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Fig. 4.9 Off-axis residual aberrations of centered reflective Schmidts - 100% obstruction. With parameter s = 1, the off-axis image is plotted, as a function of the k-ratio, onto the sphere of center C and radius (1+M)R/2 which gives the on-axis stigmatism. The 2-D size of these images (top line spots) is denoted lr and lt for the radial and tangential directions. The diameter d of the best circular off-axis image is obtained from a refocussing Af; then, the size variation of the off-axis circular image with respect to k (second line spots) shows that k = 3/2, i.e. a null power zone at ro = 1.225 rm, provides the minimal blur image. With an under-correction factor s = cosqm, k = 3/2 and slight refocussing, the off-axis blur at the field edge q = qm is improved (dotted line). The spot-diagram of this s-balanced optimization is plotted for various reduced field values (lower line spots) q/tym = 0, 1/5, 2/5, 3/5, 4/5 and 1 (same scale as for top lines). At any wavelength, the diameter of the residual images is d = 0.011 q^/O3

When adding a holed flat folding mirror, the three-reflection design provides a better detector access to the focus, and the incidence angle must be at least i = Qm + 7/16 Q.

Relations (4.19a,b) hold for incident optical beams having a circular cross-section. In these designs, the optical figure of the primary mirror is defined by Bn,0 coefficients such as given in Table 4.2-column 3. The M-value allows deriving the best fit spherical focal surface - centered at the M1 mirror vertex - and the diameter dc of the maximum residual aberration which is dominated by fifth-order astigmatism (Astm 5).

^ The resolving power of all-reflective centered system Schmidt telescopes working off-axis is dc = 0.011 (i + Vm)2/O3, s = cos (i + Vm), k = 3/2 i.e. M = 3/64O2.

The under-correction factor s allows one to balance the dominating residual Astm 5 with a small Sphe 3 amount (Fig. 4.10). This resolution formula is similar to that found for a monochromatic refractive plate telescope (4.12b), but the gain for large wavelength ranges is considerable compared to (4.14). The axisymmetric primary mirror can be readily figured by the elastic relaxation technique (cf. Sect. 5.3.2).

Fig. 4.10 Best residual aberrations of an f/4 - 5° FoV centered system reflective Schmidts used off-axis. Mirror M1 is with rotational symmetry and clear aperture diameter 2rm. The spot diagram is for k = 3/2 corresponding to a null power zone at ro = 1.224 rm, i.e. outside the clear aperture. Such a mirror can be actively aspherized from a circular plate semi-built-in at ro, i.e. by use of a moderately thicker ring than the plate k= 1.5

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