  This paper is the third part of a trilogy dealing with the principles,
performance and limitations of what I named "Telescope-Interferometers" (TIs).
The basic idea consists in transforming one telescope into a Wavefront Error
(WFE) sensing device. This can be achieved in two different ways, namely the
off axis and phase-shifting TIs. In both cases the Point-Spread Function (PSF)
measured in the focal plane of the telescope carries information about the
transmitted WFE, which is retrieved by fast and simple algorithms suitable to
an Adaptive Optics (AO) regime. Herein are evaluated the uncertainties of both
types of TIs, in terms of noise and systematic errors. Numerical models are
developed in order to establish the dependence of driving parameters such as
useful spectral range, angular size of the observed star, or detector noise on
the total WFE measurement error. The latter is found particularly sensitive to
photon noise, which rapidly governs the achieved accuracy for telescope
diameters higher than 10 m. We study a few practical examples, showing that TI
method is applicable to AO systems on telescope diameters ranging from 10 to 50
m, depending on seeing conditions and magnitude of the observed stars. We also
discuss the case of a space-borne coronagraph where TI technique provides high
sampling of the input WFE map.
