Focal-plane wavefront sensing with the vector-Apodizing Phase Plate

Context. One of the key limitations of the direct imaging of exoplanets at small angular separations are quasi-static speckles that originate from evolving non-common path aberrations (NCPA) in the optical train downstream of the instrument's main wavefront sensor split-off. Aims. In this article we show that the vector-Apodizing Phase Plate (vAPP) coronagraph can be designed such that the coronagraphic point spread functions (PSFs) can act as wavefront sensors to measure and correct the (quasi-)static aberrations without dedicated wavefront sensing holograms or modulation by the deformable mirror. The absolute wavefront retrieval is performed with a nonlinear algorithm. Methods. The focal-plane wavefront sensing (FPWFS) performance of the vAPP and the algorithm are evaluated via numerical simulations to test various photon and read noise levels, the sensitivity to the 100 lowest Zernike modes, and the maximum wavefront error (WFE) that can be accurately estimated in one iteration. We apply these methods to the vAPP within SCExAO, first with the internal source and subsequently on-sky. Results. In idealized simulations we show that for 10(7) photons the root mean square (rms) WFE can be reduced to similar to lambda/1000, which is 1 nm rms in the context of the SCExAO system. We find that the maximum WFE that can be corrected in one iteration is similar to lambda/8 rms or similar to 200 nm rms (SCExAO). Furthermore, we demonstrate the SCExAO vAPP capabilities by measuring and controlling the 30 lowest Zernike modes with the internal source and on-sky. On-sky, we report a raw contrast improvement of a factor similar to 2 between 2 and 4 lambda/D after five iterations of closed-loop correction. When artificially introducing 150 nm rms WFE, the algorithm corrects it within five iterations of closed-loop operation. Conclusions. FPWFS with the vAPP coronagraphic PSFs is a powerful technique since it integrates coronagraphy and wavefront sensing, eliminating the need for additional probes and thus resulting in a 100% science duty cycle and maximum throughput for the target.