Evaluation of Shack-Hartmann wavefront sensing artifacts due to reflectivity variations across thick layered samples using the discrete Fourier transform.

Abstract

Multiple wavefronts originating from axially and/or transversely displaced light sources are known to introduce artifactual aberrations in Shack-Hartmann wavefront sensors (SHWSs). These aberrations are primarily dominated by defocus, followed by spherical aberration and coma, depending on whether an on-axis or off-axis binary transmission pupil mask is used in the illumination path. In an earlier study, such artifactual aberrations-caused by multiple reflections from displaced sources-were predicted using rigorous diffraction-theory-based integral calculations. However, such calculations are computationally intensive, and were therefore limited to modeling only two reflecting layers. Moreover, the low Fresnel number associated with SHWS lenslets introduces a focal shift, complicating the application of the discrete Fourier transform (DFT). Here, we showed that, with an appropriate coordinate transformation, the diffraction integrals that account for focal shift can be expressed as Fourier transform integrals. Using this approach to model human retinal reflectivity from 75 axially separated layers, we demonstrate a computational speed-up of over three orders of magnitude. Our results reveal that wavefront error in multilayered structures is fundamentally sensitive to both retinal architecture and centroiding strategy. While dynamic beacon positioning remains a primary mitigation strategy, small on-axis illumination paired with polarizers offers a robust alternative for substantially minimizing these artifactual aberrations. These findings have broad implications for optical systems requiring precise wavefront sensing in volumetric samples, including microscopy, retinal imaging, and astronomy.