Small fields and large apertures

The theory of third order aberrations is based on the assumption that the aperture and the field of the lens are small enough to neglect terms of degree higher than four in the power series development of the eikonal. In practice this condition is rarely met, and yet the third order theory is quite important in the practice of lens design. The reason is that more often than not small changes in the construction parameters have a much greater effect on the third order aberrations than on the aberrations associated with the higher order terms in the eikonal. As a result it is often a useful design strategy first to make the third order aberrations zero, then to evaluate the magnitude of the higher order aberrations and to reduce them as far as possible, and finally to make minor changes in the construction parameters to introduce small amounts of third order aberration that compensate, as far as possible, for the higher order aberrations that are impervious to all attempts at correction. A numerical recipe to calculate the third order aberrations from the construction parameters is shown in appendix 2; practical routines for the fifth order aberrations may be found in [12]. The total aberrations of a lens are usually calculated by ray tracing, to be discussed in the next chapter. Several commercial computer codes are available to carry out all these calculations.

For certain lens types the series development used so far is wholly inappropriate.