Inversion algorithms for particle sizing with photon migration measurement

Abstract

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)....

Pharmaceutical Applications of Separation of Absorption and Scattering in Near-Infrared Spectroscopy (NIRS)

“…To date, FDPM has been predominately utilized to separate absorption and scattering in NIR spectral responses of pharmaceutical samples. A number of studies were performed by Dr. Sevick‐Muraca and collaborators, where they applied FDPM for the analysis of particle size in suspensions and powder media, and for the determination of constituent concentration in powder mixtures 9–12, 16, 19–21, 47…”

“…For particle size analysis, an inversion algorithm was developed to determine the particle size distribution (PSD) and volume fraction for noninteracting colloidal suspension samples (<2% volume fraction) from FDPM measurements 19. When particle interaction was accounted for by the full polydisperse hard sphere Percus–Yevick (HSPY) model, FDPM was capable of determining PSD and volume fraction for polydisperse interacting suspensions with volume fractions up to 40% 20, 47.…”

“…The two main purposes of the separation are to improve the understanding of individual roles played by absorption and scattering in NIRS, and to utilize the separated absorption and scattering spectra for qualitative and quantitative applications. To date, five techniques to separate NIR absorption and scattering of pharmaceutical related materials have been reported: spatially resolved spectroscopy,5–8 frequency‐resolved spectroscopy,9–21 time‐resolved spectroscopy,22–27 the integrating sphere based reflectance and transmittance measurements,28–31 and measurements of remission, absorption and transmission fractions through layers of material of different thicknesses 32, 33. A review of how these techniques are applied specifically to pharmaceutical application has yet to be reported.…”

Digital micro-mirror device-based detector for particle-sizing instruments via Fraunhofer diffraction

“…(3) through proper reconstruction algorithms, e.g., Chahine regularization algorithm, Tikhonov regularization algorithm, l 1 -norm-based algorithm, modified Landweber algorithm, etc. [16][17][18][19].…”

Performance evaluation of fluorescence tomography in a Siemens Inveon multimodality scanner

“…The solid agar phantom was made of distilled water, agar, Liposyn II and India ink. The optical properties of the agar phantom was decided by a heterodyned modulated-PMT-based frequency-domain instrument [5].…”