  In this paper, the design and the characterization of a novel interrogator
based on integrated Fourier transform (FT) spectroscopy is presented. To the
best of our knowledge, this is the first integrated FT spectrometer used for
the interrogation of photonic sensors. It consists of a planar spatial
heterodyne spectrometer, which is implemented using an array of Mach-Zehnder
interferometers (MZIs) with different optical path differences. Each MZI
employs a 3$\times$3 multi-mode interferometer, allowing the retrieval of the
complex Fourier coefficients. We derive a system of non-linear equations whose
solution, which is obtained numerically from Newton's method, gives the
modulation of the sensor's resonances as a function of time. By taking one of
the sensors as a reference, to which no external excitation is applied and its
temperature is kept constant, about 92$\%$ of the thermal induced phase drift
of the integrated MZIs has been compensated. The minimum modulation amplitude
that is obtained experimentally is 400 fm, which is more than two orders of
magnitude smaller than the FT spectrometer resolution.
