Relationship between particle-size and chord-length distributions in focused beam reflectance measurement: stability of direct inversion and weighting

A relationship is derived between the underlying particle-size distribution (PSD) and the measured chord-length distribution (CLD) from a Lasentec Focused Beam Reflectance Measurement (FBRM) instrument. A direct method of inverting this relationship is calculated analytically. This method is shown to be stable in some cases. The principle of the method is identical to earlier “peeling” methods, which were unstable. The reason for the improvement is finer spacing of size-intervals. The CLD is shown to be weighted by particle size; this affects the way in which mean chord-lengths should be interpreted. Two moments of the CLD represent physical quantities regardless of the particlesʹ shapes.