Ray-tracing techniques are applied to bolometry, a diagnostic particularly sensitive to machine geometry due to the effect of volume sampling. Sightlines from the ASDEX-Upgrade bolometer foils were ray-traced with a path tracing algorithm, where the optical path is represented by a statistical bundle of ray paths connecting the foil surface with the slit geometry. By using the full 3D machine model for the detector box and first wall, effects such as occlusion and vignetting were included in the bolometer’s étendue calculation. Inversion matrices calculated with the ray-tracing technique were compared with the more conventional single-ray approach and shown to be naturally more constrained, requiring less regularisation. Relative errors between the two models are shown to be significant for a sample radiation scenario. The ray-tracing technique consistently outperformed the single-ray approach when inverting a population of emission phantoms. Consequences for the overall shape of the inverted radiation distribution and total radiated power are discussed.