Principal Point

3 Key excerpts on "Principal Point"

• 

  eBook - ePub

  Foundations of Optical System Analysis and Design

  • Lakshminarayan Hazra(Author)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)

  8 ].

  It may be noted that the axial locations of the first and second principal foci can be ascertained from the above data if the refractive indices of the object and image spaces are known.

  It is sometimes useful to define a pair of conjugate axial points such that any ray incident on one of them emerges parallel to itself from the other point. This implies that in the paraxial invariance relation

  nu η =

  n ′

  u ′

  η ′

  (3.120)

  u =

  u ′

  , and so transverse magnification between these two conjugates is

  M =

  (

  η ′

  η

  )

  =

  (

  n

  n ′

  )

  (3.121)

  These two axial conjugate points are called nodal points, and are denoted by N and N′ (Figure 3.15 ). Using (3.113) and (3.114), axial locations of N and N′, with regard to the Principal Points H and H′ in the object space and image space, respectively, are given by

  HN =

  l ˜

  =

  (

  n ′

  − n

  )

  F

  (3.122)

  H ′

  N ′

  =

  l ˜

  ′

  =

  (

  n ′

  − n

  )

  F

  (3.123)

  When

  n ′

  = n

  , the values of

  l ˜

  and

  l ˜

  ′

  are zero, and the nodal points coincide with the principal or unit points.

  In Gaussian optics, the six points—namely the first and the second principal foci F and F′, the first and the second principal or unit points H and H’, and the first and the second nodal points N and N′—are called the cardinal points of an axisymmetric imaging system. For paraxial analysis, it is sufficient to know the location of the four cardinal points, which include the two foci, and either the two Principal Points or the two nodal points. The conjugate planes at the nodal points are often called the nodal planes. However, it should be noted that, except for the axial points, the equality of the convergence angles of an incident and the corresponding emergent ray does not hold good for paraxial rays passing through other points of the nodal planes. A well-known practical application of the concept of nodal points is the method of measurement of equivalent focal length of a lens system by nodal slide method.

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  eBook - PDF

  Practical Optics

  • Naftaly Menn(Author)
  • 2004(Publication Date)
  • Academic Press

    (Publisher)

  In most cases experienced in practice, 1 2 1 ♦ Geometrical Optics in the Paraxial Area Figure 1.1 Optical beams: (a) parallel, (b,c) homocentric and (d) non-homocentric. imaging systems are based on lenses (exceptions are the imaging systems with curved mirrors). The functioning of any optical element, as well as the whole system, can be described either in terms of ray optics or in terms of wave optics. The first case is usually called the geometrical optics approach while the second is called physical optics. In reality there are many situations when we need both (for example, in image quality evaluation, see Chapter 2). But, since each approach has advantages and disadvantages in practical use, it is important to know where and how to exploit each one in order to minimize the complexity of consideration and to avoid wasting time and effort. This chapter is related to geometrical optics, or, more specifically, to ray optics. Actually an optical ray is a mathematical simplification: it is a line with no thick-ness. In reality optical beams which consist of an endless quantity of optical rays are created and transferred by electro-optical systems. Naturally, there exist three kinds of optical beams: parallel, divergent, and convergent (see Fig. 1.1). If a beam, either divergent or convergent, has a single point of intersection of all optical rays it is called a homocentric beam (Fig. 1.1b,c). An example of a non-homocentric beam is shown in Fig. 1.1d. Such a convergent beam could be the result of different phenomena occurring in optical systems (see Chapter 2 for more details). Ray optics is primarily based on two simple physical laws: the law of reflection and the law of refraction. Both are applicable when a light beam is incident on a surface separating two optical media, with two different indexes of refraction, n 1 and n 2 (see Fig. 1.2). The first law is just a statement that the incident angle, i , is Figure 1.2 Reflection and refraction of radiation.

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  Introduction to Optics

  • Frank L. Pedrotti, Leno M. Pedrotti, Leno S. Pedrotti(Authors)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  Chief Ray The chief , or principal, ray is a ray from an object point that passes through the axial point , in the plane of the entrance pupil . Given the conjugate nature of the entrance pupil with both the aperture stop and the exit pupil, this ray must also pass (actually or when extended) through their axial points.The chief ray in the cone of rays leaving object point is shown in all three systems of Figure 3-1. The chief ray in the cone of rays leaving the axial point O always coincides with the optical axis. Before adding to our collection of new concepts that arise from a con-sideration of apertures in optical systems, we consider a system slightly more complex than those of Figure 3-1. In Figure 3-2, we specify a particular optical system consisting of two lenses, L 1 and L 2, with an aperture A placed be-tween them, as shown. The first question to be answered is: Which element serves as the effective AS for the whole system? The answer to this question is not always obvious. It can always be answered, however, by determining which of the actual elements in the given system—in this case, A, L 1, or L 2— has an entrance pupil that confines rays to their smallest angle with the axis , as seen from the object point. To decide which candidate presents the limiting aperture, it is necessary to find the entrance pupil for each by imaging each one through that part of the optical system lying to its left : O ¿ OO ¿ . II ¿ E n P ; E x P E n P . E x P E x P E x P , E x P E n P (E x P) E n P E n P E n P 1 “Preceding” is used in the sense that light must pass through those imaging elements first. If we always use light rays directed from left to right, we can simply say, “by all imaging elements to its left.” 54 Chapter 3 Optical Instrumentation L 2: By ray diagram or by calculation, the image of lens L 2, formed by L 1 (as if light went from right to left), is and is real. Both its location and size (magnification) are shown.

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