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文库首页大数据算法与数据结构级联迭代傅里叶变换算法在光学安全中的应用英文文献及翻译（可编辑）.doc

级联迭代傅里叶变换算法在光学安全中的应用英文文献及翻译（可编辑）.doc

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级联迭代傅里叶变换算法在光学安全中的应用英文文献及翻译（可编辑）.doc

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级联迭代傅里叶变换算法在光学安全中的应用英文文

献及翻译

A cascaded iterative Fourier transform algorithm

for optical security applications

Abstract:A cascaded iterative Fourier transform CIFT algorithm is

presented for optical security applications. Two phase-masks are

designed and located in the input and the Fourier domains of a 4-f

correlator respectively, in order to implement the optical encryption

or authenticity veri"cation. Compared with previous methods, the

proposed algorithm employs an improved searching strategy:

modifying the phase-distributions of both masks synchronously as

well as enlarging the searching space. Computer simulations show

that the algorithm results in much faster convergence and better

image quality for the recovered image. Each of these masks is

assigned to di%erent person. Therefore, the decrypted image can be

obtained only when all these masks are under authorization. This

key-assignment strategy may reduce the risk of being intruded.

Key words: Optical security ? optical encryption ? cascaded

iterative Fourier transform algorithm

1. Introduction

Optical techniques have shown great potential in the "eld of

information security applications. Recently Réfrégier and Javidi

proposed a novel double-random-phase encoding technique, which

encodes a primary image into a stationary white noise. This

technique was also used to encrypt information in the fractional

Fourier domain and to store encrypted information holographically.

Phase encoding techniques were also proposed for optical

authenticity veri"cation Wang et al and Li et al proposed another

method for optical encryption and authenticity veri"cation. Unlike

the techniques mentioned above, this method encrypts information

completely into a phase mask, which is located in either the input

or the Fourier domain of a 4-f correlator. For instance, given the

prede"nitions of a signi"cant image fx, y as the desired output and

a phase-distribution expjbu, v in the Fourier domain, it’s easy to

optimize the other phase function expjpx, y with a modi"ed

projection onto constraint sets

POCS algorithm [10]Therefore the image fx, y is encoded

successfully into expjpx, y

with the aid of expjbu, v. In other words, the "xed phase expjbu,

v serves as the lock while the retrieved phase expjpx, y serves as

the key of the security system. To reconstruct the original

information, the phase functions expjpx, y and expjbu, v must

match and be located in the input and the Fourier plane

respectively. Abookasis et al implemented this scheme with a joint

transform correlator for optical veri"cation

However, because the key expjpx, y contains information of

the image fx, y and the

lock expjbu, v, and the 4-f correlator has a character of linearity,

it is possible for the intruder to "nd out the phase-distribution of the

lock function by statistically analyzing the random characters of the

keys if the system uses only one lock for di%erent image. In order to

increase the secure level of such system, one approach is to use

di%erent lock function for di%erent image. Enlarging the key space is

another approach to increase the secure level. It can be achieved by

encrypting images in the fractional Fourier domain; as a result, the

scale factors and the transform order o%er additional keys. On the

other hand, note that the phase-mask serves as the key of the

system, enlarging the key space can be achieved by encoding the

target image into two or more phase masks with a modi"ed POCS

algorithm. Chang et al have proposed a multiple-phases retrieval

algorithm and demonstrated that an optical security system based

on it has higher level of security and higher quality for the

decrypted image. However, this algorithm retrieves only one phase-

distribution with a phase constraint in each iteration. As a result, the

masks are not so consistent and may a%ect the quality of the

recovered image In the present paper, we propose a modi"ed POCS

algorithm that adjusts the distributions of both phase-masks

synchronously in each iteration. As a result, the convergent speed of

the iteration process is expected to signi"cantly increase. And the

target image with much higher quality is expected to recover

because of the co-adjusting of the two masks during the iteration

process. When the iteration process is "nished, the target image is

encoded into the phase-masks successfully. Each of these masks

severs as the key of the security system and part of the encrypted

image itself as well. Moreover, the algorithm can be extended to

generate multiple phase-masks for arbitrary stages correlator. To

acquire the imum security, each key is assigned to di%erent

authority so that the decryption cannot be performed but being

authorized by all of them. This key-assignment scheme is especially

useful for military and government applications

The algorithm description is presented in Section 2. Computer

simulation of this algorithm and the corresponding discuss are

presented in Section 3

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