P

Fig. 4.5 Function 2kp2 — p4 representing the wavefront profiles with respect to parameter k = fo/fm varying from 0 to 2 by increments of 1/4. The Kerber condition, k = 3/4, applies for optimizing refractive Schmidts whereas Lemaitre's condition, k = 3/2, applies for optimizing reflective Schmidt telescopes and spectrographs

4.1.6 Optical Equation of Various Corrective Elements

Either refractive correctors, reflective correctors, or self-corrective gratings are Schmidt design manifolds. Let z, r, 9 be a cylindrical frame linked to the corrector where the r, 9 plane is tangent to its vertex; Set the z-axis as positive toward the spherical mirror of curvature 1/R, and 9 = 0 in the symmetry plane (z, x) of the system, so x = rcos 9, y = r sin 9. The general figure Zopt(r, 9) of the corrective optical element is of the form where Bn,m coefficients are derived from the An(M) wavefront coefficients and from the inclination angle i of the axial incident ray around the y axis for a mirror or from the incident angle a if the mirror is a reflective grating . These coefficients can be expressed by the form where s is an under- or over-correction factor for field optimization - factor close to unity - and y characterizes the corrector type. Coefficient Tn,m are all equal to unity for centered system correctors. Parameter y and first coefficients Bn,m are listed in Table 4.2 [34].

For a refractive plate, the rays are assumed to emerge from the aspherical surface that faces the concave mirror. The case of a non-tilted reflective corrector leads to an on-axis full obstruction but the system is usable off-axis; this family belongs to the class of centered systems. The case where the reflective corrector is tilted by an angle i has been listed in Table 4.2 with t = 1/2sin2 i (terms in t2 omitted) and this representation is also valid for Littrow-mounted reflective gratings; these cases

Table 4.2 ^ and BnmRn 1 for various corrector types. Columns 2, 3, and 5 are for centered systems [ C. S. ]. Column 4 is for non-centered systems [N-C. S. ]
0 0

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