Ingot Laser Guide Stars Wavefront Sensing

We revisit one class of z-invariant WaveFront sensor where the LGS is fired aside of the telescope aperture. In this way there is a spatial dependence on the focal plane with respect to the height where the resonant scattering occurs. We revise the basic parameters involving the geometry and we propose various merit functions to define how much improvement can be attained by a z-invariant approach. We show that refractive approaches are not viable and we discuss several solutions involving reflective ones in what has been nicknamed "ingot wavefront sensor" discussing the degrees of freedom required to keep tracking and the basic recipe for the optical design.