Bayesian inference of systematic and random errors in complex-amplitude sensing (CAS) of single particles at three wavelengths

The recently developed Complex Amplitude Sensing (CAS) technique—in its two versions, CAS-v1 for liquid-borne particles and CAS-v2 for gas-borne particles—enables robust measurements of the complex forward-scattering amplitude S ( 0 ∘ ) of single particles, from which detailed analytical information about the particles—refractive index, size, and (via the polarization resolution of CAS-v2) shape—can be obtained. Here we develop a framework for quantifying the instrument-dependent errors in the S ( 0 ∘ ) measurement and demonstrate it on gas-borne particle measurement by CAS-v2. The framework infers, for each instrument, a four-dimensional error parameter vector comprising a relative systematic error and a random-noise standard deviation in each of Re S ( 0 ∘ ) and Im S ( 0 ∘ ) , by applying a Bayesian analysis to the S ( 0 ∘ ) data points of standard spherical particles with known refractive index and size. Because the three instruments probe the same standard-particle population, the data from λ = 453 n m , 638 nm, and 834 nm are combined in a joint inference that shares the wavelength-independent mean diameter across instruments; this coupling restores uniqueness in the large-diameter, short-wavelength regime where single-wavelength inference is defeated by Mie-amplitude oscillation. We apply the framework to three CAS-v2 instruments using aerosolized polystyrene latex and silica standard particles, obtaining posterior estimates of the relative systematic error and noise parameters separately for each instrument. The inference framework is general and applies to any S ( 0 ∘ ) -measuring instrument for gas-borne and liquid-borne particles. The resulting per-instrument error anchors supply realistic, data-driven priors on the S ( 0 ∘ ) measurement errors and thereby provide the foundation for uncertainty-aware retrievals of the refractive index, size, and shape of unknown particles.