The principles and practice of astronomical imaging Fourier transform spectroscopy (FTS) at far-infrared wavelengths are described. The Mach-Zehnder interferometer design has been widely adopted for current and future imaging FTS instruments; we compare this design with two other common interferometer formats. Examples of three instruments based on the Mach-Zehnder design are presented. The techniques for retrieving astrophysical parameters from the measured spectra are discussed using calibration data obtained with the Herschel SPIRE instrument. The paper concludes with an example of imaging spectroscopy obtained with the SPIRE FTS instrument.
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