  3D snapshot microscopy enables volumetric imaging as fast as a camera allows
by capturing a 3D volume in a single 2D camera image, and has found a variety
of biological applications such as whole brain imaging of fast neural activity
in larval zebrafish. The optimal microscope design for this optical 3D-to-2D
encoding to preserve as much 3D information as possible is generally unknown
and sample-dependent. Highly-programmable optical elements create new
possibilities for sample-specific computational optimization of microscope
parameters, e.g. tuning the collection of light for a given sample structure,
especially using deep learning. This involves a differentiable simulation of
light propagation through the programmable microscope and a neural network to
reconstruct volumes from the microscope image. We introduce a class of global
kernel Fourier convolutional neural networks which can efficiently integrate
the globally mixed information encoded in a 3D snapshot image. We show in
silico that our proposed global Fourier convolutional networks succeed in large
field-of-view volume reconstruction and microscope parameter optimization where
traditional networks fail.
