Advanced control of crystal shape, size distribution, and polymorphic form (internal lattice structure) in suspension crystallization processes has been hindered by the limitations of available on-line sensors. High-speed, in situ video microscopy is a promising technology for measuring these critical solid-phase properties. Extracting the size and shape distributions from the video images requires not only suitable image analysis but also statistical estimation to correct for sampling biases inherent in imaging-based measurement. We have developed advanced image analysis algorithms that are effective for in situ images of needle-like particles[1] and particles with complicated shapes that can be modeled geometrically using a wireframe model[2]. The former algorithm has been licensed by an industrial manufacturer of in situ video imaging probes and is expected to be packaged with their next-generation model this fall. We also have derived a maximum likelihood estimator (MLE) of the particle size distribution (PSD) that corrects sampling bias due to the finite size of the imaging window, enabling unbiased estimation of the PSD as well as quantification of measurement uncertainty[3].

The derived MLE provides a necessary and useful starting point for imaging-based PSD estimation, but is based on the assumption that image analysis is perfect, i.e. that the image analyzer identifies every single particle appearing completely inside the imaging window. In reality, however, image analyzers often miss particles that are overlapping or occluded. In this talk, we present a method for estimating the number density of monodisperse particle populations at high solids concentrations with heavy particle overlap and imperfect image analysis. The method is based on a first-principles, probabilistic model that describes the degree of particle overlap as a function of particle geometry and number density. The effectiveness of the method is demonstrated using data obtained from a complicated image analysis algorithm applied to images simulated under a variety of conditions.

Reconstructing the PSD using imaging requires a large number of samples (i.e. images), but the amount of time available to acquire samples is limited by crystallization kinetics. By applying our image analysis and estimation tools to images from a simulated batch crystallization of an industrial photochemical, we demonstrate the feasibility of on-line, imaging-based, high-resolution PSD measurement given the time constraints imposed by a typical crystallization process.

[1] Paul A. Larsen, James B. Rawlings, and Nicola J. Ferrier. An algorithm for analyzing noisy, in situ images of high-aspect-aspect ratio crystals to monitor particle size distribution. Chem. Eng. Sci., 61(16):5236--5248, 2006.

[2] Paul A. Larsen, James B. Rawlings, and Nicola J. Ferrier. Model-based object recognition to measure crystal size and shape distributions from in situ video images. Chem. Eng. Sci., 62:1430--1441, 2007.

[3] Paul A. Larsen and James~B. Rawlings. Maximum likelihood estimation of particle size distribution for high-aspect-ratio particles using in situ video imaging. Submitted for publication in Technometrics, April 2007.