Orthogonal modal reconstruction of a wave front from phase difference measurements

The problem of retrieving the expansion coefficients of a wave front from p hase difference measurements in a square domain has been studied using the orthogonality properties of the Gram polynomials. An expression for the coe fficients to be obtained independently as weighted sums over the experiment al data is given and the influence of measurement noise in the estimate wil l be analysed, obtaining very good agreement with previous results of zonal and modal estimation with phase difference measurements.