Fabrication tolerances and metrology requirements for ion-exchanged micro-optic lenses: What’s good enough?

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.