We propose a new class of aperture-coded spectrometer that is optimized for the spectral characterization of diffuse sources. The instrument achieves high throughput and high spectral resolution by replacing the slit of conventional dispersive spectrometers with a more complicated spatial filter. We develop a general mathematical framework for deriving the required aperture codes and discuss several appealing code families. Experimental results validate the performance of the instrument. © 2006 Optical Society of America.