Reduction of systematic uncertainty in the transmission measurement of iron using entropy based mutual information

Neutron cross-section determination by transmission measurement is essentially a data reduction process of obtaining the cross-section from the raw data of the neutron detector counts. The data reduction parameters are dominated by systematic uncertainty with a large coefficient of correlation. All the efforts have so far been devoted only to minimize the statistical uncertainty in neutron detector counts by repeated measurements but the dominant systematic uncertainty in the data reduction parameters has either been neglected or randomized. As the conventional central limit theorem cannot be applied to reduce the highly correlated systematic uncertainty, we propose a new approach called entropy based mutual information to set theoretical limits and minimize the systematic uncertainty using an algorithm we have developed. In our algorithm one can determine the upper and lower bounds of the non-diagonal elements of the correlation matrix for maximization of mutual information. We demonstrate the utility of our approach in reducing the systematic and hence the total uncertainty of neutron cross-section of iron in the transmission measurement.