Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry

Anomalous diffraction by an arbitrarily oriented ellipsoid with three different axes is derived. From the resulting expression the relationship between the shape of the ellipsoid and the intensity pattern is immediately evident: The axial ratio of the elliptical isointensity curve equals the axial ratio of the elliptical projected area of the ellipsoid. A comparison of anomalous diffraction with calculations performed with the T-matrix method reveals that the anomalous diffraction approximation is highly accurate for single ellipsoidal red blood cells. Application of the expression for anomalous diffraction by ellipsoids to a population of red blood cells shows that, even in a red-cell suspension as examined in an ektacytometer, the axial ratio of the isointensity curves is equal to the mean axial ratio of the red blood cells in the population. In ektacytometry this relationship between cell shape and intensity pattern is commonly assumed to hold true without reference to the light-scattering properties of the cells. The results presented here show that this assumption is valid, and we offer a profound theoretical basis for it by considering in detail the light scattering by the red blood cells.