Recent backscattering interferometry studies utilise a single channel microfluidic system, typically approximately semicircular in cross-section. Here, we present a complete ray tracing model for on-chip backscattering interferometry with a semicircular cross-section, including the dependence upon polarisation and angle of incidence. The full model is validated and utilised to calculate the expected fringe patterns and sensitivities observed under both normal and oblique angles of incidence. Comparison with experimental data from approximately semicircular channels using the parameters stated shows that they cannot be explained using a semicircular geometry. The disagreement does not impact on the validity of the experimental data, but highlights that the optical mechanisms behind the various modalities of backscattering interferometry would benefit from clarification. From the analysis presented here, we conclude that for reasons of ease of analysis, data quality, and sensitivity for a given radius, capillary-based backscattering interferometry affords numerous benefits over on-chip backscattering interferometry.
Keywords: backscattering interferometry; microfluidics; ray tracing; refractive index; semicircular channel.