A study of the surface curvature of VELO prototype sensors

The curvature of the surface of prototype VELO sensors has been measured. Comparable coefficients of distortion were found for sensors manufactured by Hamamatsu and Micron. Sensors ranging in thickness from 150 um to 300 um have been measured and the degree of curvature is found to be significantly greater for thinner detectors. For the thinnest sensor the distortion compared with a flat base plane was up to 500 um. The effect of this curvature on the residuals and the alignment of the VELO has been simulated. Two scenarios were modelled: the set-up of LHCb VELO test-beam; and that of the final detector. It is concluded that the effect is not significant for current test-beam studies, but for thin sensors and large angle tracks it would become significant in LHCb, leading to a distortion of the residuals with an r.m.s. of 30 um for 300 mrad tracks. Surveying the surface of the sensors before insertion into LHCb and implementing a modified version of the reconstruction software the distortions could be compensated to a level that would not affect the overall performance of the detector.