A theoretical model is presented for the formation of small-particle shadow images in a single-lens laser-imaging system. The model uses a modification of classical Lorenz-Mie theory, presented by the authors in an earlier paper, to calculate the external electromagnetic fields resulting from the interaction of a Gaussian laser beam with a finite absorbing spherical particle. Propagation of the electric field through the imaging system components is developed from a scalar viewpoint using the thin-lens transformation and the Fresnel approximation to the Huygens–Fresnel propagation equation. The theoretical model is valid for either transparent or absorbing spheres and has no restrictions on the allowable degree or direction of aerosol defocus. Direct comparisons between theoretical calculations and experimental observations are reported for 53-μm-diameter transparent water droplets and 66-μm-diameter absorbing nickel spheres for defocus ranging from −2 mm (toward the lens) to +2 mm (away from the lens). Theory and experiment showed good agreement in the boundary edge gradient and the location of the external peaks, while observable differences existed in the magnitude of the central spots. Theoretical results, comparing water and nickel aerosols, showed observable differences in the calculated average internal intensity (AII). In contrast, the boundary edge gradient showed less dependence on changes in the optical properties of the particle. These results indicate that criteria, such as the AII, used in focus determination must be reevaluated when applying in-focus sizing algorithms to aerosols with significantly different optical properties.
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