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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  1. E. R. Dowski and W. T. Cathey, Appl. Opt. 34, 1859 (1995).
    [CrossRef] [PubMed]
  2. W. Z. Zhang, Y. P. Chen, T. Y. Zhao, Z. Ye, and F. H. Yu, Chin. Opt. Lett. 4, 515 (2006).
  3. V. P. Pauca, R. J. Plemmons, S. Prasad, T. C. Torgersen, and J. Gracht, Proc. SPIE 5205, 348 (2003).
    [CrossRef]
  4. W. Z. Zhang, Z. Ye, T. Y. Zhao, Y. P. Chen, and F. H. Yu, Opt. Express 15, 1543 (2007).
    [CrossRef] [PubMed]
  5. Q. G. Yang, J. F. Sun, and L. R. Liu, Chin. Phys. Lett. 23, 2080 (2006).
    [CrossRef]
  6. K. Kubala, E. R. Dowski, and W. T. Cathey, Opt. Express 11, 2102 (2003).
    [CrossRef] [PubMed]
  7. E. R. Dowski and K. Kubala, Proc. SPIE 5299, 155 (2004).
    [CrossRef]
  8. R. W. D. Nickalls, Math. Gaz. 77, 354 (1993).
    [CrossRef]

2007 (1)

2006 (2)

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

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

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)

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

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