Abstract

The degenerated performance of extend depth of field (EDoF) in wavefront coding system which using cubic phase mask is simulated. A periodical rotationally symmetric surface error structure is presented and combined with comparison the similarity of point spread function (PSF). The peak to valley (PV) error of the cubic surface is needed smaller than 15% compare with the sag of the cubic surface for low period error existed.

© 2009 Optical Society of America

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References

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  10. F. Yan, L. G. Zheng, and X. J. Zhang, "Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology," Opt. Eng. 47, 8 (2008).
  11. H. Dagnall, Exploring Surface Texture (Rank Taylor Hobson, 1980), Chap. 3.
  12. J. W. Goodman, Introduction of Fourier Optics (Stanford University, 1968), Chap. 4.

2008

F. Yan, L. G. Zheng, and X. J. Zhang, "Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology," Opt. Eng. 47, 8 (2008).

2007

2006

E. R. DowskiJr, "Wavefront coding for mobile phone imaging," Photon. Spectra 40, 56-58 (2006).

T. Hellmuth, "Spatial imaging with wavefront coding and optical coherence tomography," Adv. Atomic Molec. Opt. Phys. 53, 105-138 (2006)

2000

1999

1995

Cathey, W. T.

Chen, Y. P.

Dowski, E. R.

Fainman, Y.

Ford, J. E.

Hellmuth, T.

T. Hellmuth, "Spatial imaging with wavefront coding and optical coherence tomography," Adv. Atomic Molec. Opt. Phys. 53, 105-138 (2006)

Johnson, G. E.

Morrison, R. L.

Neifeld, M. A.

Rutkowski, J.

Silveira, P. E. X.

Stack, R. A.

Tamayo, I.

Tremblay, E. J.

Tucker, S. C.

Yan, F.

F. Yan, L. G. Zheng, and X. J. Zhang, "Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology," Opt. Eng. 47, 8 (2008).

Ye, Z.

Yu, F. H.

Zhang, W. Z.

Zhang, X. J.

F. Yan, L. G. Zheng, and X. J. Zhang, "Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology," Opt. Eng. 47, 8 (2008).

Zhao, T. Y.

Zheng, L. G.

F. Yan, L. G. Zheng, and X. J. Zhang, "Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology," Opt. Eng. 47, 8 (2008).

Adv. Atomic Molec. Opt. Phys.

T. Hellmuth, "Spatial imaging with wavefront coding and optical coherence tomography," Adv. Atomic Molec. Opt. Phys. 53, 105-138 (2006)

Appl. Opt.

Opt. Eng.

F. Yan, L. G. Zheng, and X. J. Zhang, "Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology," Opt. Eng. 47, 8 (2008).

Opt. Express

Opt. Lett.

Photon. Spectra

E. R. DowskiJr, "Wavefront coding for mobile phone imaging," Photon. Spectra 40, 56-58 (2006).

Other

H. Dagnall, Exploring Surface Texture (Rank Taylor Hobson, 1980), Chap. 3.

J. W. Goodman, Introduction of Fourier Optics (Stanford University, 1968), Chap. 4.

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Figures (8)

Fig. 1.
Fig. 1.

X and Y direction error structure of a manufactured phase mask measured by UA3P

Fig. 2.
Fig. 2.

The demonstration of a surface error which compose by two periods with different amplitude, the low period is 1.0 with amplitude is 1.0, and high period is 10 with amplitude 0.1.

Fig. 3.
Fig. 3.

Correlation coefficient curve of PSF at different defocus aberration for coding parameter (α=20), period error and 1 um PV structure exist and compare with no coding and ideal (no error existed) wavefront coding system.

Fig. 4.
Fig. 4.

Correlation coefficient curve of PSF at different defocus aberration for coding parameter (α=40), period error and 1 um PV structure exist and compare with no coding and ideal (no error existed) wavefront coding system.

Fig. 5.
Fig. 5.

Correlation coefficient curve of PSF at different defocus aberration for coding parameter (α=60), period error and 1u m PV structure exist and compare with no coding and ideal (no error existed) wavefront coding system.

Fig. 6.
Fig. 6.

Correlation coefficient curve of PSF at different defocus aberration for coding parameter (α=90), period error and 1 um PV structure exist and compare with no coding and ideal (no error existed) wavefront coding system.

Fig. 7.
Fig. 7.

Correlation coefficient curve of PSF at different defocus aberration for coding parameter (α=90), with 1.0 period and 15% PV error exist and compare with no coding and ideal (no error existed) wavefront coding system.

Fig. 8.
Fig. 8.

Correlation coefficient curve of PSF at different defocus aberration for coding parameter (α=40), with period 1.5, 1.1998um PV error and 0.2534um PV error along x and y direction and compare with no coding and ideal (no error existed) wavefront coding system.

Tables (2)

Tables Icon

Table 1. PV and RMS error of the phase mask (α= 40) measured by UA3P

Tables Icon

Table 2. Ratio of EDoF system with different period and 1um PV error structure exist in different phase mask

Equations (6)

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error ( x , y ) = n = 0 [ p v nx 2 · sin ( nπx + φ nx ) + p v my 2 · sin ( mπy + φ m y ) ] ,
z ( x , y ) = α ( x 3 + y 3 ) ,
h ( x , y ) = circ ( x , y ) · Exp { i [ α ( x 3 + y 3 ) + 2 π λ Z 2 x 2 + y 2 + 2 π λ Error ( x , y ) ] } ,
PSF ( x , y ) = { h } · { h } * ,
r = m n ( A mn A ̄ ) ( B mn B ̄ ) [ m n ( A mn A ) 2 ] [ m n ( B mn B ) 2 ] ,
ratio = z 2 0.25 0.25 .

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