Imaging spectrometers are increasingly used to measure the spectral radiance of Earth surface from aircraft and satellites. The design of optics for imaging spectrometers, covering the spectral range from visible through short-wave infrared, can be simplified using the Dyson and Offner concentric relay design forms. problems in integration of dispersing elements into these concentric relays are addressed. It is shown that use of dispersing prisms with curved faces can provide good performance in designs that are simple and compact.