Phasing of Ground-based Optical Arrays for Space Applications

Delivery of optical power to targets in space has many applications, including optical communication, active sensing, laser propulsion, and the removal of space debris. However, large monolithic optics required to obtain high directivity are costly and difficult to slew at the rates required to track an object in low earth orbit (LEO). Coherent combination of a large number of small transmit elements will enable high power and directivity without the drawbacks associated with large monolithic optics. The challenge of coherent combination is matching the phase of the light from all elements in the optical array in the presence of phase disturbances from several sources. Changes in temperature in optical fibers and in opto-mechanical systems cause slow phase drifts, while mechanical and acoustic vibrations cause rapid variations in relative optical path length. Transmission through a turbulent atmosphere adds yet another phase disturbance that must be compensated. Sensing and correction of these disturbances is a complex endeavor, made even more difficult by the unique challenges of illuminating an object in LEO. Both point-ahead offset for a fast moving target at long range and the presence of laser speckle in the light reflected from the target complicate atmospheric wavefront sensing. To address these challenges, we propose a novel optical phased array architecture based on a combination of three techniques: (i) atmospheric phase is sensed using a distributed Shack-Hartmann Wavefront Sensor (SHWFS) using light reflected from the target, and corrected using a calibrated feedforward phase offset, (ii) internal phase disturbances are sensed and corrected using Digitally Enhanced Heterodyne Interferometry (DEHI), and (iii) static misalignments and slow drifts not sensed by DEHI or the SHWFS are corrected using a Stochastic Parallel Gradient Descent algorithm. In this work we study the effects of optical speckle on SHWFS performance in conditions of weak turbulence. We develop a method for modeling these effects across a range of target and sensor geometries. We find that wavefront sensing based on reflected light from a rough target moving at orbital velocity in LEO is feasible provided the target is small relative to the diffraction limit of the SHWFS lenslets. We then analyze the performance of our proposed array architecture using a notional design for a laser system for de-orbit of space debris: an array of 2000 elements with an overall diameter of 9.6 m. Analytical models of the phase control dynamics in the DEHI and feedforward systems are developed, and used to estimate the residual phase error present on the transmit array. The diffraction pattern of the array is simulated, and a power budget is developed, showing that sufficient power is delivered to the target to achieve laser ablation thrust for debris objects in LEO. We validate our control system architecture using a laboratory demonstration of a three-element array. We develop a phase measurement system based on DEHI, implemented in an FPGA. Low-order atmospheric disturbances are simulated using a tip-tilt mirror, and measured using a quad-diode position sensor for correction with feedforward control. Quasi-static errors are corrected with SPGD, and the beam is steered to the desired target location. The system successfully corrects all three sources of phase disturbance. Internal disturbances are corrected to better than λ/120 RMS and all phase errors to better than λ/40 RMS. This thesis proposes and demonstrates a path towards the creation of large-scale optical transmit arrays for de-orbit of space debris and other applications.Ph.D