Читать книгу Optical Engineering Science - Stephen Rolt - Страница 93

An air spaced achromatic doublet may be optimised to eliminate both spherical aberration and coma. The fundamental power of the wavefront approach in describing third order aberration is reflected in the ability to calculate the total system aberration as the sum of the aberration of the two lenses. In the thin lens approximation, we may simply use Eqs. (4.30a) and (4.30b) to express the spherical aberration and coma contribution for each lens element. We simply ascribe a variable shape parameter, s₁ and s₂ to each of the two lenses. The two conjugate parameters are fixed. In the particular case of a doublet designed for the infinite conjugate, the conjugate parameter for the first lens, t₁, is −1. In the case of the second lens, the conjugate parameter, t₂, is determined by the relative focal lengths of the two lenses and thus fixed by the ratio of the two Abbe numbers and, from Eq. (4.52), we get:

(4.53)

Without going through the algebra in detail, it is clear that having determined both t₁ and t₂, Eqs. (4.30a) and (4.30b) give us two expressions solely in terms of s₁ and s₂. These expressions for the spherical aberration and coma must be set to zero and can be solved for both s₁ and s₂. The important point to note about this procedure is that because Eq. 4.30a contains terms that are quadratic in shape factor, this is also reflected in the final solution. Therefore, in general, we might expect to find two solutions to the equation and this, in general, is true.