# Polarization Radiometric Calibration in Laboratory for a Channeled Spectropolarimeter
## 1 Introduction  
Imaging spectrometer and imaging polarimeter are of particular importance in many fields, including atmospheric aerosol characterization [1; 2], remote sensing [3; 4; 5; 6], and material characterization [7; 8]. These fields require an imaging spectropolarimeter to simultaneously measure the spatial, spectral, and polarization information of a scene. In 1999, [PERSON] and [PERSON] first described the channeled spectropolarimetry technique, an attractive approach for polarimetry [9; 10] by which we can eliminate the disadvantages of conventional modulation principles. With a simple optical system and no movable polarization components, the entire wavelength-dependent state of polarization (SOP) and spectral information of a scene can be acquired simultaneously. In recent publications, researchers have investigated incorporating the channeled spectropolarimetry technique into different types of imaging spectrometers, such as the dispersive imaging spectrometer [3; 4; 11], Fourier transform imaging spectrometer [6; 12], and computed tomography imaging spectrometer [13; 14]. Among these incorporations, the channeled spectropolarimetry technique with the dispersive imaging spectrometer, which is called the channeled dispersive imaging spectropolarimeter (CDISP), has a simple structure and is easier to implement in terms of technology. Noteworthy is that the CDISP should gothrough a series of accurate calibration before quantitative applications. For imaging instruments, the actual spectral radiance of the detected object should be obtained through radiometric calibration. For the imaging polarimeter, the target light from the detected object will be affected by the polarization properties of an optical system when transmitted in the optical system. This will change the polarimetric state of target light and affect the measurement accuracy of polarization information. Therefore, in the process of radiometric calibration for the imaging spectropolarimeter, the polarization properties of an optical system should be considered. However, to the best of our knowledge, radiometric calibration for the imaging spectropolarimeter have not be well solved with the previous literature. [PERSON] et al. implemented radiometric calibration and polarimetric calibration for the channeled interference imaging spectropolarimeter [15], while the two types of calibration are carried out separately. The radiometric calibration is the same as that of traditional imaging spectrometer, without taking into account the influence of the polarization properties of optical system. [PERSON] et al. provided the polarimetric calibration of the channeled polarimeter with a pushbroom hyperspectral imaging sensor only [4], without considering the radiometric calibration of the instrument. [PERSON] et al. presented a method of polarimetric calibration and reconstruction for the fieldable CDISP [16]. This method took into account the polarization properties of the optical system, but only if it can accurately measure the spectral radiance of the detected object. The interaction between the polarized beam and the optical system could be called polarization radiation transmission. Modeling and analyzing the polarization radiation transmission properties of optical system is the core to obtain the polarization properties of optical system and the theoretical basis for calibration of polarization detection system. In this paper, we use a fieldable CDISP designed for remote sensing as an example to analyze the influence of polarization properties of the optical system on radiometric calibration of the imaging spectropolarimeter. Considering simultaneously alignment errors of the polarimetric spectral intensity modulation (PSIM) module and variation of the retardations at different fields of view, we establish a polarization radiometric calibration model for the fieldable CDISP.