  In this paper, we express the Chord Length Distribution (CLD) measure
associated to a given Particle Size Distribution (PSD) when particles are
modeled as suspended spheroids in a reactor. Using this approach, we propose
two methods to reconstruct the unknown PSD from its CLD. In the single-shape
case where all spheroids have the same shape, a Tikhonov regularization
procedure is implemented. In the multi-shape case, the measured CLD mixes the
contribution of the PSD associated to each shape. Then, an evolution model for
a batch crystallization process allows to introduce a Back and Forth Nudging
(BFN) algorithm, based on dynamical observers. We prove the convergence of this
method when crystals are split into two clusters: spheres and elongated
spheroids. These methods are illustrated with numerical simulations.
