普通彩色相机加载宽带滤光片构造的多通道光谱采集系统的光谱重建性能与滤光片的选用密切相关。针对上述问题, 提出基于主成分分析法的合成滤光片设计方法, 旨在获得具有较高光谱重建性能并对所有图像场景均适用的最优滤光片组合。在收集多个宽带滤光片的基础上, 测得其透射率并转换成矩阵形式; 采用主成分分析方法提取该矩阵的前2个主成分, 标准化处理后的主成分即为所求合成滤光片的透射率。为了验证上述方法获得的滤光片的性能, 利用色差和光谱均方根误差2个指标对加载了合成滤光片的仿真采集系统的光谱重建精度进行了评价。实验结果表明: 采用该方法得到的滤光片组合优于常用方法得到的滤光片组合, 用其构造的成像系统具有较高的色度重建精度和光谱重建精度, 此外, 改变目标场景颜色特性, 其重建性能保持稳定。

The spectral reconstruction precision of multi-channel spectral acquisition system based on the commercial digital camera is greatly dependent on the filters used to acquire the image. In order to obtain optimal filter pair, which has excellent spectral reconstruction performance and is applicable to all image scenes, a color filter design method based on the principal component analysis is proposed in this work. Firstly, a number of widely-used color filters are collected and their transmittances are measured and then written in matrix form. Secondly, the proposed method is adopted to extract the first two principal components of the matrix. The normalized principal components are the transmittances of the desired synthetic filters. To compare the spectral reconstruction performance of the synthetic filters with the other filter pair obtained by a common used method, two virtual spectral acquisition systems were constructed with two pairs of filters. The performance of each system was evaluated in terms of chromatic difference and spectral root mean square error. The results indicate that the synthetic filters obtained by the proposed method have a better performance than the common used methods. In addition, the performance of the synthetic filters is stable when the target image scenes change.