Optical System of a Prism–Grating Short-Wave Infrared Spectrometer for Single-Pixel Imaging

To circumvent the prohibitive cost of large-format infrared focal plane arrays and the significant spatial–spectral mismatch caused by spectral smile in conventional long-slit configurations, this work develops a low-cost short-wave infrared (SWIR, 1000–2500 nm) hyperspectral imaging system utilizing digital micromirror device (DMD) scanning paired with a single-element detector. A comprehensive analytical model for a prism–reflection grating (P-RG) compound dispersive element is established, enabling the joint optimization of the prism apex angle and grating period to achieve quantitative compensation of spectral distortion across the entire waveband. Based on this model, the optical system is integrated and optimized, while a centroid localization algorithm is implemented to facilitate online calibration of model parameters and real-time reconstruction of the hyperspectral data cube at the DMD plane. Experimental results demonstrate that both smile and keystone distortions are suppressed below 5μm throughout the 1000–2500 nm range, which is superior to the single DMD pixel pitch of 7.6μm. The full-field modulation transfer function (MTF) at the Nyquist frequency (32.9 lp/mm) exceeds 0.7, approaching the diffraction limit. Characterization confirms that the system provides 510 spectral channels with an average resolution of 3.57 nm and a spatial resolution of 2.5 μm. By effectively eliminating spectral overlap and cross-column crosstalk on the DMD encoding surface, this system provides a high-fidelity optical front-end for single-pixel imaging, offering a viable technical pathway for the development of affordable SWIR hyperspectral instrumentation.