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"Simulation of the fabrication infidelity of diffractive-optical elements by using halftone gray-scale masks", by Jinsong Liu, Martin. J. Thomson and M. R. Taghizadeh, Optical Engineering, 42(2):334-339, 2003.

A model is set up to simulate the fabrication infidelity of diffractive-optical elements using halftone gray-scale masks. The infidelity includes, for different spatial frequencies, variations in maximum exposure depth in photoresist, relative transition width between adjacent ramps, and nonlinearity. The attenuation of the modulation transfer function (MTF) of the fabrication system at a high spatial frequency is the main reason for all the fabrication infidelity. The component whose MTF attenuates most in the fabrication system is generally photoreduction.

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