An optical signal is compressively sampled. An optical component with a plurality of transmissive elements and a plurality of opaque elements is created. The location of the plurality of transmissive elements and the plurality of opaque elements is determined by a transmission function. A spectrum of the optical signal is dispersed across the optical component. Signals transmitted by the plurality of transmissive elements are detected in a single time step at each sensor of a plurality of sensors dispersed spatially with respect to the optical component. Each sensor of the plurality of sensors produces a measurement resulting in a number of measurements for the single time step. A number of estimated optical signal values is calculated from the number of measurements and the transmission function. The transmission function is selected so that the number of measurements is less than the number of estimated optical signal values.