Optimal quantization by use of an amplitude-weighted probability-density function for diffractive optical elements.

We present a method for determining the optimal quantitized phase levels for phase-only diffractive optical elements by taking into account a modified probability-density function (PDF). This modified PDF was obtained from the PDF of the phase distribution weighted by the incident amplitude distribution. We applied the proposed method to construct a multilevel Fresnel zone plate with a focal length of 8 m and a diameter of 6.2 mm upon which was incident a Gaussian beam with a 1/e width of 1.4 mm. The efficiency of a binary design was improved by 26.4% and the signal-to-noise ratio by was improved by 18.2% compared with those obtained by the uniform quantization method.