coma spike is directed towards the mirror axis.

of the Coma 3 aberration is ix = 3iR/32Q2 and ¿y = 2iR/32Q2 (Fig. 3.16), and the

Fig. 3.16 Linear size of the Coma 3 image from a concave and axisymmetric pupil mirror; object at infinity, s = 0 and V k

3.4.6 Examples of Active Optics Coma Correction

• Local correction of Coma 3 by "acomatic mirror" - Star tracking systems:

Considering that the pupil is on the concave mirror, i.e. s = 0 in (3.47), which is the case of a telescope primary mirror, star tracking or guiding imager systems are often used in an off-axis area of the focal surface. These systems generally use an optical transport re-imaging the selected sky area on a detector. In the case of non-aplanatic telescopes, the improvement of image quality can be achieved by implementing an "acomatic mirror" into the re-imaging optical transport. For an incidence angle i, the shape of the equivalent telescope mirror that would compensate for this aberration is, from (3.47),

Stating that the sum of the shapes expressed by (3.48) and by the acomatic mirror (3.39), must be zero, i.e.

we obtain the A31 coefficient of the acomatic mirror,

which compensates for Coma 3 of the telescope mirror at i angle.

Substituting this coefficient in the representation of the scaling thickness t0 given by (3.44b), (3.45b), or (3.46b), depending on the selected rigidity class - CTD, VTD, or hybrid -, we obtain the aspect ratio to a

4i aTelE

This aspect ratio provides the setting of the execution conditions of the acomatic mirror involving the scaling thickness (t0), the semi-aperture (a), the telescope optics (aTel, Q, i), the elastic constants (v, E), and the ring-force intensity (V0) per unit length.

From the geometrical properties of Coma3 wavefront (Sect. 3.4.4), the boundary conditions can be realized by axially thick cylinders linked via thin radial collars to the mirror substrate. This mirror-cylinder link allows one to generate a prismatic ring-force Vr = V0 cos O by only applying two opposite point-force F = ±a ¡VrdO = ±2aV0 at O = 0 and O = n on the cylinder rear side. Thus, the cosine modulation is naturally achieved by the cylinder axial thickness. In function of the point-force F, the design relation becomes to_ 2a

aaTel E

0 0

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