The Herschel SPIRE instrument consists of an imaging photometric camera and
an imaging Fourier Transform Spectrometer (FTS), both operating over a
frequency range of 450-1550 GHz. In this paper, we briefly review the FTS
design, operation, and data reduction, and describe in detail the approach
taken to relative calibration (removal of instrument signatures) and absolute
calibration against standard astronomical sources. The calibration scheme
assumes a spatially extended source and uses the Herschel telescope as primary
calibrator. Conversion from extended to point-source calibration is carried out
using observations of the planet Uranus. The model of the telescope emission is
shown to be accurate to within 6% and repeatable to better than 0.06% and, by
comparison with models of Mars and Neptune, the Uranus model is shown to be
accurate to within 3%. Multiple observations of a number of point-like sources
show that the repeatability of the calibration is better than 1%, if the
effects of the satellite absolute pointing error (APE) are corrected. The
satellite APE leads to a decrement in the derived flux, which can be up to ~10%
(1 sigma) at the high-frequency end of the SPIRE range in the first part of the
mission, and ~4% after Herschel operational day 1011. The lower frequency range
of the SPIRE band is unaffected by this pointing error due to the larger beam
size. Overall, for well-pointed, point-like sources, the absolute flux
calibration is better than 6%, and for extended sources where mapping is
required it is better than 7%.Comment: 20 pages, 18 figures, accepted for publication in MNRA