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Context: Telescopes like the Extremely Large Telescope (ELT) and the GiantMagellan Telescope (GMT) will be used together with extreme adaptive optics(AO) instruments to directly image Earth-like planets. The AO systems will needto perform at the fundamental limit in order to image Earth twins. A crucialcomponent is the wavefront sensor. Interferometric wavefront sensors, such asthe Zernike wavefront sensor (ZWFS), have been shown to perform close to thefundamental sensitivity limit. However, sensitivity comes at the cost oflinearity; the ZWFS has strong nonlinear behavior. Aims: The aim of this workis to increase the dynamic range of Zernike-like wavefront sensors by usingnonlinear reconstruction algorithms combined with phase sorting interferometry(PSI) and multi-wavelength measurements. Methods: The response of the ZWFS isexplored analytically and numerically. Results: The proposed iterative(non)linear reconstructors reach the machine precision for small aberrations(<0.25 rad rms). Coupling the nonlinear reconstruction algorithm with PSIincreases the dynamic range of the ZWFS by a factor of three to about 0.75 radrms. Adding multiple wavebands doubles the dynamic range again, to 1.4 radiansrms. Conclusion: The ZWFS is one of the most sensitive wavefront sensors, buthas a limited dynamic range. The ZWFS will be an ideal second-stage wavefrontsensor if it is combined with the proposed nonlinear reconstruction algorithm.

Into nonlinearity and beyond for Zernike-like wavefront sensors