tokens: b shows the components with frequencies lower than seven cycles per pupil. This cutoff frequency has been chosen to identify the peak at around five cycles per pupil visible in the PSD of Fig. 10 (5c). It has been shown in Sect. 5 that with a FPM, the COFFEE algorithm reconstructs low-order aberrations that should be absent, this phenomenon is also visible on the PSD of Fig. 10 (5b). Fig. 11. Reconstruction error of Fig. 10 (4c). The unit are in radians. ( a ) Same reconstruction error than Fig. 10 (4c), at an optimized scale. ( b ) Orders lower than seven cycles per pupil of the reconstruction error (a), obtained with a cut on the PSD and an inverse Fourier Transform. ( c ) Difference between the phase maps (a) and (b). Patterns of a few cycles per pupil are visible and can be easily identified using a spatial filter. They correspond to the peak at around five cycles per pupil of the PSD of Fig. 10 (5c). It has been shown in Sect. 5 that with a coronagraph, the COFFEE algorithm generates extra low-order aberrations. Conversely, the reconstruction is not efficient for low-order aberrations such as the two cycles per pupil case. The reconstructed phase is very different than the theoretical one, in terms of phase pattern and RMS value (0.29 radians RMS), most of the error coming from low-frequency aberrations (see Table 1 ). This test indicates that there exist some modes that are not or badly visible by COFFEE, mainly when they are blocked by the FPM. The FPM limits COFFEE’s ability to sense and consequently reconstruct low-order modes with spatial frequencies smaller than the spatial extent of the FPM, that is, smaller than 3.5 cy/pup in our case (as a reminder, the FPM has a diameter of 7.2 ± 0.9 λ / D ). On the other hand, COFFEE shows its full capability for modes with higher spatial frequencies than the size of the FPM. 5.3. Impact of segment-level aberrations on the phase reconstruction From the previous study, we can deduce that phase patterns containing low-order variations are not properly reconstructed. Given that segment-level aberrations contain low-frequency components, COFFEE cannot fully reconstruct phasing errors, and can even add low-order background phase aberrations. To theoretically investigate this effect, we reconstruct a segment-level piston error with COFFEE. To do so, we simulate in- and out-of-focus PSFs with a segment-level phase error (piston of 1 rad PV on the central segment) in the same configuration as the HiCAT Iris-AO. These PSFs are used as inputs of COFFEE to reconstruct the phase error. The results are shown in Fig. 12 . Fig. 12. Test of reconstruction of a segment-level phase error with COFFEE in simulation only: ( a ) theoretical phase to reconstruct: a 1 rad piston is applied on the central segment, ( b ) phase reconstructed with COFFEE, ( c ) difference between the two previous phases, ( d ) cross-sections of the three phases of Fig. 12 along the vertical axis. We can notice in particular the
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