  The recent IRLOS upgrade for VLT/MUSE narrow field mode (NFM) introduced a
full-pupil mode to enhance sensitivity and sky coverage. This involved
replacing the 2x2 Shack-Hartmann sensor with a single lens for full-aperture
photon collection, which also enabled the engagement of the linearized
focal-plane technique (LIFT) wavefront sensor instead. However, initial on-sky
LIFT experiments have highlighted a complex point spread function (PSF)
structure due to strong and polychromatic non-common path aberrations (NCPAs),
complicating the accurate retrieval of tip-tilt and focus using LIFT. This
study aims to conduct the first on-sky validation of LIFT on VLT/UT4, outline
challenges encountered during the tests, and propose solutions for increasing
the robustness of LIFT in on-sky operations. We developed a two-stage approach
to focal-plane wavefront sensing, where tip-tilt and focus retrieval done with
LIFT is preceded by the NCPA calibration step. The resulting NCPA estimate is
subsequently used by LIFT. To perform the calibration, we proposed a method
capable of retrieving the information about NCPAs directly from on-sky
focal-plane PSFs. We verified the efficacy of this approach in simulated and
on-sky tests. Our results demonstrate that adopting the two-stage approach has
led to a significant improvement in the accuracy of the defocus estimation
performed by LIFT, even under challenging low-flux conditions. The efficacy of
LIFT as a slow and truth focus sensor in practical scenarios has been
demonstrated. However, integrating NCPA calibration with LIFT is essential to
verifying its practical application in the real system. Additionally, the
proposed calibration step can serve as an independent and minimally invasive
approach to evaluate NCPA on-sky.
