Optical interference-based image encryption using circular harmonic expansion and spherical illumination in gyrator transform domain

In this paper, a new optical interference-based encryption method using off-axis circular harmonic component (CHC) expansion and iterative phase retrieval algorithm in gyrator transform (GT) domain is proposed. Off-axis CHC expansion is employed to divide the inverse GT spectrum of primitive image into two parts: the zero-order CHC and the sum of the other CHCs. The sum term of CHCs is further encrypted into a complex image whose amplitude constraint is devised to be the amplitude of zero-order CHC by the iterative retrieval GT algorithm. The amplitude part of CHC is the final ciphertext which has rotation-symmetric distribution. Three phase-only keys, the main keys of this proposal, are also calculated during the digital encryption process. To recover the primitive image correctly, two identical ciphertexts placed in the two interference branch should be illuminated by two spherical waves with required parameters (wavelength and radius). Moreover, rotational center of ciphertexts must be placed in a predefined position, which is off the optical axis. The transform angles of GTs, the propagation parameters of spherical waves and the relative position of rotational center of ciphertext are sensitive additional keys for correct retrieval. Numerical simulation tests have been carried out to verify the effectiveness of the proposed scheme.