  In the present paper we demonstrate the approach to use a holographic grating
on a freeform surface for advanced spectrographs design. On the example POLLUX
spectropolarimeter medium-UV channel we chow that such a grating can operate as
a cross-disperser and a camera mirror at the same time. It provides the image
quality high enough to reach the spectral resolving power of 126 359-133 106
between 11.5 and 195 nm, which is higher than the requirement. Also we show a
possibility to use a similar element working in transmission to build an
unobscured double-Schmidt spectrograph. The spectral resolving power reaches
2750 for a long slit. It is also shown that the parameters of both the gratings
are feasible with the current technologies.
