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

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-cm(2) collecting area, and a source radiance of 10 W/m(2)-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 (1/2) the aperture diameter required to resolve the light source. Comments are made on the optimum shear for nonuniform radiance distributions.