  By harnessing the quantum states of light for illumination, precise phase and
absorption estimations can be achieved with precision beyond the standard
quantum limit. Despite their significance for precision measurements, quantum
states are fragile in noisy environments which leads to difficulties in
revealing the quantum advantage. In this work, we propose a scheme to improve
optical absorption estimation precision by using the correlated photon pairs
from spontaneous parametric down-conversion as the illumination. This scheme
performs better than clasical illumination when the loss is below a critical
value. Experimentally, the scheme is demonstrated by a scanning transmission
type microscope that uses correlated photon illumination. As a result, the
signal-to-noise ratio (SNR) of a two-photon image shows a $1.36$-fold
enhancement over that of single-photon image for a single-layer graphene with a
$0.98$ transmittance. This enhancement factor will be larger when using
multi-mode squeezed state as the illumination.
