Imaging is about reproducing the field, or more often the irradiance pattern of an object or scene, at an image plane. Geometrical optics, where optical rays are assumed to travel in rectilinear fashion without diffraction, is used extensively in lens and optical system design. Geometrical optics provides useful relationships between the object and image locations and sizes and is also applied in the analysis of the pupils of an imaging system. A proficient approach for image modeling draws on both geometrical optics and diffraction theory. This chapter begins with a review of geometrical imaging concepts and relationships that are helpful for the imaging simulations that follow.

7.1 Geometrical Imaging Concepts

Not all optical systems form images. For example, a beam expander increases the size of a laser beam but doesn't image. However, our concern is with imaging, and in order to form a real image, light from an arbitrary object point must be collected and focused at the image plane. For the imaging situation shown in Fig. 7.1, the lens law (Gaussian form) describes the relationship needed under the paraxial condition (small ray angles relative to the optical axis) for "best focus" imaging:

(7.1)

Here, f is the lens (or lens system) focal length, z₁ is the distance along the optical axis from the object to the front principal plane of the lens, and z₂ is the distance from the back principal plane to the image location. Principal planes are a virtual concept for geometrical lens analysis. They are normal to the optical axis. A ray incident on the front principal plane at some height from the optical axis will exit the back principal plane at the same height. In other words, principal planes are planes of unit magnification. For a "thin" lens, the front and back principal planes are co-located in the plane with the vanishingly thin lens.