  Deep learning has become an extremely effective tool for image classification
and image restoration problems. Here, we apply deep learning to microscopy, and
demonstrate how neural networks can exploit the chromatic dependence of the
point-spread function to classify the colors of single emitters imaged on a
grayscale camera. While existing single-molecule methods for spectral
classification require additional optical elements in the emission path, e.g.
spectral filters, prisms, or phase masks, our neural net correctly identifies
static as well as mobile emitters with high efficiency using a standard,
unmodified single-channel configuration. Furthermore, we demonstrate how deep
learning can be used to design phase-modulating elements that, when implemented
into the imaging path, result in further improved color differentiation between
species.
