  Using general relativistic magnetohydrodynamic simulations of accreting black
holes, we show that a suitable subtraction of the linear polarization per pixel
from total intensity images can enhance the photon ring features. We find that
the photon ring is typically a factor of $\simeq 2$ less polarized than the
rest of the image. This is due to a combination of plasma and general
relativistic effects, as well as magnetic turbulence. When there are no other
persistently depolarized image features, adding the subtracted residuals over
time results in a sharp image of the photon ring. We show that the method works
well for sample, viable GRMHD models of Sgr A* and M87*, where measurements of
the photon ring properties would provide new measurements of black hole mass
and spin, and potentially allow for tests of the "no-hair" theorem of general
relativity.
