Karhunen–Loève functions represent the best choice for modal wavefront reconstruction. They are usually built up as a linear combination of Zernike polynomials by using principal component analysis methods; thus they are ordered by covariance. Using Shannon information theory, we provide a best reordering procedure based on the concept of mutual information. This enhances reconstruction efficiency, allowing us to reduce the basis dimension while maintaining the same fitting error in wavefront reconstruction.
© 2010 Optical Society of America
Atmospheric and Oceanic Optics
Original Manuscript: October 26, 2009
Revised Manuscript: February 10, 2010
Manuscript Accepted: March 14, 2010
Published: April 5, 2010
Marco Stangalini, Dario Del Moro, Francesco Berrilli, and Oskar von der Lühe, "Zernike basis optimization for solar adaptive optics by using information theory," Appl. Opt. 49, 2090-2094 (2010)