Radiometry of Imaging

Abstract

2.1 INTRODUCTION In Chapter 1, we showed how the position and size of the Gaussian image of an object formed by an imaging system can be determined from the radii of curvature of its surfaces and the refractive indices of the media around them. However, we did not consider the sizes of the imaging elements or the apertures in the system. Accordingly, no effort was made there to determine the cone of object rays that enters or exits from the imaging system. Such calculations are essential for the determination of the image intensity in terms of the object intensity, or the image irradiance in terms of the object radiance. We begin this chapter by introducing the concept of an aperture stop and its images, the entrance and exit pupils of an imaging system. The light cone from a point object that enters the system is limited by the entrance pupil. Similarly, the light cone that exits from the system and converges onto the image point is limited by the exit pupil. Certain special rays, such as the chief and marginal rays, are defined. Vignetting or blocking of the rays from an off-axis point object by the aperture stop and/or other elements of the system, thus changing the effective shape of the stop and pupils, is explained. A telecentric stop is defined and its advantages are briefly discussed. The field stop and its images, the entrance and exit windows and angular field of view of a system are also described. The field of radiometry deals with the determination of the amount of light radiated by a source per unit area per unit solid angle, or falling on a surface per unit area. To discuss the radiometry of imaging, we start with the radiometry of point and extended sources. Terms such as intensity of a point source, radiance of an extended source, irradiance of a surface, and a Lambertian source are introduced. The inverse square, cosine, and cosine-third laws of irradiance for a point source are explained. Similarly, the cosine law of intensity and cosine-fourth law of irradiance for an extended source are discussed. In particular, the irradiance of a surface by a Lambertian disc source is discussed. The results thus obtained are used next to discuss the radiometry of optical imaging. The radiometry of point-object imaging is discussed first and a relationship between the intensities of a point object and its point image is derived. This is followed by the radiometry of extended-object imaging. An invariant relation between the radiances of an object and its image is derived, and the irradiance of the image is discussed. Pupil distortion is discussed, showing that the transverse magnification between the entrance and exit pupils varies with the location of an area element on the pupil. The total flux in an image element may be determined by integrating across the entrance pupil or the exit pupil.