Application of the fractional Fourier transform for decryption in experimental optical cryptosystems

Abstract

In this contribution, we introduce a new practical approach to apply the fractional Fourier transform in the modelling of two optical systems: free space propagation and a single lens processor. This formulation presents a simple way to stablish a direct relationship between physical parameters of the two optical systems and a real-valued fractional order. Furthermore, we employ and compare two numerical methods for evaluating the fractional Fourier transform: the convolution and the Fresnel transform. Consequently, we apply this innovative approach to the digital decryption process in an opto-digital joint transform correlator cryptosystem, considering both the free space propagation and the single lens processor variants. We analyse both numerically and experimentally encrypted data to support our proposed method and to investigate the sensitivity of the decryption process with the fractional order. Notably, we obtain similar decryption results for both numerically and experimentally encrypted objects, demonstrating excellent agreement between the theoretical model, the numerical test, and the experiment.