Wave front characterization of Gaussian beams using shear interferometry and a weighted reconstructor

Shear interferometry is based on superposition of a wave field with a shifted copy of itself. It provides great advantages for high precision wave front sensing, because it does not require a reference wave that has to be assumed known. The precision is mainly limited by the accuracy of the shear alignment and aberrations caused by the optical components of the interferometer, which can be calibrated in most cases. The drawback of shear interferometry is that the measurement only provides finite differences of the wave front at positions separated by the shear. Thus, the wave front has to be reconstructed from the recorded data. We present an approach for wave front reconstruction from finite difference measurements, that is based on an iterative non-linear optimization procedure providing noise dependent weighting. We demonstrate that the method offers great advantages over standard reconstruction techniques for the accurate characterization of Gaussian beams by means of a shear interferometer. Numerical simulations show that estimation of the underlying wave front can be improved by 3dB without any additional measurements.