Computational spectrometer based on a broadband diffractive optic

We describe a simple, compact, low-cost spectrometer comprised of a broadband diffractive optic and a sensor array. The diffractive optic is designed to disperse incident collimated light onto the sensor array in a prescribed manner defined by its spatial-spectral point-spread function. By applying a novel nonlinear optimization method, we show that it is possible to reconstruct the unknown spectrum from the measured image on the sensor array. We experimentally reconstructed numerous spectra with resolution as small as ~1 nm and bandwidths as large as 450 nm. Furthermore, we readily resolved two spatially overlapping but spectrally distinct objects. The spectral resolution is determined by dispersion of the diffractive optic via a spectral correlation function, while the bandwidth is limited primarily by the quantum efficiency of the sensor array. Using simulations, we present a spectral extraction of solar radiation from 300 nm to 2,500 nm with a resolution of ~0.11 nm. Moreover, our technique utilizes almost all the incident photons owing to the high transmission efficiency of the broadband diffractive optic, which allows for fast spectroscopy with dim illumination. Due to its simple construction with no moving parts, our technique could have important applications in portable, low-cost spectroscopy.