Dragging four-point method along a circular path for high-precision measurement

Freeform optical surfaces are essential for realizing wide-field-of-view telescopes, and their development requires highly precise surface measurement methods. We propose the dragging four-point method (DFPM) as an improved version of the dragging three-point method (DTPM) that we previously developed. The output of the DFPM is designed to compensate for measurement errors caused by vibration. To evaluate its performance, error analyses were conducted using simulated sensor noise. The amplitude spectrum of the measurement error due to noise with a root-mean-square (RMS) of <i>σ</i>, as a function of spatial frequency <i>k</i>, was approximately proportional to <i>k</i>^-3, and the error propagation increased with the number of measurement points <i>N</i>, which was approximated as <i>R</i><i>M</i><i>S</i>≃0.004×<i>σ</i><i>N</i>^2.5.