Precision measurements of the Sunyaev-Zeldovich 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), optim
ized 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.
The Sunyaev-Zeldovich (SZ) effect is a powerful tool for studying clusters of galaxies and cosmology. Large mm-wave telescopes are now routinely detecting and mapping the SZ effect in a number of clusters, measure their comptonisation parameter and u
se them as probes of the large-scale structure and evolution of the universe. We show that estimates of the physical parameters of clusters (optical depth, plasma temperature, peculiar velocity, non-thermal components etc.) obtained from ground-based multi-band SZ photometry can be significantly biased, owing to the reduced frequency coverage, to the degeneracy between the parameters and to the presence of a number of independent components larger than the number of frequencies measured. We demonstrate that low-resolution spectroscopic measurements of the SZ effect that also cover frequencies $> 270$ GHz are effective in removing the degeneracy. We used accurate simulations of observations with lines-of-sight through clusters of galaxies with different experimental configurations (4-band photometers, 6-band photometer, multi-range differential spectrometer, full coverage spectrometers) and different intracluster plasma stratifications. We find that measurements carried out with ground-based few-band photometers are biased towards high electron temperatures and low optical depths, and require coverage of high frequency and/or independent complementary observations to produce unbiased information; a differential spectrometer that covers 4 bands with a resolution of $sim 6 GHz$ eliminates most if not all bias; full-range differential spectrometers are the ultimate resource that allows a full recovery of all parameters.
