Statistical Analysis of Phase-Inversion Neutron Specular Reflectivity

The phase-inversion approach to neutron specular reflection is elucidated in a formal setting, in order to emphasize its conceptual coherence and to facilitate study of some of its statistical properties in the context of real data. An operational notion of data degradation is introduced and illustrated with the randomizing effects of shot noise (counting noise) and the systematic bias induced by data truncation. Some basic statistical effects of phase-inversion are worked out in the new formalism and illustrated by simulated examples. A principal is advanced that phase-inversion sets the limit of available information from specular reflection.