Читать книгу Optical Engineering Science - Stephen Rolt - Страница 89

A practical example of the correction of lateral chromatic aberration is in the Huygens eyepiece. This very simple, early, eyepiece uses two plano-convex lenses separated by a distance equivalent to half the sum of their focal lengths. This is illustrated in Figure 4.23.

Since we are determining the impact of lateral chromatic aberration, we are only interested in the effective focal length of the system comprising the two lenses. Using simple matrix analysis as described in Chapter 1, the system focal length is given by:

If we assume that both lenses are made of the same material, then their focal power will change as a function of wavelength by a common proportion, α. In that case, the system focal power at the new wavelength would be given by:

For small values of α, we can ignore terms of second order in α, so the change in system power may be approximated by:

The change in system power should be zero and this condition unambiguously sets the lens separation, d, for no lateral chromatic aberration:

(4.50)

If this condition is fulfilled, then the Huygens eyepiece will have no transverse chromatic aberration. However, it must be emphasised that this condition does not provide immunity from longitudinal chromatic aberration.

Figure 4.24 Abbe diagram.