Abstract : ABSTRACT SITELLE, an imaging Fourier Transform Spectrometer, is part of the Canada–France–Hawaii instrument suite. It delivers spectral cubes covering an 11 arcmin × 11 arcmin field of view with a seeing-limited spatial resolution and a tunable spectral resolution (R ∼ 1–10 000) in selected bands of the visible range (350–900 nm). We present a complete picture of the calibration accuracy obtained with the SITELLE processing pipeline ORBS. We put a particular emphasis on the description of our phase correction method and on the assessment of the flux calibration precision. We show that the absolute flux calibration uncertainty is to be considered between −15 per cent and 5 per cent. Flexure in the instrument is likely responsible for a wavelength calibration error gradient across the field of view, with an amplitude corresponding to 15 to 25 km s−1; measurements of the night-sky emission lines when present in a science cube reduces this error to ∼2 km s−1. The astrometric calibration is limited to ∼1 arcsec by the optical distortions. Considering that imaging Fourier transform spectrometers are not as widely used as dispersive spectrometers and because SITELLE and its prototype are the first instruments of their kind to provide data in the near-UV at a high spectral resolution and over a very large field of view, we took great care in explaining most of the core concepts behind this technique as well as exploring all the practical limitations that affect the precision of our calibrations. As such, this paper aims at providing a solid ground for subsequent developments of imaging Fourier transform spectrometers in astronomy.