An analysis method for analyzing a sample includes a first step of acquiring measurement data including a first signal based on the sample and a second signal based on noise added to the first signal as a result of analysis of the sample, a second step of assuming a shape representing the first signal and a shape representing the second signal and modeling the measurement data using Bayesian inference, and a third step of estimating a probability distribution of characteristics of the sample based on the modeled measurement data.

Concentrations are determined based on a measurement of a composition (X) by Laser Induced Breakdown Spectroscopy (LIBS). The LIBS spectrum (Sx) comprises resonance peaks (Rk,Rca,Rna) corresponding to the constituents (K,Ca,Na) in the composition (X). The resonance peaks comprise spectral amplitudes (Pk,Pca,Dna,Pna) indicative of the unknown concentrations (Cna,Ck,Cca) of the constituents (K,Ca,Na). A first spectral amplitude (Pk,Pca,Dna) in the LIBS spectrum (Sx) corresponds to the unknown concentration (Ck,Cca,Cna) of a first constituent (K,Ca,Na) to be determined. A second spectral amplitude (Pna) corresponds to a maximum value of a self-reversed resonance peak (Rna) of the first or another constituent (Na) in the LIBS spectrum (Sx). An amplitude ratio (Pk/Pna, Pca/Pna, Dna/Pna) is calculated between the first spectral amplitude (Pk,Pca,Dna) and the second spectral amplitude (Pna) and the ratio is matched with calibration data to determine concentrations.

A vision system for monitoring areas of interest having a system for receiving an optical input, outputting a signal, and processing the signal. The system is configured to measure the radiance in spectral bands in which solar radiation is reduced substantially due to absorption by atmospheric constituents. This mitigates the negative effects of solar radiation such as sun glare. The system is configured to output a resultant detection signal in response to the measurements in the spectral bands selected.