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tokens: modes. Simulations suggest that the algorithm should be able to reach one-shot correction resulting in a λ /1000 nm rms WFE with approximately 10 7 photons, and that with one iteration it should be able to correct up to ∼ λ /8 of rms WFE. In Sect. 5 , we demonstrated the principle with the vAPP in SCExAO, both with the internal source and on-sky, by measuring and controlling the 30 lowest Zernike modes and improving the raw contrast between 2.5 and 4 λ / D by a factor ∼2. Furthermore, we showed that the algorithm can correct WFEs of 300 nm and 150 nm rms with the internal source and on-sky, respectively. Although the contrast gains, both with the internal source and on-sky, are moderate, it does demonstrate that the coronagraphic PSFs of the vAPP can be used for wavefront sensing. The FPWFS performance of the SCExAO vAPP can be improved in various ways: (1) better model calibration to increase the contrast gain, (2) measuring more and higher spatial frequency modes to increase the area of correction, and (3) improving the convergence speed of the algorithm. For this demonstration the model was calibrated ad hoc by tuning the pupil undersizing, rotation, and the detector pixel scale by hand. These parameters should be more accurately measured or be part of the fitted parameters. To measure more and higher spatial frequency modes we want to replace the current Zernike mode basis with a pixel-mode basis ( Paul et al. 2013a ). This should also reduce the effect of unsensed modes on the estimation, when estimating a truncated mode basis ( Paul et al. 2013b ). Improving the convergence speed of the algorithm would result in a higher correction cadence or the correction of a larger mode basis in a similar time. A relatively simple improvement would be to use the multi-processing capabilities in the latest python libraries not yet available on SCExAO, this would enable multi-core processing and give a maximum speed improvement of a factor of 40. Theoretically, the best possible performance we can then expect is a wavefront estimation with sub 1 nm WFE every six seconds for targets down to a m H = 8 (five seconds of integration and one second for estimation). Other coronagraph model improvements include the integral field spectrograph CHARIS, an accurate model of the focal-plane filter and the incoherent background due to residual turbulence effects. This is because science observations with the SCExAO vAPP are done with CHARIS. Preventing detector saturation due to bright fields of the vAPP requires a focal-plane neutral density filter that attenuates the bright fields. Therefore, exposures with the focal-plane filter in place will have a larger dynamic range. This increase in dynamic range will make the incoherent background, which is due to uncorrected atmospheric turbulence, a more prominent feature in the image compared to the current on-sky results. Thus, the incoherent background needs to be included within the coronagraph model as well (