Abstract
Three photoemission measurement modes, namely photoelectron spectroscopy (PES), constant initial state spectroscopy (CIS), and constant final state spectroscopy (CFS), were introduced into the measurement field by three research groups half a century ago, in accordance with the state-of-the-art experimental conditions at that time. Until now, these modes have been separately applied in experimental practices, resulting in respective datasets obtained through individual measurement processes. These measurement modes and density-functional theory share a common characteristic in that they quantitatively adhere to the same energy conservation law. In the density-functional theory, the transition probability distribution, which corresponds to the PES quantity in measurement, and the cross-section components, which are equivalent to the quantities of CIS and CFS in measurements, are interconnected and interconvertible under the constraints of the energy conservation law. However, such interconnectedness does not exist between the datasets obtained by the PES, CFS, and CIS modes. This work aims to bridge the gap between theory and experiment by establishing interconnectedness between datasets from the three modes through the introduction of an orderly structured matrix-like framework. This matrix-like framework, serving as a generalized data analysis tool, presents the results of the three modes in a unified form and enables the transformation of one set of data into the results of another mode.