General phase quantization approach for diffractive optical elements

We present a novel optimal phase quantization method for phase-only diffractive optical elements (DOEs) by taking into account both amplitude and phase information that are able to generate an arbitrary target pattern. In our approach, the MSE function was modified in which both the amplitude and the phase of the perfect wavefront were combined into the probability density function. The amplitude and the phase information could be obtained from a phase transmittance of a transparent lens incident by a Gaussian beam (providing the amplitude information), for example, or be directly constructed from the inverse Fourier transform of an arbitrary target pattern. By using the modified MSE function, the influence of the phase elements corresponding to larger amplitude values was emphasized and the optimal phase levels were calculated appropriately. Significant improvement was achieved for the construction of two-, four-, and eight-level Fresnel zone plates with a focal length of 8 m and an aperture of 6.2 mm, which was incident by a Gaussian beam with a 1/e-width of 1.4 mm were calculated. By use of the proposed algorithm, efficiency improved by 26.4% and SNR by 18.2% over the uniform quantization method for binary DOE s.