Abstract
The Collins diffraction transform (CDT) describes the optical wave diffraction from the generic paraxial optical system. The CDT has as special cases the diffraction domains given by the Fourier, Fresnel and fractional Fourier transforms. In this paper, we propose to describe the optical double random phase encoding (DRPE) using a nonlinear joint transform correlator (JTC) and the CDT. This new description of the nonlinear JTC-based encryption system using the CDT covers several optical processing domains, such as Fourier, Fresnel, fractional Fourier, extended fractional Fourier and Gyrator domains, among others. The maximum number of independent design parameters or new security keys of the proposed encryption system using the CDT increases three times in comparison with the same encryption system that uses the Fourier transform. The proposed encryption system using the CDT preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The viability of this encryption system is verified and analysed by numerical simulations.
Highlights
The double random phase encoding (DRPE) proposed by Réfrégier and Javidi is a well known and highly successful system for optical image encryption [1,2,3,4]
We present a novel extension of the nonlinear joint transform correlator (JTC)-based encryption system [16] to the Collins diffraction domain (CDD), with the purpose of increasing the security of the system and representing several optical processing domains, such as Fourier, Fresnel, fractional Fourier, extended fractional Fourier and Gyrator domains, among others, for the encryption and decryption systems by using the Collins diffraction transform (CDT) formalism
We have presented a novel extension of the image encryption system based on a nonlinear JTC architecture to the CDD
Summary
The double random phase encoding (DRPE) proposed by Réfrégier and Javidi is a well known and highly successful system for optical image encryption [1,2,3,4]. Other modifications of the JTC architecture in different optical processing domains to implement the DRPE system have been proposed by several authors [15,16,17,18,19,20,21,22] These new proposals simplify the optical setup of the encryption system, increase the security of the encryption system and improve the quality of the decrypted image. We present a novel extension of the nonlinear JTC-based encryption system [16] to the CDD, with the purpose of increasing the security of the system and representing several optical processing domains, such as Fourier, Fresnel, fractional Fourier, extended fractional Fourier and Gyrator domains, among others, for the encryption and decryption systems by using the CDT formalism. Optical Image Encryption System Based on a Nonlinear JTC Architecture in the Collins
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