## Abstract

A hybrid technique to simulate the imaging of space-based objects through cirrus clouds is presented. The method makes use of standard Huygens–Fresnel propagation beyond the cloud boundary and a novel vector trace approach within the cloud. At the top of the cloud, the wave front is divided into an array of input gradient vectors, which are in turn transmitted through the cloud model by use of the Coherent Illumination Ray Trace and Imaging Software for Cirrus. At the bottom of the cloud, the output vector distribution is used to reconstruct a wave front that continues propagating to the ground receiver. Images of the object as seen through cirrus clouds with different optical depths are compared with a diffraction-limited image. Turbulence effects from the atmospheric propagation are not included.

© 2002 Optical Society of America

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### Equations (10)

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(1)
$${W}_{i,j}={\mathrm{Re}}_{i,j}+i{\mathrm{Im}}_{i,j},$$
(2)
$${W}_{i,j}={M}_{i,j}exp\left(\mathit{ik}{\mathrm{\varphi}}_{i,j}\right),$$
(3)
$${\mathrm{\varphi}}_{i,j}=\frac{1}{k}{tan}^{-1}\frac{{\mathrm{Im}}_{i,j}}{{\mathrm{Re}}_{i,j}}.$$
(4)
$$\mathbf{\text{k}}_{i,j}{}^{q}=\frac{{\displaystyle \sum _{n=1}^{N}}\left|\mathbf{\text{E}}_{{\left[i,j\right]}_{n}}{}^{q}\right|\mathbf{\text{k}}_{{\left[i,j\right]}_{n}}{}^{q}}{{\displaystyle \sum _{n=1}^{N}}\left|\mathbf{\text{E}}_{{\left[i,j\right]}_{n}}{}^{q}\right|},$$
(5)
$$l_{{\left[i,j\right]}_{n}}{}^{q}=\sum _{s}{n}_{s}{l}_{s},$$
(6)
$$l_{i,j}{}^{q}=\frac{{\displaystyle \sum _{n=1}^{N}}\left|\mathbf{\text{E}}_{{\left[i,j\right]}_{n}}{}^{q}\right|l_{{\left[i,j\right]}_{n}}{}^{q}}{{\displaystyle \sum _{n=1}^{N}}\left|\mathbf{\text{E}}_{{\left[i,j\right]}_{n}}{}^{q}\right|}.$$
(7)
$$W_{i,j}{}^{q}=\sum _{n=1}^{N}E_{{\left[i,j\right]}_{n}}{}^{q}exp\left\{i\frac{2\mathrm{\pi}}{\mathrm{\lambda}}\left[l_{{\left[i,j\right]}_{n}}{}^{q}-\left(\mathbf{\text{k}}_{{\left[i,j\right]}_{n}}{}^{q}\xb7\mathbf{\text{r}}_{{\left[i,j\right]}_{n}}{}^{q}\right)\right]\right\},$$
(8)
$${W}_{i,j}=\mathrm{Re}\left(W_{i,j}{}^{1}\right)+i\mathrm{Re}\left(W_{i,j}{}^{2}\right).$$
(9)
$${P}_{\mathrm{out}}={P}_{\mathrm{in}}exp\left(\mathrm{\alpha}t\right),$$
(10)
$$n=1.3117+i2.93\times {10}^{-9}.$$