In Chapter 12 we examined the engineering challenges for the filled-aperture segmented-telescope architecture. In Chapter 13 we examined image quality and the engineering challenges and astronomical applications for the sparse-aperture telescope. In the sparse-aperture case, the apertures in the ξ, η pupil plane are distributed to synthesize a filled aperture. Here we discuss the application of Michelson stellar interferometry to both the astrometric measurements needed for the calculation of planetary orbits and the determination of the mass of exoplanets, as well as how the interferometer is used for creating an estimated image of an astronomical source. In the interferometry case, the aperture is very dilute; thus, only small portions of the ξ, η pupil plane are occupied. If the interferometer is based on the ground, the earth's rotation moves the pupils of the interferometer to different positions in the ξ, η plane as projected onto the celestial sphere. Some interferometer systems use beam-switching mirrors that switch beams from one telescope to another to build up, over time, the measurements needed to create a synthesized or estimated image of the source. This works well provided the source details are not changing with time. If the source is changing with time, the conditions on the Fourier transform relationship are not met. The Michelson stellar interferometer (MSI) provides information on the spatial structure of object space and is therefore a spatial interferometer.
To date, no space-based interferometer for either astrometry or imaging has been deployed. An interferometer, the NASA Space Interferometer Mission (SIM) has successfully completed its technology phase.