  We report the discovery of optical ghosts generated when using Volume Phase
Holographic (VPH) gratings in spectrographs employing the Littrow
configuration. The ghost is caused by light reflected off the detector surface,
recollimated by the camera, recombined by, and reflected from, the grating and
reimaged by the camera onto the detector. This recombination can occur in two
different ways. We observe this ghost in two spectrographs being developed by
the University of Wisconsin - Madison: the Robert Stobie Spectrograph for the
Southern African Large Telescope and the Bench Spectrograph for the WIYN 3.5m
telescope. The typical ratio of the brightness of the ghost relative to the
integrated flux of the spectrum is of order 10^-4, implying a recombination
efficiency of the VPH gratings of order 10^-3 or higher, consistent with the
output of rigorous coupled wave analysis. Any spectrograph employing VPH
gratings, including grisms, in Littrow configuration will suffer from this
ghost, though the general effect is not intrinsic to VPH gratings themselves
and has been observed in systems with conventional gratings in non-Littrow
configurations. We explain the geometric configurations that can result in the
ghost as well as a more general prescription for predicting its position and
brightness on the detector. We make recommendations for mitigating the ghost
effects for spectrographs and gratings currently built. We further suggest
design modifications for future VPH gratings to eliminate the problem entirely,
including tilted fringes and/or prismatic substrates. We discuss the resultant
implications on the spectrograph performance metrics.
