Читать книгу Optical Engineering Science - Stephen Rolt - Страница 103

There is no generic rule for conic refracting surfaces that generate perfect image formation for an arbitrary conjugate. However, there is a special condition for the infinite conjugate where perfect image formation results, as illustrated in Figure 5.2.

If the refractive index of the surface is n, assuming that the object is in air/vacuum, then the conic constant of the ideal surface is –n². In fact, the shape is that of a hyperboloid. The abscissa of the hyperboloid effectively produce grazing incidence for rays originating from the object. By definition, therefore, the angle that the surface normal makes with the optical axis at the abscissa is equal to the critical angle. This restricts the maximum numerical aperture that can be collected by the system. With this constraint, it is clear that the maximum numerical aperture is equal to 1/n. In summary therefore:

(5.8)

Unfortunately, no other general condition for perfect image formation results for a conic surface. However, for perfect image correction, all orders of (on axis) aberration are corrected. Thus, although no condition for perfect image formation is possible, it is still possible, nevertheless, to correct for third order spherical aberration with a single refractive surface.

Figure 5.2 Single refractive surface at infinite conjugate.