Monte Carlo Simulation of the Tomato Salad Problem

Johannes Albert Österreicher

doi:10.5566/ias.3593

Authors

Johannes Albert Österreicher Austrian Institute of Technology

DOI:

https://doi.org/10.5566/ias.3593

Keywords:

dispersoids, transmission electron microscopy, particle size distribution, aluminum alloys, spherical, corpuscle problem

Abstract

The tomato salad problem describes a stereological bias in the microscopic characterization of particulate systems, particularly in transmission electron microscopy (TEM). When a thin section is prepared from a material containing dispersed particles, the observed particle size distribution in micrographs may differ from the true distribution due to truncation effects and sampling bias. Depending on the initial size distribution, the observed mean particle size may appear smaller or larger than the actual mean. This work presents a Monte Carlo simulation of the tomato salad problem, implemented in R, to study the effects of foil thickness and particle size distribution on observed size measurements. Simulated results are compared with analytical predictions, showing good agreement. The study also highlights the impact of stochastic sampling errors, which can exceed the bias introduced by the tomato salad problem, emphasizing the need for sufficient sampling in microscopic analysis. The developed simulation may serve as an educational tool and could be extended in future work to analyze non-spherical particles and sample preparation artifacts.

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