Introduction to Nonimaging Optics, 2nd Edition

4

Étendue and the Winston–Welford Design Method

4.1 Introduction

As light travels through an optical system, it requires area and angular space. Figure 4.1 shows a spherical light source S_R (e.g., the sun) of radius r emitting light into space. As the emitted light expands, it will eventually illuminate the inner face of a spherical surface A₁ of radius d₁. When it reaches the surface, the angular spread of the light is confined to angle θ₁, defined by the tangents to S_R on the points of A₁. This angle θ₁ can be obtained from r/d₁ = sin θ₁. The area of the spherical surface A₁ is given by A1=4πd12, or by using the expression obtained for sin θ₁, we get A₁ sin² θ₁ = 4πr² = A_S, where A_S is the area of the source S_R.

We may now compare what ...