Meaning
Stereological procedure corrects the apparent size distribution of spherical particles observed in a two dimensional plane. Using Saltykov Wicksell unfolding is necessary because a random cross section rarely passes through the exact center of every particle. This mathematical adjustment converts the observed circle diameters into the true sphere diameters of the bulk population.
Geometric Probability
Intersection likelihood depends on the diameter of the sphere and the position of the cutting plane. Saltykov Wicksell unfolding uses a probability matrix to redistribute the observed counts from smaller size classes into their correct larger categories. This correction accounts for the fact that a large sphere can appear as a small circle if it is sliced near its edge.
Particle Diameter
Accuracy of the result relies on the assumption that the features are roughly spherical. When Saltykov Wicksell unfolding is applied to non-spherical objects, the resulting distribution may contain errors. Researchers must verify the shape factor of the inclusions before proceeding with the numerical correction.
This verification involves measuring the aspect ratio of hundreds of features across multiple images.
Numerical Method
Calculation process involves solving a system of linear equations to find the true frequency of each size class. Modern software packages automate this task to handle thousands of data points simultaneously. The final output is a histogram representing the actual volumetric distribution of the phase.
