Focal plane phase retrieval using deep convolutional neural networks

Abstract

Adaptive optics are widely used to correct the wavefront distortion imposed by atmospheric turbulence. Focal plane phase retrieval from intensity measurements has advantages due to the ease of implementation, potential broader application, less computations, low cost, high system bandwidth, simplified hardware and less calibration. To cope with the non-linear relation between focal plane intensity and wavefront phase the use of Machine Learning is investigated. A supervised learning deep Convolutional Neural Network is used to assess the feasibility for deriving a direct mapping between a single out of focus CCD intensity measurement and the Zernike modes belonging to it. A model of a typical free space optical communication system is used to asses 13 different CNN architectures. The first 35 Zernike modes(disregarding tip/tilt) were retrievedfromKolmogorovbasedCCDintensitymeasurementsofsize70x70withconstant amplitude, turbulence strength of 1 ≤ D/r0 ≤ 6, 7 ≤ D/r0 ≤ 12 and 13 ≤ D/r0 ≤ 18 and a SNR of 22dB. The convergence of a 128 channel six layer CNN with kernal size 3 using stride resulted in a mapping providing a residual wavefront error of 5nm, 21nm and 74nm after reconstruction of the wavefront. The results prove that a CNN can be used to map out of focus intensity data directly onto the Zernike coefficients of the wavefront. The CNN is validated by an experimental setup which was used to generate real input and output data. With a turbulence strength of 5 ≤ D/r0 ≤ 15 the mean squared phase error was found to be 72nm. The use of a deep CNN for phase retrieval implementation in free space optical communications is promising and can provide fast and accurate phase retrieval with relatively simple hardware and faster computations.