The Feret diameter or Feret's diameter is a measure of an object 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 A caliper (British spelling also calliper, or in plurale tantum sense a pair of calipers) is a device used to measure the dimensions of an object. Many types of calipers permit reading out a measurement on a ruled scale, a dial, or a digital d ...

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

microscopy Microscopy is the technical field of using microscopes to view objects and areas of objects that cannot 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 micr ...

, 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. A convex body K is called symmetric if it is centrally symmetric with respect to the origin; that is to say, a point x lies in ...

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

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

(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 polygon which is not convex * Concave set * The concavity In ca ...

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 The Martin diameter is the length of the area bisector of an irregular object in a specified measuring direction. It is used to measure particle size in microscopy Microscopy is the technical field of using microscopes to view objects and are ...

, 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
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'', the ScienceDirect collection of electronic journals, '' Trends'', th ...

, 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