We discuss some experience of solving an inverse light scattering problem for single, spherical, homogeneous particles using least squares global optimization. If there is significant noise in the data, the particle corresponding to the “best” solution may not correspond well to the “actual” particle. One way of overcoming this difficulty involves the use of peak positions in the experimental data as a means of distinguishing genuine from spurious solutions. We introduce two composite approaches which combine conventional data fitting with peak-matching and show that they lead to a more robust identification procedure.
TopIntroduction
Developments in the theory of light scattering from particulate matter mean that, in many situations, we can accurately compute the properties of scattered electromagnetic fields. There are rigorous solutions to this direct scattering problem for numerous particle types, such as homogeneous and inhomogeneous spheres, ellipsoids and others. However it is the inverse scattering problem that is of greater practical importance. This involves the determination of properties of scatterers from the knowledge of scattered fields. Here, we will concentrate on the case where the angular dependence of the scattered field is known. This type of problem arises in numerous applications, ranging from astronomy and remote sensing, through aerosol and emulsion characterization, to non-destructive analysis of single particles and living cells (Barth & Flippen, 1995, De Pieri, Ludlow & Waites, 1993, Gousbet & Grehan, 1988, Hull & Quinby-Hunt, 1997, Kolesnikova et al. 2006, Nascimento, Guardani & Giulietti, 1997, Semyanov et al. 2000, Ulanowski, Ludlow & Waites, 1987, Ulanowski & Ludlow, 1989, Wyatt, 1980).
The inverse problem has proved to be much harder to solve, even for the simplest particle shapes. Some approaches are based on generating solutions to the direct problem (after making assumptions concerning the shape, internal structure of the particle etc.) and matching these solutions to experimental data (Wyatt, 1980, Ulanowski 1988, Ulanowski & Ludlow, 1989). More recently, various neural network methods have been used (Berdnik, Gilev, Shvalov, Maltsev & Loiko, 2006, Hull & Quinby-Hunt, 1997, Nascimento et al, 1997, Ulanowski, Wang, Kaye & Ludlow, 1998). The inverse scattering problem has also been approached using global minimization of a sum of squares error function (Zakovic, 1997, Zakovic, Ulanowski & Bartholomew-Biggs, 1998). In the present paper we consider ways of counteracting the influence of data noise when using this approach. We use ideas discussed by Bartholomew-Biggs, Ulanowski and Zakovic (2005) and apply them in the context of unconstrained optimization of a composite performance function which seeks to match the experimental data in more than one way.
Experimental data are inevitably distorted by the presence of noise and numerous sources of error. These include optical aberrations, nonlinearity of the detection system, multiple scattering and particle nonsphericity. All existing inversion algorithms are sensitive to such distortion to a greater or lesser extent, which results in error (Gousbet & Grehan 1988), Shimizu & Ishimaru, 1990). This problem is especially acute in, but not limited to, measurements on single particles, and we will confine ourselves to this case.