Noise analysis of spectrometers based on speckle pattern reconstruction

Speckle patterns produced by a disordered medium or a multimode fiber can be used as a fingerprint to uniquely identify the input light frequency. Reconstruction of a probe spectrum from the speckle pattern has enabled the realization of compact, low-cost, and high-resolution spectrometers. Here we investigate the effects of experimental noise on the accuracy of the reconstructed spectra. We compare the accuracy of a speckle-based spectrometer to a traditional grating-based spectrometer as a function of the probe signal intensity and bandwidth. We find that the speckle-based spectrometers provide comparable performance to a grating-based spectrometer when measuring intense or narrowband probe signals, whereas the accuracy degrades in the measurement of weak or broadband signals. These results are important to identify the applications that would most benefit from this new class of spectrometer.