A new linear inverse method is demonstrated for recoueiy of particle-size distribution (PSD) and volume fraction of opaque colloidal suspensions from frequency domain photon migration (FDPM) measurement of multiply scattered light. To deal with the ill posedness of PSD retrievingproblem, the size distribution is approximated by the B-spline expansion. Tikhonov regularization, along with both nonnegativity and smoothing constraints, in which the L-curve method is employed to choose a regularization parameter, are also used to ensure the stable and realistic solution. The algorithm is tested using synthetic FDPM measurements at a variety of size distributions, and results are com-
IntroductionOnline measurements of particle-size distribution (PSD) and volume I'raction of colloidal suspensions arc highly desired in the particulate processes of pharmaceutical and chemical industries in order to effectively evaluate, optimize, and control manufacturing processes and product quality. However, it i, difficult to obtain these critical parameters at industrially t-clevant concentrations using real-time, online measurcnicnts. Most available online particle sizing methods, such as turbiclity (Crawley et al., 19971, angular static scattering (Frock. 1987). and dynamic light scattering (Nicoli et al., 190 1 1. arc b ; w d on single light scattering principle. Each method requires considerable sample dilution and mcasurement calibration due to the confounding effects of multiple scattcring from concentrated suspensions. Although some modifications of above methods, such as fiber optic dynamic light scattcring (FODLS) (Thomas, 1991) and modified static light scattering (SLS) (Lehner et al., 1998), have been proposed t o suppress the effects of multiple scattering, these methods are not well suited for particle sizing on multiple scattering, concentrated colloidal suspensions.In recent years, new particle-sizing methods based o n multiple light scattering principle. such as diffusive wave spectroscopy (DWS) (Horne and Davidson. 1993) and acoustic spectroscopy (AS) (Alba et al., 19991, have been applied for particle sizing in concentrated suspensions. Frequency domain photon migration (FDPM) is yet another new potential method for online characterization of multiple scattering, concentrated colloidal suspensions (Sevick-Muraca et al., 1997). Since this technique measures time-dependent propagation characteristics rather than the amount of light detected. it is self-calibrating and no external calibration is required. In addition, FDPM allows independent determination of absorption and scattering. Consequently. charactcrization of colloidal scatters is not biased by changes in the light absorption or color of suspending fluids. Because FDPM depends upon multiple scattered light, it is restricted to nondilute particulate suspensions, whereby the suspensions are typically opaque. Both size distribution and volume fraction can be directly obtained by inversion algorithms, where (Sevick-Muraca et al.? 1997; Richter et al., 1998)....
