Abstract

Hybrid imaging systems involve the joint design of an optical image-gathering module and digital processing algorithms to obtain a required final image. They have the potential to achieve imaging performance hitherto unobtainable by conventional imaging techniques. A reduction in the signal-to-noise ratio of the final image is one of their main disadvantages when one is considering linear signal processing. We analyze the effect of additive white noise at the detector on the performance of hybrid imaging systems under quasi-monochromatic incoherent illumination. We also show numerical results and computer-simulated images for an extended depth-of-field hybrid system.

© 2005 Optical Society of America

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References

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2004 (2)

S. S. Sherif, W. T. Cathey, and E. R. Dowski, Appl. Opt. 43, 2709 (2004).
[CrossRef] [PubMed]

S. S. Sherif, E. R. Dowski, and W. T. Cathey, J. Mod. Opt. 51, 1191 (2004).
[CrossRef]

2003 (1)

2002 (3)

2001 (1)

2000 (1)

1998 (1)

1995 (1)

1994 (1)

1984 (2)

Barrett, H. H.

Brady, D. J.

Cathey, W. T.

Chi, W.

Conchello, G. A.

Dowski, E. R.

Frieden, B. R.

W. T. Cathey, B. R. Frieden, W. T. Rhodes, and C. K. Rushford, J. Opt. Soc. Am. A 1, 241 (1984).
[CrossRef]

B. R. Frieden, in The Computer in Optical Research, B. R. Frieden, ed. (Springer-Verlag, 1980), Chap. 3, pp. 81–210.
[CrossRef]

George, N.

Hooker, R. B.

Johnson, G. E.

Kubala, K.

Milster, T. D.

Nagy, J.

J. Van der Gracht, J. Nagy, V. P. Pauca, and R. J. Plemmons, in Integrated Computational Imaging Systems 2001, Vol. 66 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2–4.

Pauca, V. P.

J. Van der Gracht, J. Nagy, V. P. Pauca, and R. J. Plemmons, in Integrated Computational Imaging Systems 2001, Vol. 66 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2–4.

Paxman, R. G.

Plemmons, R. J.

J. Van der Gracht, J. Nagy, V. P. Pauca, and R. J. Plemmons, in Integrated Computational Imaging Systems 2001, Vol. 66 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2–4.

Rahman, Z.

Rhodes, W. T.

Rushford, C. K.

Sherif, S. S.

S. S. Sherif, W. T. Cathey, and E. R. Dowski, Appl. Opt. 43, 2709 (2004).
[CrossRef] [PubMed]

S. S. Sherif, E. R. Dowski, and W. T. Cathey, J. Mod. Opt. 51, 1191 (2004).
[CrossRef]

S. S. Sherif and W. T. Cathey, Appl. Opt. 41, 6062 (2002).
[CrossRef] [PubMed]

S. S. Sherif and W. T. Cathey, Optical Imaging and Microscopy—Techniques and Advanced Systems, P. Török and F. Kao, eds. (Springer-Verlag, 2003), Chap. 5, pp. 111–142.
[CrossRef]

Smith, W. E.

Van der Gracht, J.

J. Van der Gracht, J. Nagy, V. P. Pauca, and R. J. Plemmons, in Integrated Computational Imaging Systems 2001, Vol. 66 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2–4.

Appl. Opt. (7)

J. Mod. Opt. (1)

S. S. Sherif, E. R. Dowski, and W. T. Cathey, J. Mod. Opt. 51, 1191 (2004).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Lett. (1)

Other (3)

J. Van der Gracht, J. Nagy, V. P. Pauca, and R. J. Plemmons, in Integrated Computational Imaging Systems 2001, Vol. 66 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2–4.

B. R. Frieden, in The Computer in Optical Research, B. R. Frieden, ed. (Springer-Verlag, 1980), Chap. 3, pp. 81–210.
[CrossRef]

S. S. Sherif and W. T. Cathey, Optical Imaging and Microscopy—Techniques and Advanced Systems, P. Török and F. Kao, eds. (Springer-Verlag, 2003), Chap. 5, pp. 111–142.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Extension of depth of field due to different logarithmic phase plates and the resulting decrease in the SNR of the final image.

Fig. 2
Fig. 2

Simulated images of a spoke using a clear rectangular aperture (left) and simulated final images with a logarithmic phase plate (right). (a), (b) ψ = 0 ; (c), (d) ψ = 5 ; (e), (f) ψ = 15 ; (g), (h) ψ = 30 .

Equations (11)

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O ( i , j ) = j = 0 N 1 [ j = 0 M 1 h digital ( i ; i ) I ( i , j ) ] h digital ( j ; j ) [ i = 0 M 1 h digital ( i ) ] 2 ,
O noisy ( i , j ) = O ( i , j )
+ j = 0 N 1 [ i = 0 M 1 h digital ( i , i ) n ( i , j ) ] h digital ( j ; j ) [ i = 0 M 1 h digital ( i ) ] 2 .
σ O noisy 2
= { j = 0 N 1 [ i = 0 M 1 h digital ( i , i ) n ( j , j ) ] h digital ( j , j ) } 2 [ i = 0 M 1 h digital ( i ) ] 4 ,
σ O noisy 2 = σ n 2 i = 0 M 1 j = 0 N 1 h digital 2 ( i ) h digital 2 ( j ) [ i = 0 M 1 h digital ( i ) ] 4 .
F noise = i = 0 M 1 j = 0 N 1 h digital 2 ( i ) h digital 2 ( j ) [ i = 0 M 1 h digital ( i ) ] 4 ,
f ( x ) = α x max 2 x 2 ( log x + β )
H digital ( f x , f y ) = H Clear - aperature ( f x , f y ) H Log - phase - plate ( f x , f y ) ,
H Log - phase - plate ( f x , f y ) 0 ,
= 0 , H Log - phase - plate ( f x , f y ) = 0 ,

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