Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions
Optical Society of America. Journal A: Optics, Image Science, and Vision
We assess the validity of an extended Nijboer-Zernike approach based on recently found, Bessel series representations of diffraction integrals comprising an arbitrary aberration and a defocus part, for the computation of optical point spread functions of circular, aberrated optical systems. These new series representations yield a flexible means to compute optical point spread functions, both accurately and efficiently, under defocus and aberration conditions that seem to cover almost all cases
... er almost all cases of practical interest. Because of the analytic nature of the formulas, there are no discretization effects limiting the accuracy as opposed to the more commonly used numerical packages based on strictly numerical integration methods. Instead, we have an easily managed criterion, expressed in the number of terms to be included in the Bessel series representations, guaranteeing desired accuracy. For this reason, the analytic method can also serve as a calibration tool for the numerically-based methods. The analysis is not limited to point-like objects but can also be used for extended objects under various illumination conditions. The calculation schemes are simple and permit to trace the relative strength of the various interfering complex amplitude terms which contribute to the final image intensity function.