Analytic von Hamos geometry optimization and calibration

We present an analytic method for the calibration of X-ray fluorescence spectra collected using cylindrically bent crystal analyzers in any arrangement with respect to the sample and detector. Cylindrically bent analyzers are often used in the von Hamos geometry at X-ray Free Electron Lasers to image and disperse fluorescence from a point source to an easily calibrated line. When not in the von Hamos configuration, cylindrically bent analyzers produce spatio-spectral patterns that cannot be calibrated using existing methods. Our formula allows us to rapidly fit and optimize geometric parameters for fluorescence data and calibrate the resulting spectra.