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.
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