THE PROJECTED AREAS OF ELLIPSOIDS AND CYLINDERS

In deriving particle size, volume and concentration from laser diffrac tion experiments, it is normally assumed that the particles are sphere s. For other shapes the projected area is not constant but rather has a range of values. Because the orientation of the body is usually rand om, it is the distribution function for the projected area which is of interest. In order to assist in the interpretation of light diffracti on measurements and image analysis, the distribution of the projected area for (tri-axial) ellipsoids and general cylinders is derived. The graph of the distribution is given for an ellipsoid with axes in the r atio 1:2:8. The distribution function for a general cylinder, given in terms of the width function of its base, is expressed in a form suita ble for numerical computation. Examples are given and also analytic re sults for the circular cylinder and cube.