ABSTRACT
Historically, particle size has been defined by an interaction with a measuring instrument such as a sieve; and particle shape, by one or two parameters such as size and aspect ratio. Recently particle silhouettes have been analyzed by sophisticated signal processing techniques such as Walsh and Fourier series, yielding numerical values which describe the particle profile shape with great accuracy. Fourier functions operate over an interval 0 through 2p. They are orthogonal, normalized, and complete. The term orthogonal means that the product of any two functions integrated over an interval is zero, unless they are identical. One practical implication of a complete series is that one can faithfully represent a given profile to an accuracy that is determined by the number of terms chosen to represent that profile. There are other orthogonal series but not all are complete, and this lack of completeness causes one to hesitate in testing their effectiveness in morphological analysis.
