2018 年 55 巻 1 号 p. 13-19
This paper presents the results of analysis of linear inverse problem for static light scattering (SLS) particle size distribution measurement.
The problem is written by Mv = w, where v is a particle size distribution (unknown), w is intensities of the scattered light of particles (known), and M is a kernel matrix based on Mie scattering theorem.
This study was made to identify characteristics of SLS problem. We made optical simulation of Mie scattering in computer to make kernel matrix. Then we did singular value decomposition to the kernel matrix and evaluated results.
It was found that the singular values has characteristic similar to diffusion equation.
Namely the matrix contains many minute singular values. It shows that SLS is an ill-posed problem which has instability for solution. Also the right singular vectors present TSVD (Truncated singular value decomposition) is not effective.
Finally, we discussed appropriate solution method for SLS.
