  We present a virtual image refocusing method over an extended depth of field
(DOF) enabled by cascaded neural networks and a double-helix point-spread
function (DH-PSF). This network model, referred to as W-Net, is composed of two
cascaded generator and discriminator network pairs. The first generator network
learns to virtually refocus an input image onto a user-defined plane, while the
second generator learns to perform a cross-modality image transformation,
improving the lateral resolution of the output image. Using this W-Net model
with DH-PSF engineering, we extend the DOF of a fluorescence microscope by
~20-fold. This approach can be applied to develop deep learning-enabled image
reconstruction methods for localization microscopy techniques that utilize
engineered PSFs to improve their imaging performance, including spatial
resolution and volumetric imaging throughput.
