3 Practical implementation

  
3.1 CONICA calibration

The estimation of CONICA stand-alone aberrations (objectives and filters) is obtained through the use of pinholes (diameter $10~ \mu$m) located at different defocused positions in the camera entrance focal plane (0, 1, 2 and 4 mm). The telescope pupil is simulated by a cold pupil placed inside CONICA. A detailed explanation of the experimental setup is given in Paper II. The defocus distances induced through the use of different pinhole pairs are summarized in Table 1.

 

 

Table 1: Defocus distances induced by the use of various pinhole pairs. 0-2 and 0-4 pairs are recommended for J-H and Kfilters respectively.

pinhole pairs	0-1	0-2	0-4	1-4	2-4
Defocus distance (mm)	1.0	2.0	4.0	3.0	2.0

The necessity of introducing enough diversity between the two images and the higher $S\!NR$ of images obtained with the pinhole 0 (which is in the focal plan) lead us to choose the pair 0-2 for J and H filters and the pair 0-4 for Kfilters. Note that the use of pinholes in the entrance focal plane is not optimal for the phase diversity algorithm since

• the known aberration is not a pure defocus (a longitudinal translation in the entrance focal plane of the camera is not completely equivalent to a detector translation in the imaging focal plane) - see Sect. 5.1.5,
• the use of different pinholes may induce errors in the aberration estimation (the PD algorithm assumes that the same object is used to obtain focused and defocused images, see Sect. 5.1.4). Shape differences between two pinholes can induce phase estimation errors,
• the focused and defocused images are not at the same position on the detector and need to be re-centered - see Sect. 6.2 - since PD can not estimate relative tip-tilt greater than $\lambda$ between the two images. Indeed, the phase is estimated modulo $2\pi$ (see Eqs. (2) and (4)),
• lastly, there may be field aberrations due to the different pinhole position in the beam - see Sect. 5.1.6.

The procedure described in Sect. 2.3 allows us to estimate a set of aberrations for each CONICA configuration, that is a filter plus a camera objective.

3.2 Dichroic calibration

The estimation of the NAOS dichroic aberrations is obtained through the use of the AO system. A focused image of a fiber source, located in the entrance focal plane of NAOS, is recorded in closed-loop in order to avoid the common-path aberrations from the optical train between the source and the dichroic. Then a given defocus is introduced on the DM with the AO loop still closed to record the defocused image. (See Paper II for a complete description of this procedure.) This approach gives the input data for the estimation of the NAOS dichroic aberrations together with the CONICA aberrations. The value of the separated dichroic aberrations is obtained by subtracting the value of the previously estimated CONICA aberrations.

The introduction of a defocus by the DM avoids the difficulties of object defocussing highlighted above for the CONICA calibration. Now, the same object is considered and thus the two images are located at the same position on the detector.