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A theoretical framework is developed to estimate the optimal binning of X-rayspectra. We derived expressions for the optimal bin size for model spectra aswell as for observed data using different levels of sophistication. It is shownthat by taking into account both the number of photons in a given spectralmodel bin and their average energy over the bin size, the number of modelenergy bins and the size of the response matrix can be reduced by a factor of$10-100$. The response matrix should then contain the response at the bincentre as well as its derivative with respect to the incoming photon energy. Weprovide practical guidelines for how to construct optimal energy grids as wellas how to structure the response matrix. A few examples are presented toillustrate the present methods.

Optimal binning of X-ray spectra and response matrix design