Abstract: We have measured the resistance R (T, I, B(sub ext) of a superconducting transition edge sensor over the entire transition region on a fine scale, producing a four-dimensional map of the resistance surface. The dimensionless temperature and current sensitivities (alpha equivalence partial derivative log R/partial derivative log T|(sub I) and beta equivalence partial derivative log R/partial derivative log I|(sub T) of the TES resistance have been determined at each point. alpha and beta are c…