Allowable deviations in index profiles, dopant distributions, and concentration dependence of diffusion coefficients are determined for collimating microlenses. Examples of high (and low) numerical aperture lenses are given for silver/sodium (and lithium/sodium) ion exchanges. Using the full lens aperture, one can ensure diffraction-limited performance only when the index is measured to within 1.0 x 10(-4) (4.3 x 10(-5)) of the optimum values. Fabrication tolerances for diffraction-limited performance over 80% of the numerical aperture are expressed in terms of the concentration-dependent diffusion coefficient, which typically must be held to within +/-4.7% (+/-11.5%) of ideal values.

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