Modal wave-front reconstruction with zernike polynomials and Karhunen-Loeve functions

Modal wave-front reconstruction by use of Zernike polynomials and Karhunen-Loeve functions from average slope measurements with circular and annular apertures is discussed because of its practical applications in astronomy. A new error source, referred to as the remaining error, is formulated theoretically and evaluated numerically. The total reconstruction error is found to be the sum of the uncompensated wave-front residual error, the measurement error, and the remaining error. Numerical calculation shows that modal wave-front reconstruction with atmospheric Karhunen-Loeve functions results in a smaller residual error than with Zernike polynomials. (C) 1996 Optical Society of America