The art of rectifying a laser beam carrying amplitude and phase distortions has been demonstrated through several competing methods. Both wavefront sensor and wavefront sensor-less approaches show that the closed-loop correction of a laser beam can be accomplished by exploiting high-resolution sampling of the beam distortion in its spatial or time domain, respectively. Moreover, machine-learning-based wavefront sensing has emerged recently, and uses training data on an arbitrary sensing architecture to map observed data to reasonable wavefront reconstructions. This offers additional options for beam correction and optical signal decoding in atmospheric or underwater propagation. Ideally, wavefront sensing can be achieved through any resolution in spatial samples, provided that more frequent sampling in the time domain can be achieved for a reduced number of spatial samples. However, such trade-offs have not been comprehensively studied or demonstrated experimentally. We present a fundamental study of lossy wavefront sensing that reduces the number of effective spatial samples to the number of actuators in a deformable mirror for a balanced performance of dynamic wavefront corrections. As a result, we show that lossy wavefront sensing can both simplify the design of wavefront sensors and remain effective for beam correction. In application, this concept provides ultimate freedom of hardware choices from sensor to sensorless approaches in wavefront reconstruction, which is beneficial to the frontier of study in free-space optical communication, lidar, and directed energy.
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21 January 2020: A correction was made to the Algorithm.
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