Evaluation of Polarization Observation Accuracy of SGLI VNR-PL Using In-Orbit Calibration Data

Abstract

The Second Generation Global Imager (SGLI) on the Global Change Observation Mission—Climate (GCOM-C) “SHIKISAI” has polarization observation channels at wavelengths of red (673.5 nm—P1) and near infrared (868.5 nm—P2), and it is expected to extract information of aerosols on land with higher accuracy than conventional observation methods by utilizing the scattering by atmospheric particles obtained by polarization observation. The polarization observation of SGLI adopts a method to derive the Stokes parameters I, Q, and U by observing three polarized azimuths. In this paper, the polarization observation accuracy means the polarization degree accuracy and polarization azimuth accuracy, which can be expressed as a relative value of I, Q, and U, and does not include the accuracy of radiance. In order to evaluate the polarization observation accuracy of SGLI on orbit, variations of the Q/I and U/I have been investigated using three kinds of calibration data. The effects of calibration methods and aging have been successfully eliminated by comparing independent evaluations of three kinds of calibration data. As a result, it was concluded that the variations of Q/I and U/I are achieved within a slight variation range of ±0.07% at the P1 telescope and ±0.04% at the P2 telescope.

1. Introduction

The Global Change Observation Mission (GCOM) aims to establish and demonstrate a global, long-term satellite observing system to measure essential geophysical parameters and facilitate an understanding of global water circulation and climate change, which could eventually contribute to improving future climate projections through a collaborative framework with climate model institutions. GCOM consists of two polar-orbiting satellite observing systems—GCOM-Water (GCOM-W) and GCOM-Climate (GCOM-C). The Second Generation Global Imager (SGLI) is an optical sensor on-board GCOM-C. SGLI is a successor of the Global Imager (GLI) on-board the Advanced Earth Observing Satellite-II (ADEOS-II), and this is an optical sensor that is capable of multi-channel observation at wavelengths from near-UV to thermal infrared (380~12 μm) [1]. GCOM-C with SGLI was launched on 23 December 2017. After the initial function verification, calibration, and validation for 1 year, various GCOM-C scientific products have been released to the public since December 2018 [2].

SGLI includes two independent radiometers—VNR (visible and near-infrared radiometer) and IRS (infrared scanning radiometer). VNR is a push-broom radiometer that consists of non-polarization (VNR-NP) with 11 spectral channels, polarization, and multi-directional observation (VNR-PL) with two spectral channels and three polarization angles. IRS is a whisk-broom radiometer which has a short-wavelength infrared spectral region (IRS-SWI) and a thermal infrared spectral region (IRS-TIR).

An overview of the SGLI-VNR is shown in Figure 1. The SGLI-VNR consists of non-polarized (NP) observation telescopes, polarized (PL) observation telescopes, and a solar diffuser. NP telescopes consist of 3 telescopes, namely NP-Nadir, NP-Left, and NP-Right, and each telescope has 11 channels from VN1 for 380 nm to VN11 for 868.5 nm. PL Telescopes consist of two telescopes—PL1 for 673.5 nm and PL2 for 868.5 nm. A tilting mechanism enables PL telescopes to observe the earth by rotating ±45 degrees in an along-track direction. Each PL telescope has three polarized angles to calculate the Stokes parameters I, Q, and U. The polarized angles are extracted by positioning a polarizing filter composed of three polarizers, with each polarization azimuth above the liner CCD.

The polarization observation channel’s specification is summarized in

Table 1. Polarization observation channel specification.

Radiometer	Channel	λ	∆λ	Lstd	Lmax	SNR at Lstd	IFOV
		[nm]		[W/m2/sr/μm]			[m]
VNR-PL	P1	673.5	20	25	250	250	1000
	P2	868.5	20	30	300	250	1000

. λ and ∆λ are the center wavelength and bandwidth, respectively. The specification of the standard radiance (Lstd), maximum radiance (Lmax), signal-to-noise ratio (SNR), and instantaneous field of view (IFOV) for each channel are shown in Table 1.

The polarized observation of the SGLI-VNR is capable of observation with a 1150 km swath width at a 1 km ground spatial resolution. This is one of the unique features that is not found in other polarized observation sensors.

One of the challenges in predicting global average temperature increases is reducing the uncertainty of the effects of aerosols on temperature fluctuations. It is known that polarization observation is effective for aerosol observation.

POLDER (Polarization and Directionality of the Earth’s Reflectances) is the most famous earth observation satellite sensor that has polarization channels with visible and near-infrared wavelengths; however, the ground surface reflectance in visible and near-infrared wavelengths is high, so it has been difficult to accurately estimate terrestrial aerosols only in the visible and near-infrared wavelengths.

SGLI has polarization channels with a red wavelength (P1, 673.5 nm) and near-infrared wavelength (P2, 868.5 nm); furthermore, it has near-ultraviolet and violet wavelength non-polarization channels with low ground surface reflectivity [3]. Using SGLI’s simultaneous observations of non-polarization channels with near-ultraviolet and violet wavelengths and polarization channels with red and near-infrared wavelengths, it is expected to be possible to accurately estimate terrestrial aerosols, reduce the uncertainty of the influence of aerosols on temperature fluctuations, and improve the prediction accuracy of global average temperature increases.

The polarization observations of the SGLI calculates the Stokes parameters I, Q, and U from the output of the three polarization bands; thus, the error of the output ratio among each band has a significant effect on the polarization observation accuracy.

In a pre-launch calibration test, input/output characteristics for converting output values to the incident radiance and optical properties of condensing optics and polarization filters were measured and formulized for each polarization band and for each pixel to achieve high polarization observation accuracy. These results were applied to the Level-1 processing algorithms and radiometry model data.

The following two points are planned to be performed in the in-orbit calibration and validation of polarization observation in the VNR-PL:

• A trend evaluation of the effect on polarization observation by fluctuations in the sensitivity ratio among polarization bands in orbit;
• An absolute accuracy validation of the polarization observation.

In-orbit calibration evaluated the effect on polarization observation accuracy by the variation of the output ratio among polarization bands and the variation of the observed polarization azimuth angle using the calibration data of an internal lamp, solar diffuser, and lunar calibration maneuver. In the future, we plan to evaluate the absolute of the polarization observation accuracy using these calibration data and improve the accuracy by correcting the sensitivity between each band.

In this paper, the result of pre-launch calibration test on polarization observation accuracy is described. After that, the evaluation result of the effect on polarization observation accuracy using in-orbit calibration data is described.

2. Polarization Observation Model and Pre-Launch Calibration

VNR-PL consists of two sensors—P1 and P2 telescopes. The P1 and P2 telescopes observe a 673.5 nm wavelength band and 868.5 nm wavelength band, respectively. Each telescope consists of three line sensors—S09 (φ_S09 ≈ +60°), S10 (φ_S10 ≈ 0°), and S11 (φ_S11 ≈ −60°)—to observe three polarization azimuth angles. The φ_S09, φ_S10, and φ_S11 mean polarization azimuth angles of polarizers are set above three line sensors. These three line sensor outputs enable us to obtain three components (I, Q, and U), excluding the circularly polarized component (V) from the four components of the Stokes vector (I, Q, U, and V). The following Equation (1) is the general formula for calculating I, Q, and U.

$$\left(\begin{array}{c}\mathrm{I}\\ \mathrm{Q}\\ \mathrm{U}\end{array}\right)={\left(\begin{array}{ccc}1& \cos 2{\mathsf{\phi }}_{\mathrm{S}09}& \sin 2{\mathsf{\phi }}_{\mathrm{S}09}\\ 1& \cos 2{\mathsf{\phi }}_{\mathrm{S}10}& \sin 2{\mathsf{\phi }}_{\mathrm{S}10}\\ 1& \cos 2{\mathsf{\phi }}_{\mathrm{S}11}& \sin 2{\mathsf{\phi }}_{\mathrm{S}11}\end{array}\right)}^{-1}\left(\begin{array}{c}{\mathrm{I}}_{\mathrm{S}09}\\ {\mathrm{I}}_{\mathrm{S}10}\\ {\mathrm{I}}_{\mathrm{S}11}\end{array}\right)$$

(1)

where I_S09, I_S10, and I_S11 mean the radiance of three polarization bands calculated from the output of the three line sensors, respectively.

Degree of polarization P and polarization azimuth angle θ are calculated by Equations (2) and (3) using I, Q, and U.

$$\mathrm{P}=\frac{\sqrt{{\mathrm{Q}}^2+{\mathrm{U}}^2}}{\mathrm{I}}$$

(2)

$$\mathsf{\theta }=\left\{\begin{array}{ll}\frac{1}{2}{\tan }^{-1}\frac{\mathrm{U}}{\mathrm{Q}}& :\mathrm{Q}>0\\ \frac{1}{2}{\tan }^{-1}\frac{\mathrm{U}}{\mathrm{Q}}+{90}^{°}& :\mathrm{U}\ge 0,\mathrm{Q}<0\\ \frac{1}{2}{\tan }^{-1}\frac{\mathrm{U}}{\mathrm{Q}}-{90}^{°}& :\mathrm{U}<0,\mathrm{Q}<0\\ {90}^{°}& :\mathrm{Q}=0\end{array}\right.$$

(3)

When the matrix that converts the observed radiance into a Stokes vector is replaced with Equation (4), P and θ are represented by Equations (5) and (6), respectively.

$$\left(\begin{array}{ccc}{\mathrm{n}}_{11}& {\mathrm{n}}_{12}& {\mathrm{n}}_{13}\\ {\mathrm{n}}_{21}& {\mathrm{n}}_{22}& {\mathrm{n}}_{23}\\ {\mathrm{n}}_{31}& {\mathrm{n}}_{32}& {\mathrm{n}}_{33}\end{array}\right)={\left(\begin{array}{ccc}1& \cos 2{\mathsf{\phi }}_{\mathrm{S}09}& \sin 2{\mathsf{\phi }}_{\mathrm{S}09}\\ 1& \cos 2{\mathsf{\phi }}_{\mathrm{S}10}& \sin 2{\mathsf{\phi }}_{\mathrm{S}10}\\ 1& \cos 2{\mathsf{\phi }}_{\mathrm{S}11}& \sin 2{\mathsf{\phi }}_{\mathrm{S}11}\end{array}\right)}^{-1}$$

(4)

$$\mathrm{P}=\frac{\sqrt{\left({\mathrm{n}}_{21}{}^2+{\mathrm{n}}_{31}{}^2\right){\left(\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}\right)}^2+\left({\mathrm{n}}_{22}{}^2+{\mathrm{n}}_{32}{}^2\right)+\left({\mathrm{n}}_{23}{}^2+{\mathrm{n}}_{33}{}^2\right){\left(\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}\right)}^2}}{{\mathrm{n}}_{11}\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}+{\mathrm{n}}_{12}+{\mathrm{n}}_{13}\frac{{\mathrm{I}}_{\mathrm{S}11}}{{\mathrm{I}}_{\mathrm{S}10}}}$$

(5)

$$\mathsf{\theta }=\left\{\begin{array}{ll}\frac{1}{2}{\tan }^{-1}\frac{{\mathrm{n}}_{31}\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}+{\mathrm{n}}_{32}+{\mathrm{n}}_{33}\frac{{\mathrm{I}}_{\mathrm{S}11}}{{\mathrm{I}}_{\mathrm{S}10}}}{{\mathrm{n}}_{21}\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}+{\mathrm{n}}_{22}+{\mathrm{n}}_{23}\frac{{\mathrm{I}}_{\mathrm{S}11}}{{\mathrm{I}}_{\mathrm{S}10}}}& :\mathrm{Q}>0\\ \frac{1}{2}{\tan }^{-1}\frac{{\mathrm{n}}_{31}\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}+{\mathrm{n}}_{32}+{\mathrm{n}}_{33}\frac{{\mathrm{I}}_{\mathrm{S}11}}{{\mathrm{I}}_{\mathrm{S}10}}}{{\mathrm{n}}_{21}\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}+{\mathrm{n}}_{22}+{\mathrm{n}}_{23}\frac{{\mathrm{I}}_{\mathrm{S}11}}{{\mathrm{I}}_{\mathrm{S}10}}}+{90}^{°}& :\mathrm{U}\ge 0,\mathrm{Q}<0\\ \frac{1}{2}{\tan }^{-1}\frac{{\mathrm{n}}_{31}\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}+{\mathrm{n}}_{32}+{\mathrm{n}}_{33}\frac{{\mathrm{I}}_{\mathrm{S}11}}{{\mathrm{I}}_{\mathrm{S}10}}}{{\mathrm{n}}_{21}\frac{{\mathrm{I}}_{\mathrm{S}09}}{{\mathrm{I}}_{\mathrm{S}10}}+{\mathrm{n}}_{22}+{\mathrm{n}}_{23}\frac{{\mathrm{I}}_{\mathrm{S}11}}{{\mathrm{I}}_{\mathrm{S}10}}}-{90}^{°}& :\mathrm{U}<0,\mathrm{Q}<0\\ {90}^{°}& :\mathrm{Q}=0\end{array}\right.$$

(6)

where P and θ are determined by the ratio of I_S09, I_S10, and I_S11; thus, the accuracy of P and θ are determined by the ratio of I_S09, I_S10, and I_S11. In other words, polarization observation accuracy is affected not by the accuracy of I_S09, I_S10, and I_S11 themselves but the accuracy of the ratio of I_S09, I_S10, and I_S11.

The sensitivity characteristics of the sensor and the polarization characteristics of the optical system are corrected for each pixel in order to improve the calculation accuracy of I, Q, and U in the pre-launch calibration of the VNR-PL. Equations (7)–(9) show formulas for calibrating the radiance of the three polarization bands.

$${\mathrm{I}}_{\mathrm{S}09}={\mathrm{b}}_{\mathrm{S}09}{\mathrm{DN}}_{\mathrm{S}09}^{\mathrm{obs}}+{\mathrm{c}}_{\mathrm{S}10}{{\mathrm{DN}}_{\mathrm{S}09}^{\mathrm{obs}}}^2+{\mathrm{d}}_{\mathrm{S}10}{{\mathrm{DN}}_{\mathrm{S}09}^{\mathrm{obs}}}^3+{\mathrm{e}}_{\mathrm{S}10}{{\mathrm{DN}}_{\mathrm{S}09}^{\mathrm{obs}}}^4$$

(7)

$${\mathrm{I}}_{\mathrm{S}10}={\mathrm{b}}_{\mathrm{S}10}{\mathrm{DN}}_{\mathrm{S}10}^{\mathrm{obs}}+{\mathrm{c}}_{\mathrm{S}10}{{\mathrm{DN}}_{\mathrm{S}10}^{\mathrm{obs}}}^2+{\mathrm{d}}_{\mathrm{S}10}{{\mathrm{DN}}_{\mathrm{S}10}^{\mathrm{obs}}}^3+{\mathrm{e}}_{\mathrm{S}10}{{\mathrm{DN}}_{\mathrm{S}10}^{\mathrm{obs}}}^4$$

(8)

$${\mathrm{I}}_{\mathrm{S}11}={\mathrm{b}}_{\mathrm{S}11}{\mathrm{DN}}_{\mathrm{S}11}^{\mathrm{obs}}+{\mathrm{c}}_{\mathrm{S}11}{{\mathrm{DN}}_{\mathrm{S}11}^{\mathrm{obs}}}^2+{\mathrm{d}}_{\mathrm{S}11}{{\mathrm{DN}}_{\mathrm{S}11}^{\mathrm{obs}}}^3+{\mathrm{e}}_{\mathrm{S}11}{{\mathrm{DN}}_{\mathrm{S}11}^{\mathrm{obs}}}^4$$

(9)

where ${\mathrm{DN}}_{\mathrm{S}09}^{\mathrm{obs}}$, ${\mathrm{DN}}_{\mathrm{S}10}^{\mathrm{obs}}$, and ${\mathrm{DN}}_{\mathrm{S}11}^{\mathrm{obs}}$ mean outputs [DN] after the offset correction for each sensor. b_S09, b_S10, b_S11, c_S09, c_S10, c_S11, d_S09, d_S10, d_S11, e_S09, e_S10, and e_S11 mean coefficients determined by pre-launch calibration. I_S09, I_S10, and I_S11 mean radiance [W/m²/sr/mm] after the sensitivity characteristics correction.

Incident light on the VNR-PL is received by a detector through a condenser lens system, band pass filter, and polarizers with three polarized azimuth angles above the detector. The model of the VNR-PL optical system was constructed using the results of pre-launch calibration in consideration of the following phenomena:

(a)

There is a component that eliminates the polarization state in the optical system;

(b)

The polarization state of the incident light to the polarization filter above the detector has a pixel dependency that is symmetric with respect to the central pixel because of the rotating of the relationship between the sagittal direction and tangential direction as the detector location in the optical system;

(c)

The polarizers mounted on the VNR-PL have pixel dependence in the polarized azimuth by manufacturing tolerance.

Equation (10) shows the formula for calculating I, Q, and U.

$$\left(\begin{array}{c}\mathrm{I}\\ \mathrm{Q}\\ \mathrm{U}\end{array}\right)={\left(\begin{array}{ccc}1& \left(1-{\mathrm{a}}_{\mathrm{S}09}\right)\cos 2{\mathsf{\phi }}_{\mathrm{S}09}& \left(1-{\mathrm{a}}_{\mathrm{S}09}\right)\sin 2{\mathsf{\phi }}_{\mathrm{S}09}\\ 1& \left(1-{\mathrm{a}}_{\mathrm{S}10}\right)\cos 2{\mathsf{\phi }}_{\mathrm{S}10}& \left(1-{\mathrm{a}}_{\mathrm{S}10}\right)\sin 2{\mathsf{\phi }}_{\mathrm{S}10}\\ 1& \left(1-{\mathrm{a}}_{\mathrm{S}11}\right)\cos 2{\mathsf{\phi }}_{\mathrm{S}11}& \left(1-{\mathrm{a}}_{\mathrm{S}11}\right)\sin 2{\mathsf{\phi }}_{\mathrm{S}11}\end{array}\right)}^{-1}\left(\begin{array}{c}{\mathrm{I}}_{\mathrm{S}09}\\ {\mathrm{I}}_{\mathrm{S}10}\\ {\mathrm{I}}_{\mathrm{S}11}\end{array}\right)$$

(10)

where a_S09, a_S10, and a_S11 mean depolarization ratios modeled by phenomenon (a), and φ_S09, φ_S10, and φ_S11 mean sum of the polarization rotation of the optical systems and the polarization azimuth of the polarizer modeled by phenomena (b) and (c). These have unique values for each pixel from the results of the pre-launch calibration.

In the pre-launch calibration, the sensor outputs were measured while rotating the polarizer (100% linear polarizer or 5% partial polarizer) set between the light source and the sensor for two rounds. Upon rotating the 5% partial polarizer, it measured two radiance conditions of about 90 % of the saturation level of the sensor (L_max) and equivalent to the observation target in orbit (L_std). As an example of measured pre-launch calibration data, the sensor outputs while rotating the polarizer for two rounds and the light incident angle of view of +0.5 degree for the P1 telescope are shown in Figure 2.

Figure 2a–c show the outputs of the three polarization bands while rotating the 100% linear polarizer for two rounds, the outputs of the three polarization bands while rotating the 5% partial polarizer for two rounds at the radiance conditions of L_max, and the outputs of the three polarization bands while rotating the 5% partial polarizer for two rounds at the radiance conditions of L_std, respectively.

The number of measurement data while rotating the polarizer for two rounds was about 4620 points. For each measurement point, P and θ were calculated.

The accuracy of P and θ were calculated as polarization observation accuracy. Each accuracy value was calculated by the root mean square of difference between the observed value and characteristics of incident light at about 4620 points of measurement data. The accuracy of P was calculated by Equation (11) from the difference between P_obs and P_in. P_obs and P_in are the degree of polarization observed and degree of polarization of incident light, respectively. The accuracy of θ was calculated by Equation (12) from the difference between θ_obs and θ_in. θ_obs and θ_in are the observed polarization azimuth angle and polarization azimuth angle of incident light, respectively.

$$\mathrm{Degree}\mathrm{of}\mathrm{polarization}\mathrm{accuracy}=\sqrt{ \overline{{\left(\frac{{\mathrm{P}}_{\mathrm{obs}}-{\mathrm{P}}_{\mathrm{in}}}{{\mathrm{P}}_{\mathrm{in}}}\right)}^2}}$$

(11)

$$\mathrm{Polarization}\mathrm{azimuth}\mathrm{angle}\mathrm{accuracy}=\sqrt{\overline{{\left({\mathsf{\theta }}_{\mathrm{obs}}-{\mathsf{\theta }}_{\mathrm{in}}\right)}^2}}$$

(12)

Pre-launch calibration data for polarization observation were measured at ten angles of view in the P1 and P2 telescopes. The results of the accuracy of P and θ after rotating the 5% partial polarizer are shown in Figure 3.

Figure 3a,b are the result of the accuracy of P and θ at ten angles of view in the P1 telescope and P2 telescope after rotating the 5% partial polarizer in two radiance conditions, respectively. The angle of view shown on the horizontal axis in Figure 3 corresponds to the pixel direction of the line sensor. The left vertical axis and the right vertical axis show the accuracy of P and θ, respectively. The accuracy of P is ratio of difference between P_obs and P_in to P_in, therefore, in the case of rotating 5% partial polarizer, the P accuracy of 4% means that the difference between P_obs and P_in is 0.2%.

3. In-Orbit Calibration and Validation

Degree of polarization (P) and polarization direction are particularly important for polarization observation. These are calculated from the relative values of Stokes parameters I, Q, and U.

POLDER is one of the most famous in-orbit observation sensors with a polarization observation function. Polarization observation of the POLDER is realized by switching the polarization filter above the CCD sensor [4]. Therefore, the sensitivity degradation does not affect the relative values of Stokes parameters I, Q, and U. The sensitivity degradation of the CCD sensor does not affect the degree of polarization and polarization direction. POLDER has no on-board calibration system, so in-flight calibration methods that use the sunlight reflected within the sun’s glitter have been developed. The expected accuracy is about 0.5% in the near-infrared channel and about 2% in the visible channels in terms of percent polarization [5].

On the other hand, the SGLI-VNR has on-board radiometric calibration systems. During the polarization observation of the VNR-PL, the sensitivity change in each CCD sensor greatly influences the polarization observation accuracy because the output of the three polarization bands composed of independent lines of CCD are used to calculate I, Q, and U. Therefore, it is important for polarization observation in the VNR-PL to monitor the variations in the sensitivity ratio among the polarization bands in-orbit.

The SGLI-VNR in-orbit calibration methodology and frequency is shown

Table 2. SGLI VNR in-orbit calibration methodology and frequency.

Calibration Methodology		Frequency
On-board calibrator
	Solar diffuser	Once every eight days
	Internal lamp	Once every eight days
	Dark image	Once every eight days
Calibration maneuver
	Lunar calibration maneuver	Monthly
	Solar angle correction maneuver	Yearly
	90 deg. yaw maneuver	Yearly

[6].

An explanation of the SGLI-VNR on-board calibration and output fluctuation trends of each polarization bands 1 year since launch is reported by Urabe et al. [1]. The trend data for internal lamp calibration, solar diffuser calibration, and lunar calibration maneuver are used for the in-orbit calibration and verification of polarization observations. Among the three calibrations, a diffuser is used for internal lamp calibration and solar diffuser calibration. Figure 4 shows a configuration of the internal lamp and solar diffuser calibrations.

The left panel of Figure 4 is a side view of the SGLI-VNR’s internal lamp and solar diffuser calibrations. The right panel of Figure 4 shows details of the LED and monitor bench.

The diffuser plate is normally shielded from direct solar illumination and atomic oxygen by being stored inside the SGLI-VNR structure. This is only deployed for internal lamp solar diffuser calibrations once every eight days. +X_sat and +Z_sat are the satellite traveling direction and the nadir direction, respectively. +X_diff and +Y_diff are in-plane direction of diffuser, and +Z_diff is vertical direction of diffuser in the diffuser coordinate system. Regarding the internal lamp and solar diffuser calibrations, the diffuser plate faces the direction tilted 45 degrees with respect to the satellite traveling direction by the rotation of the diffuser mechanism. Then, the PL telescopes face toward the diffuser plate, while LEDs face the direction of the irradiating diffuser plate by the rotation of the tilting mechanism.

Polarization observation accuracy is affected not by a variation of the sensor’s output but a variation of the output ratio among each polarization band. Therefore, the trends of each sensor output ratio and change amount of the polarization components Q/I and U/I need to be described.

3.1. Internal Lamp Calibration

Internal lamp calibration is one of the methods for monitoring in-orbit radiometric performance. In the internal lamp calibration, the PL telescopes observe the scattered light of the LED lamp irradiated to the diffuser plate with three polarization bands. White LED lamps and near-infrared LED lamps are used for the P1 and P2 telescopes, respectively. There are some variable factors in the internal lamp calibration data, namely the sensor sensitivity, the reflection characteristics of the diffusion plate, the polarization characteristics of the LED light, and the lamp’s emitting angle dependence.

The internal lamp calibration trends of P1 the P2 telescopes are shown in Figure 5a,b, respectively. The data after a lapse of 95 days since launch with stable temperature control were evaluated. The vertical axis shows the ratio of the average output of effective pixels after a lapse of 95 days since launch.

The internal lamp calibration trends of the three polarization bands of both telescopes have been decreasing at a similar rate among the three polarization bands. It is thought that the decrease in the sensor’s output is due to the deterioration of the lamp. Since polarization observation accuracy is affected not by changes in the sensor’s output but by changes in the output ratio among each polarization band, trends of I_S09/I_S10 and I_S11/I_S10 and trends of ΔQ/I and ΔU/I will be described. I_S09/I_S10 and I_S11/I_S10 are the mean ratios of I_S09 to I_S10 and I_S11 to I_S10, respectively. ΔQ/I and ΔU/I are the mean change amounts of the polarization characteristics of Q/I and U/I, respectively.

The I_S09/I_S10 and I_S11/I_S10 trends of the internal lamp calibration are shown in Figure 6a,b, respectively. The ΔQ/I and ΔU/I trends calculated by the change in I_S09/I_S10 and I_S11/I_S10 are shown in Figure 7a,b, respectively.

As shown in Figure 6, the variations of I_S09/I_S10 and I_S11/I_S10 in the P2 telescope are generally within ±0.1%; however, in the P1 telescope, I_S09/I_S10 slightly decreases, while I_S11/I_S10 increases. As a result, ΔU/I is on a downward trend in the P1 telescope, decreasing by about 0.2% in the 2 years since launch. The ΔQ/I in the P1 telescope, and ΔQ/I and ΔU/I in P2 telescope, are stable in the range of ±0.1%.

If the cause of this change is due to a change in the sensitivity of the sensor, it affects the polarization observation accuracy. However, since it may be caused by a change in the characteristics of the light source or diffuser, this result cannot conclude that this change affects the polarization observation accuracy.

3.2. Solar Diffuser Calibration

Solar diffuser calibration is another method for monitoring in-orbit radiometric performance. The SGLI-VNR observes solar light scattered by the diffuser panel once in eight days. The SGLI-VNR is equipped with a deployable diffuser to illuminate the uniformly scattered sunlight to CCD elements for the solar diffuser calibration. The long-term change in the CCD response to diffused sunlight may arise from the degradation of either the sensitivity of the telescopes or the bidirectional reflectance distribution function (BRDF) of the diffuser. Since multilayer insulation’s (MLI) stray light and the diffuser plate’s degradation with a varying in-plane distribution caused by ultraviolet (UV) irradiation to the stored diffuser plate were confirmed during the initial study, it was necessary to take these matters into consideration [1].

In the solar diffuser calibration, three polarization bands observe the scattered light of solar light on the diffuser panel. The polarization characteristics of scattered light on the diffuser panel is evaluated by using the following method.

For example, as can be seen from the polarization reflection characteristics of the Spectralon^®—the material of the solar diffuser on SGLI—S-polarized reflectance is generally higher than the P-polarized reflectance [7]. For this reason, the polarization azimuth angle observed by the three polarization bands should be equal to the S-polarized direction of the scattered light of sunlight on the diffuser panel. Polarization observation evaluations using solar diffuser calibration data have been conducted to analyze polarization observation accuracy by the difference between the S-polarized direction of the scattered light of sunlight on the diffuser panel and the polarization azimuth angle observed by the three polarization bands. Since the solar diffuser calibration data contains stray light reflected from the structure covered by MLI, the range of effective CCD pixels and zenith angles at the diffuser coordinate system is limited (shown in

Table 3. Limited range of solar diffuser calibration data.

Parameters	P1	P2	Unit
Zenith angles at the diffuser coordinate system	52–54	52–54	deg.
Range of effective CCD pixels	301–407	51–157	pixel

) to minimize the effect by stray light. The center zenith angle of the limited range in the solar diffuser calibration data is 53 degrees. The center pixel in the P1 and P2 telescopes are 354 pixels and 104 pixels, respectively.

The line-of-sight unit vectors of the center pixel of the limited range (x, y, z) are shown in

Table 4. The line-of-sight unit vectors of the center pixels of limited range.

Parameters		P1	P2
Line-of-sight unit vector of the center pixel of limit range	x	0.00027	0.00337
	y	0.09398	0.38937
	z	−0.99557	−0.92108

. The line-of sight unit vectors are defined by the polarization band of S10.

The incident angle of sunlight to the diffuser is not constant due to changes in the eccentricity of the earth’s orbit, the inclination of the earth’s axis, the satellite orbital plane, and so on. Thus, the S-polarized direction of the scattered light of sunlight on the diffuser is calculated by the relation of the solar zenith angle and solar azimuth angle.

When the solar zenith angle is θ_s and the solar azimuth angle is φ_s, the specular reflection direction vectors of sunlight in the diffuser coordinate system (x′, y′, z′) are represented by Equations from (13) to (15) using θ_s and φ_s from the relationship shown in Figure 4.

$$\mathrm{x}{}^{\prime }=\frac{\sqrt{2}}{2}\left(\sin {\mathsf{\theta }}_{\mathrm{s}}\sin {\mathsf{\phi }}_{\mathrm{s}}+\cos {\mathsf{\theta }}_{\mathrm{s}}\right)$$

(13)

$$\mathrm{y}{}^{\prime }=-\sin {\mathsf{\theta }}_{\mathrm{s}}\cos {\mathsf{\phi }}_{\mathrm{s}}$$

(14)

$$\mathrm{z}{}^{\prime }=\frac{\sqrt{2}}{2}\left(\sin {\mathsf{\theta }}_{\mathrm{s}}\sin {\mathsf{\phi }}_{\mathrm{s}}-\cos {\mathsf{\theta }}_{\mathrm{s}}\right)$$

(15)

The S-polarized direction of the scattered light of sunlight on the diffuser panel φ_s-pol is represented by Equation (16) using (x, y, z) and (x′, y′, z′). The equation is derived from the following assumptions.

• Sunlight is non-polarized light;
• The reflected light in the diffuser has an S-polarization reflectance higher than the P-polarization reflectance.

$${\mathsf{\phi }}_{\mathrm{s}-\mathrm{pol}}={\tan }^{-1}\frac{\mathrm{z}\mathrm{x}{}^{\prime }}{{\mathrm{zy}}^{{}^{\prime }}\sqrt{1-{\mathrm{y}}^2}-\mathrm{y}\left(\mathrm{x}\mathrm{x}{}^{\prime }+\mathrm{y}\mathrm{y}{}^{\prime }\right)}$$

(16)

I, Q, and U are calculated by using the same line and the same pixel outputs of the three polarization bands for all observation data in the limited range. Here, each average value of I, Q, and U is represented as I_{IN_ave}, Q_{IN_ave}, and U_{IN_ave}, respectively.

The measured values of the polarization azimuth φ_obs and the degree of polarization P_obs are calculated by Equations (17) and (18) using I_{IN_ave}, Q_{IN_ave}, and U_{IN_ave}.

$${\mathsf{\phi }}_{\mathrm{obs}}=\frac{1}{2}{\tan }^{-1}\frac{{\mathrm{U}}_{\mathrm{IN}\_\mathrm{ave}}}{{\mathrm{Q}}_{\mathrm{IN}\_\mathrm{ave}}}+{90}^{°}:{\mathrm{Q}}_{\mathrm{IN}\_\mathrm{ave}}<0$$

(17)

$${\mathrm{P}}_{\mathrm{obs}}=\sqrt{{\mathrm{Q}}_{\mathrm{IN}\_\mathrm{ave}}{}^2+{\mathrm{U}}_{\mathrm{IN}\_\mathrm{ave}}{}^2}/{\mathrm{I}}_{\mathrm{IN}\_\mathrm{ave}}$$

(18)

In solar diffuser calibration, since the line-of-sight angle is different among polarization bands, each polarization band observes light at different scatter angles by the diffuser panel. In addition, there is a potential error in the correction equation determined by the calibration before launch.

In order to absorb these effects, radiance conversion polynomial of Equations (7)–(9) are changed to Equations (7′)–(9′) by multiplying the polarization band-to-band correction coefficients k_S09, k_S10, and k_S11, and the polarization azimuth angle and degree of polarization are calculated using Equations (7′)–(9′).

$${\mathrm{I}}_{\mathrm{corr}\_\mathrm{S}09}={\mathrm{k}}_{\mathrm{S}09}{\mathrm{I}}_{\mathrm{S}09}={\mathrm{k}}_{\mathrm{S}09}({\mathrm{b}}_{\mathrm{S}09}{\mathrm{I}}_{\mathrm{S}09}^{\mathrm{obs}}+{\mathrm{c}}_{\mathrm{S}09}{{\mathrm{I}}_{\mathrm{S}09}^{\mathrm{obs}}}^2+{\mathrm{d}}_{\mathrm{S}09}{{\mathrm{I}}_{\mathrm{S}09}^{\mathrm{obs}}}^3+{\mathrm{e}}_{\mathrm{S}09}{{\mathrm{I}}_{\mathrm{S}09}^{\mathrm{obs}}}^4)$$

(7′)

$${\mathrm{I}}_{\mathrm{corr}\_\mathrm{S}10}={\mathrm{k}}_{\mathrm{S}10}{\mathrm{I}}_{\mathrm{S}10}={\mathrm{k}}_{\mathrm{S}10}\left({\mathrm{b}}_{\mathrm{S}10}{\mathrm{I}}_{\mathrm{S}10}^{\mathrm{obs}}+{\mathrm{c}}_{\mathrm{S}10}{{\mathrm{I}}_{\mathrm{S}10}^{\mathrm{obs}}}^2+{\mathrm{d}}_{\mathrm{S}10}{{\mathrm{I}}_{\mathrm{S}10}^{\mathrm{obs}}}^3+{\mathrm{e}}_{\mathrm{S}10}{{\mathrm{I}}_{\mathrm{S}10}^{\mathrm{obs}}}^4\right)$$

(8′)

$${\mathrm{I}}_{\mathrm{corr}\_\mathrm{S}11}={\mathrm{k}}_{\mathrm{S}10}{\mathrm{I}}_{\mathrm{S}10}={\mathrm{k}}_{\mathrm{S}11}({\mathrm{b}}_{\mathrm{S}11}{\mathrm{I}}_{\mathrm{S}11}^{\mathrm{obs}}+{\mathrm{c}}_{\mathrm{S}11}{{\mathrm{I}}_{\mathrm{S}11}^{\mathrm{obs}}}^2+{\mathrm{d}}_{\mathrm{S}11}{{\mathrm{I}}_{\mathrm{S}11}^{\mathrm{obs}}}^3+{\mathrm{e}}_{\mathrm{S}11}{{\mathrm{I}}_{\mathrm{S}11}^{\mathrm{obs}}}^4)$$

(9′)

The polarization band-to-band correction coefficients k_S09, k_S10, and k_S11 shown in

Table 5. Polarization band-to-band correction coefficient.

Polarization Band-to-Band Correction Coefficient	P1	P2
kS09	0.99764	1.00174
kS10	0.99887	1.00603
kS11	1.00349	0.99223

were determined from the calibration data of seven solar diffusers, which were extracted approximately once every three months.

Trends of the S-polarized direction of the scattered light of sunlight on the diffuser panel (φ_s-pol), the measured values of polarization azimuth (φ_obs), measured values of degree of polarization (P_obs), and difference between φ_obs and φ_s-pol are shown in Figure 8. Figure 8a,c are the trends of φ_s-pol, φ_obs, and P_obs in the P1 and P2 telescopes. Figure 8b,d show trends of the difference between φ_obs and φ_s-pol in the P1 and P2 telescopes, respectively.

The φ_s-pol and φ_obs are almost identical, and the measured value of the degree of polarization is gradually decreasing in the P1 telescope. The reduction in the degree of polarization is considered to be due to the influence of the degradation of the diffusion plate. Since each polarization band observes different light scattered by the diffuser panel, the change in degree of polarization may have an effect on the difference between φ_s-pol and φ_obs. Regarding the P2 telescope, the φ_s-pol and φ_obs are almost identical, and the measured value of the degree of polarization is changed in accordance with the polarization azimuth angle as a behavior not seen in the P1 telescope. The difference between φ_s-pol and φ_obs seems to have systematic errors. Each polarization band of the polarization observation channel observes a different position on the diffuser and has a different viewing angle. A polarization band-to-band correction coefficient is incorporated to compensate for the difference, but the coefficient cannot compensate for changes in the angle of incidence of sunlight on the diffuser, which changes each time the solar diffuser calibrates. The failure to compensate for the change in the angle of incidence of sunlight on the diffuser may be the cause of the systematic error between φ_s-pol and φ_obs.

The deviation between the φ_s-pol and φ_obs, which is converted to the Q/I component and U/I component, are calculated for the P1 and P2 telescopes, respectively. The results of converting the difference between φ_s-pol and φ_obs to the Q/I component and U/I component (ΔQ/I and ΔU/I) are shown in Figure 9. ΔQ/I and ΔU/I are calculated by Equations (19) and (20) under the condition that the measured degree of polarization does not change.

$$\mathsf{\Delta }\mathrm{Q}/\mathrm{I}={\mathrm{P}}_{\mathrm{obs}}\cos 2\mathsf{\varphi }-{\mathrm{Q}}_{\mathrm{IN}\_\mathrm{ave}}/{\mathrm{I}}_{\mathrm{IN}\_\mathrm{ave}}$$

(19)

$$\mathsf{\Delta }\mathrm{U}/\mathrm{I}={\mathrm{P}}_{\mathrm{obs}}\sin 2\mathsf{\varphi }-{\mathrm{U}}_{\mathrm{IN}\_\mathrm{ave}}/{\mathrm{I}}_{\mathrm{IN}\_\mathrm{ave}}$$

(20)

The variations of ΔQ/I and ΔU/I that can be caused by the sensor are very small in the range of ±0.07% and ±0.04% in the P1 and P2 telescopes, respectively. These results suggest that that the in-orbit polarization observation accuracy is very stable.

3.3. Lunar Calibration Maneuver Calibration

Lunar calibration maneuver differs from internal lamp calibration and solar diffuser calibrations in that the SGLI observes the object (the Moon) without a solar diffuser plate. Thus, it is not necessary to consider the effects of the degradation of the solar diffuser plate. Regarding the trend of polarization observation using a lunar calibration maneuver, we evaluated the polarization characteristics of the Moon observed from the data of the 11 pixels by 29 lines, including the Moon. The polarization characteristics trend of the Moon observed at the angle of view at 0 degrees or +1 degrees is shown in Figure 10. Figure 10a,b are the polarization characteristics trends of the Moon observed by the P1 and P2 telescopes, respectively.

The variation width of Q/I is more than 2%, and the variation width of U/I is about 0.6% in both the P1 and P2 telescopes. In addition, the temporal variations of P1 and P2 show a similar trend. The main factor of this variation is estimated to be that the polarization characteristics of the light reflected from the Moon have changed for the following two reasons:

• The Moon observed from the SGLI-VNR appears to rotate due to seasonal variation;
• The phase angle defined as the angle of the “Sun-SGLI-Moon” is slightly different for each lunar calibration.

The above two effects are the same in the P1 and P2 telescopes; therefore, in the lunar calibration maneuver, the difference trends of Q/I and U/I between the P1 and P2 telescopes were evaluated. The difference trends of Q/I and U/I between the P1 and P2 telescopes are shown in Figure 11.

The variation widths for Q/I and U/I are 0.50% and 0.36%, respectively. The results of these variation widths are significantly reduced from the results with a single telescope (shown in Figure 10).

According to the lunar calibration data, it seems that the reflected light of the Moon is polarized. In this paper, the effect on polarization observation accuracy after launch is discussed; however, the phenomenon in which the reflected light of the Moon is polarized would be helpful for the calibration of the absolute accuracy of the polarization observation. For example, if the reflected light is polarized due to the effect of the lunar phase angle, it might calibrate the absolute accuracy of the polarization observation from the observed polarization azimuth angle and the direction of the waned Moon.

3.4. Inter-Comparison

The results of the internal lamp calibration, solar diffuser calibration, and lunar calibration maneuver are summarized as follows:

• In the trend of internal lamp calibration, ΔU/I in the P1 telescope was on a downward trend by about 0.2%, and ΔQ/I in the P1 telescope and ΔQ/I and ΔU/I in the P2 telescope were stable within the range of ±0.10%;
• In the trend of solar diffuser calibration, the variations in ΔQ/I, ΔU/I were very small. The variations in the P1 and P2 telescopes were within the range of ± 0.07% and ±0.04%, respectively;
• In the trends of the lunar calibration maneuver data, the variation in the difference between the P1 and P2 telescopes for the Q/I component was within 0.50%, and that of U/I component was within 0.36%.

The variations in ΔQ/I and ΔU/I in the P2 telescope were small for internal lamp calibration and solar diffuser calibration; therefore, the polarization observation accuracy should be stable in the P2 telescope in orbit.

The variation in ΔQ/I in the P1 telescope was small for internal lamp calibration, however that of ΔU/I has been on a downward. By contrast, the variations in ΔQ/I and ΔU/I in the trend of the solar diffuser calibration data of P1 were within ±0.07% calculated under the conditions that the observed polarization degree does not change.

Here, assuming that the deviation of the observed polarization azimuth angle from the S-polarized direction of the scattered light of sunlight on the diffuser panel occurred only in the U/I component, the variation in ΔU/I calculated under the condition that ΔQ/I does not change is shown in Figure 12. The formula for calculating ΔU/I is described in Equation (21).

$$\mathsf{\Delta }\mathrm{U}/\mathrm{I}=\left({\mathrm{U}}_{\mathrm{IN}\_\mathrm{ave}}-{\mathrm{Q}}_{\mathrm{IN}\_\mathrm{ave}}\tan 2\mathsf{\varphi }\right)/{\mathrm{I}}_{\mathrm{IN}\_\mathrm{ave}}$$

(21)

The variation in ΔU/I under the condition that ΔQ/I does not change decreased about 0.2% based on the data after a lapse of 95 days since launch. Figure 13 shows the U/I component variation in the P1 telescope by three sets of calibration data under the following conditions:

• ΔU/I trend of internal lamp calibration based on the data after a lapse of 95 days since launch;
• ΔU/I trend of solar diffuser calibration under the condition that ΔQ/I does not change based on the data after a lapse of 95 days since launch;
• ΔU/I trend of lunar calibration maneuver when ΔU/I is the difference in U/I between the P1 and P2 telescopes based on the data after a lapse of 95 days since launch.

Figure 13a,b show a fluctuation trend of ΔU/I and a fluctuation trend graph of the three-month moving average of ΔU/I in the P1 telescope, respectively.

Figure 13 suggests the following:

• The fluctuation trend of U/I in the P1 telescope for the internal lamp calibration data is gradually and monotonically decreased;
• The fluctuation trend of U/I in the P1 telescope for the solar diffuser calibration data is almost stable, except for having decreased by about 0.2% from a lapse of 360 to 460 days since launch;
• The fluctuation trend of U/I in the P1 telescope for the lunar calibration maneuver was on a downward trend before a lapse of 360 days after launch. After that, this trend increased and returned to its initial value.

Each fluctuation trend of the three calibrations of U/I in the P1 telescope is different from the other two. If the decrease in ΔU/I in internal lamp calibration is due to a change in sensitivity deviation among polarization bands, similar changes should be identified in solar diffuser calibration and lunar calibration maneuver; however, such a trend is not identified. Thus, the sensitivity deviation among the polarization bands is not the factor of the decrease in U/I in the P1 telescope by internal lamp calibration. The degradation of the lamp and solar diffuser may be affected by the decrease in U/I in the P1 telescope by internal lamp calibration.

The degradation of the lamp characteristics may cause not only lower radiance but changes on the polarization characteristics of lamp, as well as changes in the balance of two white LEDs’ radiance, resulting in changes in the light-receiving ratio among each polarization band. In addition, the degradation of the diffuser induces changes in the polarization characteristics of the scattered light.

ΔU/I variation in the P1 telescope is considered to be stable within the range of ±0.07% for the following reasons:

• The fluctuation trends of ΔU/I converted from the deviation from the S-polarized direction of the scattered light of sunlight on the diffuser panel in the solar diffuser calibration is stable in the range of ±0.07%, and it is almost at a 0% position at the time of 730 days since launch, as shown in Figure 9a;
• Relative changes in the U/I of the P1 and P2 telescopes for lunar calibration maneuver are also almost at a 0% position at the time of 730 days since launch, as shown in Figure 13b.

In conclusion, the ΔQ/I and ΔU/I variations are within ±0.07% for the P1 telescope, and ±0.04% for the P2 telescope; therefore, the polarization observation accuracy of both P1 and P2 telescopes are stable in orbit.

The effect of the variations caused by the sensor does not depend on the degree of polarization of the observed light; it is thought that there is almost the same effect on atmospheric aerosol observations with a polarization intensity of several tens of percent. The maximum impact on the degree of polarization with variations in ΔQ/I = 0.07% and ΔU/I = 0.07% is approximately 0.1%. If the same light observed with a degree of polarization of 30% 95 days after launch is observed on 730 days after launch, the observed degree of polarization is considered to be within 30 ± 0.1%. The SGLI was not calibrated with absolute accuracy, so it is not directly comparable, and the ±0.1% fluctuation of the degree of polarization is very small compared with about 0.5% of the expected accuracy in POLDER’s near-infrared channel.

4. Conclusions

The in-orbit effect of the SGLI VNR-PL’s polarization observation accuracy has been evaluated by using the fluctuation trends of internal lump calibration, solar diffuser calibration, and lunar calibration maneuver. The result of the conversion to fluctuation of the Q/I and U/I components from the difference between the observed polarization azimuth and S-polarized direction of the scattered light of sunlight on the diffuser panel in the solar diffuser calibration is stable. As a result of the comprehensive evaluation, we observed that the polarization observation accuracy is stable because the in-orbit fluctuations of Q/I and U/I are within ±0.07% in the P1 telescope and ±0.04% in the P2 telescope.

The SGLI has on-board radiometric calibration systems, and we investigated the calibration method of polarization observation using its calibration systems. In the present, we are investigating the absolute accuracy calibration of polarization observation accuracy using Lunar calibration data without diffusers. As a result, if it is insufficient to calibrate absolute polarization observation accuracy, it is necessary to consider methods such as accuracy calibration using the sun’s glitter, which have been developed by POLDER. In the future, we plan to establish a method for further improving the calibration of absolute polarization observation accuracy.