7.1 Respons matrices

A theoretical framework is developed in order to estimate the optimum binning of X-ray spectra. Expressions are derived for the optimum bin size for the model spectra as well as for the observed data using different levels of sophistication. It is shown that by not only taking into account the number of photons in a given spectral model bin but also its average energy (not necessarily equal to the bin center) the number of model energy bins and the size of the response matrix can be reduced by a factor of 10–100. The response matrix should then not only contain the response at the bin center, but also its derivative with respect to the incoming photon energy. Practical guidelines are given how to construct the optimum energy grids as well as how to structure the response matrix. Finally a few examples are given to illustrate the present methods.