We investigate the assessment of uncertainty in the inference of aerosol size distributions from backscatter and extinction measurements that can be obtained from a modern elastic/Raman lidar system with a Nd:YAG laser transmitter. To calculate the uncertainty, an analytic formula for the correlated probability density function (PDF) describing the error for an optical coefficient ratio is derived based on a normally distributed fractional error in the optical coefficients. Assuming a monomodal lognormal particle size distribution of spherical, homogeneous particles with a known index of refraction, we compare the assessment of uncertainty using a more conventional forward Monte Carlo method with that obtained from a Bayesian posterior PDF assuming a uniform prior PDF and show that substantial differences between the two methods exist. In addition, we use the posterior PDF formalism, which was extended to include an unknown refractive index, to find credible sets for a variety of optical measurement scenarios. We find the uncertainty is greatly reduced with the addition of suitable extinction measurements in contrast to the inclusion of extra backscatter coefficients, which we show to have a minimal effect and strengthens similar observations based on numerical regularization methods.
© 2008 Optical Society of America
Remote Sensing and Sensors
Original Manuscript: September 26, 2007
Manuscript Accepted: November 27, 2007
Published: March 31, 2008
Benjamin R. Herman, Barry Gross, Fred Moshary, and Samir Ahmed, "Bayesian assessment of uncertainty in aerosol size distributions and index of refraction retrieved from multiwavelength lidar measurements," Appl. Opt. 47, 1617-1627 (2008)