Optimisation of through-vial Raman analysis of turbid samples by modelling the Raman intensity-depth decay response

Raman spectroscopy enables non-destructive chemical analysis and can be performed through-vial, eliminating air exposure. However, signal attenuation arises from refraction, absorption, and scattering within the sample, while distortions and spectral interference from the vial further degrade signal collection and data quality. This study investigates depth-dependent Raman intensity decay in polystyrene (PS) particle suspensions as a model for turbid liquids and proposes a framework of equations and approaches based on Mie scattering theory and the Beer-Lambert law to predict Raman intensity decay in a range of samples. Experimental validation was performed using aqueous suspensions containing 495 nm, 350 nm, and 200 nm PS particles using an 830 nm laser, with Raman spectra acquired at incremental depths. Peak areas corresponding to PS, water, and glass were recorded. Mie theory was used to model the UV-visible extinction response, yielding estimated absorbance and, combined with the intensity decay due to refraction established from non-turbid samples, Raman intensity decay lengths. Estimated decay lengths for PS and water showed good agreement with experimental values, typically within 20%. This framework enables rapid optimisation of focal depth and consistent comparison between samples and experiments for quantitative through-container Raman analysis in pharmaceuticals, materials science, and nanotechnology.