Imaging properties of phase-shifting apodizers

Abstract

We discuss the imaging properties of Phase Shifting Apodizers (PSAs) in terms of their Optical Transfer Function (OTF). The capability to transfer spatial frequencies from the input to the output of an optical imaging system, in the presence of focus error, is quantified by inspecting the three-dimensional Modulation Transfer Function (3D-MTF). We have found that, in the search of novel apodizers for increasing the focal depth in imaging optical systems, it is not sufficient to analyze the axial impulse response of that system. Some apodizers, even when they increase the focal depth along the optical axis, provide poor imaging properties with respect to defocus. Yet we identify specific values for some important parameters of the PSA that allow us to achieve high focal depth without severally sacrificing the optical performance of the system. We present computer simulations of the 3D-MTF of the system that incorporates these apodizers as well as the output images that can be obtained with it.