S. van Haver

Zernike representation and Strehl ratio of optical systems with variable numerical aperture

We consider optical systems with variable numerical aperture (NA) on the level of the Zernike coefficients of the correspondingly scalable pupil function. We thus present formulas for the Zernike coefficients and their first two derivatives as a function of the scaling factor ε ≤ 1, and we apply this to the Strehl ratio and its derivatives of NA-reduced optical systems. The formulas for the Zernike coefficients of NA-reduced optical systems are also useful for the forward calculation of point-spread functions and aberration retrieval within the Extended Nijboer–Zernike (ENZ) formalism for optical systems with reduced NA or systems that have a central obstruction. Thus, we retrieve a Gaussian, comatic pupil function on an annular set from the intensity point-spread function in the focal region under high-NA conditions.

On the modeling of optical systems containing elements of different scales

In optical systems often components of widely varying scales occur. The scale, expressed in units of wavelength, determines what kind of model is needed for the component. For objects with size of the order of the wavelength, rigorous electromagnetic models are required. We discuss several home-made rigorous methods such as the Finite Element Method, the Finite Difference Time Domain Method and the Rigorous Coupled Wave Method and describe our experience with them. For lenses of high numerical aperture, the Extended Nijboer Zernike method is considered. An important issue is how to propagate the field from the exit plane of one component to the entrance plane of the other. We explain a numerical integration method by which the diffraction integral can be computed with an error that is independent of the propagation distance.