We explore how the Peccei-Quinn (PQ) axion parameter space can be constrained by the frequency-dependence dimming of radiation from astrophysical objects. To do so we perform accurate calculations of photon-axion conversion in the presence of a variable magnetic field. We propose several tests where the PQ axion parameter space can be explored with current and future astronomical surveys: the observed spectra of isolated neutron stars, occultations of background objects by white dwarfs and neutron stars, the light curves of eclipsing binaries containing a white dwarf. We find that the lack of dimming of the light curve of a detached eclipsing white dwarf binary recently observed, leads to relevant constraints on the photon-axion conversion. Current surveys designed for Earth-like planet searches are well matched to strengthen and improve the constraints on the PQ axion using astrophysical objects radiation dimming.