Feasibility Exploration of Throughfold as a Predictor for Target Loading and Associated Error Bounds

Various applications of the Fredholm integral equation appear m different fields of study. An application of particular interest to the Air Force arises in determination of target loading from nuclear effects simulations. Current techniques first unfold the incident spectrum then determine target loading; resulting spectrum and loading are assumed exact. This study investigates the feasibility of a new method, through-fold, for directly determining defensible error bounds on target loading. Through-fold uses a priori information to define input data and represents target response with a linear combination of instrument responses plus a remainder to derive a quadratic expression for exact target loading. This study uses a simplified, linear version of the quadratic expression. Through-fold feasibility is tested by comparing error bounds based on three target loading functions. The three test cases include an exact linear combination of instrument responses, the same combination plus a positive remainder, and the same combination plus a negative remainder. Total error bounds reduced from 100% to 35% in cases #1 and #2. In case #3 error bound was reduced to 48%. These results indicate that through-fold has promise as a predictor of error bounds on target loading