Abstract

The point spread function (PSF) characteristics of wavelengths for a wavefront coding imaging system are investigated. Although the phase delayed by the mask changes with wavelength, the shape of the PSF is nearly invariant with respect to wavelength. However, the position of the PSF shifts with axial chromatic aberration. If the wideband light is separated into several channels and separated channel images are restored using the same filter, then color traces may be observed in the recombined color images.

© 2011 Optical Society of America

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References

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2011 (1)

2010 (3)

2007 (1)

1999 (1)

1998 (1)

1996 (1)

1995 (1)

Barwick, S.

Cathey, W. T.

Chen, Y.

Deaver, D. M.

Demenikov, M.

Diaz, F.

Dowski, E. R.

Findlay, E.

Goudail, F.

Harvey, A. R.

Huignard, J.

Li, Y.

Loiseaux, B.

Taylor, M. G.

Tucker, S. C.

van der Gracht, J.

Wach, H. B.

Ye, Z.

Yu, F.

Zhang, W.

Zhao, H.

Zhao, T.

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Figures (5)

Fig. 1
Fig. 1

PSFs of F and C light.

Fig. 2
Fig. 2

Shift between PSF peak positions of d and C light with ACA and that of the in-focus PSF at λ F

Fig. 3
Fig. 3

Hilbert space angles between the in- focus F light PSF and the PSFs of d or C light with the presence of ACA, where the three parameters in the parentheses of the legend are C or d light, the amount of ξ (in micrometers) and pixel width (in micrometers), respectively.

Fig. 4
Fig. 4

Simulation results for F, d, and C light with Δ ω = 0 , 2 λ F , and 4 λ F , respectively. (a)–(c) Restored image of F, d, and C light using the filter calculated from the in-focus F light PSF; (d) the recombined color image from (a)–(c); (e) repeat of the reconstruction in (d) but taking into account the PSF shifts; (f) the recombined color image from the monochromatic cases using multiple filters derived from the in-focus C, d, and F light PSFs, respectively.

Fig. 5
Fig. 5

Enlarged version of simulation results. The first and third columns are images recombined in a manner similar to that in Fig. 4d; the other two columns are images done as in Fig. 4e. The amount of ξ, PW, and PSF shift of d and C light for each image are listed, respectively, in the following parentheses, where the units of the parameters are in micrometers: (a) (2, 2, 0.35, 1.99), (b) (2, 2, 0, 0), (c) (2, 4, 0.35, 1.99), (d) (2, 4, 0, 0), (e) (4, 2, 0.02 , 0.84), (f) (4, 2, 0, 0), (g) (4, 4, 0.02 , 0.84), and (h) (4, 4, 0, 0).

Tables (1)

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Table 1 Imaging System Parameters

Equations (8)

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ϕ ( x , λ ) = exp [ j 2 π ξ ( x / L ) 3 / λ ] ,
Δ ω = L 2 ( f λ f λ ) / ( 2 f λ f λ ) .
q ( x , λ ) = Rect ( x / L ) exp [ j 2 π k λ ξ ( x / L ) 3 / λ ] × exp [ j 2 π ( ω 20 + Δ ω ) ( x / L ) 2 / λ ] ,
h ( u , λ ) = | L L exp { j 2 π λ [ k λ ξ x 3 L 3 + ( ω 20 + Δ ω ) x 2 L 2 u x d i ] } d x | 2 ,
y ( u ) = 8 π ( ω 2 + 3 L k λ ξ u / d i ) 3 / 2 / [ 27 λ ( k λ ξ ) 2 ] .
h ( u , λ ) = { λ [ 1 + sin ( y ( u ) ) ] 2 ( ω 2 + 3 L k λ ξ u / d i ) 1 / 2 d i ω 2 3 L k λ ξ u d i ( 3 k λ ξ 2 ω ) L λ 4 ( ω 2 + 3 L k λ ξ u / d i ) 1 / 2 d i ( 3 k λ ξ 2 ω ) L < u d i ( 3 k λ ξ + 2 ω ) L 0 others .
u peak = 3 d i ( 2 λ 2 k λ ξ ) 1 / 3 / ( 8 L ) d i ω 2 / ( 3 L k λ ξ ) .
Δ u peak = 3 d i ( 2 ξ ) 1 / 3 ( k λ 1 / 3 λ 2 / 3 λ 2 / 3 ) 8 L d i ( ω 2 k λ ω 20 2 ) 3 L k λ ξ .

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