WAVEFRONT SENSING BY HETERODYNE SHEARING INTERFEROMETRY (WAVEFRONT RECONSTRUCTION).

Abstract

The operation of a grating lateral shear heterodyne interferometer as a wavefront sensor for atmospherically perturbed wavefronts is analyzed. A novel wavefront sensor design is given and its feasibility is proven by laboratory experiments. The applications in mind are closed-loop active optical systems for compensating atmospheric perturbations and open-loop atmospheric wavefront measuring device. The optical properties of the turbulent atmosphere are summed up and the resulting wavefront sensor requirements are given. Among them are the property of sell-referencing, high white light efficiency, independence of scintillation effects, and high spatial and temporal sampling rates. Then the general heterodyne grating shearing interferometer is introduced. A description of the phase measurement by the heterodyne process in the frequency domain has been derived. The heterodyne process is interpreted as convolutions of the signal with a pair of filter functions, which isolate a particular harmonic term of the signal and provide its phase. The representation of the convolutions in the frequency domain provides an elegant way to analyse the systematic errors of the heterodyning with general, non-sinusoidal signals. Also the random phase errors of the heterodyne process have been determined using Gaussian error propagation. An algorithm is derived to carry out the wavefront reconstructions from the measured differences on a square array of discrete data points. It is based on a modal expansion in complex exponentials, leading to a simple filtering operation in the spatial frequency domain. The algorithm provides unbiased reconstructions over the finite data set. It has minimal error propagation in a least squares sense. It is computationally efficient in that the number of operations required for a reconstruction is approximately proportional to the number of wavefront points, if a Fast-Fourier-Transform algorithm is used. Finally, a compact wavefront sensor design is described fulfilling the requirements posed by the turbulent atmosphere. It determines wavefronts at 24 by 24 points at a sampling rate of 60 Hz. A rms-wavefront error of better than λ/20 can be achieved with astronomical light sources of sixth stellar magnitude. Laboratory experiments proved the feasibility of the design.