The Feret diameter or Feret's diameter is a measure of an object's size along a specified direction. In general, it can be defined as the distance between the two parallel planes restricting the object perpendicular to that direction. It is therefore also called the caliper diameter, referring to the measurement of the object size with a

caliper Calipers or callipers are an instrument used to measure the linear dimensions of an object or hole; namely, the length, width, thickness, diameter or depth of an object or hole. The word "caliper" comes from a corrupt form of caliber. Many ty ...

. This measure is used in the analysis of particle sizes, for example in

microscopy Microscopy is the technical field of using microscopes to view subjects too small to be seen with the naked eye (objects that are not within the resolution range of the normal eye). There are three well-known branches of microscopy: optical mic ...

, where it is applied to projections of a three-dimensional (3D) object on a 2D plane. In such cases, the Feret diameter is defined as the distance between two parallel tangential ''lines'' rather than ''planes''.

Mathematical properties

From Cauchy's theorem it follows that for a 2D

convex body In mathematics, a convex body in n-dimensional Euclidean space \R^n is a compact convex set with non- empty interior. Some authors do not require a non-empty interior, merely that the set is non-empty. A convex body K is called symmetric if it ...

, the Feret diameter averaged over all directions (〈F〉) is equal to the ratio of the object

perimeter A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimet ...

(P) and pi, i.e.,〈F〉= P/. There is no such relation between〈F〉and P for a

concave Concave or concavity may refer to: Science and technology * Concave lens * Concave mirror Mathematics * Concave function, the negative of a convex function * Concave polygon A simple polygon that is not convex is called concave, non-convex or ...

object.

Applications

Feret diameter is used in the analysis of particle size and its distribution, e.g. in a powder or a polycrystalline solid; Alternative measures include Martin diameter, Krumbein diameter and Heywood diameter. The term first became common in scientific literature in the 1970s and can be traced to L.R. Feret (after whom the diameter is named) in the 1930s. It is also used in biology as a method to analyze the size of cells in tissue sections.

References

{{reflist, refs= {{cite book, author=Henk G. Merkus, title=Particle Size Measurements: Fundamentals, Practice, Quality, url=https://books.google.com/books?id=lLx4GzA-7AUC&pg=PA15, accessdate=12 December 2012, date=1 January 2009, publisher=Springer, isbn=978-1-4020-9016-5, pages=15– W. Pabst and E. Gregorová
Characterization of particles and particle systems
{{Webarchive, url=https://web.archive.org/web/20130717070642/http://www.vscht.cz/sil/keramika/Characterization_of_particles/CPPS%20_English%20version_.pdf , date=2013-07-17 . vscht.cz {{cite book, author=Yasuo Arai, title=Chemistry of Powder Production, url=https://books.google.com/books?id=6Bgew6-rNgwC&pg=PA216, accessdate=12 December 2012, date=31 August 1996, publisher=Springer, isbn=978-0-412-39540-6, pages=216– {{cite book, author=M. R. Walter, title=Stromatolites, url=https://books.google.com/books?id=WquTlXfp-FwC&pg=PA47, accessdate=13 December 2012, date=1 January 1976, publisher=

Elsevier Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, ...

, isbn=978-0-444-41376-5, pages=47– L. R. Feret La grosseur des grains des matières pulvérulentes, Premières Communications de la Nouvelle Association Internationale pour l’Essai des Matériaux, Groupe D, 1930, pp. 428–436. Particulates Length