…the electric forces can disentangle themselves from material bodies and can continue to subsist as conditions or changes in the state of space.
—H. Hertz 
Chapter 2 developed a geometric model for optical propagation and detection and described algorithms for object estimation on the basis of this model. While geometric analysis is of enormous utility in analysis of patterns formed on image or projection planes, it is less useful in analysis of optical signals at arbitrary points in the space between objects and sensors. Analysis of the optical system at all points in space requires the concept of “the optical field.” The field describes the state of optical phenomena, such as spectra, coherence, and polarization parameters, independent of sources and detectors.
Representation, analysis, transformation, and measurement of optical fields are the focus of the next four chapters. The present chapter develops a mathematical framework for analysis of the field from the perspective of sensor systems. A distinction may be drawn between optical systems, such as laser resonators and fiber waveguides, involving relatively few spatial channels and systems, such as imagers and spectrometers, involving a large number of degrees of freedom. The degrees of freedom are typically typically expressed as pixel values, modal amplitudes or Fourier components. It is ...