Lens Design

A Practical Guide

Haiyin Sun

• Publisher: CRC Press
• Year: 2016
• ISBN:
  9781351722247
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

A Practical Guide to Lens Design focuses on the very detailed practical process of lens design. Every step from setup specifications to finalizing the design for production is discussed in a straight forward, tangible way. Design examples of several widely used modern lenses are provided. Optics basics are introduced and basic functions of Zemax are described. Zemax will be used throughout the book.

1 Basic Optics

This chapter summarizes some of the most basic optics. Readers, even without the knowledge of college-level optics, may be able to gain enough basic optics knowledge from reading this chapter and move on to the next chapter. However, a systematic study of optics elsewhere is still recommended.

1.1 SNELL’S LAW AND PARAXIAL APPROXIMATIONS

1.1.1 SNELL’S LAW

Snell’s law describes how an optical interface between two materials refracts an optical ray passing through the interface [1]. Snell’s law is the foundation of all geometric optics and has the following mathematical form:

n2⁢sin(θ2)=n1⁢sin(θ1)(1.1)

where n₁ and n₂ are the refractive indexes of the two materials forming the interface, θ₁ and θ₂ are the incident angle and the refracted angle of the ray with respect to the local normal of the interface. Figure 1.1a and b show the schematic of a plane and a spherical optical interfaces refract a ray.

1.1.2 PARAXIAL APPROXIMATIONS

When θ₁ and θ₂ are small, sin(θ₁) ≈ θ₁ and sin(θ₂) ≈ θ₂, Snell’s law reduces to its first order paraxial approximation form:

θ2=sin−1⁢[n1n2⁢sin(θ1)]≈n1n2⁢θ1(1.2)

If Equation 1.2 is not accurate enough, we can include the third-order term and have

θ2=sin−1⁢[n1n2⁢sin(θ1)]≈n1n2⁢θ1+n16⁢n2⁢θ13⁢(n12n22−1)(1.3)

or further include the fifth-order term. Paraxial approximation can significantly simplify the calculation involved in tracing a ray through optical elements. This was important in pre-computer era. Equations 1.1 1.2, and 1.3 are plotted in Figure 1.2 for n₂/n₁ = 1.5 and n₂/n₁ = 1.9. We can see from Figure 1.2 that for the purpose of analysis, paraxial approximation is good for incident angle θ₁ < 30° or so, the third-order approximation is good for incident angle θ₁ < 60° or so. But for accurate design, the accurate form of Equation 1.1 (Snell’s law) needs be used.

FIGURE 1.1 Two optical interfaces refract an optical ray passing through them, respectively. (a) Planar interface with n₁ < n₂. (b) Spherical interface with n₁ < n₂.

FIGURE 1.2 Solid curve: Snell’s law, Equation 1.1. Dotted curve: the first-order (paraxial) approximation, Equation 1.2. Dashed curve: the third-order approximation, Equation 1.3. (a) n₂/n₁ = 1.5. (b) n₂/n₁ = 1.9.

From Figure 1.1b, we can see that when a ray incident on a spherical surface and the height of the ray is much smaller than the radius of the spherical interface, the paraxial condition can also be met. In real optical systems, paraxial condition is often not met. Fortunately, the enormous calculation power of computers makes paraxial approximation unnecessary. However, many optical concepts were developed based on paraxial approximation before the invention of computers and are still widely used.

1.2 FREQUENTLY USED CONCEPTS AND TERMINOLOGIES FOR LENSES

1.2.1 POSITIVE LENSES AND NEGATIVE LENSES

Lenses can be generally divided into two categories: positive and negative. A positive lens convergently refracts the rays passing through it or, in other words, focuses the rays. A positive lens has a positive focal length. A negative lens divergently refracts the rays passing through it. A negative lens has a negative focal length. Figure 1.3a and b show some examples of positive and negative lenses, respectively, where R₁ and R₂ are the radii of the two surfaces of one lens.

1.2.2 OPTICAL AXIS AND FOCAL POINTS

The optical axis of a lens or an optical system is its rotational symmetric axis. Figure 1.4a and b show the optical axis of a positive lens and a negative lens, respectively. When optical rays parallel to the optical axis pass through a positive lens from left to right, the refracted or f...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Author
• Chapter 1 Basic Optics
• Chapter 2 Optical Aberrations
• Chapter 3 Optical Glasses
• Chapter 4 Lens Specifications and Parameters
• Chapter 5 Design Process: From Start to Finish
• Chapter 6 Image Optics: Design Examples
• Chapter 7 Design Using the Multiconfiguration Function
• Chapter 8 Nonsequential Raytracing Design
• Chapter 9 Tolerance Analysis
• Chapter 10 Design for Production
• Index