Читать книгу Optical Engineering Science - Stephen Rolt - Страница 88

The most obvious effect of chromatic aberration is that light is broad to a different focus for different wavelengths. This effect is known as longitudinal chromatic aberration and is illustrated in Figure 4.21.

As can be seen from Figure 4.21, light at the shorter, ‘blue’ wavelengths are focused closer to the lens, leading to an axial (longitudinal) shift in the paraxial focus for the different wavelengths. In summary, longitudinal chromatic aberration is associated with a shift in the paraxial focal position as a function of wavelength. Thus the effect of longitudinal chromatic aberration is to produce a blur spot or transverse aberration whose magnitude is directly proportional to the aperture size, but is independent of field angle. However, there are situations where, to all intents and purposes, all wavelengths share the same paraxial focal position, but the principal points are not co-located. That is to say, whilst all wavelengths are focused at a common point, the effective focal length corresponding to each wavelength is not identical. This scenario is illustrated in Figure 4.22.

Figure 4.21 Longitudinal chromatic aberration.

Figure 4.22 Transverse chromatic aberration.

The effect illustrated is known as transverse chromatic aberration or lateral colour. Whilst no distinct blurring is produced by this effect, the fact that different wavelengths have different focal lengths inevitably means that system magnification varies with wavelength. As a result, the final image size or height of a common object depends upon the wavelength. This produces distinct coloured fringing around an object and the size of the effect is proportional to the field angle, but independent of aperture size.

Hitherto, we have cast the effects of chromatic aberration in terms of transverse aberration. However, to understand the effect on the same basis as the Gauss-Seidel aberrations, it is useful to express chromatic aberration in terms of the OPD. When applied to a single lens, longitudinal chromatic aberration simply produces defocus that is equal to the focal length divided by the Abbe number. Therefore, the longitudinal chromatic aberration is given by:

(4.49a)

f is the focal length of the lens and r the pupil position.

Figure 4.23 Huygens eyepiece.

Similarly, the transverse chromatic aberration can be expressed as an OPD:

(4.49b)

Examining Eqs. (4.49a) and (4.49b) reveals that the ratio of transverse to longitudinal aberration is given by the ratio of the field angle to the numerical aperture. In practice, for optical elements, such as microscope and telescope objectives, the field angle is very much smaller than the numerical aperture and thus longitudinal chromatic aberration may be expected to predominate. For eyepieces, the opposite is often the case, so the imperative here is to correct lateral chromatic aberration.