The Sizes of Spheres from Profiles in a Thin Slice I. Opaque Spheres

Thin slices through specimens are made into slides for use in microscopy. If a specimen consists of opaque spherical particles in a transparent medium, there will be seen through the slice circular profiles of particles and sections through particles. For a random slice, the size distribution of these profiles can be related to the size distribution of the population of spheres. The extensive literature dealing with this relationship is surveyed. An important generalization of practical importance is made with the introduction of a resolution interval which excludes from observation those profiles that are too large or too small. How this affects the relationship between the profile and sphere size distributions is considered, and some special cases are used as illustrations. In Part II (COLEMAN, 1983) the corresponding results for the case of transparent spheres in an opaque specimen are given.

[1]  S. D. Wicksell,et al.  THE CORPUSCLE PROBLEM. A MATHEMATICAL STUDY OF A BIOMETRIC PROBLEM , 1925 .

[2]  P. Goldsmith.  The calculation of true particle size distributions from the sizes observed in a thin slice , 1967 .

[3]  S. Komenda,et al.  Die mikroskopische Bestimmung der Größenverteilung von Kugelelementen, die zufällig in gewisser Umwelt verstreut sind , 1969 .

[4]  W. L. Nicholson,et al.  Estimation of linear properties of particle size distributions , 1970 .

[5]  H. Riedwyl,et al.  Bestimmung der Größenverteilung von Kugeln aus Schnittkreisradien , 1970 .

[6]  Estimating the distribution of spherical and elliptical bodies in conglomerates from plane sections. , 1970 .

[7]  N Keiding,et al.  Maximum likelihood estimation of the size distribution of liver cell nuclei from the observed distribution in a plane section. , 1972, Biometrics.

[8]  Robert S. Anderssen,et al.  Abel type integral equations in stereology. II. Computational methods of solution and the random spheres approximation , 1975 .

[9]  R. Anderssen.  Stable Procedures for the Inversion of Abel′s Equation , 1976 .

[10]  R. E. Miles,et al.  Precise and general conditions for the validity of a comprehensive set of stereological fundamental formulae , 1976 .

[11]  R. E. Miles.  Estimating aggregate and overall characteristics from thick sections by transmission microscopy , 1976 .

[12]  W. J. Whitehouse.  Errors in area measurement in thick sections, with special reference to trabecular bone , 1976, Journal of Microscopy.

[13]  D. Greeley,et al.  Practical approach to the estimation of the overall mean caliper diameter of a population of spheres and its application to data where small profiles are missed , 1978 .

[14]  P. E. Rose.  Improved tables for the evaluation of sphere size distributions including the effect of section thickness , 1980, Journal of microscopy.