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"Fabrication of diffractive-optical elements by using halftone gray-scale masks", by Jinsong Liu, Andrew. J. Waddie and M. R. Taghizadeh, Optics Communications, 208(1-3): 31-40, 2002.

The fabrication of diffractive optical elements (DOEs), especially the DOEs with variable spatial frequency features, by using halftone gray-scale masks is investigated. Three aspects of the DOEs profile infidelity have been studied. The first two infidelities are, with the reduced periods, the decrease in maximum depth in photoresist and the increase in relative transition width between adjacent ramps. Imaging error is found to be responsible for the infidelities. The infidelities can be reduced by using a certain aperture or a larger photoreduction, while proximity-printing nearly eliminates the infidelites. The third infidelity is the uncertainty of the nonlinearity between the gray values in mask data and the final depth in photoresist. Both the nonlinearity and the uncertainty of the nonlinearity can be reduced to some extent by using a reduced gamut of gray values of 0.3-0.8 and an appropriate exposure dose from the primary mask to the secondary mask before the compensation function is finally measured and imposed on the gray-scale values.

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