  We provide approximate analytic expressions for above-threshold ionization
(ATI) transition probabilities and photoelectron angular distributions (PADs).
These analytic expressions are more general than those existing in the
literature and include the residual binding potential in the electron continuum
propagation. They successfully reproduce the ATI side lobes and specific
holographic structures such as the near-threshold fan-shaped pattern and the
spider-like structure that extends up to relatively high photoelectron
energies. We compare such expressions with the Coulomb quantum orbit
strong-field approximation (CQSFA) and the full solution of the time-dependent
Schr\"odinger equation for different driving-field frequencies and intensities,
and provide an in-depth analysis of the physical mechanisms behind specific
holographic structures. Our results shed additional light on what aspects of
the CQSFA must be prioritized in order to obtain the key holographic features,
and highlight the importance of forward scattered trajectories. Furthermore, we
find that the holographic patterns change considerably for different field
parameters, even if the Keldysh parameter is kept roughly the same.
