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A novel method for image encryption under spatially incoherent illumination is proposed. The LED array is used as the spatially incoherent source. Both the encryption process and decryption process are numerically simulated. Experiments are carried out to demonstrate the basic ideal of the proposed method. The incoherent light is modulated by the spatial light modulator on the input plane as the input image to be encrypted. Then a random phase only mask is used as the key to encode the image, finally a Fourier lens is adopted to image the encrypted image on the output plane. The encrypted intensity distribution is recorded by a CCD. In the numerical simulations, the random phase only mask is generated by a rand function. The incoherent image is composed of many source points, and any two points of these sources are spatially incoherent, but each point is self-spatially coherent. Under this property, the point spread function for the encryption system can be considered as the interference of two beams, one is the spherical beam and the other is the random phase beam. Once the point spread function is given, the system’s optical transfer function can be calculated easily. Then the encryption system can be considered as a decryption system, and the output image is the same as the original image. The encrypted image can be calculated with the system’s optical transfer function and the output image. The random phase mask, the distance between the random phase mask and the SLM, and the wavelength of the laser can be seen as the keys of the encryption systems. Only when all these parameters are correct, can one get the right decrypted image. The factors which could affect the practical experiment, such as quantization noise and displacement tolerances are also investigated. Compared with the conventional coherent encryption system, the incoherent encryption system proposed in this paper is free of the flaws of the optical elements, the dust particles on the elements, and other unstable factors of the environment. What’s more, the cost of the incoherent encryption system is lower since only a phase only mask and a imaging lens are used.
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