In a method for measuring radiation, the radiation is temporally and/or spatially separated by a modulator to direct at least N different combinations of radiation incident on each region into at least two and fewer than N distinct directions. The total intensity of radiation in each direction is measured with a detector for each modulator configuration and the detector outputs are analyzed statistically to obtain information relating to the spectral properties of the radiation. In this way substantially all of the energy received at the entrance aperture of a measurement device is encoded into multiple outputs and the multiplexed output is received by a small number of detectors.