HARTMANN SENSING WITH ALBRECHT GRIDS

The modal coefficients of a wavefront can be estimated by suitably wei ghted integrals of the wavefront slopes. When the basis functions chos en to expand the wavefront are orthogonal (e.g. Zernike polynomials), the reconstruction problem becomes orthogonal itself, so that each coe fficient can be estimated independently from the others. Modal cross-c oupling can in this way be avoided. The obtained coefficients correspo nd to a direct least-squares fit between the real and estimated wavefr onts, The evaluation of the modal integrals from the finite data set o f measurements supplied by Shack-Hartmann sensors or shearing interfer ometers requires the use of efficient numerical integration methods. I n this paper it is shown that Albrecht cubatures are a good candidate to perform this task. The wavefront slopes have to be measured at the nodal points of the chosen cubature, which in general are located in a n unevenly spaced grid. Numerical results show that the method of orth ogonal reconstruction with Albrecht cubatures allow to recover the mod al coefficients with better accuracy than other usual approaches, incl uding the standard non-orthogonal least-squares fit between the gradie nts of the original and reconstructed wavefronts.