A multiband spatial heterodyne spectrometer for determining spectra in first and second wavelength bands has a beam splitter configured to split incident light and to direct the incident light upon a first and a second diffraction grating. The gratings are configured for Littrow reflection of incident light of the first wavelength band at a first order and Littrow reflection of incident light of the second wavelength band at a second order. Light reflected by the first and the second diffraction grating forms diffraction patterns that are imaged by an electronic camera. A dispersive device such as a prism or diffraction grating separates the imaged interference patterns onto separate rows of pixel sensors corresponding to the wavelength bands. A processing device receives information from the detector and computes spectra therefrom. In embodiments, the spectrometer is configured to compute hyperspectral images of a target.