Abstract

We consider optimization of hybrid imaging systems including a phase mask for enhancing the depth of field and a digital deconvolution step. We propose an image quality criterion that takes into account the variability of the system’s point-spread function along the expected defocus range and the noise enhancement induced by deconvolution. Considering the classical cubic phase mask as an example, we show that the optimization of this criterion may lead to filter parameters that are significantly different from those usually proposed to ensure the strict invariance of the PSF.

© 2009 Optical Society of America

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References

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2009 (2)

2008 (1)

2007 (1)

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

2005 (1)

2004 (1)

2002 (1)

1995 (1)

Bagheri, S.

Barbastathis, G.

Caron, N.

Cathey, W. T.

Dowski, E. R.

Li, G.

Liu, L.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Sheng, Y.

Sherif, S. S.

Silveira, P.

Sun, J.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Wang, D.

Yang, Q.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Zhang, H.

Zhou, F.

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Figures (4)

Fig. 1
Fig. 1

SNR o u t and SNR min as functions of α for ST object with SNR i n = 34   dB .

Fig. 2
Fig. 2

PSF and MTF at α = 15.74 and α = 90 .

Fig. 3
Fig. 3

Results obtained with the ST with (a) a conventional imaging system and with hybrid imaging system at (b) α = 15.74 and (c) α = 90 . The left column is at ψ = 0 , the middle column is at ψ = 7.62 , and the right column is at ψ = 15.75 . SNR i n = 34   dB .

Fig. 4
Fig. 4

Optimal parameters versus ψ d e f o c   max and its corresponding SNR o u t , for the ST and Lena.

Equations (13)

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I ( r ) = h ψ ( r ) * O ( r ) + n ( r ) ,
h ψ ( r ) = | F { P ( r ) exp [ i ( φ ( r ) + ψ r 2 ) ] } | 2 ,
ψ = π R 2 λ ( 1 f 1 d o 1 d i ) ,
S n n ( ν ) = | n ̃ ( ν ) | 2 ,     S O O ( ν ) = | O ( ν ) | 2 ,
SNR i n ( dB ) = 10 log 10 S O O ( ν ) d ν S n n ( ν ) d ν .
MSE ψ = | O ̂ ( r ) O ( r ) | 2 .
MSE ψ = | d ̃ ( ν ) h ̃ ψ c ( ν ) 1 | 2 S O O ( ν ) d ν + | d ̃ ( ν ) | 2 S n n ( ν ) d ν .
MSE m e a n = 1 n MSE i = 1 n MSE MSE ψ i ,
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 ) .
SNR o u t ( dB ) = 10 log 10 [ S O O ( ν ) d ν MSE m e a n ] ,
φ ( x , y ) = α x 3 + α y 3 ,
SNR min ( dB ) = min i SNR ψ i ( dB ) ,
SNR ψ i ( dB ) = 10 log 10 [ S O O ( ν ) d ν MSE ψ i ] .

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