Tolerance analysis method for Shack-Hartmann sensors using a variable phase surface

Even after good calibration, the measurement accuracy of a Shack- Hartmann sensor can be affected by the fabrication and alignment tolerances of the wavefront sensing optical system. The shifts of the Shack-Hartmann spots caused by misalignments correspond to ray intercept errors on the detector that typically have to be converted into a meaningful input wavefront measurement error. This conversion cannot be directly obtained from a conventional tolerance analysis using optical design software, because of the intrinsic wavefront sampling by the lenslet array. The tolerancing method proposed in this paper solves the problem of converting conventional merit function degradation into input wavefront measurement error without employing a separate wavefront reconstruction algorithm. Using the proposed method, this investigation shows the effect of fabrication and misalignment errors on the accuracy of a calibrated Shack- Hartmann sensor, as a function of input wavefront vergence.