Abstract

We consider optimization of hybrid imaging systems including a pupil mask for enhancing the depth of field and a digital deconvolution step. In a previous paper [Opt. Lett. 34, 2970 (2009) ] we proposed an optimization criterion based on the signal-to-noise ratio of the restored image. We use this criterion in order to optimize different families of phase or amplitude masks and to compare them, on an objective basis, for different desired defocus ranges. We show that increasing the number of parameters of the masks allows one to obtain better performance.

© 2010 Optical Society of America

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References

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  1. C.-L. Tisse, H. Nguyen, R. Tessieres, M. Pyanet, and F. Guichard, “Extended depth-of-field using sharpness transport across colour channels,” Proc. SPIE 7061, 706105 (2008).
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    [CrossRef]
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    [CrossRef]
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2009 (3)

2008 (3)

2007 (1)

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

2005 (1)

2004 (2)

2003 (2)

R. Balboa and N. Grzywacz, “Power spectra and distribution of contrasts of natural images from different habitats,” Vision Res. 43, 2527–2537 (2003).
[CrossRef] [PubMed]

W. Chi and N. Georges, “Computational imaging with the logarithmic asphere: theory,” J. Opt. Soc. Am. A 20, 2260–2273 (2003).
[CrossRef]

2000 (1)

E. Dowski, R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

1998 (1)

1995 (1)

Balboa, R.

R. Balboa and N. Grzywacz, “Power spectra and distribution of contrasts of natural images from different habitats,” Vision Res. 43, 2527–2537 (2003).
[CrossRef] [PubMed]

Caron, N.

Cathey, T.

Chi, W.

Cormack, R.

E. Dowski, R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

Diaz, F.

Dowski, E.

Georges, N.

Goudail, F.

Grzywacz, N.

R. Balboa and N. Grzywacz, “Power spectra and distribution of contrasts of natural images from different habitats,” Vision Res. 43, 2527–2537 (2003).
[CrossRef] [PubMed]

Guichard, F.

C.-L. Tisse, H. Nguyen, R. Tessieres, M. Pyanet, and F. Guichard, “Extended depth-of-field using sharpness transport across colour channels,” Proc. SPIE 7061, 706105 (2008).
[CrossRef]

Huignard, J. -P.

Johnson, G.

Levin, A.

A. Levin, “4-D frequency analysis of computational cameras for depth of field extension,” in Frontiers in Optics, OSA Technical Digest (2009), paper FThX1.

Li, G.

Liu, L.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Loiseaux, B.

Narayanswamy, R.

Nguyen, H.

C.-L. Tisse, H. Nguyen, R. Tessieres, M. Pyanet, and F. Guichard, “Extended depth-of-field using sharpness transport across colour channels,” Proc. SPIE 7061, 706105 (2008).
[CrossRef]

Ojeda-Castañeda, J.

Pyanet, M.

C.-L. Tisse, H. Nguyen, R. Tessieres, M. Pyanet, and F. Guichard, “Extended depth-of-field using sharpness transport across colour channels,” Proc. SPIE 7061, 706105 (2008).
[CrossRef]

Robinson, D.

Sarama, S.

E. Dowski, R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

Sauceda, A.

Sheng, Y.

Sherif, S.

Silveira, P.

Stork, D.

Sun, J.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Tessieres, R.

C.-L. Tisse, H. Nguyen, R. Tessieres, M. Pyanet, and F. Guichard, “Extended depth-of-field using sharpness transport across colour channels,” Proc. SPIE 7061, 706105 (2008).
[CrossRef]

Tisse, C. -L.

C.-L. Tisse, H. Nguyen, R. Tessieres, M. Pyanet, and F. Guichard, “Extended depth-of-field using sharpness transport across colour channels,” Proc. SPIE 7061, 706105 (2008).
[CrossRef]

Wach, H.

Wang, D.

Yang, Q.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Zhang, H.

Zhou, F.

Appl. Opt. (6)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (2)

E. Dowski, R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

C.-L. Tisse, H. Nguyen, R. Tessieres, M. Pyanet, and F. Guichard, “Extended depth-of-field using sharpness transport across colour channels,” Proc. SPIE 7061, 706105 (2008).
[CrossRef]

Vision Res. (1)

R. Balboa and N. Grzywacz, “Power spectra and distribution of contrasts of natural images from different habitats,” Vision Res. 43, 2527–2537 (2003).
[CrossRef] [PubMed]

Other (1)

A. Levin, “4-D frequency analysis of computational cameras for depth of field extension,” in Frontiers in Optics, OSA Technical Digest (2009), paper FThX1.

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Figures (17)

Fig. 1
Fig. 1

Objects used to optimize the different masks.

Fig. 2
Fig. 2

R I Q mean as a function of α cub for the spoke target and Lena, with ψ defoc   max = 15.75 , using either the ideal filter or the generic one.

Fig. 3
Fig. 3

Optimal cubic phase mask parameter α cub , opt as a function of the desired depth of field.

Fig. 4
Fig. 4

R I Q mean as a function of the logarithmic phase mask parameters α log and β log , for the spoke target and ideal deconvolution filter, with ψ defoc   max = 15.75 .

Fig. 5
Fig. 5

Profile along the x direction of the different phase masks with their optimal parameters.

Fig. 6
Fig. 6

Optimal logarithmic phase mask parameters α log , opt and β log , opt as functions of the desired depth of field.

Fig. 7
Fig. 7

R I Q mean as a function of the fractional-power phase mask parameters, for the spoke target and ideal deconvolution filter, with ψ defoc   max = 15.75 .

Fig. 8
Fig. 8

Optimal fractional-power phase mask parameters α frac , opt and β frac , opt as functions of the desired depth of field.

Fig. 9
Fig. 9

R I Q mean as a function of the exponential phase mask parameters, for the spoke target and ideal deconvolution filter, with ψ defoc   max = 15.75 .

Fig. 10
Fig. 10

Optimal exponential phase mask parameters α exp , opt and β exp , opt as functions of the desired depth of field.

Fig. 11
Fig. 11

Optimal exponential phase mask parameters α exp , opt β exp , opt and α exp , opt β exp , opt 2 / 2 as functions of the desired depth of field.

Fig. 12
Fig. 12

R I Q mean as a function of the amplitude mask parameter for the spoke target and ideal deconvolution filter, with ψ defoc   max = 15.75 .

Fig. 13
Fig. 13

Optimal amplitude mask parameter as a function of the desired depth of field.

Fig. 14
Fig. 14

Images obtained with the amplitude mask, at the focal plane, with ψ defoc   max = 15.75 .

Fig. 15
Fig. 15

R I Q mean obtained with the different phase masks for the spoke target and Lena using either their ideal or the generic deconvolution filter.

Fig. 16
Fig. 16

Images of the spoke target obtained at different defocus values with the different masks using their optimal parameters and the ideal deconvolution filter, with ψ defoc   max = 15.75 .

Fig. 17
Fig. 17

Images of Lena obtained at different defocus values with the different masks using their optimal parameters and the generic deconvolution filter, with ψ defoc   max = 15.75 .

Equations (23)

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I ψ ( r ) = h ψ ( r ) O ( r ) + n ( r ) ,
ψ = π R 2 λ ( 1 d O + 1 d I 1 f ) ,
S N R i n ( dB ) = 10 log 10 [ S O O ( ν ) d ν / S n n ( ν ) d ν ] ,
O ̂ ψ ( r ) = d ( r ) I ψ ( r ) .
M S E ψ = | O ̂ ψ ( r ) O ( r ) | 2 = | d ̃ ( ν ) h ̃ ψ ( ν ) 1 | 2 S O O ( ν ) d ν + | d ̃ ( ν ) | 2 S n n ( ν ) d ν ,
M S E mean = 1 n MSE i = 1 n MSE M S E ψ i .
R I Q mean ( dB ) = 10 log 10 [ S O O ( ν ) d ν / M S E mean ] ,
R I Q ψ ( dB ) = 10 log 10 [ S O O ( ν ) d ν / M S E ψ ] .
φ cub ( x , y ) = α cub ( x 3 + y 3 ) ,
φ tot ( x , y ) = φ cub ( x , y ) + ψ ( x 2 + y 2 ) = α cub ( x ψ 3 α cub ) 3 + α cub ( y ψ 3 α cub ) 3 ψ 2 ( x + y ) 3 α cub 2 ψ 3 81 α cub 2 .
M S E translat ( δ x ) = | h ̃ 0 ( ν ) h ̃ ψ ( ν ) exp ( 2 i π ν δ x ) | 2 .
δ x ̂ = arg   min δ x [ M S E translat ( δ x ) ] ,
h ̃ ψ c ( ν ) = h ̃ ψ ( ν ) exp ( 2 i π ν δ x ̂ ) .
M S E ψ = | d ̃ ( ν ) h ̃ ψ c ( ν ) 1 | 2 S O O ( ν ) d ν + | d ̃ ( ν ) | 2 S n n ( ν ) d ν .
d ̃ ( ν ) = 1 n d i = 1 n d h ̃ ψ i c ( ν ) 1 n d i = 1 n d | h ̃ ψ i c ( ν ) | 2 + S n n ( ν ) S O O ( ν ) .
φ log ( x , y ) = α log   sgn ( x ) x 2   log ( | x | + β log ) + α log   sgn ( y ) y 2   log ( | y | + β log ) ,
φ frac ( x , y ) = α frac ( sgn ( x ) | x | β frac + sgn ( y ) | y | β frac ) .
φ exp ( x , y ) = α exp x [ exp ( β exp x 2 ) 1 ] + α exp y [ exp ( β exp y 2 ) 1 ] .
φ exp ( x , y ) = α exp β exp ( x 3 + y 3 ) + α exp β exp 2 ( x 5 + y 5 ) / 2 ,
A ( x , y ) = 1     if   0 x 2 + y 2 α amp 1
= 0     otherwise ,
A ( x , y ) = 1     if   0 β amp x 2 + y 2 α amp 1
= 0     otherwise ,

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