Wavefront fitting using Gaussian functions

Details Wavefront fitting using Gaussian functions Wavefront fitting using Gaussian functions

May 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999optco.163..259m&link_type=abstract

Optics Communications, Volume 163, Issue 4-6, p. 259-269.

Physics

Optics

2

Wavefront Approximation, Radial Basis Function (Rbf), Interpolation, Adaptive Optics

Scientific paper

Often the polynomial description of a wavefront shape is inaccurate because sharp local deformations are difficult to represent. In this case an analytical representation in terms of Gaussians may give better results. We have made a study of properties of Gaussians in fitting wavefronts. We analyzed an specific array of Gaussian functions and show their easy Fourier transformation. In Fourier space some criteria are proposed for setting the Gaussian width, the separation between these functions and making an estimation of the wavefront fitting error. Two simulated wavefronts are fitted and a comparison with a Zernike polynomial is made. It is well known that when fitting using Zernike polynomials one needs to find the optimal number of terms beyond which the errors in the approximation become larger. We show that using Gaussians the accuracy of the fit increases with the number of terms. We demonstrate some interesting properties, such as their facility to fit local deformations and fast parameter determination.

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