Fig. 1. Conceptual illustration of STRSS. (a) Comparison of spatial, temporal, and spatial-temporal random speckle spectrometers. (b) Schematic representation of the proposed spectrometer and the process of constructing the spatial-temporal speckle transmission matrix. (c) Illustration of the process of applying random voltage to the electrodes and pixels.

Fig. 2. Fabricated spectrometer. (a) Microscope image of the fabricated device. (b) Photograph of the packaged chip. (c) Magnified image of the optical splitter. (d) Magnified image of the MZI array. (e) Magnified image of the tunable diffraction network.

Fig. 3. Characterization of the STRSS. (a) Reconstruction results when the number of sampling channels is 16, 64, and 128, respectively. The reference spectrum is a dual-peak signal with an interval of 100 pm. (b) Relative error of reconstruction under a different number of rounds. The blue line represents a narrowband spectrum, while the orange line corresponds to a broadband spectrum. (c) Normalized transmission matrix of the proposed spectrometer with 160 sampling channels. (d) Calculated spectral self-correlation function. (e) Calculated spectral cross-correlation function. (f) Calculated singular values (σi) of the transmission matrix.

Fig. 4. Diagram of the experimental setup.

Fig. 5. Illustration of the experimental results. (a) Reconstruction results of single-peak spectra located at 1534.60 nm, 1546.50 nm, and 1558.74 nm, respectively. (b) Reconstruction results for three dual-peaks at various locations, each separated by an interval of 100 pm. (c) Reconstruction result of a triple-peak spectrum. The triple peaks consist of a dual-peak with an interval of 100 pm and a single peak further apart. (d) Reconstruction result of a dual-peak with an interval of 200 pm. (e) Reconstruction results of broadband spectra covering the entire C-band.