Equivalent circle diameter , defined

In addition, more detailed measurements of equivalent circle diameter (ECD), which is defined as the diameter of a circle with an area equivalent to the area of the particle, and has units of length ... 

Once an image has been segmented, the microstructural characteristics can be measured, for example ice crystal and air bubbles size. Figure 6.1 shows that the ice crystals and air bubbles are not spherical. Therefore, several different measurements of size can be made, for example the maximum diameter, the minimum diameter, or the equivalent circular diameter i.e. the diameter of a circle with the same area). The shape factor (defined by equation 6.3) is a measure of how far a particle is from being circular it takes a value of one for a sphere and becomes smaller as the particle becomes less spherical. 

Let QP be a diameter of the unit sphere then, since great circles defined by Q and P are not unique, all turns TK defined by pairs of opposite points are equivalent. Since rTn can be chosen on any great circle, it commutes with any turn T. The operation of adding I, to a turn T is described as conjugation,... 

Particle shape index is defined as the projected area of the particle divided by the area of a circle having a diameter equivalent to the maximum projected length of the particle. 

Particle size ambiguous term which refers to a variety of measurands that correlate with the outer dimensions of a particle particle size is either defined as a characteristic length in a two-dimensional projection of the particle (e.g. Feret diameter xperet) Of characteristic length of a regular body (e.g. sphere, circle, ellipse) that is equivalent to the particle with respect to a defined geometrical or physical particle property. 

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