  Laser guide star (LGS) wave-front sensing (LGSWFS) is a key element of
tomographic adaptive optics system. However, when considering Extremely Large
Telescope (ELT) scales, the LGS spot elongation becomes so large that it
challenges the standard recipes to design LGSWFS. For classical Shack-Hartmann
wave-front sensor (SHWFS), which is the current baseline for all ELT
LGS-assisted instruments, a trade-off between the pupil spatial sampling
[number of sub-apertures (SAs)], the SA field-of-view (FoV) and the pixel
sampling within each SA is required. For ELT scales, this trade-off is also
driven by strong technical constraints, especially concerning the available
detectors and in particular their number of pixels. For SHWFS, a larger field
of view per SA allows mitigating the LGS spot truncation, which represents a
severe loss of performance due to measurement biases. For a given number of
available detectors pixels, the SA FoV is competing with the proper sampling of
the LGS spots, and/or the total number of SAs. We proposed a sensitivity
analysis, and we explore how these parameters impacts the final performance. In
particular, we introduce the concept of super resolution, which allows one to
reduce the pupil sampling per WFS and opens an opportunity to propose potential
LGSWFS designs providing the best performance for ELT scales.
