Gaussian Optics Lenses are an important part of most optical systems. Good results in optical measurements often rely on the best selection of lenses. In this chapter we develop the relations governing the passage of light rays through imaging elements on the basis of the paraxial approximation using matrix algebra. We also mention the aberrations occurring when rays deviate from this ideal Gaussian behaviour. Finally we go through some of the standard imaging systems. | Optical Metrology. Kjell J. Gasvik Copyright 2002 John Wiley Sons Ltd. ISBN 0-470-84300-4 2 Gaussian Optics INTRODUCTION Lenses are an important part of most optical systems. Good results in optical measurements often rely on the best selection of lenses. In this chapter we develop the relations governing the passage of light rays through imaging elements on the basis of the paraxial approximation using matrix algebra. We also mention the aberrations occurring when rays deviate from this ideal Gaussian behaviour. Finally we go through some of the standard imaging systems. REFRACTION AT A SPHERICAL SURFACE Consider Figure where we have a sphere of radius R centred at C and with refractive index n . The sphere is surrounded by a medium of refractive index n. A light ray making an angle a with the . axis is incident on the sphere at a point A at height x above the . axis. The ray is incident on a plane which is normal to the radius R and the angle of incidence 0 is the angle between the ray and the radius from C. The angle of refraction is 0 and the refracted ray is making an angle a with the .-axis. By introducing the auxiliary angle we have the following relations 0 - a 0 a x sin n sin 0 n sin 0 The last equation follows from Snell s law of refraction. By assuming the angles to be small we have sin sin 0 0 sin 0 0 and by combining Equations we get the relation a x a Px a. n R n n n 2-2 16 GAUSSIAN OPTICS Figure Refraction at a spherical interface where n n P ------- R is called the power of the surface. The spherical surface in Figure might be the front surface of a spherical lens. In tracing rays through optical systems it is important to maintain consistent sign conventions. It is common to define ray angles as positive counterclockwise from the . axis and negative in the opposite direction. It is also common to define R as positive when the vertex V of the surface is to the left of the centre C and negative when it
