A New Wave-Front Reconstruction Method for Adaptive Optics Systems Using Wavelets

A new technique for wave-front reconstruction from gradient measurements on a square data set is presented. This technique is based on obtaining the Haar wavelet image decomposition of the original wave-front by appropriate filtering and down-sampling of the gradient measurement data. The use of the wavelet decomposition leads to an algorithm with complexity of
O
(
N
), where N is the number of data points in the reconstruction, and at the same time allows denoising of the data using the wavelet coefficients. The proposed technique is illustrated with two examples and its reconstruction accuracy, computational speed and denoising performance are discussed. Results indicate that the proposed technique is a computationally efficient and accurate technique for wave-front and/or image reconstruction from gradient measurements.