Abstract

Microscopy by holographic means is attractive because it permits true three-dimensional (3D) visualization and 3D display of the objects. We investigate the necessary condition on the object size and spatial bandwidth for complete 3D microscopic imaging with phase-shifting digital holography with various common arrangements. The cases for which a Fresnel holographic arrangement is sufficient and those for which object magnification is necessary are defined. Limitations set by digital sensors are analyzed in the Wigner domain. The trade-offs between the various holographic arrangements in terms of conditions on the object size and bandwidth, recording conditions required for complete representation, and complexity are discussed.

© 2008 Optical Society of America

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References

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2007

2006

A. Stern and B. Javidi, “Improved resolution digital holography using generalized sampling theorem,” J. Opt. Soc. Am. A 23, 1227-1235 (2006).
[CrossRef]

T. Namura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45, 4873-4877 (2006).
[CrossRef]

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

S. Yeom, I. Moon, and B. Javidi, “Real-time 3-D sensing, visualization and recognition of dynamic biological microorganisms,” Proc. IEEE 94, 550-566 (2006).
[CrossRef]

2005

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4402-4506 (2005).
[CrossRef]

2004

2003

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938-1946 (2003).
[CrossRef] [PubMed]

C.-S. Guo, L. Zhang, and Z. Y. Rong, “Effects of the fill factor of CCD pixels on digital holograms: comment on papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution',” Opt. Eng. (Bellingham) 42, 2768-2771 (2003).
[CrossRef]

2002

2001

1998

1979

1967

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Meas. Sci. Technol.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Opt. Eng. (Bellingham)

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. (Bellingham) 43, 239-250 (2004).
[CrossRef]

C.-S. Guo, L. Zhang, and Z. Y. Rong, “Effects of the fill factor of CCD pixels on digital holograms: comment on papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution',” Opt. Eng. (Bellingham) 42, 2768-2771 (2003).
[CrossRef]

Opt. Express

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4402-4506 (2005).
[CrossRef]

D. Kim and B. Javidi, “Distortion-tolerant 3-D object recognition using single exposure on-axis digital holography,” Opt. Express 12, 5539-5548 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Proc. IEEE

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

S. Yeom, I. Moon, and B. Javidi, “Real-time 3-D sensing, visualization and recognition of dynamic biological microorganisms,” Proc. IEEE 94, 550-566 (2006).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 9.

A. Lohmann, M. E. Testorf, and J. Ojeda-Castaneda, “Holography and the Wigner function,” in The Art and Science of Holography, a Tribute to Emmett Leith and Yuri Denisyuk, J.H.Caulfield, ed. (SPIE, 2004), Chap. 8.

B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer Verlag, 2002).

T. Kreis, ed., Handbook of Holographic Interferometry (Wiley, VCH, 2005).

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, 1968), Chap. 11.

A. Vanderlught, Optical Signal Processing (Wiley, 1992), Chap. 3.

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Figures (4)

Fig. 1
Fig. 1

Schematic of PSDH microscope. BS1, BS2: beam splitters; M1, M2: mirrors; RP: retarder plates.

Fig. 2
Fig. 2

(a) Support of the object field in the Wigner domain, (b) the support of the object field at the sensor plane, (c) the sensor acceptance range (bold rectangle). The entire object information is captured if the propagated object field fits the acceptance range of the sensor.

Fig. 3
Fig. 3

Wigner chart of the (a) original field, (b) the field in the image plane, and (c) together with the sensor limitations.

Fig. 4
Fig. 4

(a) Object planes O 1 and O 2 imaged in planes O 1 and O 2 , respectively. (b) The Wigner chart (shaded) of the field on plane O 2 due to object points in O 1 is obtained by x shearing of Wigner chart of the field in O 1 due to the same object points (dashed lines).

Equations (21)

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H ( x , y ; φ R ) = u H ( x , y ) 2 + u R ( x , y ) 2 + u H * ( x , y ) u R ( x , y ) + u H ( x , y ) u R * ( x , y ) = [ A H ( x , y ) ] 2 + A R 2 + 2 A R A H cos [ Φ H ( x , y ) φ R ] ,
Φ R ( x , y ) = H ( x , y ; φ R = 3 π 2 ) H ( x , y ; φ R = π 2 ) H ( x , y ; φ R = 0 ) H ( x , y ; φ R = π ) .
W u 0 ( x , ν ) = u 0 ( x + x 2 ) u 0 * ( x x 2 ) exp ( j 2 π x ν ) d x ,
W u H ( x , ν ) = W u H ( x λ z ν , ν ) ,
u s ( x ) = [ u H ( x ) * rect ( x α Δ ) ] comb ( x Δ ) rect ( x W s ) ,
W H W s ,
B H B s = 1 α Δ ,
MLB 1 Δ ,
W 0 W s λ z B 0 ,
B 0 1 α Δ ,
SBP F = W s B s W H B H = SBP 0 + λ z B 0 2 .
u i ( x ) = λ z 1 e j ( π λ M f ) x 2 u 0 ( x M ) ,
W u i ( x , ν ) = W u 0 ( x M , M ν x λ f M ) .
W 0 = W H M W s M .
B 0 M Δ min ( 1 , 1 α Δ W 0 λ f ) .
M Δ δ min ( 1 , 1 α Δ W 0 ( λ f ) ) .
SBP i = W s B s W H B H = SBP 0 + M W 0 2 λ f .
W 0 W s λ d B 0 M ,
SBP d = SBP 0 + M W 0 2 λ f + λ d ( B 0 M + W 0 λ f ) 2 .
W 0 W s λ M 1 M 2 D B 0 M 1 .
B 0 M 1 Δ min ( 1 , 1 α Δ W 0 λ f ) .

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