We describe new results obtained with the integrated Mach-Zehnder (iMZ) self referenced wavefront sensor (WFS) allowing to extract independently phase and amplitude from intensity variations in the pupil images produced by the interferometer. This kind of wavefront sensor meets extreme adaptive optics requirements, high speed (1 kHz) and high accuracy (< 10 nm at 5-10 cm spatial scale), as well as the reconstruction of phasing errors on segmented telescopes and scintillation measurements. In this paper we present the calibration method we have developed and validated experimentally to accurately extract the phase and the amplitude of the wavefront from the Mach-Zehnder signal, using several diversities in the phase patterns. We also present a new phase modulation method which combined with an unwrapping algorithm increases the dynamical range of the wavefront sensor up to several microns, otherwise limited to ± lambda/4 without these new strategies. Numerical simulations of the Mach-Zehnder performances for various turbulence phase will be presented to address the ultimate sensor accuracy. We will also report on our latest laboratory calibration results, using a deformable mirror and a spatial light modulator to introduce the required phase modulations.