  Recent studies have shown convolutional neural networks (CNNs) can be trained
to perform modal decomposition using intensity images of optical fields. A
fundamental limitation of these techniques is that the modal phases can not be
uniquely calculated using a single intensity image. The knowledge of modal
phases is crucial for wavefront sensing, alignment and mode matching
applications. Heterodyne imaging techniques can provide images of the
transverse complex amplitude & phase profile of laser beams at high resolutions
and frame rates. In this work we train a CNN to perform modal decomposition
using simulated heterodyne images, allowing the complete modal phases to be
predicted. This is to our knowledge the first machine learning decomposition
scheme to utilize complex phase information to perform modal decomposition. We
compare our network with a traditional overlap integral & center-of-mass
centering algorithm and show that it is both less sensitive to beam centering
and on average more accurate.
