New x-ray imaging crystal spectrometers, currently operating on Alcator C-Mod, NSTX, EAST, and KSTAR, record spectral lines of highly charged ions, such as Ar(16+), from multiple sightlines to obtain profiles of ion temperature and of toroidal plasma rotation velocity from Doppler measurements. In the present work, we describe a new data analysis routine, which accounts for the specific geometry of the sightlines of a curved-crystal spectrometer and includes corrections for the Johann error to facilitate the tomographic inversion. Such corrections are important to distinguish velocity induced Doppler shifts from instrumental line shifts caused by the Johann error. The importance of this correction is demonstrated using data from Alcator C-Mod.