  Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), one of three
core programs in the Sloan Digital Sky Survey-IV (SDSS-IV), is an
integral-field spectroscopic (IFS) survey of roughly 10,000 nearby galaxies. It
employs dithered observations using 17 hexagonal bundles of 2 arcsec fibers to
obtain resolved spectroscopy over a wide wavelength range of 3,600-10,300A. To
map the internal variations within each galaxy, we need to perform accurate
{\it spectral surface photometry}, which is to calibrate the specific intensity
at every spatial location sampled by each individual aperture element of the
integral field unit. The calibration must correct only for the flux loss due to
atmospheric throughput and the instrument response, but not for losses due to
the finite geometry of the fiber aperture. This requires the use of standard
star measurements to strictly separate these two flux loss factors (throughput
versus geometry), a difficult challenge with standard single-fiber spectroscopy
techniques due to various practical limitations. Therefore, we developed a
technique for spectral surface photometry using multiple small fiber-bundles
targeting standard stars simultaneously with galaxy observations. We discuss
the principles of our approach and how they compare to previous efforts, and we
demonstrate the precision and accuracy achieved. MaNGA's relative calibration
between the wavelengths of H$\alpha$ and H$\beta$ has a root-mean-square (RMS)
of 1.7%, while that between [NII] $\lambda$6583A and [OII] $\lambda$3727A has
an RMS of 4.7%. Using extinction-corrected star formation rates and gas-phase
metallicities as an illustration, this level of precision guarantees that flux
calibration errors will be sub-dominant when estimating these quantities. The
absolute calibration is better than 5% for more than 89% of MaNGA's wavelength
range.
