Abstract

A recent publication [Opt. Express 16, 20540–20561 (2008)] presented a way for extending the depth of field (DOF) of imaging systems using a binary phase mask made of annular rings delivering a π-phase shift. Usually, such masks are designed with respect to some central wavelength; they will thus deliver a different phase shift for other wavelengths. This issue is reexamined in this paper, where it is shown that polychromatic masks that deliver the same phase shift over a wide range of wavelengths provide improved imaging over an extended DOF. The simulation results demonstrate the improved performance of imaging systems using such masks.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. D. Parikh and G. Jancke, “Localization and segmentation of a 2D high capacity color barcode,” presented at IEEE Workshop on Applications of Computer Vision, Copper Mountain, CO (2008).

2012 (1)

2008 (1)

2001 (1)

1998 (1)

1996 (1)

1995 (1)

Arieli, Y.

Ben-Eliezer, E.

Cathey, W. T.

Dowski, E. R.

Ebstein, S. M.

Eisenberg, N.

Gan, F.

Haim, H.

Jancke, G.

D. Parikh and G. Jancke, “Localization and segmentation of a 2D high capacity color barcode,” presented at IEEE Workshop on Applications of Computer Vision, Copper Mountain, CO (2008).

Konforti, N.

Marom, E.

Milgrom, B.

Noach, S.

Ozeri, S.

Parikh, D.

D. Parikh and G. Jancke, “Localization and segmentation of a 2D high capacity color barcode,” presented at IEEE Workshop on Applications of Computer Vision, Copper Mountain, CO (2008).

Wang, H.

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Figures (15)

Fig. 1.
Fig. 1.

DOF phase mask. The phase ring (yellow) provides a π-phase shift.

Fig. 2.
Fig. 2.

MTF curves for clear aperture (calculated for RGB wavelengths) at (top) ψ=0, (center) ψG=3, and (bottom) ψG=6. The dashed line indicates the acceptable minimum contrast value chosen here to be 5%.

Fig. 3.
Fig. 3.

MTF curves for MPM (calculated for RGB wavelengths) at (top) ψ=0, (center) ψG=3, and (bottom) ψG=6. The dashed line indicates the acceptable minimum contrast value chosen here to be 5%.

Fig. 4.
Fig. 4.

RGB Chess–Bar template imaged with a clear aperture system for ψ=0. The horizontal dashed lines indicate the location of the traces displayed at the left.

Fig. 5.
Fig. 5.

RGB Chess–Bar template imaged with a clear aperture system for ψG=6. The horizontal dashed lines indicate the location of the traces displayed at the left.

Fig. 6.
Fig. 6.

RGB Chess–Bar template imaged with MPM incorporated for ψ=0. The horizontal dashed lines indicate the location of the traces displayed at the left.

Fig. 7.
Fig. 7.

RGB Chess–Bar template imaged with MPM incorporated for ψG=6. The horizontal dashed lines indicate the location of the traces displayed at the left.

Fig. 8.
Fig. 8.

MTF curves for PCM (calculated for RGB wavelengths) at (top) ψ=0, (center) ψG=3, and (bottom) ψG=6. The dashed line indicates the acceptable minimum contrast value chosen here to be 5%.

Fig. 9.
Fig. 9.

Cutoff frequency versus ψ for (top) red, (center) green, and (bottom) blue bands obtained with clear aperture (solid line), with MPM incorporated (dashed line), and with PCM incorporated (dotted line).

Fig. 10.
Fig. 10.

RGB Chess–Bar template imaging with PCM ψ=0. The horizontal dashed lines indicate the location of the traces displayed at the left.

Fig. 11.
Fig. 11.

RGB Chess–Bar template imaging with PCM, ψG=6 (for green). The horizontal dashed lines indicate the location of the traces displayed at the left.

Fig. 12.
Fig. 12.

PCM cross section. Both parts of the mask have the same ring radii, while in the positive mask (blue), the ring is etched into the substrate, and in the negative mask (green), the surrounding area is etched.

Fig. 13.
Fig. 13.

PCM for the visible region phase shift profile. (Top) positive, negative, and joint phase shift, (bottom) zoom-in on the joint phase shift.

Fig. 14.
Fig. 14.

HCCB example.

Fig. 15.
Fig. 15.

Imaging simulation results of a sample HCCB for ψG=6 condition for a (left) clear aperture with (center) MPM incorporated and with (right) PCM incorporated.

Tables (2)

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Table 1. First Horizontal Group (ν=0.17νmax) Contrast Values

Tables Icon

Table 2. Last Horizontal Group (ν=0.3νmax) Contrast Values

Equations (9)

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ψ=πR2λ(1zimg+1zobj1f),
maxrminψDOF[ν:MTF(ν,r,ψ)=Cd],
φmask=2πλh(n(λ)1),
maxrminψDOF,λ{λi}[ν:MTF(λ,ν,r,ψ)=Cd],
φMPM=2πλh(n(λ)1).
φPCM=φ1+φ2=2πλh1(n1(λ)1)+2πλh2(n2(λ)1).
minh1,h2[λ1λ2(φPCM(λ,n1,h1,n2,h2)φdesired)2dλ],
φPCM=2πλh1[(n1(λ)+α(1n2(λ)))1],
φPCM=2πλh1[n*(λ)1],

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