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在热成象系统的分析中,时常需要对微分辐射率(((?)W_λ)/((?)T))进行积分。由于适当的工作,验证了波长限λ_1和λ_2之间积分的级数解。当然不是完整形式的解,但该级数容易借助于使用小型计算机得到数值解。该级数的求导借普朗克黑体辐射定律开始:式中,W_λ是辐射率并且是波长的函数,C_1和C_2是第一和第二辐射常数,T是绝对温度。得到W_λ对T的偏导数的简单形式:
In thermal imaging system analysis, it is often necessary to integrate the differential emissivity (((?) W_λ) / ((? T)). Due to the proper work, the series solution of the integral between the wavelength limits λ_1 and λ_2 is verified. This is not, of course, a complete solution, but it is easy to get a numerical solution by using a small computer. The derivation of this series starts with the Planckian law of black-body radiation: where W_λ is the emissivity and is a function of wavelength, C_1 and C_2 are the first and second radiation constants, and T is the absolute temperature. Get the simple form of the partial derivative of W_λ for T: