Fabrication tolerances in geodesic lenses: A rule of thumb

A rule of thumb has been derived for geodesic lenses which allows one to evaluate, with a good precision, the change of the focal length as a function of the depth change
\Delta z_0
due to fabrication errors. This rule of thumb has been tested on a large number of perfect geodesic lenses designed following a relatively simple analytic procedure. Considering the use of geodesic lenses in an integrated data processor with a high resolution detector array, the thumb rule can be used with an accuracy particularly good to evaluate the increase of the beam spot size at a prespecified focal line, due to the error
\Delta z_0
. It has been confirmed that, in order to build lenses with resolution capability compatible with a
12-{\mu}
m spacing of the detector array, we have to get a precision control of
\sim 0.5 {\mu}
m during the fabrication. Such a tolerance seems to be achievable at least in the near future.