It is shown how the direct irradiance model for stratified source‐free light fields in natural and laboratory hydrosols may be inverted so as to obtain from in situ irradiance measurements the volume absorption coefficient and mean backscatter coefficient consistent with the irradiance field. That is, the resultant optical properties may be arbitrary functions of depth in the hydrosol and the corresponding direct model will nevertheless exactly reproduce the original light field using the optical properties determined by the inverse model. In this way we obtain compatible light fields and optical properties within a hydrosol so that, given one, we can reproduce the other. The properties of the inversion algorithm are illustrated through its application to artificially generated light fields, and the effects of noise in the light field are studied. The algorithm is then used to obtain depth‐dependent absorption and backscatter coefficients from in situ irradiance measurements in the Sargasso Sea.