  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.
