  We present a new technique to measure multi-wavelength "Super-deblended"
photometry from highly confused images, which we apply to Herschel and
ground-based far-infrared (FIR) and (sub-)millimeter (mm) data in the northern
field of the Great Observatories Origins Deep Survey (GOODS). There are two key
novelties. First, starting with a large database of deep Spitzer 24{\mu}m and
VLA 20cm detections that are used to define prior positions for fitting the
FIR/submm data, we perform an active selection of useful priors independently
at each frequency band, moving from less to more confused bands. Exploiting
knowledge of redshift and all available photometry, we identify hopelessly
faint priors that we remove from the fitting pool. This approach significantly
reduces blending degeneracies and allows reliable photometry to be obtained for
galaxies in FIR+mm bands. Second, we obtain well-behaved, nearly Gaussian flux
density uncertainties, individually tailored to all fitted priors in each band.
This is done by exploiting extensive simulations that allow us to calibrate the
conversion of formal fitting uncertainties to realistic uncertainties depending
on quantities directly measurable. We achieve deeper detection limits with high
fidelity measurements and uncertainties at FIR+mm bands. As an illustration of
the utility of these measurements, we identify 70 galaxies with z>3 and
reliable FIR+mm detections. We present new constraints on the cosmic star
formation rate density at 3<z<6, finding a significant contribution from z>3
dusty galaxies that are missed by optical-to-near-infrared color selection.
Photometric measurements for 3306 priors, including over 1000 FIR+mm detections
are released publicly with our catalog.
