , y ) = 1 - i 4 I R { [ I H ( x , y ; 0 ) - I H ( x , y ; π / 2 ) ] + i [ I H ( x , y ; π / 2 ) - I H ( x , y ; π ) ] } ,
U I ( X , Y ; Z ) = - - U ( x , y ) exp { i k 2 Z [ ( X - x ) 2 + ( Y - y ) 2 ] } d x d y .
U I ( x , y ; - z O ) = U O ( x , y ) .
U I ( X , Y ) = exp [ i k 2 Z ( X 2 + Y 2 ) ] - - U ( x , y ) × exp [ i k 2 Z ( x 2 + y 2 ) ] × exp [ - i k Z ( X x + Y y ) ] d x d y .
λ z O N O Δ x Δ x = 1 ,             λ z O M O Δ y Δ y = 1.
I H Q ( δ ) = [ f { Q I H ( δ ) I H max - 1 } ] I H max Q - 1 ,
D ( b ; 8 ) = ( { n = 1 512 m = 1 512 [ I b ( m , n ) 2 - I 8 ( m , n ) 2 ] 2 } ) 1 / 2 × { n = 1 512 m = 1 512 [ I 8 ( m , n ) 2 ] 2 } - 1 / 2 ,

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