# On-Orbit Polarization Calibration for Multichannel Polarimetric Camera
## 2 The Multichannel Polarimetric Camera and Main Polarization Elements
### Main Polarization Parameters of the Polarimetric Camera  
Comparing with Figures 1 and 2, we can know that the polarimetric camera is much more complex than the method of using a rotating linear polarizer. According to the Fresnel formula, when the light is reflected or refracted on the optical surface, the polarization state of the reflected or refracted light is changed because of the polarizing effects. Therefore, it is necessary to consider the polarizing effects of the optical elements in the polarimetric camera. However, due to the restriction of space and power on the satellite, it is unpractical to take the on-orbit polarization calibration for every optical element. A realizable way is proposed to analyze the polarizing effects of the polarimetric camera and take calibration to the main polarization elements, whose polarizing effects are more notable [15]. As we know, the polarizing effects are related to the optical structure, material, wavelength, aperture and coating [13]. In this multichannel polarimetric camera, the collimating lens, the beam splitters and the converging lens can be designed and optimized into approximately unpolarized elements, because their diameters and aperture angles are small. [16] The degree of polarization of the optics decreases as the angle of view decreases. At a 670 nm channel, an optical component with a field of view of 0.3 rad has a degree of polarization lower than 0.01. That means we should consider the polarizing effects of the pre-optical system and linear analyzers. The polarizing effects cannot be eliminated by optimization design. The pre-optical system of the polarimetric camera is an off-axis three-mirror reflective configuration, which is commonly used for space remote sensing detection. The mirrors are made of aluminum and the effect of the coating for polarization can be ignored which has low phase retardance [17]. For a filmless optical system, the polarization characteristics are determined by the incident angle, exit angle, incident wavelength, and refractive index of the interface, which can be calculated by the Fresnel formula. The entrance pupil diameter is 150 mm and the focal length is 500 mm. The polarizing effects of the optical system at the exit pupil are analyzed by means of the POLDSPSEQ macro in CODE V [18]. The design model of the optical system and the analysis result are shown in Figure 3. The polarizing effects is expressed by the diattenuation \(\varepsilon_{1}\) and the phase retardance \(\theta\)[13], where the diattenuation is defined by \(\varepsilon_{1}=(R_{s}-R_{p})/(R_{s}+R_{p})\), in which \(R_{s}\) and \(R_{p}\) represent the maximum and minimum intensity reflectance, respectively [14]. When the incent light is unpolarized light, the polarization state at the exit pupil can also describe the polarizing effects, which contains partially linear polarized light, partially circular polarized light, and partially elliptical polarized light. Figure 2: (**a**) Schematic of the multichannel polarimetric camera and (**b**) optical design model of the multichannel polarimetric camera. The incident light is represented by the red solid lines. The three channels (analyzer channels at 0\({}^{\circ}\), 60\({}^{\circ}\), and 120\({}^{\circ}\)) are indicated by the red dotted boxes. Figure 3b shows that the polarization state of the exit light is a partially linear polarized light. We can see from Figure 3c,d that the diattenuation \(\varepsilon_{1}\) and the retardance are changed according to the field of view and the wavelength. The parameters rise as the increase of the field of view. The material or the coating of the mirrors decides their changes as the wavelength. For the material of aluminum, the diattenuation \(\varepsilon_{1}\) at 870 nm is larger than the other wavelength. On the contrary, the retardance at 870 nm is smaller than the other wavelength.