论文信息 - Zernike expansion of separable functions of cartesian coordinates.

Zernike expansion of separable functions of cartesian coordinates.

A Zernike expansion over a circle is given for an arbitrary function of a single linear spatial coordinate. The example of a half-plane mask (Hilbert filter) is considered. The expansion can also be applied to cylindrical aberrations over a circular pupil. A product of two such series can thus be used to expand an arbitrary separable function of two Cartesian coordinates.

Colin J R Sheppard | Sam Campbell | Michael D Hirschhorn

[1] F Roddier,et al. Curvature sensing and compensation: a new concept in adaptive optics. , 1988, Applied optics.

[2] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[3] R. Noll. Zernike polynomials and atmospheric turbulence , 1976 .

[4] B. Nijboer,et al. The diffraction theory of optical aberrations: Part II: Diffraction pattern in the presence of small aberrations , 1947 .

[5] G Conforti. Zernike aberration coefficients from Seidel and higher-order power-series coefficients. , 1983, Optics letters.

[6] B. Nijboer,et al. The diffraction theory of optical aberrations*)Part I: General discussion of the geometrical aberrations , 1943 .

[7] William J. Tango,et al. The circle polynomials of Zernike and their application in optics , 1977 .

[8] Fraunhofer diffraction by semicircular apertures , 1977 .

[9] R K Tyson. Conversion of Zernike aberration coefficients to Seidel and higher-order power-series aberration coefficients. , 1982, Optics letters.

[10] D. Malacara. Optical Shop Testing , 1978 .

[11] A. I. Mahan,et al. Far-Field Diffraction Patterns of Single and Multiple Apertures Bounded by Arcs and Radii of Concentric Circles*† , 1964 .

[12] A. Bhatia,et al. On the circle polynomials of Zernike and related orthogonal sets , 1954, Mathematical Proceedings of the Cambridge Philosophical Society.

[13] D. K. Hamilton,et al. Differential phase contrast in scanning optical microscopy , 1984 .