Inverse Problems in Scattering

[Steve Drake]

Hi Guys,

I am doing a bit of work with dynamic light scattering (DLS) data. It is one of the many areas of science where we encounter an inverse problem.

The forward problem is: For a known sized particle, calculate its scattered spectrum (that is easy). The inverse problem is: from the scattered spectrum, calculate the size(s) of the partcile(s) that made the spectrum (that is hard).

What I would like to know is how, given an experimental data set, do you invert that data set to get the original sample properties? I just read some books and they don't seem to go into the maths.

Any help would be greatly appreciated. I am pretty good at MATLAB and would like to code my own inversion routines.

Thanks

 

[Bobbywhy]

I’m not qualified to be positively sure, but here are three papers which may contain the mathematical method you are asking about:

“Photon Scattering with the Lorentz Integral Transform Method”
http://arxiv.org/abs/1107.2320

“Single-Scattering Optical Tomography: Simultaneous Reconstruction of Scattering and Absorption”
http://arxiv.org/abs/0811.4434

“The Legacy of the IST”
http://arxiv.org/abs/math/0206282

 

[opticspcs]

You can the simulated CONTIN program, (http://www.mathworks.cn/matlabcentral/fileexchange/6523-rilt ), it is relative simple. It can recover the particle size distribution fom dynamic light scattering data.

Best regards.

 

[Steve Drake]

You can the simulated CONTIN program, (http://www.mathworks.cn/matlabcentral/fileexchange/6523-rilt ), it is relative simple. It can recover the particle size distribution fom dynamic light scattering data.

Best regards.

Hi mate,

thanks for the reply to my very old topic hah. I had a go at that cause the original CONTIN is too complicated for me to use. rILT seems to work but its very slow. I have been using other methods in the mean time.

Thanks.

 

[sardar]

for bringing up this topic! Inverse problems in scattering are indeed a complex and challenging area of research. As you mentioned, the inverse problem in dynamic light scattering involves determining the size(s) of particles from their scattered spectrum. This is a non-trivial task as the scattered spectrum is affected by multiple factors such as particle size, shape, and concentration, as well as experimental conditions like wavelength and angle of incidence.

There are various approaches to solving inverse problems in scattering, and the choice of method often depends on the specific problem at hand. Some commonly used techniques include least squares fitting, maximum likelihood estimation, and Bayesian inference. These methods involve using mathematical models and algorithms to analyze the scattered data and estimate the underlying particle properties.

As for implementing these methods, it is certainly possible to code your own inversion routines in MATLAB. However, I would recommend consulting with experts in the field or seeking out specialized software designed for inverse problems in scattering. These resources can provide valuable insights and tools to help ensure accurate and reliable results.

Overall, the field of inverse problems in scattering is constantly evolving and there is still much to be explored and understood. I wish you all the best in your research and hope you are able to make significant contributions to this fascinating area of science.