Angular truncation errors in integrating nephelometry

Abstract

Ideal integrating nephelometers integrate light scattered by particles over all directions. However, real nephelometers truncate light scattered in near-forward and near-backward directions below a certain truncation angle (typically 7°). This results in truncation errors, with the forward truncation error becoming important for large particles. Truncation errors are commonly calculated using Mie theory, which offers little physical insight and no generalization to nonspherical particles. We show that large particle forward truncation errors can be calculated and understood using geometric optics and diffraction theory. For small truncation angles (i.e., <10°) as typical for modern nephelometers, diffraction theory by itself is sufficient. Forward truncation errors are, by nearly a factor of 2, larger for absorbing particles than for nonabsorbing particles because for large absorbing particles most of the scattered light is due to diffraction as transmission is suppressed. Nephelometers calibration procedures are also discussed as they influence the effective truncation error.