Zernike polynomiales for opticl system with horizantal rectangular aperture

Abstract AR

For small aberrations, the Strehl ratio of an imaging system depends on the aberration variance.

Its aberration function is expanded ٨؛ terms of Zernike polynomials, which are orthogonal over a circulai• aperture.

Their advantage lies in the fact that they can be identified with classical aberrations balanced to yield minimum variance, and thus maximum Strehl ratio.

In recent paper, we derived closed form of Zernike polynomials that are orthonormal over a horizontal rectangular pupil (parallel to the x-axies) with area equal 7t.

Using tile circle polynomials as the basis functions for their orthogonalization over such pupil, we derive dosed-form polynomials that are orthonormal over rectangular pupil by using Gram-shmii method These polynomials are unique in that they are not only orthogonal across such pupils, but also represent balanced classical aberrations, just as the Zemike circle polynomials are unique in these respects but also represent balanced classical aberrations.