an example, a small astronomical refracting telescope might comprise a 75 mm diameter objective lens with a focal length of 750 mm (f/10) and might use a ×10 eyepiece. Eyepiece magnification is classified in the same way as for microscope eyepieces and so the focal length of this eyepiece would be 25 mm, as derived from Eq. (2.12b). The angular magnification (f1/f2) would be ×30 and the size of the pupil about 3 mm, which is smaller than the pupil of the eye.
In the preceding discussion, the basic description of the instrument function assumes ocular viewing, i.e. viewing through an eyepiece. However, increasingly, across a range of optical instruments, the eye is being replaced by a detector chip. This is true of microscope, telescope, and camera instruments.
2.11.4 Camera
In essence, the function of a camera is to image an object located at the infinite conjugate and to form an image on a light sensitive planar surface. Of course, traditionally, this light sensitive surface consisted of a film or a plate upon which a silver halide emulsion had been deposited. This allowed the recording of a latent image which could be chemically developed at a later stage. Depending upon the grain size of the silver halide emulsion, feature sizes of around 10–20 μm or so could be resolved. That is to say, the ultimate system resolution is limited by the recording media as well as the optics. For the most part, this photographic film has now been superseded by pixelated silicon detectors, allowing the rapid and automatic capture and processing of images. These detectors are composed of a rectangular array of independent sensor areas (usually themselves rectangular) that each produce a charge in proportion to the amount of light collected. Resolution of these detectors is limited by the pixel size which is analogous to the grain size in photographic film. Pixel size ranges from a one micron to a few microns.
Optically from a paraxial perspective, the camera is an exceptionally simple instrument. Its purpose is simply to image light from an object located at the infinite conjugate onto the focal plane, where the sensor is located. As such, from a system perspective one might regard the camera as a single lens with the sensor located at the second focal point. This is illustrated in Figure 2.10.
If this system is the essence of simplicity, then the Pinhole Camera, a very early form of camera, takes this further by dispensing with the lens altogether! A pinhole camera relies on a very small system aperture (a pinhole) defining the image quality. In this embodiment of the camera, all rays admitted by the entrance pupil follow closely the chief ray. However, light collection efficiency is low. Whilst in the paraxial approximation, the camera presents itself as a very simple instrument, as indeed early cameras were, the demands of light collection efficiency require the use of a large aperture which results in the breakdown of the paraxial approximation. As we shall see in later chapters, this leads to the creation of significant imperfections, or aberrations, in image formation which can only be combatted by complex multi-element lens designs. Thus, in practice, a modern camera, i.e. its lens, is a relatively complex optical instrument.
Figure 2.10 Basic camera.
In defining the function of the camera, we spoke of the imaging of an object located at infinity. In this context, ‘infinity’ means a substantially greater object distance than the lens focal length. For the traditional 35 mm format photographic camera, a typical standard lens focal length would be 50 mm. The ‘35 mm’ format refers to the film frame size which was 36 mm × 24 mm (horizontal × vertical). As mentioned in Chapter 1, the focal length of the camera lens determines the ‘plate scale’ of the detector, or the field angle subtended per unit displacement of the detector. Overall, for this example, plate scale is 1.15° mm−1. The total field covered by the frame size is ±20° (Horizontal) × ±13.5° (Vertical). ‘Wide angle’ lenses with a shorter focal length lens (e.g. 28 mm) have a larger plate scale and, naturally a wider field angle. By contrast, telephoto lenses with longer focal lengths (e.g. 200 mm), have a smaller plate scale, thus producing a greater magnification, but a smaller field of view.
Modern cameras with silicon detector technology are generally significantly more compact instruments than traditional cameras. For example, a typical digital camera lens might have a focal length of about 8 mm, whereas a mobile phone camera lens might have a focal length of about half of this. The plate scale of a digital camera is thus considerably larger than that of the traditional camera. Overall, as dictated by the imaging requirements, the field of view of a digital camera is similar to its traditional counterpart, although, in practice, equivalent to that of a wide field lens. Therefore, in view of the shorter focal length, the detector size in a digital camera is considerably smaller than that of a traditional film camera, typically a few mm. Ultimately, the miniaturisation of the digital camera is fundamentally driven by the resolution of the detector, with the pixel size of a mobile phone camera being around 1 μm. This is over an order of magnitude superior to the resolution, or ‘grain size’ of a high specification photographic film.
Further Reading
1 Haija, A.I., Numan, M.Z., and Freeman, W.L. (2018). Concise Optics: Concepts, Examples and Problems. Boca Raton: CRC Press. ISBN: 978-1-1381-0702-1.
2 Hecht, E. (2017). Optics, 5e. Harlow: Pearson Education. ISBN: 978-0-1339-7722-6.
3 Keating, M.P. (1988). Geometric, Physical, and Visual Optics. Boston: Butterworths. ISBN: 978-0-7506-7262-7.
4 Kidger, M.J. (2001). Fundamental Optical Design. Bellingham: SPIE. ISBN: 0-81943915-0.
5 Kloos, G. (2007). Matrix Methods for Optical Layout. Bellingham: SPIE. ISBN: 978-0-8194-6780-5.
6 Longhurst, R.S. (1973). Geometrical and Physical Optics, 3e. London: Longmans. ISBN: 0-582-44099-8.
7 Smith, F.G. and Thompson, J.H. (1989). Optics, 2e. New York: Wiley. ISBN: 0-471-91538-1.
3 Monochromatic Aberrations
3.1 Introduction
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
