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Extensive numerical simulations have been carried out to verify the feasibility, security, and robustness of these four color image encryption schemes.A method is proposed and demonstrated to improve a diffraction grating displacement sensor to simultaneously achieve nanometer-level resolution and an extended range of operation. The method exploits the polarization phase-shifting optical path to extract two sinusoidal signals with a quadrature phase shift. The interpolation circuit is applied to nonlinearly convert two sinusoidal signal