LIGO Document G0900467-v2

Characterizing Coherent Scatter from Interferometer Mirror Roughness

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Images of cavity mode “beam spots” on LIGO interferometer mirror surfaces from non-specular view points reveal an apparently random pattern of intensities. Heuristically this has been assumed to be associated with the near fractal distribution of residual surface roughness from the polishing process, and plausibly random distribution of micro-flaw points in or on the HR coatings. We have developed a more quantitative theory of the expected coherent light scattering from the known extremely shallow () roughness. This essentially statistical treatment assumes homogeneous and isotropic surface ensembles typify actual specimen surfaces, the only free parameter being the PSD (over the ensemble) of intensity in polar angle. This approach is fundamentally related to that developed to quantify the statistical properties of “laser speckle” where, however, the roughness is not shallow (no specular reflection). The theory predicts several characteristic features of both beam spot images and point field strength measurement (via PD monitors in the scatter field). These are compared to the available data. This comparison allows a characteristic distinction to be made between the anticipated (from polishing meterological data) scatter due to residual roughness and hard point scatter from post-polishing flaws.
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