  Precision measurements of the Sunyaev-Zel'dovich effect in clusters of
galaxies require excellent rejection of common-mode signals and wide frequency
coverage. We describe an imaging, efficient, differential Fourier transform
spectrometer (FTS), optimized for measurements of faint brightness gradients at
millimeter wavelengths. Our instrument is based on a Martin-Puplett
interferometer (MPI) configuration. We combined two MPIs working synchronously
to use the whole input power. In our implementation the observed sky field is
divided into two halves along the meridian, and each half-field corresponds to
one of the two input ports of the MPI. In this way, each detector in the FTS
focal planes measures the difference in brightness between two sky pixels,
symmetrically located with respect to the meridian. Exploiting the high
common-mode rejection of the MPI, we can measure low sky brightness gradients
over a high isotropic background. The instrument works in the range $\sim$
1$-$20 cm$^{-1}$ (30$-$600 GHz), has a maximum spectral resolution $1/(2 \ OPD)
= 0.063 \ cm^{-1}$ (1.9 GHz), and an unvignetted throughput of 2.3 cm$^2$sr. It
occupies a volume of 0.7$\times$0.7$\times$0.33 m$^3$ and has a weight of 70
kg. This design can be implemented as a cryogenic unit to be used in space, as
well as a room-temperature unit working at the focus of suborbital and
ground-based mm-wave telescopes. The first in-flight test of the instrument is
with the OLIMPO experiment on a stratospheric balloon; a larger implementation
is being prepared for the Sardinia radio telescope.
