The purpose of this procedure is to model the full-wave response of an antenna for use in two-way propagation models and experimental inverse scattering. We have developed a model for our antennas which provides the incident field on transmit (the field produced in the absence of objects) and the measured voltage on receive (an angle-dependent coherent sum of all incoming fields), and can predict the signal measured between transmitting and receiving antennas. We model the antenna radiation characteristics of a single antenna by expanding the incoming and outgoing electric fields in vector spherical harmonics and relate these to the outgoing and incoming modes on a feeding waveguide through a linear model. The model parameters are called transmit and receive coefficients. To model the propagation of fields between two antennas, the outgoing field of the transmitter is expanded in the reference frame of the receiver using the translation relation for vector spherical harmonics. Treating the two antennas as the ports of a two-port network, we can derive an expression for the S-parameters that would be measured between these antennas. This relation can be used to relate any two antennas in a multi-antenna setup in the absence of an object. We determine the transmit coefficients numerically. After constructing a physical antenna, a CAD model is developed and is used to simulate the fields radiated by the antenna. The numerical field measurements are then used to determine the transmit coefficients by inverting a model relating the coefficients to the fields. The commercial simulation package Ansoft HFSS is well suited for the problem because it gives field measurements and S-parameters. Having the antenna model, it must be included in the inverse scattering algorithm. Inverse scattering algorithms are often cast in terms of a volume or surface integral equation. The integral equation gives the total or scattered field off an object given the background Green’s function, object dielectric properties, electric field in the object, and incident field. In order to include the antenna model, we can make use of the addition theorem for the Green’s function to expand the scattered field as incoming waves in the frame of a receiver. This allows us now to use the receiver model of the antenna to account for the angle-dependent radiation pattern of the antenna when taking S-parameter measurements. Also, the transmit coefficients are used to provide the now-known incident field in the algorithm. This directly links the physics equation (for the fields) in our algorithms to the S-parameter measurements we take. This antenna model is important because it directly links measured quantities to field quantities. The model also allows us to very concisely include the effects of the antenna in the inverse scattering algorithms and link measured data to predicted data which is vital to imaging algorithms. Including an antenna model in an inverse scattering algorithm is a new development in the inverse scattering community and applicable in other remote sensing fields, such as seismology and oil exploration. This development is key for making experimental inverse scattering widely successful.

# Antenna and Propagation Model for Free-space Measurements and Experimental Inverse Scattering

*Technology #4752*

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- Mahta Moghaddam
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- Joohee Kim
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*US Patent Pending*