## Abstract

Distributed aperture synthesis is an exciting technique for recovering high-resolution images from an array of small telescopes. Such a system requires optical field values measured at individual apertures to be phased together so that a single, high-resolution image can be synthesized. This paper describes the application of sharpness metrics to the process of phasing multiple coherent imaging systems into a single high-resolution system. Furthermore, this paper will discuss hardware and present the results of simulations and experiments which will illustrate how aperture synthesis is performed.

© 2010 OSA

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### Equations (6)

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(1)
$$I\left(x,y\right)={\left|{U}_{LO}\left(x,y\right)\right|}^{2}+{\left|{U}_{t}\left(x,y\right)\right|}^{2}+{U}_{LO}\left(x,y\right)\text{\hspace{0.17em}}{U}_{t}^{*}\left(x,y\right)+{U}_{LO}^{*}\left(x,y\right)\text{\hspace{0.17em}}{U}_{t}\left(x,y\right),$$
(2)
$$\begin{array}{l}\multicolumn{1}{c}{F\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}I\left(x,y\right)\right\}=F\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}{\left|{U}_{LO}\left(x,y\right)\right|}^{2}\right\}+F\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}{\left|{U}_{t}\left(x,y\right)\right|}^{2}\right\}}\\ \multicolumn{1}{c}{+F\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}{U}_{LO}\left(x,y\right)\text{\hspace{0.17em}}{U}_{t}^{*}\left(x,y\right)\right\}+F\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}{U}_{LO}^{*}\left(x,y\right)\text{\hspace{0.17em}}{U}_{t}\left(x,y\right)\right\}\text{\hspace{0.17em}}.}\end{array}$$
(3)
$$\begin{array}{l}\multicolumn{1}{c}{F\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}I\left(x,y\right)\right\}={A}_{LO}^{2}\text{\hspace{0.17em}}\delta \left({f}_{x},{f}_{y}\right)+F\left\{\text{\hspace{0.17em} \hspace{0.17em}}{\left|{U}_{t}\left(x,y\right)\right|}^{2}\right\}}\\ \multicolumn{1}{c}{+F\left\{\text{\hspace{0.17em}}{A}_{LO}\mathrm{exp}\left(jk\left({\theta}_{x}x+{\theta}_{y}y\right)\right)\text{\hspace{0.17em}}{U}_{t}^{*}\left(x,y\right)\right\}}\\ \multicolumn{1}{c}{+F\left\{\text{\hspace{0.17em}}{A}_{LO}\mathrm{exp}\left(-jk\left({\theta}_{x}x+{\theta}_{y}y\right)\right)\text{\hspace{0.17em}}{U}_{t}\left(x,y\right)\right\},}\end{array}$$
(4)
$$\begin{array}{l}\multicolumn{1}{c}{F\text{\hspace{0.17em}}\left\{\text{\hspace{0.17em}}I\left(x,y\right)\right\}={A}_{LO}^{2}\text{\hspace{0.17em}}\delta \left({f}_{x},{f}_{y}\right)+F\left\{\text{\hspace{0.17em} \hspace{0.17em}}{\left|{U}_{t}\left(x,y\right)\right|}^{2}\right\}}\\ \multicolumn{1}{c}{+{A}_{LO}\text{\hspace{0.17em}}F\left\{\text{\hspace{0.17em}}{U}_{t}^{*}\left(x,y\right)\right\}\ast \delta \left({f}_{x}-{f}_{x0},{f}_{y}-{f}_{y0}\right)}\\ \multicolumn{1}{c}{+{A}_{LO}\text{\hspace{0.17em}}F\left\{\text{\hspace{0.17em}}{U}_{t}\left(x,y\right)\right\}\ast \delta \left({f}_{x}+{f}_{x0},{f}_{y}+{f}_{y0}\right),}\end{array}$$
(5)
$$S={\displaystyle \colorbox[rgb]{}{$\int {I}^{\gamma}\left(x,y\right)dxdy,$}}$$
(6)
$${S}_{A}={{\displaystyle \colorbox[rgb]{}{$\int dxdy\left|\genfrac{}{}{0.1ex}{}{1}{N}{\displaystyle \colorbox[rgb]{}{$\sum _{n=1}^{N}{I}_{n}\left(x,y\right)$}}\right|$}}}^{\gamma},$$