A new approach is described for obtaining spectral imagery over a broad range of infrared wavelengths, with high efficiency, and with a single grating element and focal plane array. The approach represents a simplification and mass reduction over the traditional approach involving multiple focal plane arrays, dispersing elements, and optical beamsplitters. The new approach has significant advantages for space-based hyperspectral imagers operating in the infrared over a broad range of wavelengths (e.g., MWIR and LWIR), where the reduction in cryocooled mass relative to the multichannel approach translates into noteworthy savings in cryocooling requirements and launch costs. Overlapping grating orders are focused onto a multiwaveband focal plane array to create spectral images of a scene simultaneously in multiple wavelength regions. The blaze of the grating is chosen so that all spectral orders are dispersed with high grating efficiency. Such an approach extends the spectral range of dispersive spectrometers to several octaves of wavelength, while preserving the compact packaging and cryogenic requirements of conventional (one octave) instruments. We conclude with a description of a ground-based demonstration of an MWIR and LWIR embodiment of the concept.