## Abstract

In this paper, we propose a novel method for image encryption by employing the diffraction imaging technique. This method is in principle suitable for most diffractive-imaging-based optical encryption schemes, and a typical diffractive imaging architecture using three random phase masks in the Fresnel domain is taken for an example to illustrate it. The encryption process is rather simple because only a single diffraction intensity pattern is needed to be recorded, and the decryption procedure is also correspondingly simplified. To achieve this goal, redundant data are digitally appended to the primary image before a standard encrypting procedure. The redundant data serve as a partial input plane support constraint in a phase retrieval algorithm, which is employed for completely retrieving the plaintext. Simulation results are presented to verify the validity of the proposed approach.

© 2014 Optical Society of America

Full Article |

PDF Article
### Equations (10)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$U(\eta ,\xi )=\frac{\mathrm{exp}(j2\pi {d}_{1}/\lambda )}{j\lambda {d}_{1}}\iint U(x,y){M}_{1}(x,y)\phantom{\rule{0ex}{0ex}}\times \mathrm{exp}[j\pi [{(x-\eta )}^{2}+{(y-\xi )}^{2}]/\lambda {d}_{1}]\mathrm{d}x\mathrm{d}y,$$
(2)
$$U(\eta ,\xi )={\mathrm{FrT}}_{\lambda}[U(x,y){M}_{1}(x,y);{d}_{1}].$$
(3)
$$I(\mu ,\nu )=|{\mathrm{FrT}}_{\lambda}[{\mathrm{FrT}}_{\lambda}\{{\mathrm{FrT}}_{\lambda}[U(x,y){M}_{1}(x,y);{d}_{1}]{\times {M}_{2}(\eta ,\xi );{d}_{2}\}{M}_{3}(p,q);{d}_{3}]|}^{2},$$
(4)
$$\rho =\frac{\text{Quantity of the redundant data}(\text{Pixels})}{\text{Quantity of the original image}(\text{Pixels})}.$$
(5)
$${U}_{n}(\mu ,\nu )={\mathrm{FrT}}_{\lambda}[{\mathrm{FrT}}_{\lambda}\{{\mathrm{FrT}}_{\lambda}[{T}_{n}(x,y){M}_{1}(x,y);{d}_{1}]\phantom{\rule{0ex}{0ex}}\times {M}_{2}(\eta ,\xi );{d}_{2}\}{M}_{3}(p,q);{d}_{3}].$$
(6)
$$\overline{{U}_{n}(\mu ,\nu )}=I{(\mu ,\nu )}^{1/2}{U}_{n}(\mu ,\nu )/|{U}_{n}(\mu ,\nu )|.$$
(7)
$$\overline{{T}_{n}(x,y)}=|{\mathrm{FrT}}_{\lambda}[{\mathrm{FrT}}_{\lambda}\{{\mathrm{FrT}}_{\lambda}[\overline{{U}_{n}(\mu ,\nu )};-{d}_{3}]{\times {M}_{3}^{*}(p,q);-{d}_{2}\}{M}_{2}^{*}(\eta ,\xi );-{d}_{1}]|}^{2},$$
(8)
$${T}_{n+1}(x,y)=RD[(x,y);\rho ]\overline{{T}_{n}(x,y)},$$
(9)
$$\text{Error}=\sum {[|{T}_{n}(x,y)|-|{T}_{n+1}(x,y)|]}^{2}.$$
(10)
$$\mathrm{CC}=\frac{E\{[{U}_{o}-E({U}_{o})][{U}_{r}-E({U}_{r})]\}}{\sqrt{E\{{[{U}_{o}-E({U}_{o})]}^{2}\}E\{{[{U}_{r}-E({U}_{r})]}^{2}\}}},$$