定量遥感要求对星载或机载遥感数据进行大气影响订正。精确的大气订正则需要知道下垫面的方向性反射(或辐射)特征, 而这正是定量遥感所要知道的。这就形成了一个死循环。为了解开这个死结, MODIS可见/近红外产品采用了考虑地表BRDF的迭代订正。然而迭代订正的收敛性是有待研究的问题。胡宝新等用大量的模拟来表明该算法的收敛性, 但模拟很难耗尽各式各样的可能情况。本文旨在从理论上研究该订正环的收敛性并阐明收敛的条件。

Quantiative remote sensing requires atmospheric correction, which requires directional reflectance or emittancc of the earth surface as the boundary condition of the radiative transfer problem. But the actual reflectance or eminence characteristics of the earth surface are what the quantitative remote sensing aims at. This presents as a deadlock. In order to solve the problem, Hu et al. suggested a BRDF-based correction loop. However the convergence of such an iteration loop is to be studied. Hu et al. used simulations to show the loop converging. But it's not easy to exhaust all the possible cases by simulations. This paper is to analyse theoretically the loop's convergence and its conditions.