# Four-Channel Polarimetric-Spectral Intensity Modulation Imager
## 1 Introduction  
With the increasing demand for optical remote sensing information acquisition, many researchers are deeply studying polarization spectral imaging technology and the technique is widely used in many fields, including atmospheric aerosol characterization [1; 2], remote sensing [3; 4; 5; 6], and material characterization [7; 8; 9; 10; 11; 12]. These fields require an imaging spectropolarimeter to simultaneously measure the spatial, spectral, and polarization information of a scene. Polarimetric-spectral intensity modulation (PSIM) imaging is one of these polarization spectral imaging technologies. It measures the polarization information of the target by inserting an intensity modulation module into the traditional spectrometer system. PSIM was first proposed by [PERSON] and OKA [13; 14]. The system has a simple structure, and there are no moving parts in it. In order to detect polarization spectra, [PERSON] combined PSIM with a grating or dispersion prism [15] which can acquire the spectrometer and polarimeter of a target [15]. [PERSON] et al. combined the Fourier transform spectrometer with PSIM to obtain a Fourier transform spectral imaging polarizer [7]. Computed tomography imaging spectropolarimeter was proposed by [PERSON] et al., which can simultaneously obtain information from a Stokes spec, polarimeter, and image [16]. [PERSON] et al. designed a PSIM polarization measurement method of coded aperture based on intensity-modulated, coded aperture measurement [17], which comprises spectral polarization intensity modulation and a compressive sensing spectral imaging system. [PERSON] et al. analyzed the angle error of a channeled spectropolarimeter [18]. [PERSON] et al. proposed tempo-spatially modulated imaging spectropolarimetry based on a polarization modulation array in order to realize the demodulation of target polarization spectral information [19]. The polarization spectrum instrument based on PSIM needs to recover the polarization spectrum data by Fourier transform channel filtering. It is necessary to calibrate the phase delay of the instrument for high precision polarization spectral data demodulation. [PERSON] used 22.5\({}^{\circ}\) and 45\({}^{\circ}\) linearly polarized beams to calibrate this. [PERSON] used auxiliarywaveplates to calibrate this instead [20; 21]. However, PSIM applies the channel filtering method to Stokes data demodulation, which results in a limited Stokes spectral resolution and a crosstalk between channels [22; 23; 24]. [PERSON] et al. combined the PSIM with two orthogonal optical axes using a Wollaston prism, and obtained two orthogonal interferograms on the detector. By processing the positive interferograms, the space range between each channel was enlarged, channel crosstalk was avoided, and spectral resolution was improved. However, the data demodulation still uses Fourier transform, which has the problem of edge jitter [25]. [PERSON] et al. combined four PSIMs with the Savart polarizer. The four PSIMs have different thicknesses, resulting in different phase delays. Four groups of interferogram are obtained on the detector, and the data demodulation is realized by the spatial processing of four interferograms. However, it has high requirements for PSIM thickness [26]. [PERSON] proposes an efficient calibration method for the spectral modulation transfer function via channel shifting in a channeled spectropolarimeter using PSIM [27]. [PERSON] proposes a reconstruction method, incorporating the complete physical model into a traditional deep neural network for a channeled spectropolarimeter [28]. In this paper, a Four-Channel Polarimetric Spectrometer (FCPS) is proposed for the simultaneous measurement of the target spectrum and polarization states based on PSIM. To measure the modulated spectra, this paper proposes a spatial data demodulation method that can demodulate Stokes vector information using a calibrated system matrix. Spatial data demodulation can avoid the influence of channel crosstalk.