linear transmittance that opaque surfaces exhibit and the traditional exponential transmittance encountered in participating media and unstructured geometries. This covers a large part of the spectrum of geometric structures encountered in complex scenes. In order to handle the spatially varying transmittance correlation effects, we further extend the theory of non-exponential participating media to a heterogeneous transmittance model. Our model is compact in storage and computationally efficient both for evaluation and for reverse-mode gradient computation. Applying our model to optimization algorithms yields significant improvements in volumetric scene appearance quality. We further show improvements for relevant applications, such as scene appearance prefiltering, image-based scene reconstruction using differentiable rendering, neural representations, and compare it to a conventional exponential model.