In the solar reflective band, the on-board calibration method based on solar diffuser (SD) allows for full-aperture, full-field-of-view, end-to-end absolute radiometric calibration of optical remote sensors. The bidirectional reflectance distribution function (BRDF) of the SD is a key parameter that can affect on-board calibration accuracy. The SD is typically made from fired polytetrafluoroethylene (PTFE), a material that suffers from non-Lambertian reflective properties, non-specular peaks for in-plane reflections, and susceptibility to contamination and degradation. These characteristics can affect the accuracy of on-board calibration. In the present study, we present the measurement results from the BRDF absolute measurement facility for the SD used in on-board calibration. The measurement angles ranged from 0° to 75° for the incident zenith angle, 15° to 75° for the reflected zenith angle, and 60° to 360° for the azimuthal difference. The results show that the relative difference in the SD BRDF at different reflection angles can exceed 350% at a 75° incidence angle. We then analyze the influence of the SD BRDF characteristics on on-board calibration in terms of the measurement accuracy of the SD BRDF, the calculation of the SD attenuation factor, and the placement error of the SD. The analysis shows that the SD BRDF characteristics can affect on-board calibration accuracy by more than 1% if the geometric relationship between the incident and reflected vectors in the on-board calibration is not properly set. Finally, based on the analysis and measurement results, we propose suitable angular geometric relations for on-board calibration that can effectively reduce the relative change in the BRDF across the field of view of the remote sensor during on-board calibration. These angular geometric relations can serve as a reference for the design of future on-board calibrators.

In this paper, we measure the BRDF (with angles ranging from 0° to 75° for the incident zenith angle, 15° to 75° for the reflected zenith angle, and 60° to 360° for the azimuthal difference) of the SD for on-board calibration. Additionally, we measure the BRDF of the SD under various geometrical conditions after 100 h of irradiation, using the same batch of SD samples, with a high-accuracy absolute BRDF measurement facility. Based on these measurements, the effect of the SD BRDF characteristics on the accuracy of on-board calibration is analyzed. The factors influenced by the SD BRDF characteristics include the measurement uncertainty of the SD BRDF, the degradation of the SD, and the variation of the SD BRDF due to placement errors. Finally, the combined effect of these three factors on the accuracy of on-board calibration is analyzed using the example of a remote sensor with an SD stability monitor.

According to the SD BRDF measurement, Fig. 6 shows that the SD for the on-board calibration is not an ideal Lambertian surface. When the geometric relationship between the incident and reflected zenith angles is 75° and the azimuth difference is 180°, the SD BRDF is close to 1. This is determined by the nature of the uniformly rough surface. Figure 8 shows the relationship between the SD BRDF and the incident zenith angle, as well as the reflected azimuth angle at large reflected zenith angles. It can be seen that when the azimuth angle between the incident and reflected vectors is small, the SD BRDF hardly changes with the incident zenith angle. However, as the azimuth angle increases, the BRDF increases rapidly with the increase in the incident zenith angle. According to the degradation of the SD BRDF measurement, Fig. 10 shows that the degradation of the SD BRDF does not remain constant. Instead, it is related to the incident and reflected angles. For a small incident angle, the degradation of the SD BRDF at 400 nm does not vary much with the reflected angle and is better than 0.8%. When the incident zenith angle increases to 65° and 75°, the relative changes in SD BRDF degradation are 2% and 2.9% respectively. The results of the analysis of the three factors affecting the on-board calibration accuracy are shown in Table 5. Table 5 demonstrates that if the angles for the on-board calibrator are set unreasonably, the accuracy of the on-board calibration will be reduced by 1.1%.

An SD for the on-board calibration is not an ideal Lambertian surface and in some cases, particularly at large incident zenith angles, the BRDF characteristics of the SD deviate significantly from those of an ideal Lambertian surface. At an incident zenith angle of 75°, the proportion of the first reflections is increased, leading to a significant increase in the BRDF in the specular direction, reaching approximately 310% of the BRDF of an ideal Lambertian surface. Furthermore, the BRDF measurement results of the SD after the 100 h irradiation and the same batch of samples of this SD demonstrate that the degradation of the SD BRDF is not isotropic. When the incident zenith angle is 75°, the relative variation of the BRDF degradation for each reflected angle is close to 3%. When the on-board calibration angle is not reasonably designed, the above two characteristics will affect the accuracy of the on-board calibration of remote sensors. The analysis demonstrates that if the angles for the on-board calibrator are set unreasonably, the accuracy of the on-board calibration will be reduced by 1.1%. Based on the measurement and analysis results in this paper, a range of reflected angles suitable for the on-board calibration is given when the incident zenith angle is both 50° and 55°. Within this specified angle range, the relative change of the SD BRDF in the field of view of the remote sensor during the on-board calibration process is minimal. In this case, it is possible to reduce the influence of the SD BRDF characteristics on the on-board calibration.