It is easily seen that in the case of a readout beam, even with the largest possible allowed by clipping losses, the resulting thermal lens is currently a serious spurious effect and will be even greater in advanced interferometers. For a fundamental mode with a width of 6.65 cm on the cavity input mirrors, the curvature radius of the thermal lens is about 4 km for 1 W thermalized, on the same order as the nominal curvature radius of the mirror.
This is why thermal compensation systems (TCS) have been designed. The general principle is to use an auxiliary source of heat for heating the cold parts of the mirror in order to achieve a more homogeneous temperature distribution. The source of heat may be a classical radiator able to radiate infrared energy in a vacuum, for instance, a hot ring near the rear face of the mirror [30, 25, 13, 14, 22, 43]. It may also be an auxiliary laser projector, which can be programmed to scan the mirror surface to produce a given power mask .
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