Spatial-spectral coupling multispectral imaging is an innovative technology that integrates spatial and spectral information using color filter array sensors and multi-bandpass narrowband filters. This approach allows each pixel to capture data from multiple spectral bands. Due to the inherent coupling of spatial and spectral data, traditional radiometric calibration methods are insufficient for accurately determining radiometric response coefficients. Research on the calibration of such multispectral cameras remains limited. Current methods often focus solely on spectral response, using theoretical energy contribution ratios for each band as decomposition coefficients. However, these methods lack a well-defined radiometric response model and have not undergone sufficient experimental validation, leading to inaccuracies. Therefore, further research is needed to develop precise calibration methods and to solve for accurate radiometric response coefficients in this multi-band spatial-spectral coupled imaging system. Improving the radiometric accuracy of these systems will ensure reliable data for a wide range of applications.

In this study, we use a four-channel multispectral camera to construct a radiometric response model based on radiative transfer theory, describing the complete spectral radiative transfer process. A laboratory radiometric calibration method using a combination of multiple light sources is proposed, enabling variation in both the spectral and radiometric dimensions. This approach generates an overdetermined system of equations for the radiometric response coefficients. By calculating the energy contribution ratios for each band from the spectral response and converting these ratios into initial estimates of the radiometric response coefficients, the method avoids incorrect local optima when solving the overdetermined equations. The gradient descent method is then applied to compute the optimal radiometric response coefficients, ensuring practical physical relevance. This approach, which integrates theoretical calculations with experimental calibration data, significantly enhances the reliability of the derived radiometric response coefficients.

Using the proposed calibration method, we determine optimal radiometric response coefficients for the four spectral bands (Table 3). These coefficients are then used in both laboratory and field accuracy verification, with the results as follows. 1) Laboratory accuracy verification: data not involved in deriving the optimal radiometric response coefficients are used. The mean relative error of the retrieved radiance for all bands is found to be less than 5% (Fig. 8). 2) Field calibration: a relationship between the reflectance of a diffuse reflection panel and the exit radiance is established. Radiance data are collected using the multispectral camera, while reflectance data are measured with an ASD device. Field calibration coefficients are calculated (Table 4), and reflectance validation shows that the error distribution across all bands is uniform, with a mean relative error within 6% (Table 6, Fig. 11). 3) Uncertainty analysis: the uncertainty in the radiometric calibration transfer chain is analyzed, revealing that the absolute calibration uncertainty for each band is less than 5% (Table 7).

In this study, we propose a comprehensive radiometric response model for spatial-spectral coupling multispectral camera, based on radiative transfer theory. We introduce a laboratory calibration method using multiple light sources, allowing for variation in both spectral and radiometric dimensions. The initial radiometric response coefficients are derived from theoretical spectral response calculations, and the gradient descent method is used to determine the optimal coefficients. We validate the calibration accuracy through both laboratory and field experiments. Our model and method significantly enhance the radiometric accuracy of spatial-spectral coupling multispectral imaging systems, eliminating uncertainties caused by overlapping radiometric responses between different spectral bands. These findings hold significant theoretical and practical values for advancing research and applications of this technology.