  Different astrophysical methods can be combined to detect possible deviations
from General Relativity. In this work, we consider a class of $f(R)$ gravity
models selected by the existence of Noether symmetries. In this framework, it
is possible to determine a set of static and spherically symmetric black hole
solutions, encompassing small departures from the Schwarzschild geometry. In
particular, when gravity is the only dominating interaction, we exploit the
ray-tracing technique to reconstruct the image of a black hole, the epicyclic
frequencies, and the black hole shadow profile. Moreover, when matter dynamics
is also affected by an electromagnetic radiation force, we take into account
the general relativistic Poynting-Robertson effect. In light of the obtained
results, the proposed strategy results to be robust and efficient: on the one
hand, it allows to investigate gravity from strong to weak field regimes; on
the other hand, it is capable of detecting small departures from General
Relativity, depending on the current observational sensitivity.
