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This paper studies the effects on Zernike coefficients of aperture scaling,translation and rotation, when a given aberrated wavefront is described on theZernike polynomial basis. It proposes a new analytical method for computing thematrix that enables the building of the transformed Zernike coefficients fromthe original ones. The technique is based on the properties of Zernikepolynomials Fourier Transform and, in the case of a full aperture withoutcentral obstruction, the coefficients of the matrix are given in terms ofintegrals of Bessel functions. The integral formulas are exact and do notdepend on any specific ordering of the polynomials.

Transformation of Zernike coefficients: A Fourier based method for scaled, translated and rotated wavefront apertures