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tokens: translation error of one pitch implies a 20% error in the 7 λ / D × 7 λ / D region around the center, whereas it reaches 60% in the largest DH (28 λ / D × 28 λ / D ). The more uncertainties there are on the positions of the actuators, the narrower the region of correction. We now consider that the modeled DM is not translated relative to the true one but is rotated around the pupil center. We calculate the estimated field and the RMSE for each rotation error. Results are plotted in blue on the right of Fig. 5 . As for the translation error, the larger the DH the more sensitive the PW is to the rotation error. For example, the RMSE is 10% for the largest DH (28 λ / D × 28 λ / D ) and 5% for the smallest one. Actuator 498 is at about two actuators from the pupil center such that a rotation of 10° corresponds to a translation of 0.35 pitch. From the translation error plot (center plot of Fig. 5 ), a 0.35 pitch translation error gives a RMSE of ∼10% for the largest DH and ∼5% for the smallest one. We therefore expect the PW estimation to be more sensitive to an error on the angular position of the DM if the actuator-probes are further away from the center of the pupil. We confirm this statement by executing the same study for a pair of actuator-probes closer to the edge of the pupil: actuators 283 and 251. The results plotted in red on the right of Fig. 5 confirm the following statement: the closer the pair of actuator-probes is to the center of the pupil, the more robust is the PW with respect to a rotational error. 4. Wavefront control Once the electric field E S 0 is estimated, DMs are controlled to minimize the stellar speckle intensity inside a DH. In this section, we present two wavefront control techniques (SCC and EFC) assuming small aberrations ( α and β ) and a single DM placed in the pupil plane. Both techniques use an iterative process and a control matrix. 4.1. SCC and EFC common strategy Classical AO systems measure and minimize the phase aberrations β in the pupil plane. In the context of HCI, this strategy is not optimal because the amplitude aberrations α also induce stellar speckles in the science image. Moreover, DMs cannot control all the high spatial frequencies because of the limited number of actuators. Therefore, even if there are no amplitude aberrations, one DM cannot completely null the phase β . That is why Malbet et al. (1995) proposed to minimize the stellar speckle intensity inside a DH in the science image instead of the phase in a pupil plane. This has two main advantages. The field induced by both amplitude and phase aberrations can be minimized. And a stronger attenuation can be reached using the frequency-folding phenomenon and by decreasing the size of the DH ( Bordé Traub 2006 ; Give’On et al. 2006 ). We assume a single DM placed in the pupil plane and we consider that the focal plane field E DM = iC [ Aφ ] induced on the science detector is a linear combination of the DM actuator voltages : where G is the