Abstract

Wavefront coding as an optical–digital hybrid imaging technique can be used to extend the depth of field. The key to wavefront coding lies in the design of suitable phase masks to achieve the invariant imaging properties over a wide range of defocus. In this Letter, we propose another phase mask with a tangent function to enrich the odd symmetrical kind of phase masks. The performance of the tangent phase mask is evaluated by comparison with a cubic mask, improved-1 logarithmic mask, improved-2 logarithmic mask, and sinusoidal mask. The results demonstrate that the tangent phase mask has superior performance in extending the depth of field.

© 2014 Optical Society of America

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References

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2013

2010

2007

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

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

2004

1995

Caron, N.

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

Cathey, W. T.

Dowski, E. R.

Larivière-Bastien, M.

Li, Y.

Liu, L.

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

Ojeda-Castañeda, J.

Sauceda, A.

Sheng, Y.

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

Sherif, S. S.

Sun, J.

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

Thibault, S.

Yang, Q.

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

Zhao, H.

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Figures (4)

Fig. 1.
Fig. 1.

Phase profiles of cubic, improved-1 logarithmic, improved-2 logarithmic, sinusoidal, and tangent phase masks.

Fig. 2.
Fig. 2.

Defocused MTFs of (a) cubic, (b) improved-1 logarithmic, (c) improved-2 logarithmic, (d) sinusoidal, and (e) tangent masks.

Fig. 3.
Fig. 3.

Normalized integral areas of MTF of cubic, improved-1 logarithmic, improved-2 logarithmic, sinusoidal, and tangent phase masks.

Fig. 4.
Fig. 4.

Hilbert space angles of cubic, improved-1 logarithmic, improved-2 logarithmic, sinusoidal, and tangent phase masks.

Tables (1)

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Table 1. Optimum Parameters of the Five Phase Masks

Equations (7)

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fCubic(x,y)=ax3+ay3,
fImproved-1logarithmic(x,y)=sgn(x)ax2log(||x|+b|)+sgn(y)ay2log(||y|+b|),
fImproved-2logarithmic(x,y)=sgn(x)ax4log(||x|+b|)+sgn(y)ay4log(||y|+b|),
fSinusoidal(x,y)=ax4sin(bx)+ay4sin(by),
fTangent(x,y)=ax2tan(bx)+ay2tan(by).
11|HCubic(u,a,ω=0)|du=11|HImproved-1logarithmic(u,a,b,ω=0)|du=11|HImproved-2logarithmic(u,a,b,ω=0)|du=11|HSinusoidal(u,a,b,ω=0)|du=11|HTangent(u,a,b,ω=0)|du,
θ(ω)=cos1(|H(u,0)||H(u,ω)||H(u,0)||H(u,ω)|),

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