## Abstract

A specially designed phase mask embedded in the lens assembly of an imaging system is shown to provide different response in the three major color bands, R, G and B of a detector array. Each channel provides optimal performance for different depth of field regions, such that the three channels jointly provide an imaging system with wide depth of field. The approach is useful in particular for Barcode imagers.

© 2010 OSA

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### Equations (12)

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(1)
$${P}^{\prime}(u,v)=P(u,v)\text{\hspace{0.17em}}\mathrm{exp}[j\psi ({u}^{2}+{v}^{2})]$$
(2)
$$\psi =\frac{\pi {D}^{2}}{4\lambda}\left(\frac{1}{{s}_{obj}}+\frac{1}{{s}_{img}}-\frac{1}{f}\right)$$
(3)
$$COF\equiv {\nu}_{c}=\frac{D}{2\lambda {R}_{gs}}$$
(4)
$$\xi =\frac{{v}_{x}}{{\nu}_{c}},\text{\hspace{1em}}\eta =\frac{{v}_{y}}{{\nu}_{c}}$$
(5)
$${v}_{x}=\frac{u\left(D/2\right)}{\lambda {R}_{gs}},\text{\hspace{1em}}{v}_{y}=\frac{v\left(D/2\right)}{\lambda {R}_{gs}}$$
(6)
$$OTF(\xi ,\eta )=\frac{{\displaystyle \underset{\Omega}{\iint}P\left(u+\frac{\xi}{2};v+\frac{\eta}{2}\right){P}^{\ast}\left(u-\frac{\xi}{2};v-\frac{\eta}{2}\right)\text{\hspace{0.17em}}\mathrm{exp}[j\psi 2\text{\hspace{0.17em}}(u\text{\hspace{0.17em}}\xi +v\text{\hspace{0.17em}}\eta )]\text{\hspace{0.17em} \hspace{0.17em} d}u\text{d}v}}{{\displaystyle \underset{\Omega}{\iint}{\left|P\left(u;v\right)\right|}^{2}\text{\hspace{0.17em} d}u\text{d}v}}$$
(7)
$$\psi \propto \left(\frac{1}{\lambda}\right)$$
(8)
$$\frac{{\psi}_{{\lambda}_{1}}}{{\psi}_{{\lambda}_{2}}}=\frac{{\lambda}_{2}}{{\lambda}_{1}}$$
(9)
$${\phi}_{\lambda}=\frac{2\pi h[n(\lambda )-1]}{\lambda}$$
(10)
$$h=\frac{{\lambda}_{B}}{n\left({\lambda}_{B}\right)-1}\frac{{\phi}_{{\lambda}_{B}}}{2\pi}$$
(11)
$$\frac{{\varphi}_{{\lambda}_{1}}}{{\varphi}_{{\lambda}_{2}}}=\frac{{\lambda}_{2}}{{\lambda}_{1}}\text{\hspace{0.17em}}\frac{n({\lambda}_{1})-1}{n({\lambda}_{2})-1}\cong \frac{{\lambda}_{2}}{{\lambda}_{1}}$$
(12)
$$\frac{CO{F}_{{\lambda}_{1}}}{CO{F}_{{\lambda}_{2}}}=\frac{\lambda 2}{{\lambda}_{1}}$$