Fig. 1. Mie phase function and Lengdre extension with different Nstr=4，8，16，32，64. (a) Particle mean radius=0.5 μm; (b) Particle mean radius=1.0 μm

Fig. 2. Sky radiance calculated using CART with the different Nstr of 4, 8, 16, and 32

Fig. 3. Comparisons of Lengdre extension with different Nstr（4，8，16，32，64） and the H-G phase function. (a) g=0.8; (b) g=0.95

Fig. 4. Aerosol scattered sky radiance calculated by using of CART with the Nstr of 4, 8, 16, and 32 for the case of H-G phase fucntion with g=0.95

Fig. 5. Relationship between the time-consuming of CART multiple scattering calculation and the Nstr of Lengendre extension

Fig. 6. Comparisons of atmospheric thermal radiation vs. zenith angle and target altitude between CART calculations and fittings

Fig. 7. Scene atmospheric thermal radiation vs. zenith angle and target altitude calcaulted with CART

Fig. 8. Comparisons of atmospheric average transmittance vs. zenith angle and target altitude between CART calculations and fittings

Fig. 9. Scene atmospheric transmittance vs. zenith angle and target altitude calcaulted with CART