Liquid foam is a dense packing of gas bubbles in a small amount of surfactant liquid, which has well-organized structure and behaves as typical soft condensed matter. Forced drainage is the flow of constantly input liquid through the network of interstitial channels between bubbles in foams under actions of gravity and capillarity, which is one of major mechanisms causing liquid foam evolution. Firstly in this paper, we improved the newly proposed method introduced by Hutzler et al. (2005) by considering the light transmission ratio to eliminate the incident light intensity discrepancy along the one dimensional foam formed within a slender Hele-Shaw silicon rectangular tube. After the film rupture and the bubble coarsening were carefully slowed down, forced foam drainages in one dimension were studied by using the improved light scattering technique. We found that the characteristic quantities, such as the drainage wave front velocity and liquid fraction evolution, are consistent with traditional foam drainage results based on Poiseuille-type flow assumption in Plateau borders. And the light transmission ratio is found not to be the reciprocal of the liquid fraction as similar with the transmission probability in diffuse-transmission spectroscopy technique, but prevails the relationship T=0.293+1.038e-29.39(0.01<0.13). We then deduced the viscous energy of foams based on Kelvin cell structure during forced drainage process and calculated the surface energy of foam using the software of Surface Evolver. The evolution of the two kinds of energy at local area of foam was predicted based on the quasi-static assumption of Kelvin cell structure evolution along with liquid fraction variation. The study of foam drainage from a view of energy will be useful in the further study on foam drainage and foam stability control in various applications.