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Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration.

We have investigated two approximation methods for estimating the normalized point source sensitivity (PSSN), which is a recently developed optical performance metric for telescopes. One is an approximation based on the power spectral density (PSD) of the wavefront error. The other is the root-square-sum of the wavefront slope. We call these approximations β approximation and SlopeRMS approximation, respectively. Our analysis shows that for the Thirty Meter Telescope (TMT), the uncertainty of the β approximation is less than 1×10(-3) if the PSSN is better than 0.95, assuming the input PSD estimation is accurate. In addition, we find that the SlopeRMS approximation is a simple method for estimating the worst-case PSSN value in the specific situation when the PSSN is dominated by low-frequency aberrations. Therefore, the SlopeRMS approximation is expected to be useful for specifying a mirror surface for mirror vendors. Accordingly, TMT has a plan to adopt the SlopeRMS approximation for its M2 and M3 polishing specification.