Learning Optimal Multicolor PSF Design for 3D Pairwise Distance Estimation

Measuring the 3-dimensional (3D) distance between 2 spots is a common task in microscopy, because it holds information on the degree of colocalization in a variety of biological systems. Often, the 2 spots are labeled with 2 different colors, as each spot represents a different labeled entity. In computational microscopy, neural networks have been employed together with point spread function (PSF) engineering for various imaging challenges, specifically for localization microscopy. This combination enables “end-to-end” design of the optical system’s hardware and software, which is learned simultaneously, optimizing both the image acquisition and reconstruction together. In this work, we employ such a strategy for the task of direct measurement of the 3D distance between 2 emitters, labeled with differently colored fluorescent labels, in a single shot, on a single optical channel. Specifically, we use end-to-end learning to design an optimal wavelength-dependent phase mask that yields an image that is most informative with regards to the 3D distance between the 2 spots, followed by an analyzing net to decode this distance. We utilize the fact that only the distance between the 2 spots is of interest, rather than their absolute positions; importantly, the use of 2 colors, instead of 1, inherently enables subdiffraction distance estimation. We demonstrate our approach experimentally by distance measurement between pairs of fluorescent beads, as well as between 2 fluorescently tagged DNA loci in yeast cells. Our results represent an appealing demonstration of the usefulness of neural nets in task-specific microscopy design and in optical system optimization in general.