2.1

Geometric calibration

To evaluate the geometric performance of the CAI-2, the observation of ground control point (GCP) and cross-correlation methods were used. At first, the absolute direction vector of each pixel in the reference bands (Band 4 and Band 9) derived using GCP was calculated. After that, the difference of the direction vector for the other bands with respect to the reference band was calculated using cross-correlation between images. The direction vector data ware calibrated using these observation data.

2.2

Radiometric performance

In the radiometric calibration, the lunar calibration is performed using the Moon as the reference light source to evaluate the radiometric performance of the CAI-2. The schematic diagram of the lunar calibration is shown in Figure 3.

Figure 3.

Schematic diagram of the CAI-2 lunar calibration. The satellite body is oriented to the Moon, and the Moon is scanned by controlling the satellite attitude in the AT direction.

As shown in Figure 3, the Moon image is obtained by scanning the field of view by controlling the satellite attitude in the Along Track (AT) direction. An example of the observed Moon image is shown in Figure 4. Due to the slow scanning, the Moon image is vertically elongated.

Figure 4.

An example of the observed Moon image of Band 4 taken on December 2018.

The ROLO model⁵ was used as the lunar reflectance model, and the full disk integrated spectral irradiance of the Moon measured by the CAI-2 was compared with the model using the following procedure⁶:

The wavelength of the disk equivalent reflectance of the Moon obtained by the ROLO model is not identical with the wavelength of the CAI-2. The wavelengths of the ROLO model are discrete and only available at wavelengths from 347 nm to 2390 nm. Therefore, the obtained reflectance data of the ROLO model was fitted with a logarithmic curve, extrapolated to 340 nm, and replaced with the data corresponding to the observed wavelength of the CAI-2. The fitted reflectance data are shown in Figure 5. The approximation curve is slightly larger than that of the ROLO model in the range of 1000-1300 nm, but it is well approximated in the shorter wavelength range than 1000 nm and around 1600 nm.

Figure 5.

An example of the disk equivalent spectral reflectance of the Moon produced by the ROLO model and the approximation curve. (a) Forward-looking observation; (b) Backward-looking observation. The dots are reflectance of the ROLO model. The red lines are the approximation curve.

The irradiance model of the Moon H’ was calculated from the disk equivalent reflectance and solar spectra. As the solar spectra, the solar spectral model of Wehrli (1986)⁷, which was used in the ROLO model, was used to avoid the influence of the uncertainty of the solar spectral irradiance model. The comparison between the observed lunar irradiance H and the calculated irradiance H’ based on the ROLO model is shown in Table 4. In Table 4, some bands show a deviation of up to 10%. Such deviation could be caused by errors in the ground-based radiometric calibration, uncertainties in the satellite’s orbital position and attitude, and uncertainties in the lunar reflectance model itself. According to previous study, the absolute error of the lunar reflectance model might be up to 5-10%⁸.

Table 4.

The comparison between the observed lunar irradiance and the calculated irradiance based on the ROLO model at the beginning of initial checkout phase (December 2018).

2.3

Dark level and dark noise

The CAI-2 acquires dark calibration data by imaging the ocean around midnight. To avoid the influence of sunshine, the data is acquired during the time when the satellite is in the shade of the Earth. Examples of the obtained dark calibration data are shown in Figure 6. Although the fixed pattern of lines due to the variation of the dark signal of each pixel is clearly seen in the dark signal of Band5, these stripe patterns are corrected by performing dark subtraction.

Figure 6.

Examples of uncorrected raw dark signals taken above the mid-night ocean (December 2020). (a) Band4; (b) Band5. The stripe pattern of lines due to the variation of the dark signal of each pixel is clearly seen in the dark signal of Band5.

Bands 1 to 4 and 6 to 9 have 8 pre-scan pixels to monitor the variation of dark current. No pre-scan pixels exist in the InGaAs detectors for Bands 5 and 10, therefore the first six pixels of the 1024 pixels are masked to create a region of dark pixels. The dark current level is monitored by the output of these pre-scan pixels and masked pixels. The dark level of each band was evaluated by calculating the average value of all pixels for approximately 100 lines of raw data before pre-scan correction. The dark noise of each band was also evaluated by calculating the standard deviation (1σ) of approximately 100 lines of each pixel after subtracting the pre-scan or masked pixel data, by averaging the standard deviation for all pixels. Table 5 shows the comparison of the dark level and dark noise between the data obtained from the pre-flight test on the ground and the data obtained from the on-orbit dark calibration. There was no significant change in the dark level and dark noise from the ground test. It was confirmed that the performance at the ground test was maintained.

Table 5.

The comparison of the dark level (digital number: DN) and the dark noise (standard deviation of digital number: DN rms) between the data obtained during the ground pre-flight test (PFT) and the on-orbit dark calibration at the beginning of the initial checkout phase (December 2018).

3.1

Radiometric performance

Following the initial calibration phase, the radiometric performance of the CAI-2 has been continuously evaluated. In this chapter, the evaluation results of the radiometric response trend data for two years after the initial calibration phase are presented. As described in Section 2.2, the comparison of on-orbit lunar observations with the ROLO model has a slightly large difference due to the inclusion of the effects of geometric uncertainties in the orbital position and attitude, as well as the uncertainties in the lunar reflectance model itself. The observed irradiance error of the Moon due to geometry such as lunar phase variation and orbital error affects all bands in the same ratio. In order to reduce the influence of such geometric factors, the observed irradiance in Bands 1, 2, 3, 5 and Bands 6, 7, 8, 10 were normalized by Bands 4 and 9, respectively, with a wavelength of 865 nm, which is considered less affected by radiation and contamination. And the relative variation was calculated from the initial calibration phase in February 2019. The relative response change γ from the initial calibration phase is derived by the following equation:

where x is the index of each Band, α is the ratio of the observed lunar irradiance H to the calculated irradiance H’, β is the relative value of α for each band with respect to Band 4 for the forward bands and Band 9 for the backward bands, and γ is the variation of β at each calibration based on the initial calibration phase referred as β_Band(x),ref. The calculated results of the relative response change γ from the initial calibration phase are shown in Figure 7.

Figure 7.

Results of the relative response change γ from the initial calibration phase (February 2019). Forward Bands normalized by Band 4 (a) and Backward Bands normalized by Band 9 (b). The dark blue dots indicate Band 1 and Band 6.

The radiometric response evaluation using the lunar calibration data and the ROLO model showed a response degradation in the UV Bands. Relative to Band 4 and Band 9 (865 nm), Band 1 (340 nm) and Band 6 (380 nm) showed a degradation of about 8% and 3% in two years, respectively. The degradation was found in shorter wavelengths of UV bands. It might be affected by contamination and UV radiation rather than the longer wavelength bands. In the other longer wavelength bands, the observed degradation was less than 1.5% relative to Band 4 or Band9. These results suggest that the radiometric performance of the CAI-2 is generally maintained for two years after initial calibration phase.

3.2

Dark level and dark noise

The evaluation of dark level and dark noise has been continuously carried out using the methods described in Section 2.3. The trend graph is shown in Figure 8. Although there was some variation especially in Band 10, there was no significant increase in the dark level and the dark noise in all bands. Both the dark level and the dark noise are considered stable during the two years of evaluation from the initial calibration phase.

Figure 8.

Trend graph of the dark level (a), and the dark noise (b). The dark violet dots indicate Band 10. Band 5 and Band 10 have slightly higher amounts of dark level and dark noise than the other bands due to the difference in detectors.