Linear systems characterization of the topographical spatial resolution of optical instruments

• Peter de Groot, Zoulaiha Daouda, Leslie Deck, and Xavier Colonna de Lega
• received 02/26/2024; accepted 04/29/2024; posted 04/29/2024; Doc. ID 521868
• Abstract: Lateral resolving power is a key performance attribute for Fizeau interferometers,confocal microscopes, interference microscopes, and other instruments that measure surfaceform and texture. Within a well-defined scope of applicability, limited by surface slope, texture,and continuity, a linear response model provides a starting point for characterizing spatialresolution under idealized conditions. Presently, the instrument transfer function (ITF) is astandardized way to quantify linear response to surface height variations as a function of spatialfrequency. Here we build upon the ITF idea and introduce terms, mathematical definitions, andappropriate physical units for applying a linear systems model to surface topographymeasurement. These new terms include topographical equivalents of the point spread, linespread, and edge spread functions, as well as a complex-valued transfer function that extendsthe ITF concept to systems with spatial-frequency dependent topography distortions. As anexample, we consider the experimental determination of lateral resolving power of a coherencescanning interference microscope using a step-height surface feature to directly measure theITF. The experiment illustrates the proposed mathematical definitions and provides a directcomparison to theoretical calculations performed using a scalar diffraction model.