Abstract

The point spread function (PSF) of a wavefront coding (WFC) system with a cubic phase mask is analyzed with a wide viewing angle based on physical optics for what is believed to be the first time. Two coordinate transformations are made to generate a pupil function, from which we obtain the encoded PSF of the WFC system with defocus parameters W020 and object angles α and β. The encoded PSFs are further side extended as the object angles get wider. When αβ<0, the included angle Φ of encoded PSF will skew to an obtuse angle. When αβ=0, Φ remains orthogonal; when αβ>0, Φ will skew to an acute angle. Furthermore, the effect of skew and side extension is even symmetric about W020. As a result, the wide viewing angle has a bad effect on the imaging quality of the WFC system.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007 (1)

2006 (2)

W. Z. Zhang, Y. P. Chen, T. Y. Zhao, Z. Ye, and F. H. Yu, Chin. Opt. Lett. 4, 515 (2006).

Q. G. Yang, J. F. Sun, and L. R. Liu, Chin. Phys. Lett. 23, 2080 (2006).
[CrossRef]

2004 (1)

E. R. Dowski and K. Kubala, Proc. SPIE 5299, 155 (2004).
[CrossRef]

2003 (2)

V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
[CrossRef]

K. Kubala, E. R. Dowski, and W. T. Cathey, Opt. Express 11, 2102 (2003).
[CrossRef] [PubMed]

1995 (1)

1993 (1)

R. W. D. Nickalls, Math. Gaz. 77, 354 (1993).
[CrossRef]

Cathey, W. T.

Chen, Y. P.

Dowski, E. R.

Gracht, J.

V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
[CrossRef]

Kubala, K.

Liu, L. R.

Q. G. Yang, J. F. Sun, and L. R. Liu, Chin. Phys. Lett. 23, 2080 (2006).
[CrossRef]

Nickalls, R. W. D.

R. W. D. Nickalls, Math. Gaz. 77, 354 (1993).
[CrossRef]

Pauca, V. P.

V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
[CrossRef]

Plemmons, R. J.

V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
[CrossRef]

Prasad, S.

V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
[CrossRef]

Sun, J. F.

Q. G. Yang, J. F. Sun, and L. R. Liu, Chin. Phys. Lett. 23, 2080 (2006).
[CrossRef]

Torgersen, T. C.

V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
[CrossRef]

Yang, Q. G.

Q. G. Yang, J. F. Sun, and L. R. Liu, Chin. Phys. Lett. 23, 2080 (2006).
[CrossRef]

Ye, Z.

Yu, F. H.

Zhang, W. Z.

Zhao, T. Y.

Appl. Opt. (1)

Chin. Opt. Lett. (1)

Chin. Phys. Lett. (1)

Q. G. Yang, J. F. Sun, and L. R. Liu, Chin. Phys. Lett. 23, 2080 (2006).
[CrossRef]

Math. Gaz. (1)

R. W. D. Nickalls, Math. Gaz. 77, 354 (1993).
[CrossRef]

Opt. Express (2)

Proc. SPIE (2)

V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
[CrossRef]

E. R. Dowski and K. Kubala, Proc. SPIE 5299, 155 (2004).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Wide angle incidence scheme.

Fig. 2
Fig. 2

Encoded PSFs at different incidence angle when W 020 = 0 λ .

Fig. 3
Fig. 3

Encoded PSFs at different incidence angle when W 020 = 10 λ .

Fig. 4
Fig. 4

Enlarged view of PSF, where a , b is the length of the sides and Φ is the included angle between the sides.

Fig. 5
Fig. 5

Profile of included angle and length of sides distribution with variable object angle α and β with W 020 = 0 λ : (a) included angle, (b) length of side a, (c) length of side b.

Fig. 6
Fig. 6

Profile of angles and sides distribution varied with the defocus parameter W 020 when α = 30 ° : (a) angle distribution; (b) side distribution, where solid lines represent the length of side a; the dashed lines represent the length of side b.

Fig. 7
Fig. 7

Decoded PSFs at different incidence angle when W 020 = 0 λ .

Equations (5)

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z ( x , y ) = W r m s ( x 3 + y 3 ) + W 020 ( x 2 + y 2 ) ,
{ x = x cos θ + y sin θ cos γ + z sin θ sin γ y = x sin θ + y cos θ cos γ + z cos θ sin γ z = z cos γ y sin γ .
p z 3 + q z 2 + m z + n = 0 ,
z 1 cos γ W r m s ( A 3 + B 3 ) + W 020 ( A 2 + B 2 ) + y sin γ 1 [ 3 W r m s tan γ ( A 2 sin θ + B 2 cos θ ) + 2 W 020 tan γ ( A sin θ + B cos θ ) ] .
z [ W r m s ( cos 3 θ sin 3 θ ) cos γ ] x 3 + [ W r m s ( cos 3 θ + sin 3 θ ) ( 1 + 2 sin 2 γ ) ] y 3 + [ 3 W r m s sin θ cos θ ( sin θ cos θ ) ( 1 + sin 2 γ ) cos γ ] x y 2 + [ W 020 ( cos γ + 2 sin γ tan γ ) ] y 2 + [ 3 W r m s sin θ cos θ ( sin θ + cos θ ) cos 2 γ ] x 2 y + [ W 020 cos γ ] x 2 + y tan γ .

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