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XMM-Newton Science Analysis System


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Meta Index / Home Page / Photometry / Point-Spread Function Fitting

Interpolation method

The interpolation scheme used to interpolate the PSF at any point from the centre of a source is one that is published in Transactions on Mathematical Software, Vol 32, No 3, September 1996, pages 357-361. The subroutine performs interpolation of a bivariate function, z(x,y), on a rectangular grid in the x-y plane and is based on the revised Akima method. The interpolating function is a piecewise function composed of a set of bicubic (bivariate third-degree) polynomials, each applicable to a rectangle of the input grid in the x-y plane. Each polynomial is determined locally and has the accuracy of a bicubic polynomial, i.e., it interpolates accurately when all the data points lie on a surface of a bicubic polynomial.