Focal ratio degradation (FRD) is a major contributor to light loss in astronomical instruments employing multimode optical fibres. We present a powerful diagnostic model that uniquely quantifies the various sources of FRD in multimode fibres. There are three main phenomena that can contribute to FRD: scattering, diffraction and modal diffusion. We propose a Voigt FRD model where the diffraction and modal diffusion are modelled by the Gaussian component and the end-face scattering is modelled by the Lorentzian component. The Voigt FRD model can be deconvolved into its Gaussian and Lorentzian components and used to analyse the contribution of each of the three major components. We used the Voigt FRD model to analyse the FRD of modern astronomical grade fibre for variations in (i) end-face surface roughness, (ii) wavelength, (iii) fibre length and (iv) external fibre stress. The elevated FRD we observed was mostly due to external factors, i.e. fibre end effects such as surface roughness, subsurface damage and environmentally induced microbending caused by the epoxy, ferrules and fibre cable design. The Voigt FRD model has numerous applications such as a diagnostic tool for current fibre instrumentation that show elevated FRD, as a quality control method for fibre manufacture and fibre cable assembly and as a research and development tool for the characterization of new fibre technologies.