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High-power laser facilities may be restricted in operations by the risk of damage to optics due to the backscattering of laser light from the intended target. A portion of this backscattered light can re-enter the beam line and at sufficient fluence may damage (burn) optical apparatus. Here, the observed cumulative burn pattern on mirrors at the National Ignition Facility (NIF) due to stimulated Brillouin scattering (SBS) at the target is explained using detailed simulations. Our methodology involves using a measurement of a phase plate profile installed at the NIF to provide the laser input to a three-dimensional simulation of laser-plasma interaction in a target typical of that fielded at the NIF. Light scattered by SBS at the target is then followed back to the final aperture of the beam line, back through the phase plate, and to a mirror where damage typically occurs. We find that mirror damage patterns are largely dictated by the phase imprint of the phase plate on the returning SBS light. Our simulations show that the instantaneous SBS signal at the mirror varies on a picosecond time scale and is also highly modulated in space. Temporal averaging of the simulated SBS light pattern on the mirror reveals a pattern in close agreement with the experimentally observed damage. Understanding these burn patterns (distribution, modulation depth) may lead to future phase plate designs that limit damage throughout the optics assembly of high-powered laser facilities. [ABSTRACT FROM AUTHOR]