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Optical Engineering Science. Stephen RoltЧитать онлайн книгу.

Optical Engineering Science - Stephen Rolt


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      The optical invariant is a generalised constraint that relates system lateral and angular magnification and applies to any arbitrary pair of rays. A very specific descriptor is created when the ray pair consists of the chief ray and the marginal ray. This special case of the optical invariant is known as the Lagrange invariant. The Lagrange invariant, H is given by:

      (2.6)equation

      If we now simply evaluate H at the entrance and exit pupils where, by definition, hchief is zero, then the product nhmarginalθchief is constant. The Lagrange invariant then simply articulates the fact that the angular and lateral magnifications are inversely related. In fact, the Lagrange invariant captures a more fundamental constraint to an optical system. If the object plane is uniformly illuminated, then the total light flux emanating from the plane is proportional to the square of the maximum field angle. The proportion of that flux that is admitted by the entrance pupil is itself proportional to the square of the marginal ray height. Therefore, the total flux passing through an optical system is proportional to the square of the Lagrange invariant, H2. Thus the Lagrange invariant is an expression of the conservation of energy as light propagates through an optical system. This will become of paramount significance when, in later chapters, we consider source brightness or radiance and the impact of the optical system on optical flux flowing through it.

      (2.7)equation

      E is of course infinite at the focal point of a system. The variable is of great significance in the analysis of optical imperfections or aberrations where the distance of a component from the aperture stop is of critical importance.

      These introductory chapters provide a complete description of ideal optical systems. That is to say, in the paraxial approximation, where imaging imperfections, or aberrations may be ignored, the analysis presented is substantially complete. Some very simple optical instruments are introduced at this point; their deficiencies are discussed later.

      2.11.1 Magnifying Glass or Eye Loupe

      For the two cases illustrated in Figure 2.7, the eye's focussing power remains the same. Therefore, addition of a lens of focal length f will change the closest approach distance, d0, to:

equation Geometrical illustration of a simple magnifying lens.

      (2.8)equation

      In describing magnifying lenses, as suggested earlier, d0 is defined to be 250 mm. Thus, a lens with a focal length of 250 mm would have a magnification of ×2 and a lens with a focal length of 50 mm would have a magnification of ×6. In practice, simple lenses are only useful up to a magnification of ×10. This is partly because of the introduction of unacceptable aberrations, but also because of the impractical short working distances introduced by lenses with a focal length of a few mm. For higher magnifications, the compound microscope must be used.

      Naturally, the pupil of this simple system is defined by the pupil of the eye itself. The size of the eye's pupil varies from about 3 mm in bright light, to about 7 mm under dim lighting conditions, although this varies with individuals.

      2.11.2 The Compound Microscope

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      The entire co-ordinate system is referenced to the position of the objective lens. Of particular relevance here is the first focal length. From the above matrix we have the following equation for the system focal length:

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