Abstract

Focus analysis techniques from computer vision are applied to digital holography to determine the depth (range) of multiple objects and their surfaces from a single hologram capture. With this method the depths of objects can be determined from a single hologram capture without the need for manual focusing and without prior information on object location. Variance and the Laplacian of Gaussian are analyzed as focus measures, and techniques are proposed for focus plane determination from the focus measure curves. The algorithm is described in detail and demonstrated through simulation and optical experiment.

© 2008 Optical Society of America

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2005

2004

M. Liebling and M. Unser, “Autofocus for digital fresnel holograms by use of a fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424-2430 (2004).
[CrossRef]

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396-400 (2004).

2003

2001

1999

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373-385 (1999).
[CrossRef] [PubMed]

1997

1994

1989

J. Gillespie and R. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recogn. Lett. 9, 19-25 (1989).
[CrossRef]

1986

J. Canny,“A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

1980

D. Marr and E. C. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187-217 (1980).
[CrossRef]

1976

R. Jarvis, “Focus optimisation criteria for computer image processing,” Microscope 24, 163-180 (1976).

Bongartz, J.

Cai, L.

Callens, N.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895-5908 (June 2006).

Canny, J.

J. Canny,“A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

Conchello, J. A.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373-385 (1999).
[CrossRef] [PubMed]

Cooper, J.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373-385 (1999).
[CrossRef] [PubMed]

Coppola, G.

De Nicola, S.

Dubois, F.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895-5908 (June 2006).

Ferraro, P.

Finizio, A.

Frey, S.

Giel, D.

Gillespie, J.

J. Gillespie and R. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recogn. Lett. 9, 19-25 (1989).
[CrossRef]

Hering, P.

Hildreth, E. C.

D. Marr and E. C. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187-217 (1980).
[CrossRef]

E. C. Hildreth, “Implementation of a theory of edge detection,” MIT Artificial Intelligence Laboratory Technical Report 579 (MIT, 1980).

Jarvis, R.

R. Jarvis, “Focus optimisation criteria for computer image processing,” Microscope 24, 163-180 (1976).

Jin, H.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396-400 (2004).

Jüptner, W.

Karpova, T.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373-385 (1999).
[CrossRef] [PubMed]

King, R.

J. Gillespie and R. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recogn. Lett. 9, 19-25 (1989).
[CrossRef]

Kroktov, E.

E. Kroktov, “Focusing,” Int. J. Comput. Vision 1, 223-237(October 1987).

Li, Y.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396-400 (2004).

Liebling, M.

Ma, L.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396-400 (2004).

Marr, D.

D. Marr and E. C. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187-217 (1980).
[CrossRef]

McNally, J. G.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373-385 (1999).
[CrossRef] [PubMed]

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

Nayar, S. K.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

Pierattini, G.

Schnars, U.

Schockaert, C.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895-5908 (June 2006).

Thelen, A.

Unser, M.

Wang, H.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396-400 (2004).

Yamaguchi, I.

Yourassowsky, C.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895-5908 (June 2006).

Yu, L.

Zhang, T.

Appl. Opt.

IEEE Trans. Pattern Anal. Mach. Intell.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

J. Canny,“A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679-698 (1986).
[CrossRef] [PubMed]

Int. J. Comput. Vision

E. Kroktov, “Focusing,” Int. J. Comput. Vision 1, 223-237(October 1987).

J. Opt. Soc. Am. A

Methods

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373-385 (1999).
[CrossRef] [PubMed]

Microscope

R. Jarvis, “Focus optimisation criteria for computer image processing,” Microscope 24, 163-180 (1976).

Opt. Lett.

Pattern Recogn. Lett.

J. Gillespie and R. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recogn. Lett. 9, 19-25 (1989).
[CrossRef]

Proc. R. Soc. London Ser. B

D. Marr and E. C. Hildreth, “Theory of edge detection,” Proc. R. Soc. London Ser. B 207, 187-217 (1980).
[CrossRef]

Other

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895-5908 (June 2006).

E. C. Hildreth, “Implementation of a theory of edge detection,” MIT Artificial Intelligence Laboratory Technical Report 579 (MIT, 1980).

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Figures (14)

Fig. 1
Fig. 1

Focus curve for a flat void cell.

Fig. 2
Fig. 2

Focus curve for a blank void cell.

Fig. 3
Fig. 3

Focus curve for an edge cell.

Fig. 4
Fig. 4

Focus measure suppressed by surrounding flat void.

Fig. 5
Fig. 5

Calculation of local peak height.

Fig. 6
Fig. 6

Peak widths for true and false peaks.

Fig. 7
Fig. 7

Object intensity distributions for test computer-generated holograms: (a)  20 cm , (b)  25 cm , (c)  30 cm .

Fig. 8
Fig. 8

(a) Three- and (b) two-dimensional depth maps for measurement simulation using variance.

Fig. 9
Fig. 9

(a) Three- and (b) two-dimensional depth maps for measurement simulation using LoG.

Fig. 10
Fig. 10

Composite reconstruction for measurement using (a) variance and (b) LoG .

Fig. 11
Fig. 11

Defocus irradiance profiles in holography.

Fig. 12
Fig. 12

(a) Three- and (b) two-dimensional depth maps for the range measurement using variance.

Fig. 13
Fig. 13

(a) Three- and (b) two-dimensional depth maps for the range measurement using LoG.

Fig. 14
Fig. 14

Composite reconstruction for the range measurement. (a) Variance, (b) LoG.

Equations (11)

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f r ( x r , y r ) = j λ e j k d d f h ( x h , y h ) exp { i k 2 d [ ( x r x h ) 2 + ( y r y h ) 2 ] } d x h d y h ,
2 f = d 2 f d x 2 + d 2 f d y 2 .
f filtered ( x , y ) = 2 [ G ( x , y ) * f image ( x , y ) ] = 2 G ( x , y ) * f image ( x , y ) ,
G ( x , y ) = 1 2 π σ 2 exp ( ( x 2 + y 2 ) 2 σ 2 ) ,
2 G ( x , y ) = 1 σ 3 ( 2 π ) 1 / 2 ( 1 x 2 + y 2 σ 2 ) exp [ ( x 2 + y 2 ) 2 σ 2 ] .
NA = hologram   radius hologram   radius 2 + object   distance 2 ,
20 ×
x y
20 cm
25 cm
30 cm

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