  The mid-infrared spectrum contains rich diagnostics to probe the physical
properties of galaxies, among which the pervasive emission features from
polycyclic aromatic hydrocarbons (PAHs) offer a promising means of estimating
the star formation rate (SFR) relatively immune from dust extinction. This
paper investigates the effectiveness of PAH emission as a SFR indicator on
sub-kpc scales by studying the Spitzer/IRS mapping-mode observations of the
nearby grand-design spiral galaxy M51. We present a new approach of analyzing
the spatial elements of the spectral datacube that simultaneously maximizes
spatial resolution and spatial coverage, while yielding reliable measurements
of the total, integrated $5-20\,\mu$m PAH emission. We devise a strategy of
extracting robust PAH emission using spectra with only partial spectral
coverage, complementing missing spectral regions with properly combined
mid-infrared photometry. We find that in M51 the PAH emission correlates
tightly with the extinction-corrected far-ultraviolet, near-ultraviolet, and
H$\alpha$ emission, from scales$\sim 0.4$ kpc close to the nucleus to 6 kpc out
in the disk of the galaxy, indicating that PAH serves as an excellent tracer of
SFR over a wide range of galactic environments. But regional differences exist.
Close to the active nucleus of M51 the 6.2 $\mu$m feature is weaker, and the
overall level of PAH emission is suppressed. The spiral arms and the central
star-forming region of the galaxy emit stronger 7.7 and 8.6 $\mu$m PAH features
than the inter-arm regions.
