Читать книгу Optical Engineering Science - Stephen Rolt - Страница 55

In the first two chapters, we have been primarily concerned with an idealised representation of geometrical optics involving perfect or Gaussian imaging. This treatment relies upon the paraxial approximation where all rays present a negligible angle with respect to the optical axis. In this situation, all primary optical ray behaviour, such as refraction, reflection, and beam propagation, can be represented in terms of a series of linear relationships involving ray heights and angles. The inevitable consequence of this paraxial approximation and the resultant linear algebra is apparently perfect image formation. However, for significant ray angles, this approximation breaks down and imperfect image formation, or aberration, results. That is to say, a bundle of rays emanating from a single point in object space does not uniquely converge on a single point in image space.

This chapter will focus on monochromatic aberrations only. These aberrations occur where there is departure from ideal paraxial behaviour at a single wavelength. In addition, chromatic aberration can also occur where first order paraxial properties of a system, such as focal length and cardinal point locations, vary with wavelength. This is generally caused by dispersion, or the variation in the refractive index of a material with wavelength. Chromatic aberration will be considered in the next chapter.

A simple scenario is illustrated in Figure 3.1 where a bundle of rays originating from an object located at the infinite conjugate is imaged by a lens. Figure 3.1a presents the situation for perfect imaging and Figure 3.1b illustrates the impact of aberration.

In Figure 3.1b, those rays that are close to the axis are brought to a focus at the paraxial focus. This is the ideal focus. However, those rays that are further from the axis are brought to a focus at a point closer to the lens than the paraxial focus. In fact, the behaviour illustrated in Figure 3.1b is representative of a simple lens; marginal rays are brought to a focus closer to the lens than the chief ray. However, in general terms, the sense of the aberration could be either positive or negative, with the marginal rays coming to a focus either before or after the paraxial focus.