**Stereology**

The aim of quantitation in EM is obtain precise estimates of sizes and number of structures/particles with the minimum of work. To do this we use an approach called stereology. The aim is achieved in two steps:

1. Organising a sampling scheme. Rather easy to implement sampling schemes that give all items/locations equal chance of being included in an EM micrographs that are later examine using the chosen estimators.

A typical sampling scheme uses Systematic Uniform Random (SUR) sampling to organise the samples used. SUR means a set of samples taken at intervals through the specimen but always with the first sample placed at a random position within the intervals used. The random position ensures the sample is unbiased and the systematic array ensures coverage of the specimen. For example an SUR sample of organ would consist of a set of evenly space slices with the first slice of the array placed at random. For some types of estimation it may also necessary to randomize orientation. Once a section or an array of sections has been placed at random within thereference space of interest then usually the section is imaged using an SURarray of micrographs in which features are probed using arrays of geometrical features such as points and lines. In some cases the number of features might be counted and also multiple parallel slices could be used as probes (details to follow).

2. Applying estimators and doing counts. Estimation of sizes or numbers by counting encounters of structures with a set of geometrical "probes" such as points, lines or planes.

An example of a probe would be the one for estimating the area of organelle profiles or parts of them in a micrograph. A regular array of equally spaced points is placed at random over the image and encountered of the points with all organelles profiles or parts thereof arecounted. The number of points landing on the "phase" of interest multiplied by the area associated with each of the points on the lattice provides an estimate of profile area.

Another example is for 3D analysis of volume. If a series of points is randomly positioned within a designated space (the reference space), then the fraction of points that "land" on a "phase" or component of interest contained within the space is an unbiased estimator of the fractional volume or volume density of the component in the reference space. In many systems this can be achieved on SUR micrographs taken from random or SUR sections. An SUR array of points can be overlaid onto the micrograph and used for point counting (details to follow).