The distribution of photoelectrons acquired in angle-resolved photoemission spectroscopy can be mapped onto the 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-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-1. The mapping methodology is also usable in other spectroscopic methods such as momentum-resolved electron-energy loss spectroscopy.