Modal wave-front reconstruction with Zernike polynomials and Karhunen–Loève functions

Modal wave-front reconstruction by use of Zernike polynomials and Karhunen–Loève 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–Loève functions results in a smaller residual error than with Zernike polynomials.