EE 231 Introduction to Optics Geometrical optics and

EE 231 Introduction to Optics Geometrical optics and Imaging theory lesson 1 Andrea Fratalocchi www. primalight. org 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 1 1

Nature of light: Rays vs. Waves Before the nineteenth century, light was considered to be a stream of particles. Newton and Fermat were the main architect of this vision. Newton believed that light ‘particles’ left the object and stimulated the ‘sense of light’ upon entering in the eyes. The modern theory of images is still mainly based on such a ‘particle’ approach, based on Fermat principle Sir Isaac Newton (1642 -1726) 10/29/2020 Christian Huygens, conversely, argued that light is a wave and light propagation is described by a wave motion and not by a particle. Thomas Young in 1801 provides the first clear experiment showing the wave nature of light. Young experiments shown interferences effects that could not be explained by particles. Pierre de Fermat (1607 -1665) Andrea Fratalocchi (www. primalight. org) Christiaan Huygens (16291695) EE 231: Geometrical Optics and Imaging theory Thomas Young (1773 -1829) slide 2 2

Nature of light: Rays vs. Waves Who is right? 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 3 3

Nature of light: Rays vs. Waves Who is right? All of them: to every wave it can be associated a particle behavior, which holds true in approximate conditions. Wave Optics 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory Ray optics slide 4 4

Plane waves Nature of light: Rays q How do I associate rays to waves? Rays are constructed from surfaces of constant phase, which define the wavefront. Rays are orthogonal to the wavefront of a wave. Spherical waves 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 5 5

Nature of light: Rays q How do light rays propagate? Fermat Principle. Optical rays traveling between two points A and B follow a path such that the time of travel (or the optical pathlength) between the two points is minimum The refractive index of a material is n=c 0/c, i. e. , the ratio between the speed of light in vacuum and the speed of light in the medium. Therefore, the time T taken by light to travel a distance L is T=L/c=n. L/c 0. The time T is proportional to the optical pathlength, or optical path, n. L 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 6 6

Nature of light: Rays q Propagation of rays in an homogeneous medium In an homogeneous medium the refractive index is constant everywhere. The path of minimum distance between to points A and B is a straight line, which implies that: In an homogeneous medium light rays travel in straight lines 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 7 7

Nature of light: Rays q Propagation of rays at the interface between two different media v What path would you choose? 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 8 8

Nature of light: Rays q Propagation of rays at the interface between two different media v What path would you choose? 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 9 9

Nature of light: Rays q Propagation of rays at the interface between two different media v What path would you choose? The optical path is: 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 10 10

Nature of light: Rays q Propagation of rays at the interface between two different media v What path would you choose? The optical path is: Snell Law, demonstrated via Fermat principle 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 11 11

Nature of light: Rays q Propagation of rays at the interface between two different media Snell law 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 12 12

Nature of light: Rays q Propagation of rays at the interface between two different media Snell law is nonlinear, however for small angles and it becomes: Paraxial Snell law 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 13 13

Nature of light: Rays and Maxwell Equations Fermat principle 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 14 14

Nature of light: Rays and Maxwell Equations Fermat principle Path of minimum time 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 15 15

Nature of light: Rays and Maxwell Equations Fermat principle 10/29/2020 Equation of rays Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 16 16

Nature of light: Rays and Maxwell Equations Fermat principle Equation of rays Eikonal equation 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 17 17

Nature of light: Rays and Maxwell Equations Fermat principle Equation of rays Eikonal equation 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 18 18

Nature of light: Rays and Maxwell Equations Fermat principle Equation of rays Maxwell equations Equation of rays Wave Optics 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory Ray optics slide 19 19

Nature of light: Rays vs. Waves Who is right? All of them: Fermat and Newton were probing a specific limit of waves, which under short wavelengths conditions become equivalent to a stream of particles. In optics, this limit is called geometrical optics or ray optics Wave Optics 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory Ray optics slide 20 20

Nature of light: Ray optics Fermat principle 1. Propagation of straight lines in homogeneous media 2. Law of reflection and refraction at discontinuous interfaces between materials of different refractive index 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 21 21

Nature of light: Ray tracing examples 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 22 22

Ray and Geometrical Optics Ø References 1) A. Yariv, P. Yeh, Photonics, 6 th Ed. , Chapter 2 2) M. Born and E. Wolf, Principle of Optics, 6 th Ed. , Chapter 3. 10/29/2020 Andrea Fratalocchi (www. primalight. org) EE 231: Geometrical Optics and Imaging theory slide 23 23