Feret s diameter

To obtain a value for the dimensions of an irregular particle, several measurement approaches can be used Martin s diameter (defined as the length of a line that bisects the particle image), Feret s diameter (or end-to-end measurement, defined as the distance between two tangents on opposite sides of the particle parallel to some fixed direction), and the projected area diameter (defined as the diameter of a circle having the same area as that of the particle observed perpendicular to the surface on which the particle rests). With any technique, a sufficiently large number of particles is required in order to obtain a statistically valid conclusion. This is best accomplished by using a... 

Image analysis can be used to determine a variety of morphometric parameters including area, Feret s diameter, Martin s diameter, aspect ratio (ratio of minimum to maximum Feret diameter), perimeter, length, width, and form factor (the ratio of area/[perimeter]2), which can be related to specific particle shapes. Some of these functions are illustrated in Fig. 10 [14]. In addition, quantitative methods have been developed to measure particle shape [2,15,16]. 

As we just suggested, particle size and shape are important physical properties influencing powder flow and compaction. Particle size is a simple concept and yet a difficult one to quantitate. Feret s diameter, Martin s diameter, projected area diameter, specific surface diameter, Stokes diameter, and volume diameter are but several of the measurements that have been used to quantify particle size using a variety of methods. 

Greatest Feret s Diameter (GFD), 78 147 Greatest temperature difference (GTD),... 

Horizontal belt pressure filters, 11 379 Horizontal belt vacuum filter, 11 354-355 Horizontal box heaters, 19 511 Horizontal current classifiers, 16 619 Horizontal Feret s Diameter (HFD), 16 147 Horizontal injection wells, 16 613 Horizontal leaf filters, 11 366-367 Horizontal magnetic field-type (HMC), 23 857... 

Learning, types of, 15 475t Least Bounding Rectangle (LBR), 18 148 Least Feret s Diameter (LFD), 18 147 Least-squares curve fitting, 14 237 Leather... 

Feret s diameter, l.) (the mean value of the distance between pairs of parallel tangents to the projected outline of the particle), and Martin s diameter, Du (the mean chord length of the projected outline of the particle[96] D DM=I 7.1. S A//b) are used in automated analysis of microscopic images [49,50],... 

Martin s diameter and Feret s diameter of a particle depend on the particle orientation under which the measurement is made. Thus, obtaining a statistically significant measurement for these diameters requires a large number of randomly sampled particles which are measured in an arbitrarily fixed orientation. Since Martin s diameter, Feret s diameter, and projected area diameter are based on the two-dimensional image of the particles, they are generally used in optical and electron microscopy. The principles of microscopy as a sizing method are discussed in 1.2.2.2. 

Two commonly encountered definitions of particle size are Feret s diameter and Martin s diameter. These refer to estimates of approxi-... 

Feret s diameter = 15 scale units Martin s diameter = 10 scale units Projected area diameter = 13 scale units... 

This measurement problem can be simplified somewhat by using the projected area diameter instead of Feret s or Martin s diameter. This is defined as the diameter of a circle having the same projected area as the particle in question. Figure 1.1 illustrates these three definitions. In general, Feret s diameter will be larger than the projected area diameter which will be larger than Martin s diameter. 

Figure 1.1 Illustration of three common definitions of particle diameter. In general, Martin s diameter is less than the equivalent area diameter, which in turn is less than Feret s diameter.

Microscopy Projected Area diameter Feret s diameter Martin s diameter Perimeter diameter Uiuolled diameter... 

Feret s diameter (Fig. 20-5) is the perpendicular projection, in a fixed direction, of the tangents to the extremities of the particle profile. Martin s diameter is a line, parallel to a fixed direction, which divides the particle profile into two equal areas. Since the magnitude of these statistical diameters varies with particle orientation, these diameters have meaning only when a sufficient number of measurements are averaged. 

Church [39] proposed the use of the ratio of the expected values of Martin s and Feret s diameters as a shape factor for a population of elliptical particles. Cole [40] introduced an image-analyzing computer (the Quantimet 720) to compare longest chord, perimeter and area for a large number of particles. Other parameters have been proposed by Pahl el. al [7,41], Beddow [42] and Laird [29]. 

Longest dimension. A measured diameter equal to the maximum value of Feret s diameter. 

Feret s diameter (df). This is defined as the distance between two tangents on opposite sides of the particle, which are parallel to some fixed direction. 

Fig. 1 Influence of particle orientation on statistical diameters. The change in Feret s diameter is shown by the distances, df. Martin s diameter (dm) corresponds to the dashed lines.

Statistical diameters are often used in microscopy as they can be easily and rapidly measured, but the disadvantage is that they do not give information about the particle properties such as volume, mass, or surface area. However, for quality control applications this information may not be important. Figure 5 illustrates the most commonly used diameters. The USP <776> defines Martin s and Feret s diameter and other less commonly used diameters as (7) ... 

Feret s diameter The distance between imaginary parallel lines tangent to a randomly oriented particle and perpendicular to the ocular scale also called a graticule. Martinis diameter The diameter of the particle at the point that divides a randomly oriented particle into two equal projected areas. 

Feret s Diameter Feret s diameter is determined from the projected area of the particles by using a slide gauge. In general it is defined as the distance between two parallel tangents of the particle at an arbitrary angle. In practice, the minimum Xjrmm d maximum Feret diameters the mean Feret diameter Xp, and the Feret diameters obtained at 90 to the direction of the minimum and maximum Feret diameters X/rmax9o used. The minimum Feret diameter is often used as the diameter equivalent to a sieve analysis. 

Feret s Diameter A statistical particle diameter the length of a line drawn parallel to a chosen direction and taken between parallel planes drawn at the extremities on either side of the particle. This diameter is thus the maximum projection of the particle onto any plane parallel to the chosen direction. The value obtained depends on the particle orientation thus, these measurments have significance only when a large enough number of measurements are averaged together. See also Martin s Diameter. 

Figure 4. Selected measures of. size on a single particle (modilied from Muller, 1967). See Table II for delinitions. Df . Feret s diameter Dm Marlin s diameter, Dk Krumbein s diameter Dmd Middle diameter Dl Long diameter.

Feret s Diameter The distance between a pair of parallel lines which are oriented in a given direction (normally parallel to the vertical cross-hair in a microscope field of view) and which touch the extreme points on the perimeter of the projected outline of the particle. 

These and other diameters are defined in general texts such as Cadle [16] and Orr [1,2]. Martin s and Feret s diameters are statistical diameters associated with microscopy and image analysis. By definition, Martin s diameter is the distance between opposite sides of a particle measured i a line tnsecting the projected area. Feret s diameter is the distance betweoi parallel tangents cm opposite sides of the particle profile. To isure statistical significance, all measuremoits are made in the same directi[Pg.207]

---