RESUMEN
In this Letter, a compact spectrometer based on upconversion and downconversion luminescence for operation in the infrared, visible, and ultraviolet bands is presented. The proposed spectrometer has three components that are used for dispersion, frequency conversion, and detection. The conversion component converts the incident signal beam into a spectral window appropriate for the detection component. The detection component images the speckle pattern generated by scattering or diffraction in the random structure of the dispersion component. With the two-dimensional intensity data captured from both the speckle pattern and a calibration measurement process, one can reconstruct the spectra of the signal beam by solving a matrix equation. A smoothing simulated annealing algorithm has been implemented to improve the accuracy of the spectral reconstruction. We have analyzed possible sources of error in the algorithm and the corresponding limits of operation. The reported broadband, compact, high-resolution, luminescence-based spectrometer is well suited for portable spectroscopy applications.