## Abstract

Multi-transmitter aperture synthesis is a method in which multiple transmitters can be used to improve resolution and contrast of distributed aperture systems. Such a system utilizes multiple transmitter locations to interrogate a target from multiple look angles thus increasing the angular spectrum content captured by the receiver aperture array. Furthermore, such a system can improve the contrast of sparsely populated receiver arrays by capturing field data in the region between sub-apertures by utilizing multiple transmitter locations. This paper discusses the theory behind multi-transmitter aperture synthesis and provides experimental verification that imagery captured using multiple transmitters will provide increased resolution.

©2010 Optical Society of America

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### Equations (9)

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(1)
$${U}_{T}\left({x}_{T},{y}_{T}\right)=\frac{{e}^{jkz}{e}^{j\frac{k}{2z}\left({x}_{T}^{2}+{y}_{T}^{2}\right)}}{j\lambda z}\text{F}\left\{U\left(x-{x}_{n},y-{y}_{n}\right)\right\},$$
(2)
$${U}_{T}\left({x}_{T},{y}_{T}\right)=\tilde{g}({x}_{T},{y}_{T})\text{F}\left\{U\left(x,y\right)\otimes \delta (x-{x}_{n},y-{y}_{n})\text{}\right\}\text{},$$
(3)
$${U}_{T}\left({x}_{T},{y}_{T}\right)={e}^{j\frac{2\pi}{\lambda z}\left({x}_{T}{x}_{n}+{y}_{T}{y}_{n}\right)}{U}_{T}\text{'}\left({x}_{T},{y}_{T}\right),$$
(4)
$${U}_{T}\text{'}\left({x}_{T},{y}_{T}\right)=\tilde{g}({x}_{T},{y}_{T})\text{F}\left\{U\left(x,y\right)\text{}\right\}\text{ }.$$
(5)
$${U}_{refl}\left({x}_{T},{y}_{T}\right)={e}^{j\frac{2\pi}{\lambda z}\left({x}_{T}{x}_{n}+{y}_{T}{y}_{n}\right)}{U}_{T}\text{'}\left({x}_{T},{y}_{T}\right)r\left({x}_{T},{y}_{T}\right),$$
(6)
$${U}_{R}\left(x,y\right)=P\left(x,y\right)\frac{{e}^{jkz}{e}^{j\frac{k}{2z}\left({x}^{2}+{y}^{2}\right)}}{j\lambda z}\text{F}\left\{{e}^{j\frac{2\pi}{\lambda z}\left({x}_{T}{x}_{n}+{y}_{T}{y}_{n}\right)}{U}_{T}\text{'}\left({x}_{T},{y}_{T}\right)r\left({x}_{T},{y}_{T}\right)\right\},$$
(7)
$${U}_{R}\left(x,y\right)=P\left(x,y\right)\frac{{e}^{jkz}{e}^{j\frac{k}{2z}\left({x}^{2}+{y}^{2}\right)}}{j\lambda z}{U}_{r}\left(x-{x}_{n},y-{y}_{n}\right),$$
(8)
$${U}_{r}\left(x,y\right)=\text{F}\left\{{U}_{T}\text{'}\left({x}_{T},{y}_{T}\right)r\left({x}_{T},{y}_{T}\right)\right\}.$$
(9)
$${S}_{A}={{\displaystyle \int dxdy\left|\frac{1}{N}{\displaystyle \sum _{n=1}^{N}{I}_{n}\left(x,y\right)}\right|}}^{\gamma},$$