We describe the procedure used to flux calibrate the three-band submillimetre photometer in the Spectral and Photometric Imaging REceiver (SPIRE) instrument on the Herschel Space Observatory. This includes the equations describing the calibration scheme, a justification for using Neptune as the primary calibration source, a description of the observations and data processing procedures used to derive flux calibration parameters (for converting from voltage to flux density) for every bolometer in each array, an analysis of the error budget in the flux calibration for the individual bolometers, and tests of the flux calibration on observations of primary and secondary calibrators. The procedure for deriving the flux calibration parameters is divided into two parts. In the first part, we use observations of astronomical sources in conjunction with the operation of the photometer internal calibration source to derive the unscaled derivatives of the flux calibration curves. To scale the calibration curves in Jy/beam/V, we then use observations of Neptune in which the beam of each bolometer is mapped using Neptune observed in a very fine scan pattern. The total instrumental uncertainties in the flux calibration for the individual bolometers is ~0.5% for most bolometers, although a few bolometers have uncertainties of ~1-5% because of issues with the Neptune observations. Based on application of the flux calibration parameters to Neptune observations performed using typical scan map observing modes, we determined that measurements from each array as a whole have instrumental uncertainties of 1.5%. This is considerably less than the absolute calibration uncertainty associated with the model of Neptune, which is estimated at 4%.
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