•A non-invasive optical particle-characterization method for submicron particles.•Accurate measurement of real and imaginary parts of complex refractive index.•Accurate measurement of volume-equivalent particle-size distribution.•Applicable to both spherical and non-spherical particles•A novel Bayesian computational approach for solving inverse scattering problem. Nondestructive inline measurements of submicron-sized particles and gas bubbles are required in many fields of study, including environmental, industrial, and biomedical research. The single particle extinction and scattering (SPES) method is a promising technique for this purpose because of its sensitivity to both the complex refractive index and the size of individual particles. Herein an original modification of the SPES instrument that suppresses measurement bias and background noise is presented. In addition, relevant theory and a practical algorithm for data analysis are presented. The inverse scattering problem of estimating the physical characteristics of a particle from SPES data using Bayesian theory for model selection is formulated, and the performance of the algorithm using simulated data for spherical and non-spherical particles is evaluated. The results suggest that a cluster of SPES data points for an ensemble of particles contains sufficient information to retrieve the complex refractive index and volume equivalent size-distribution of the particles, regardless of particle shape. The Bayesian inversion method also allows incorporation of informative data from other analytical methods (e.g., electron microscope, upstream size-sorting device) through the model and parameter priors. As practical examples, the SPES method was used to constrain the complex refractive index and size distribution of water-insoluble aerosols contained in rainwater. The results suggest that the SPES method itself or its use in combination with other conventional analytical methods can quantify the complex refractive index and size distribution of almost any type of submicron particle (including gas bubbles) in environmental, industrial, and biomedical samples.