Abstract
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.
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