Ill-posed inverse problem in diffraction optics. tolerance analysis of diffractive lenses and gratings

A method is proposed for the prediction of deviations of the phase polynomial coefficients of diffractive optical elements from their nominal values due to fabrication errors. This problem represents an ill-posed inverse problem in diffraction optics. Its solution is based on the regularization technique resulting in an approximate stable (rather than exact but unstable) solution of the inverse problem. The proposed method can become a useful tool, providing optical designers with a possibility of including these deviations into the tolerance analysis of optical devices.