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The in-line hologram of a micrometer-scale colloidal sphere can be analyzed with the Lorenz–Mie theory of light scattering to obtain precise measurements of the sphere's diameter and refractive index. The same technique also can be used to characterize porous and irregularly shaped colloidal particles provided that the extracted parameters are interpreted with effective-medium theory to represent the properties of an equivalent effective sphere. Here, we demonstrate that the effective-sphere model consistently accounts for changes in the refractive index of the medium as it fills the pores of porous particles and therefore yields quantitative information about such particles' structure and composition. In addition to the sample-averaged porosity, holographic perfusion porosimetry gauges the polydispersity of the porosity. We demonstrate these capabilities through measurements on mesoporous spheres, fractal protein aggregates and irregular nanoparticle agglomerates, all of which are noteworthy for their industrial significance. 

Holographic particle characterization uses in-line holographic microscopy and the Lorenz-Mie theory of light scattering to measure the diameter and the refractive index of individual colloidal particles in their native dispersions. This wealth of information has proved invaluable in fields as diverse as soft-matter physics, biopharmaceuticals, wastewater management, and food science but so far has been available only for dispersions in transparent media. Here, we demonstrate that holographic characterization can yield precise and accurate results even when the particles of interest are dispersed in turbid media. By elucidating how multiple light scattering contributes to image formation in holographic microscopy, we establish the range conditions under which holographic characterization can reliably probe turbid samples. We validate the technique with measurements on model colloidal spheres dispersed in commercial nanoparticle slurries.