This chapter dealt with a theory that describes propagation through free space as a process of the propagation of EM waves, these waves being directly related to the acceleration of charged particles. A description of these waves is then provided based on Maxwell's equations and the derivation of the scalar Helmholtz equations. Then a description of the sources of these waves as being retarded potentials that then produce fields was provided. Although the basis of this explanation is charge and current densities on the geometrical structure that constitutes an antenna, direct measurement methods to assess these sources are not viable, therefore an alternative equivalent fields model was developed which in turn suggested other measurement methodologies.

The theoretical development of planar near-field antenna measurements is usually based on this plane wave spectrum (PWS) representation of electromagnetic (EM) fields. This generalized interpretation can be shown to stem from the free-space solution of the scalar wave equation, which itself follows directly from classical EM theory and Maxwell's equations where the four Maxwell equations are postulated, mathematical generalizations of a great many macroscopic experimental observations of electricity and magnetism. The validity of these phenomenological physical laws is attested to by the extraordinarily good agreement attained between measurement and prediction.

As shown in Chapter 5. for plane rectilinear near-field scanning, probe pattern characterisation errors contribute to the overall facility error budget as a singular mapping. Essentially then, this means that an error in the probe pattern at a particular direction in space will correspond to a similar error at that angle being introduced into any antenna pattern that has been corrected with this data. Furthermore, this can potentially constitute one of the largest and most repeatable, measurement uncertainties. Thus it is clear that in order to obtain reliable measurements, the electromagnetic (EM) properties of the near-field probe must be known very accurately indeed. Throughout this work, it has been assumed that relative measurements are taken, that is, without reference to absolute gain. If an absolute gain is required, then it is assumed that a substitution method is used employing a calibrated gain standard in order that the measurements can be correctly normalized. The importance of this for the characterisation of the near-field probe is that if the same probe and probe pattern used to correct the measurement of the antennas under test (AUTs) and the standard gain horn (SGH) then the gain of the probe will be unimportant. Thus, within this chapter, characterisation of the gain of the probe is not discussed and the gain of the probe will be normalized to unity for convenience. This chapter briefly describes the properties that are desirable in a near-field probe before proceeding to describe methods for obtaining and then using reliable probe pattern data.

The concept of measurement is interpreted differently in different sciences and there fore by definition in different areas of engineering and technology. As described in Chapter 1 the information extraction model is a particularly applicable concept for the cognitive evaluation of antenna measurements. In near-field scanning we are primarily concerned with microwave frequencies and as millions of years of human evolution have left our species without sense organs that respond to such frequencies, sensory cognition is largely irrelevant, leaving only rational cognition as a tool for the evaluation of microwave phenomena.

This list and very short description of postulated alternative mechanisms of interaction is not meant to be exhaustive or comprehensive. It is included to show that a wide range of interpretations of the interaction of charged particles across space and time are available. All of them can appropriately be used over a range of applicable circumstances and they all fail outside their range of applicability. Certain of them lend themselves to more than one formal structure, for example, it is possible to describe classical electromagnetism in terms of the Maxwell tensor in a four-vector relativistic space time and many of them fit more or less neatly into more over arching concepts for example, local gauge invariant field theories or Fisher information exchange concepts. However, the material in this overall text has been written so that while it is specific to classical electromagnetism, as this is anticipated to be the most widely used model recognized by the target readership, none of the above postulated mechanisms are inconsistent with the material in the book.

Within this text reference is made to a great many coordinate systems and the transformations between them. Implicit within this is the assumption that the tabulating grids are plaid, monotonic and equally spaced. Whilst not necessary from a theoretical stand point these conditions greatly simplify the recording process for a robotic positioner as well as simplifying the tasks of numerical integration, differentiation and interpolation. The following section presents a concise description of the most important coordinate systems and then goes on to discuss methods for representing the relationships between them like antenna mechanical system (AMS), antenna electrical system (AES), far-field plotting systems, direction cosine, azimuth over elevation, elevation over azimuth, elevation over azimuth, polar spherical, azimuth and elevation (true-view), range of spherical angles, transformation between coordinate systems, coordinate systems and elemental solid angles, relationship between coordinate systems, azimuth, elevation and roll angles, euler angles, quaternion, elemental solid angle for a true-view coordinate system.

This appendix discusses the calculation of semi-major axis, semi-minor axis and tilt angle of a rotated ellipse.