Abstract

Wavefront coding is a powerful technique that can be used to extend the depth of field of an incoherent imaging system. By adding a suitable phase mask to the aperture plane, the optical transfer function of a conventional imaging system can be made defocus invariant. Since 1995, when a cubic phase mask was first suggested, many kinds of phase masks have been proposed to achieve the goal of depth extension. In this Letter, a phase mask based on sinusoidal function is designed to enrich the family of phase masks. Numerical evaluation demonstrates that the proposed mask is not only less sensitive to focus errors than cubic, exponential, and modified logarithmic masks are, but it also has a smaller point-spread-function shifting effect.

© 2010 Optical Society of America

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References

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2009 (1)

2008 (1)

2007 (3)

2004 (2)

2003 (1)

2002 (1)

2000 (1)

1995 (1)

1966 (1)

Barakat, R.

Caron, N.

N. Caron and Y. Sheng, Proc. SPIE 6832, 68321G (2007).
[CrossRef]

Cathey, W.

Cathey, W. T.

Dowski, E.

Dowski, E. R.

Fainman, Y.

Feng, H. J.

Ford, J. E.

Houston, A.

Johnson, G. E.

Kubala, K.

Li, G.

Li, Q.

Liu, L.

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

Morrison, R. L.

Neifeld, M. A.

Ojeda-Castañeda, J.

Robinson, D.

D. Robinson and D. G. Stork, Computational Optical Sensing and Imaging (Optical Society of America, 2009).

Rutkowski, J.

Sauceda, A.

Sheng, Y.

N. Caron and Y. Sheng, Proc. SPIE 6832, 68321G (2007).
[CrossRef]

Sherif, S. S.

Silveira, P. E. X.

Stack, R. A.

Stork, D. G.

D. Robinson and D. G. Stork, Computational Optical Sensing and Imaging (Optical Society of America, 2009).

Sun, J.

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

Tamayo, I.

Tremblay, E. J.

Wang, D.

Yang, Q.

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

Ye, R.

Zhang, H.

Zhao, H.

Zhou, F.

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Figures (6)

Fig. 1
Fig. 1

Phase contour corresponding to different parameters (left: α = 306.6884 , β = 1.56 ; right: α = 200 , β = 8 ).

Fig. 2
Fig. 2

Defocused MTF with W 20 changing from 0 to 9 π and Th equaling 0.25.

Fig. 3
Fig. 3

Comparison of FI curves among different phase masks.

Fig. 4
Fig. 4

2D normalized PSF comparison (rows: cubic, exponential, logarithmic, sinusoidal; columns: Th = 0.21 , 0.23 , 0.25 , 0.27 , 0.30 , 0.33 ).

Fig. 5
Fig. 5

Comparison of 1D normalized PSF.

Fig. 6
Fig. 6

Digital restoration results (rows: W 20 = π , 3 π , 6 π , and 9 π ; columns: clear aperture, cubic, exponential, logarithmic, sinusoidal).

Tables (1)

Tables Icon

Table 1 Optimum Parameters for Each Mask a

Equations (2)

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f ( x , y ) = α x 4 sin ( β x ) + α y 4 sin ( β y ) ,
Iterate : for ( paras ( ) = Para [ i ] , i + + ) H ( u , W 20 , paras ( ) ) = F F T ( | F F T ( P ( x , W 20 , paras ( ) ) ) | 2 ) [ Value ( i ) = arg min ( ψ ψ ( | W 20 H | 2 d u ) d W 20 ) subject to { ( L B ) paras ( ) ( U B ) | H ( u , W 20 = 0 , paras ( ) ) | d u T h } ] End : PARA = Minimize ( Value ) .

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