  In the present paper, we consider the optical design of a zoom system for the
active refocusing in laser guide star wavefront sensors. The system is designed
according to the specifications coming from the Extremely Large Telescope
(ELT)-HARMONI instrument, the first-light, integral field spectrograph for the
European (E)-ELT. The system must provide a refocusing of the laser guide as a
function of telescope pointing and large decentring of the incoming beam. The
system considers four moving lens groups, each of them being a doublet with one
aspherical surface. The advantages and shortcomings of such a solution in terms
of the component displacements and complexity of the surfaces are described in
detail. It is shown that the system can provide the median value of the
residual wavefront error of 13.8-94.3 nm and the maximum value <206 nm, while
the exit pupil distortion is 0.26-0.36% for each of the telescope pointing
directions.
