Modeling is clearly at the center of this book’s endeavors, from pursuing an understanding of the MQS regime, to developing representations that may be useful in object identification and to examining their performance in fast forward models for discrimination algorithms. This chapter pursues a variety of methods to compute the response of any TOIs to excitation by arbitrary impinging primary fields. The first focus is on methods that proceed from first principles; such methods have been particularly useful for illuminating the underlying MQS physics and phenomenology. These methods are more involved than simpler response models, such as the TIDRM, whose input–output connection is something of a parameterized black box. In particular, first-principles methods use formulations developed explicitly from the governing physics. They rely on equations inherent to such physics and typically proceed by enforcing physical, universal boundary conditions. This way of proceeding makes them more rigorous and less dependent on conveniences and idealizations; however, they are also more cumbersome and less useful for discrimination processing than the simpler formulations. Many numerical techniques are available that might serve well for first-principles modeling, i.e., integral and differential formulations, in the FD and TD. The method of auxiliary sources (MAS) presented here has proven notably successful and efficient. This method and essentially all comparable, firstprinciples numerical and analytical modeling approaches must exploit some form of the concepts in Section 6.2. In particular, specialized formulations must be used to handle the regime in which external field penetration of an object is still physically significant (in terms of response) but when it is very small relative to object dimensions. Techniques that deal with this scenario effectively have turned out to be applicable over a surprisingly broad portion of the entire MQS band for certain common target types. They have also provided basic revelations in connection with uniqueness issues in inversions for electrogmagnetic properties.
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