## Abstract

The technique of Fourier synthesis holography to image through scattering materials is analyzed in detail. A broad spectral source is decomposed into its Fourier components, and a hologram is formed at each wavelength and stored in the computer. Upon synthesis in the computer, a clear image can be formed of the obscured object. Post-data-acquisition processing such as selection of the gating time delay and autocorrelation shaping are also demonstrated.

© 1995 Optical Society of America

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### Equations (5)

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(1)
$${G}_{s}(f)=G(f)\sum _{m=-\infty}^{\infty}\mathrm{\delta}(m\mathrm{\Delta}f),$$
(2)
$${u}_{t}={u}_{o}+{u}_{r}=H(f)G(f)\sum _{m=-\infty}^{\infty}\mathrm{\delta}(m\mathrm{\Delta}f)+\text{exp}(i2\mathrm{\pi}\mathrm{\alpha}x)G(f)\sum _{m=-\infty}^{\infty}\mathrm{\delta}(m\mathrm{\Delta}f),$$
(3)
$${I}_{h}=\hspace{0.17em}\mid {u}_{o}+{u}_{r}{\mid}^{2}=\hspace{0.17em}\mid {u}_{o}{\mid}^{2}+\mid {u}_{r}{\mid}^{2}+\text{exp}(-i2\mathrm{\pi}\mathrm{\alpha}x)H(f)G(f){G}^{*}(f)\sum _{m=-\infty}^{\infty}\mathrm{\delta}(m\mathrm{\Delta}f)+\text{exp}(i2\mathrm{\pi}\mathrm{\alpha}x){H}^{*}(f){G}^{*}(f)G(f)\sum _{m=-\infty}^{\infty}\mathrm{\delta}(m\mathrm{\Delta}f),$$
(4)
$$I(m\mathrm{\Delta}f)=H(f)\mathbf{G}(f)\sum _{m=-\infty}^{\infty}\mathrm{\delta}(m\mathrm{\Delta}f),$$
(5)
$$I(l\mathrm{\Delta}t)=\left[h(t)*\mathbf{g}(t)*\sum _{k=-\infty}^{\infty}\mathrm{\delta}(k\mathrm{\Delta}T)\right]\sum _{l=-\infty}^{\infty}\mathrm{\delta}(l\mathrm{\Delta}t),$$