## 1 Introduction  
With the rapid development of aerospace remote sensing, resource surveys, medical biology, military reconnaissance, agriculture, and other fields, there is an urgent need for high-performance infrared imaging detection instruments, and higher requirements have been put forward for the real-time detection of transient targets, weak signal detection ability, compact structure, and stability. The multidimensional information acquisition technology developed on the basis of infrared imaging spectroscopy and polarization imaging technology, known as infrared polarization spectroscopy imaging technology, has unique advantages. It can obtain the imaging, spectral, and polarization information of the detected target at the same time, greatly improving the amount of information obtained by optical detection, providing a more abundant, more scientific, and more objective scientific basis and information source for target detection, recognition, and confirmation [1; 2; 3; 4; 5; 6; 7]. In 2018, Xi'an Jiaotong University proposed a channel polarization spectroscopy measurement system based on a liquid crystal variable retarder (LCVR). The system adjusts the zero optical path difference position by controlling the optical path difference delay of an LCVR and time-sharing each channel to realize the function of polarization spectroscopy imaging. It improves the resolution of reconstructed spectra while maintaining the high resolution of images [8]. In 2021, the University of Saskatchewan in Canada proposed a multispectral polarization imaging instrument for the contour imaging of atmospheric aerosols. The instrument incorporates a liquid crystal polarization rotator and an acousto-optic tunable filter to capture polarized multispectral images of the atmospheric edge, thereby enhancing both the image resolution and signal-to-noise ratio [9]. In 2021, a static full-Stokes Fourier transform infrared spectrometer was proposed and built by the Shandong University of Technology, which includes a liquid crystal polarization modulator and a birefringent shear interferometer as the core devices. The 4D data cube containing spatial, spectral, and polarization information can be obtained synchronously, and the optical path difference and full-Stokes polarization information with good linear distribution can be obtained with a high signal-to-noise ratio [10]. Image and spectral information processing is one of the key technologies in the development of spectral imaging systems. In the field of polarization spectrum and image data processing, Xi'an Jiaotong University conducted a study in 2010, while the University of Burgundy conducted a study in 2019, on the image formation and data distribution characteristics of polarization interferometric imaging spectrometry in spatio-temporal mixed modulation mode, proposing principles and methods for multi-spectral data acquisition and processing [11; 12; 13]. In 2021, the Changchun University of Science and Technology used guided filtering and a pulse-coupled neural network to preprocess a polarization angle image, and then obtained the polarization features by combining the polarization degree image, after which the multi-scale analysis method was used to extract and fuse the features of the high-frequency part, making the image details more affluent and obvious [14]. At present, most of such systems work in the visible light and near infrared band, and there are few studies on the mid-infrared band [15; 16; 17]. The thermal imaging of the infrared spectrum is characterized by its detection ability for targets in all-weather conditions and its reduced susceptibility to interference from weather and external factors, thus offering significant advantages in accurate target recognition. In this paper, we propose a static infrared polarization snapshot spectral imaging system for infrared target recognition, which is based on an infrared micro-nanowire-grating polarizer array device, an infrared micro-lens array device, and a rooftop-shaped infrared multi-stage micro-reflector.