Читать книгу Optical Engineering Science - Stephen Rolt - Страница 60

The first term, spherical aberration, has a simple fourth order dependence upon pupil function and no dependence upon field. This is illustrated in Eq. (3.21):

(3.21)

This aberration shows no dependence upon field angle and no dependence upon the orientation of the ray fan. Since, in the current analysis and for a non-zero field angle, the object is offset along the y axis, then the pupil orientation corresponding to p_y defines the tangential ray fan and the pupil orientation corresponding to p_x defines the sagittal ray fan. This is according to the nomenclature set out in Chapter 2. So, the aberration is entirely symmetric and independent of field angle. In fact, the opening discussion in this chapter was based upon an illustration of spherical aberration.

Spherical aberration characteristically produces a circular blur spot. The transverse aberration may, of course, be derived from Eq. (3.21) using Eq. (3.12). For completeness, this is re-iterated below:

(3.22)

A 2D geometrical plot, of ray intersection at the paraxial focal plane, as produce by an evenly illuminated entrance pupil is referred to as a geometrical point spread function. Due to the symmetry of the aberration, this spot is circular. However, since the transformation in Eq. (3.22) is non-linear, the blur spot associated with spherical aberration is non uniform. For spherical aberration alone (no defocus or other aberrations), the density of the geometrical point spread function is inversely proportional to the pupil function, p. That is to say, spherical aberration manifests itself as a blur spot with a pronounced peak at the centre, with the density declining towards the periphery. This is illustrated in Figure 3.11. The spot, as shown in Figure 3.11, with a pronounced central maximum, is characteristic of spherical aberration and should be recognised as such by the optical designer.

As suggested earlier, the size of this spot can be minimised by moving away from the paraxial focus position. The ray fan and OPD fan for this aberration look like those illustrated in Figures 3.3 and 3.8. Overall, the characteristics of spherical aberration and the balancing of this aberration is very much as described in the treatment of generic third order aberration, as set out earlier.

Figure 3.11 Geometrical spot associated with spherical aberration.