Use of an ac heterodyne lateral shear interferometer with real–time wavefront correction systems

TLDR

Comments are made on the optimum shear for nonuniform radiance distributions. The study analyzes the accuracy of an ac heterodyne lateral shear interferometer in measuring wavefront aberrations using a white‑light extended source, with shot noise as the predominant noise source. The analysis evaluates wavefront measurement accuracy by modeling the interferometer’s response to a white‑light extended source under shot‑noise‑limited conditions. The analysis shows that for uniform circular or square sources above a minimum size, accuracy depends only on source radiance, not angular subtense; with a 1‑ms integration, 25‑cm² area, and 10 W/m²‑sr radiance, rms error is ≈1/30 wave, and the optimum shear is ≈½ the aperture diameter for both source shapes.

Abstract

An analysis is performed to determine the accuracy with which an ac heterodyne lateral shear interferometer can measure wavefront aberrations if a white light extended source is used with the interferometer, and shot noise is the predominate noise source. The analysis shows that for uniform circular or square sources larger than a derived minimum size, the wavefront measurement accuracy depends only upon the radiance of the source and not upon the angular subtense of the source. For a 1-msec integration time, a 25-cm2 collecting area, and a source radiance of 10 W/m2-sr the rms wavefront error is approximately 1/30 wave, assuming the signal is shot noise limited. It is shown that for both uniform circular and square sources an optimum shear distance is approximately ½ the aperture diameter required to resolve the light source. Comments are made on the optimum shear for nonuniform radiance distributions.