Single-beam image encryption using spatially separated ciphertexts based on interference principle in the Fresnel domain

A new optical security system for image encryption based on optical interference principle and translation property of Fresnel transform (FrT) has been proposed in this article. The algorithm of this proposal is specially designed for single-beam optical decryption and can thoroughly resolve the silhouette problem existing in the previous interference-based scheme. Different from earlier schemes using interference of phase-only masks (POMs), the inverse FrT of primitive image is digitally decomposed into a random POM and a complex field distribution. Information associated with the primitive images can be completely smoothed away by the modulation of this random POM. Through the translation property of FrT, two linear phase-only terms are then used to modulate the obtained random POM and the complex distribution, respectively. Two complex ciphertexts are generated by performing digital inverse FrT again. One cannot recover any visible information of secret image using only one ciphertext. Moreover, to recover the primitive image correctly, the correct ciphertexts must be placed in the certain positions of input plane of decryption system, respectively. As additional keys, position center coordinates of ciphertexts can increase the security strength of this encryption system against brute force attacks greatly. Numerical simulations have been given to verify the performance and feasibility of this proposal. To further enhance the application value of this algorithm, an alternative approach based on Fourier transform has also been discussed briefly.