Topographic spatial resolution enhancement of coherence scanning interferometry based on extended Fourier optics model through pupil modulation

Lateral resolving power is a critical performance metric in coherence scanning interferometry (CSI) for characterizing surface form and texture. Pupil modulation enhances lateral resolving power by reducing the Airy disk size within the point spread function (PSF). In modern metrology, the instrument transfer function (ITF) serves as a comprehensive metric for evaluating lateral resolving power. This study presents an extended Fourier optics model integrated for CSI to simulate surface topography measurements, in which the ITF can be computed for various central obscuration ratios, taking the step-height surface as the sample. Under linear response conditions, the ITF is approximately equal to the corresponding modulation transfer function (MTF) at each central obscuration ratio. Comparisons of the MTF across different central obscuration ratios indicate that pupil modulation enhances the ITF in the high spatial frequency range. As an example, direct measurement of the ITF on a step-height surface validates the accuracy of our model predictions, while experiments with a Siemens star further demonstrate that pupil modulation improves topographic spatial resolution at high spatial frequencies.