8 September 1998 Optimal beam steering using time-delayed wavefront measurements in airborne laser target engagements
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In Airborne Laser (ABL) target engagements, beam steering should account for the effects of turbulence-induced wavefront tilt. Due to the finite temporal response of adaptive-optical systems, steering commands must be based upon time-delayed wavefront measurements. The dynamics of the ABL target engagement scenario and turbulence-induced anisoplanatism cause the time-delayed wavefront measurements to be decorrelated from the required wavefront tilt correction. This decorrelation leads to suboptimal beam steering when time-delayed wavefront measurements are used directly in the control loop. To assess beam steering performance, we calculate the aperture-averaged mean square residual phase error after tilt correction, as a function of measurement time delay, and show that this quantity is minimized by the minimum mean square error (MMSE) estimate of tilt given a set of time-delayed wavefront measurements. Therefore, a temporal MMSE tilt estimator is constructed using time-delayed tilt plus higher-order aberration measurements. We define the tilt correction interval (tau) c as the time delay at which the residual phase error is 1% larger than its value at zero time delay. Our results show that (tau) c using the MMSE tilt estimator with modal measurements through Zernike 15 is over 3 times larger than (tau) c using time-delayed tilt measurements only. Accordingly, the beam steering bandwidth for ABL target engagements is reduced by more than 70% when higher order modal measurements are used in optimal tilt correction.
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Matthew R. Whiteley, Michael C. Roggemann, Byron M. Welsh, "Optimal beam steering using time-delayed wavefront measurements in airborne laser target engagements", Proc. SPIE 3381, Airborne Laser Advanced Technology, (8 September 1998); doi: 10.1117/12.323929; https://doi.org/10.1117/12.323929

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