Zernike Polynomiales for OpticI Ssytem With Horizantal Rectangular Aperture

For small aberrations, the Strehl ratio of an imaging system depends on the aberration variance. Its aberration function is expanded in terms o f Zernike polynomials, which are orthogonal over a circular 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 7L Using the circle polynomials as the basis functions for their orthogonalization over such pupil, we derive closed-form polynomials that are orthonormal over rectangular pupil by using Gram-shout method These polynomials are unique in that they are not only orthogonal across such pupils, but also represent balanced classical aberrations, just as the Zernike circle polynomials are unique in these respects but also represent balanced classical aberrations.