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哈尔滨理工大学学士学位论文
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哈尔滨理工大学学士学位论文
附录A 英文原文
Chapter 4 Paraxial World
J. M. Geary Introduction to lens design
4.1 Introduction
When you call up a ray trace in ZEMAX via Analysis - Calculations - RayTraceyou obtain surface height and angle data for a single ray selected via Settings. Youwill see two tables of data. The upper table is for the real ray; the lower, for ihEparaxial ray In this chapter we will concentrate an where the numbers in the paraxial table come from, and answer the yuestion: What is a paraxial ray?
In this book, most designs will be preceded by a thin lens pyre-design. This will be done using manual first-order calculations. The basis for such calculationsare the paraxial ray trace equations (PRTE). Real fray tracing is best left to thecomputer, but paraxial ray tracing is relatively easy. Though an approximation, it is nonetheless quite powerful. The EFL, BFL, f-number, magnification, principal plane locations, pupil locations, and image location can all be found using PRTE. Further, the paraxial ray heights and angles found an optical surfaces will also be used to calculate the Seidel aberrations.
4.2 Paraxial Ray Trace Equations
The PARTE are a pair of linear equations:
The first equation bends the ray (and will be derived in Section 4.5). The second equation provides the transfer height at the following optical surface (or plane of interest). Figures 4.1 and 4.2 illustrate the meaning of each equation.
As an example, we trace the ray from an axial object located 25 units from an optical element having n=0.05 (with units of inverse length), and incident on that surface at a height of 5 units (as illustrated in Figure 4.3).
We first use Equation 4.2 to find the incidence angle on the optical surface. Fig. 4.1Ray bending at a powered surface
Fig. 4.2 Ray transfer to next optical surface.
Fig 4.3 Example of PARTE (thin lens). We next use Equation 4.1 to find the amount of bending performed by the element. (Note in this example we have assumed that n=n=1.This is valid if is the power of a thin lens in air.)
Finally, we again employ Equation 4.2 to find the teat image axial location Please note that any ray launched from the object to any height cm the optical element would yield the same image distance, t;. This is illustrated in Figure 4.4
4.3 Gaussian Lens Formula
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哈尔滨理工大学学士学位论文
We will now derive a formula which relates the object and image conjugates. This is a basic formula learned in high school physics.
Fig. 4.4All paraxial rays yield the name emerge distance
Fig. 4.5 Real triplet
Fig. 4.6 PRTE triplet. This is the Gaussian formula for a thin lens derived via the PRTE. Note that / in Figure 4.4 is (according to the convention in Figure 3.1) negative.
4.4 What Lenses Look Like in the PRTE World
Figure 4.5 shows a lens system known as a Cooke triplet. You will design one of these lenses later on. However, in the PRTE world the triplet has the look shown
Fig. 4.7 Rear ray trace at art optical surface: a. significant y height; b. paraxial y height. in Figure 4.6 All dimensions are the same. This include thicknesses, and axial separations. The curved surfaces are replace with flat surface but these surfaces have power. They can bend surface is given by: s lens diameters, axial are replaced with flat rays. The power of a surface is given by
where n' is the index to the right of the surface, n is the index to the left, C is the curvature (11R).
All the first order properties; of a real lens system can be determined using the surrogate paraxial system and the PRTE.
4.5 Determination of Surface Power
Consider the optical refractive surface in Figure 4.7a. We show a ray hitting the surface at a height y and bending. At the ray-surface intersection point, we also show the normal to the surface, and a dashed line parallel to the optical axis. Ray angles (U and U')and incident and refracted angles (and) are also shown. Now imagine sliding the intersection point downward so it is close to the optical axis. If we blow up the scale, we get the picture shown in Figure 4.7b. Using this latter picture and some math we can come up with Equation 4.4.
We start by obtaining an expression for a. From Figure 4.7b we see that:
Next we relate the incident and refracted angles to alpha and the ray angles:
Next we write an expression for Snell's Law for small angles:
Now substitute Equations 4.6 into Equation 4.7 and rearrange: - 28 -