The iterative projection method, originally proposed by Kaczmarz and Cimmino, was recently applied to particle size analysis with forward light scattering. Modification was made to improve the convergent procedure. However, there are still limitations. It is found that the solutions are oscillatory when the method is applied to a set of underdetermined linear equations without any additional constraints. A new version of the projection method, combined with the constraints of nonnegativity and smoothness, is proposed and is studied in the presence of experimental noise. Compared with the early versions of the projection method, this one shows fast convergence, is more stable against random noise, and is insensitive to particle size distributions.
© 2008 Optical Society of America
Original Manuscript: October 1, 2007
Revised Manuscript: February 2, 2008
Manuscript Accepted: February 28, 2008
Published: April 4, 2008
Jianqi Shen, Bin Yu, Huarui Wang, Haitao Yu, and Yehuan Wei, "Smoothness-constrained projection method for particle analysis based on forward light scattering," Appl. Opt. 47, 1718-1728 (2008)