An x-ray spectrometer system comprising an x-ray imaging system with at least one achromatic imaging x-ray optic and an x-ray detection system. The optical train of the imaging system is arranged so that its object focal plane partially overlaps an x-ray emitting volume of an object. An image of a portion of the object is formed with a predetermined image magnification at the x-ray detection system. The x-ray detection system has both high spatial and spectral resolution, and converts the detected x-rays to electronic signals. In some embodiments, the detector system may have a small aperture placed in the image plane, and use a silicon drift detector to collect x-rays passing through the aperture. In other embodiments, the detector system has an energy resolving pixel array x-ray detector. In other embodiments, wavelength dispersive elements may be used in either the optical train or the detector system.