Learning Optimal Wavefront Shaping for Multi-Channel Imaging.

Fast acquisition of depth information is crucial for accurate 3D tracking of moving objects. Snapshot depth sensing can be achieved by wavefront coding, in which the point-spread function (PSF) is engineered to vary distinctively with scene depth by altering the detection optics. In low-light applications, such as 3D localization microscopy, the prevailing approach is to condense signal photons into a single imaging channel with phase-only wavefront modulation to achieve a high pixel-wise signal to noise ratio. Here we show that this paradigm is generally suboptimal and can be significantly improved upon by employing multi-channel wavefront coding, even in low-light applications. We demonstrate our multi-channel optimization scheme on 3D localization microscopy in densely labelled live cells where detectability is limited by overlap of modulated PSFs. At extreme densities, we show that a split-signal system, with end-to-end learned phase masks, doubles the detection rate and reaches improved precision compared to the current state-of-the-art, single-channel design. We implement our method using a bifurcated optical system, experimentally validating our approach by snapshot volumetric imaging and 3D tracking of fluorescently labelled subcellular elements in dense environments.