Determining the Backward Scattering Coefficient with Fixed-Angle Backscattering Sensors—Revisited

Modern sensors for measuring the volume scattering function (VSF) at a fixed angle in the backward scattering direction were first developed in the early 1980's at SRI International. 1 At the time, considerable thought and debate were devoted to methods for calibrating the instruments to provide an absolute measurement of the VSF. The idea of measuring the scattering by spherical particles, for which the resulting VSF could be calculated from electromagnetic theory (so-called Mie theory), and then relating the scattering signal to the calculated VSF, was rejected for several important reasons. Principally, this method requires a priori knowledge of the sensor's relative response throughout its scattering volume, and it was recognized that this could not be accurately calculated from a simple analysis of the optical geometry. The method that was eventually developed was to measure the sensor's response to a diffusely reflecting plate with a known surface scattering function. This measurement, made across the entire scattering volume, provides an absolute calibration in units of the VSF (m -1 sr -1 ). In the early 1990's, when the authors developed the first multispectral backscattering sensors, they refined this calibration method and extended it to provide an estimate of the backscattering coefficient following a conjecture by Oishi. 2 We revisit these methods using new calculations of the VSF and, most important, new measurements of the VSF in the back hemisphere made with the HOBI Labs' HydroBeta. We show that the reflecting-plate method is the most reliable way to accurately calibrate VSF instruments, fixed- or multi-angle. We also show a further analysis of Oishi's conjecture, taking into account practical sensors' response to volume scattering rather than assuming an ideal sensor.