Hao, X, Qu, JJ (2009). Fast and highly accurate calculation of band averaged radiance. INTERNATIONAL JOURNAL OF REMOTE SENSING, 30(5), 1099-1108.
Conversion between brightness temperature and band averaged radiance is frequently used in radiative transfer model simulations, algorithm development and remote sensing applications. While the formula looks quite simple, direct conversion is not very efficient. In this paper, a fast conversion algorithm for band averaged radiance calculations from brightness temperature is proposed based on the Chebyshev polynomial approximation, and is validated with the thermal infrared bands of the moderate resolution imaging spectroradiometer (MODIS). Due to the orthogonality of the Chebyshev polynomial, the look-up-tables (LUTs) can be constructed very easily, and only need the Chebyshev expansion coefficients and two constants. Error analysis and performance testing of approximations at different orders demonstrate that band averaged radiance can be calculated very accurately with the seventh to tenth Chebyshev expansion at a speed that is over 50 times faster than direct calculation using numerical integration. A toolkit is also implemented based on the proposed algorithm; this is freely available upon request.