Single particle raster image analysis of diffusion
Journal article, 2017

As a complement to the standard RICS method of analysing Raster Image Correlation Spectroscopy images with estimation of the image correlation function, we introduce the method SPRIA, Single Particle Raster Image Analysis. Here, we start by identifying individual particles and estimate the diffusion coefficient for each particle by a maximum likelihood method. Averaging over the particles gives a diffusion coefficient estimate for the whole image. In examples both with simulated and experimental data, we show that the new method gives accurate estimates. It also gives directly standard error estimates. The method should be possible to extend to study heterogeneous materials and systems of particles with varying diffusion coefficient, as demonstrated in a simple simulation example. A requirement for applying the SPRIA method is that the particle concentration is low enough so that we can identify the individual particles. We also describe a bootstrap method for estimating the standard error of standard RICS.

Bias correction

Maximum likelihood


Confocal laser scanning microscopy

Fluorescent beads



Marco Longfils

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Erich Schuster

SIK – the Swedish Institute for Food and Biotechnology

Niklas Lorén

Chalmers, Physics, Eva Olsson Group

SuMo Biomaterials

Aila Särkkä

University of Gothenburg

SuMo Biomaterials

Chalmers, Mathematical Sciences, Mathematical Statistics

Mats Rudemo

SuMo Biomaterials

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

Journal of Microscopy

0022-2720 (ISSN) 1365-2818 (eISSN)

Vol. 266 1 3-14

Subject Categories

Other Physics Topics

Probability Theory and Statistics

Areas of Advance

Materials Science



More information

Latest update