  In this paper, we are interested in the estimation of Particle Size
Distributions (PSDs) during a batch crystallization process in which particles
of two different shapes coexist and evolve simultaneously. The PSDs are
estimated thanks to a measurement of an apparent Chord Length Distribution
(CLD), a measure that we model for crystals of spheroidal shape. Our main
result is to prove the approximate observability of the infinite-dimensional
system in any positive time. Under this observability condition, we are able to
apply a Back and Forth Nudging (BFN) algorithm to reconstruct the PSD.
