Transformation of Volume Holographic Pupils for Microscopic Imaging

Volume holograms (VHs) are good candidates for pupils of microscopic imaging systems thanks to their three–dimensional structure, providing additional design flexibility compared to conventional two–dimensional pupils [1]. Transformations of VH pupils promise richer opportunities to design more sophisticated point–spread–functions (PSFs). In addition, this allows for in vivo adjustment of a microscopic system for different imaging purposes. One can simply change the mechanical deformations applied on the VHs to achieve various PSFs, without having to replace the pupils. Previously we have investigated the exterior deformations of the VH pupils using a superposition of point indenters [2]. However, not all PSFs are achievable by multiple point indenters. Here we propose bulky mechanical deformations besides point load, including compression, shearing, bending, twisting, etc. They offer more general and sophisticated PSF designs for various microscopic imaging applications. Through transformation, the system performance can be tuned to fit more design criterions such as spectral composition of the PSF, anisotropic behavior, etc. This general approach is called transformational volume holography. Numerically, it is straightforward to compute the final PSF given a certain type of transformation. However, these computations are normally unstable and require 3D integrations, which pose unattainable demands on extensive CPU and memory cost. What is more, a physically intuitive relationship between the transformation of the VH pupils and the resulting PSFs is lost. Here we focus on finding quasi–analytical expressions for calculating the PSFs, since analytical equations are always much easier to compute, and give better physical intuitions. For some