  We present a general surface brightness correction method for compact
extended sources imaged in the slow-scan pointed observation mode of the
Far-Infrared Surveyor (FIS) aboard the AKARI Infrared Astronomical Satellite.
Our method recovers correct surface brightness distribution maps by re-scaling
archived raw FIS maps using the surface-brightness-dependent inverse FIS
response function. The flux of a target source is then automatically corrected
for as the simple sum of surface brightnesses within the adopted contour
encircling the perimeter of the target (i.e., contour photometry). This
correction method is contrasted to the previous aperture photometry method for
point sources, which directly corrects for the target flux with a
flux-dependent scaling law. The new surface brightness correction scheme is
applicable to objects of any shape from unresolved point sources to resolved
extended objects, as long as the target is not deemed diffuse, i.e., the total
extent of the target source does not exceed too much more than a single FIS
scan width of 10 arcmin. The new correction method takes advantage of the
well-defined shape (i.e., the scale invariance) of the point-spread function,
which enables us to adopt a power-law FIS response function. We analyze the
point-source photometric calibrator data using the FIS AKARI Slow-scan Tool
(FAST) and constrained the parameters of the adopted power-law FIS response
function. We conclude that the photometric accuracy of the new correction
method is better than 10% error based on comparisons with the expected fluxes
of the photometric calibrators and that resulting fluxes without the present
correction method can lead up to 230% overestimates or down to 50%
underestimates.
