Abstract

By using exponential evaluations of the Strehl ratio and appropriate Dini-sampling formulas in concert, an approximate formula is derived for fast calculation of intensity distributions in the central bright core of rotationally symmetric aberrational diffraction patterns. Since the formula involves no special functions, it is convenient both for numerical and analytical purposes. Numerical examples show that for moderate amounts of rotationally symmetric aberrations, the formula gives excellent results inside the unity disk (compared with a radius of 1.22 for the Airy disk) at the image plane. In the case of balanced (Zernike) spherical aberrations, our formula reduces to the perfect Airy pattern multiplied by corresponding Strehl ratio. A useful tool for the optical system designer, it can easily be implemented using any desk-top calculator for evaluating parameters as encircled energy, truncated radius of gyration, or to compute the central part of polychromatic diffraction patterns.

© 1986 Optical Society of America

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