The conventional problem of linear transport theory is to find the distribution function given the various scattering functions. Here, the inverse question is asked. Given the results of some simple experiment how can one construct the kernels? First, the simple problem of one velocity neutron diffusion is considered, and it is found that the methods and solution are quite similar to that for the problem of deducing a potential given the scattering data. The solution given is constructive and seems to be efficient.