Functions to map photoelectron distributions in a variety of setups in angle-resolved photoemission spectroscopy

The distribution of photoelectrons acquired in angle-resolved photoemission spectroscopy can be mapped onto energy-momentum space of the Bloch electrons in the crystal. The explicit forms of the mapping function $f$ depend on the configuration of the apparatus as well as on the type of the photoelectron analyzer. We show that the existence of the analytic forms of $f^{\text{-}1}$ is guaranteed in a variety of setups. The variety includes the case when the analyzer is equipped with a photoelectron deflector. Thereby, we provide a demonstrative mapping program implemented by an algorithm that utilizes both $f$ and $f^{\text{-}1}$. The mapping methodology is also usable in other spectroscopic methods such as momentum-resolved electron-energy loss spectroscopy.