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the spherical aberration change having reversed sign and, with m2 = —4, only one quarter of that of a classical Cassegrain. The DK form is, therefore, not only favourable for transverse decenter but also for axial despace. The Gregory DK form (DKG) has the same value, but with positive sign with m2 = +4. The favourable nature of the DK solution is particularly clear in the afocal form, when, from (3.405), the sensitivity becomes zero with bs2 = 0. The physical explanation is instructive. If the secondary is at the prime focus, it introduces zero (Sj)2 because y2 is zero in Eqs. (3.20). As the secondary is moved towards the primary, the first (spherical) term of (Sj)2 increases, reaching a maximum in the afocal position, if r2 is kept constant. It reduces as |d1| is further reduced, because A2 reduces although y2 increases, reaching zero when the centre of curvature of the secondary is at the prime focus. Hence the differential of (Sj)2 is zero in the afocal case. By contrast, the aspheric term t2 increases monotonically with y4, leading to Eq. (3.405).

## Telescopes Mastery

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