  AGN are known to account for a major portion, if not all, of the cosmic X-ray
background radiation. The dominant sharp spectral feature in their spectra is
the 6.4 keV fluorescent line of iron, which may contribute to as much as ~ 5-10
% of the CXB spectral intensity at ~ 2-6 keV. Owing to cosmological redshift,
the line photons detected at the energy E carry information about objects
located at the redshift z=6.4/E-1. In particular, imprinted in their angular
fluctuations is the information about the large-scale structure at redshift z.
This opens the possibility of performing the Fe K_alpha line tomography of the
cosmic large-scale structure. We show that detection of the tomographic signal
at ~100 sigma confidence requires an all-sky survey by an instrument with an
effective area of ~10 m^2 and field of view of ~1 deg^2. The signal is
strongest for objects located at the redshift z~1 and at the angular scales
corresponding to l ~ 100-300, therefore an optimal detection can be achieved
with an instrument having a rather modest angular resolution of ~ 0.1-0.5 deg.
For such an instrument, the CCD-type energy resolution of ~ 100-200 eV FWHM is
entirely sufficient for the optimal separation of the signals coming from
different redshifts. The gain in the signal strength that could potentially be
achieved with energy resolution comparable to the line width is nullified by
the photon counting and AGN discreteness noise. Among the currently planned and
proposed missions, these requirements are best satisfied by LOFT, even though
it was proposed for an entirely different purpose. Among others, clear
detection should be achieved by WFXT (~ 20-35 sigma) and ATHENA (~ 10-20
sigma). eROSITA, in the course of its 4 years all-sky survey, will detect the
tomographic signal only marginally.
