Abstract
We develop a rapidly converging algorithm for stabilizing a large channel-count diffractive optical coherent beam combination. An 81-beam combiner is controlled by a novel, machine-learning based, iterative method to correct the optical phases, operating on an experimentally calibrated numerical model. A neural-network is trained to detect phase errors based on interference pattern recognition of uncombined beams adjacent to the combined one. Due to the non-uniqueness of solutions in the full space of possible phases, the network is trained within a limited phase perturbation/error range. This also reduces the number of samples needed for training. Simulations have proven that the network can converge in one step for small phase perturbations. When the trained neural-network is applied to a realistic case of 360 degree full range, an iterative scheme exploits random walking at the beginning, with the accuracy of prediction on phase feedback direction, to allow the neural-network to step into the training range for fast convergence. This neural-network-based iterative method of phase detection works tens of times faster than the commonly used stochastic parallel gradient descent approach (SPGD) using a single-detector and random dither when both are tested with random phase perturbations.
Highlights
Coherent beam combination is a way to derive high energy and power from lasers which are limited in output, by adding outputs together [1,2]
We show the physical model of spatial convolution with the diffractive optical element (DOE), and discusses the principle of interference pattern recognition with a neural network (NN) algorithm which learns the mapping from pattern to phase, yielding the phase errors directly
The neural-network is trained as a phase detector based on pattern recognition of interference patterns emerging from a DOE
Summary
Coherent beam combination is a way to derive high energy and power from lasers which are limited in output, by adding outputs together [1,2]. We show the physical model of spatial convolution with the DOE, and discusses the principle of interference pattern recognition with a NN algorithm which learns the mapping from pattern to phase, yielding the phase errors directly. In order to perform actual measurements on a 9 × 9 diffractive combiner without incurring the cost and complexity of building a phase-controlled beam array using discrete optics, we opted to generate a beam array using a spatial light modulator [18,19] This provides for control of all parameters of each beam, enabling measurements of the actual DOE phase function and tests of combining and control. Equation (2) indicates that our stabilization goal is to control σφ99%
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