Wavefront sensor based on varying transmission filters: theory and expected performance

The use of Wavefront Sensors (WFS) is nowadays fundamental in the field of instrumental optics. This paper discusses the principle of an original and recently proposed new class of WFS. Their principle consists in evaluating the slopes of the wavefront errors by means of varying density filters placed into the image plane of the tested optical system. The device, sometimes called 'optical differentiation WFS' is completed by a digital data-processing system reconstructing the wavefront from the obtained slopes. Various luminous sources of different wavelengths and spectral widths can be employed. The capacities of the method are discussed from the geometrical and Fourier optics points of view, then by means of numerical simulations showing that the ultimate accuracy can be well below lambda/10 and lambda/100 Peak-to-Valley (PTV) and RMS respectively, provided that certain precautions are taken.