An x-ray spectrometer includes at least one x-ray optic configured to receive x-rays having an incident intensity distribution as a function of x-ray energy and at least one x-ray detector configured to receive x-rays from the at least one x-ray optic and to record a spatial distribution of the x-rays from the at least one x-ray optic. The at least one x-ray optic includes at least one substrate having at least one surface extending at least partially around and along a longitudinal axis. A distance between the at least one surface and the longitudinal axis in at least one cross-sectional plane parallel to the longitudinal axis varies as a function of position along the longitudinal axis. The at least one x-ray optic further includes at least one mosaic crystal structure and/or a plurality of layers on or over at least a portion of the at least one surface. The plurality of layers has a first plurality of first layers comprising a first material and a second plurality of second layers comprising a second material. The first layers and the second layers alternate with one another in a direction perpendicular to the at least one surface.