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The authors report on the angle resolved light scattering characteristics of individual polystyrene spheres on three silicon surfaces. A He-Ne laser (632.8 nm) focused to a 15 micrometers 1/e2 diameter was employed to illuminate 0.804 micrometers diameter spheres on optically smooth ((sigma) >= (lambda) ) silicon surfaces: monocrystalline silicon (bare silicon), polycrystalline silicon (polysilicon), and roughened silicon ('black silicon'). These surfaces provided a roughness spectrum ranging between the smooth, virtually featureless surface of the bare silicon to one of dense, very coarse needle- like features on the black silicon. Scattering was measured as a function of incident beam polarization for incident angles of 30, 45, and 75.3 degrees (Brewster's angle). Experimental measurements show that the beam incident angle and polarization are important factors controlling substrate background scatter. The substrate influences sphere detectability in two ways: first, by directly scattering incident radiation into the detector and second, by reflecting a portion of the forward scattered light originating from the sphere. The results obtained are qualitatively explained with reference to the silicon surface reflectance which varies significantly as beam incident angle and polarization are changed. As surface roughness approached a value comparable to the sphere size, detectability diminished; that is, the measured cross sections were lower under these conditions. Surface roughness not only added to the background signal, but also reduced the amount of energy scattered by the sphere reaching the detector. A modification to Lorenz-Mie theory is introduced to explain the experimental findings. The approach taken is to calculate the scattering components for a sphere in free space, then attenuate those components which are reflected from the substrate into the detector. The computation includes the variation in substrate reflectivity as the ray incident angle and polarization change. The assumptions and validity of this approach are discussed, as well as future possible improvements to the model.
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