Recently, it has been shown that the complex amplitude for neutrons specularly reflected from a film can be determined exactly at all accessible wave-vector transfers, including those for which the Born approximation is invalid, through the use of buried reference layers of finite thickness. Given the phase of reflection, it is then possible to solve the one-dimensional inverse-scattering problem directly, without resort to potentially ambiguous fitting procedures, to obtain a unique scattering length density depth profile for a laminar thin-film structure. Here we describe an extension of that phase determination method which utilizes controlled variations of the scattering length density of the incident and/or substrate medium instead of reference layers of finite thickness. This technique is of practical importance for thin-film systems involving either gas-liquid or solid-liquid interfaces in which the scattering length density of the liquid can be varied in a known way, as in an aqueous media consisting of a mixture of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}.$

• Received 21 July 1998

DOI:https://doi.org/10.1103/PhysRevB.58.15416