中文摘要：

针对辐射率的漫射近似、P3近似等正向模型在描述小源探距离及低约化反照率介质下光子传输时存在的局限性,推导了用于小源探距离低反照率无限媒质中各向同性稳态点光源下辐射传输方程在P5近似下的解析解,并将P3近似、P5近似计算的辐射率分别和蒙特卡洛模拟结果进行对比.结果表明：在高约化反照率（0.97）条件下,P5近似和蒙特卡洛模拟结果的最大相对误差为13.17%,而P3为41.57%.在低约化反照率（0.69）条件下,最大相对误差分别为27.78%,286.70%.在其他光学参数下,P5近似与蒙特卡洛模拟的最大相对误差均小于P3.在P5适用的范围内舍弃最大特征根相关项,可以简化解析表达式,提高计算速度,且对P5的计算结果影响甚微.稳态辐射率测量系统仿体验证表明,在高、低约化反照率介质中的小源探距离下,由P5近似计算得到的辐射率和实验测量结果相符.

英文摘要：

In order to describe photon migration at small source detector separation and in media with low reduced albedo where diffuse approximation and P3 approximation have limitations,the solution of radiance transfer equation in the P5 approximation for the case of an isotropic continuous-wave point source in an infinite medium was derived.The P3 and P5were compared with Monte Carlo simulation to verify the correctness of the derived solution.Under the condition of high reduced albedo（0.97）,the maximum relative error between P3 and Monte Carlo simulation is about 41.57% while that between P5 and Monte Carlo simulation is just about 13.17%.In the case of low reduced albedo（0.69）,the maximum relative error is about 27.78%,286.70%,respectively.In the situations of other optical parameters,the maximum relative errors between P5 and Monte Carlo simulation are also no more than that between P3 and Monte Carlo simulation.By abandoning the expressions related to the maximum eigenvalue which has little impact to the result of P5 calculation in the validity condition of P5,a simpler analytical expression can be obtained to accelerate the calculation of P5 approximation.Experiments on a solid phantom with a continuous-wave radiance measurement system are conducted and the results show that the radiance calcualted from P5 approximation meets well with that from the experimental measuring at small source detector separation and in media with high or low albedo.