中文摘要：

颗粒粒度反演需要求解第一类Fredholm积分方程，此问题是动态光散射中的难点之一，其中，双峰颗粒的反演更是亟待解决的问题．为保证反演结果的非负性，采用了trustregionreflec—tiveNewton和activeset算法实现的非负Tikhonov，非负TSVD算法对双峰颗粒数据进行了反演．结果表明采用前者实现的非负Tikhonov和非负TSVD不能区别间隔粒径较近双峰，而采用后者实现的非负Tikhonov和非负TSVD能区别出．

英文摘要：

Particle size distribution inversion requires solving the first kind of Fredholm integration, which is a core problem in dynamic light scattering. Moreover, the inversion of bimodal particles, a more difficult issue, should be considered. In view of the nonnegative characteristic of inversion results, we employed the trust region reflective Newton and active set algorithms to im- plement nonnegative Tikhonov and TSVD algorithm and adopted these approaches to investigate inverse problems for bimodal particles. Simulated and experimental results show that both no negative Tikhonov and nonnegative TSVD, implemented by trust region reflective Newton, fail to resolve bimodal particles with small peaks ratio, while both of them, implemented by active set, succeed in this case.