Introduction

In this chapter, we will study lens aberrations and their effects on light distributed on the image plane. We would like to calculate the image irradiance for a given optical imaging system, especially when there is defocus because this is the most frequent problem in consumer images. First, we derive the relation between the scene radiance and the image irradiance for an ideal optical imaging systemwhich has no lens aberrations and is in perfect focus. Next, we study how the distribution of light on the image plane is affected by some defects in the optical imaging process. The theory of wavefront aberrations is formulated and it is used to calculate the point spread function (PSF) and the OTF in the presence of focus error. Results from geometrical optics and physical optics are compared.

Some terms are used very often in the discussion of image light distribution. Sometimes, however, they are defined differently by different authors. We will define some of these terms here based on the international standard as specified in ISO 9334. The image of an ideal point object is a two-dimensional function, f(x, y), on the image plane, on which the coordinates (x, y) are defined. If we normalize this function so that it integrates to 1, the normalized f(x, y) is the PSF of the imaging system. The Fourier transform of the PSF is the OTF, F(νx, νy), where νx and νy are the horizontal and vertical spatial frequencies in the image plane. By the definition of the PSF, the OTF is equal to 1 at zero frequency, i.e., F(0, 0) = 1. An OTF can be a complex function.