## Abstract

We describe some basic optical image-processing operations with
acousto-optic (AO) Bragg diffraction. Instead of using frequency-plane
filters, we place an AO cell behind the object. We then realize experimentally
one-dimensional edge enhancement, which utilizes a high-pass filtering effect
in the undiffracted order from the AO cell. A numerical simulation compares
well with the experimental results. With two AO cells oriented orthogonally to
each other, a second-order mixed derivative operation, evident from the
four-corner enhancement of a square, is also
demonstrated.

© 1997 Optical Society of America

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### Equations (4)

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(1)
$${H}_{0}\left({k}_{x}\right)=exp\left[j\left(\frac{k_{x}{}^{2}L}{2{k}_{0}}-\frac{{k}_{x}Q{\mathrm{\Lambda}}_{0}}{4\mathrm{\pi}}\right)\right]\left\{cos{\left[{\left(\frac{{k}_{x}Q{\mathrm{\Lambda}}_{0}}{4\mathrm{\pi}}\right)}^{2}+{\left(\frac{\mathrm{\alpha}}{2}\right)}^{2}\right]}^{1/2}+\left(\frac{{\mathit{jk}}_{x}Q{\mathrm{\Lambda}}_{0}}{4\mathrm{\pi}}\right)\frac{sin{\left[{\left({k}_{x}Q{\mathrm{\Lambda}}_{0}/4\mathrm{\pi}\right)}^{2}+{\left(\mathrm{\alpha}/2\right)}^{2}\right]}^{1/2}}{{\left[{\left({k}_{x}Q{\mathrm{\Lambda}}_{0}/4\mathrm{\pi}\right)}^{2}+{\left(\mathrm{\alpha}/2\right)}^{2}\right]}^{1/2}}\right\},$$
(2)
$${H}_{1}\left({k}_{x}\right)=exp\left[j\left(\frac{k_{x}{}^{2}L}{2{k}_{0}}-\frac{{k}_{x}\mathit{Q}{\mathrm{\Lambda}}_{0}}{4\mathrm{\pi}}\right)\right]\times \left(-j\frac{\mathrm{\alpha}}{2}\right)\frac{sin{\left[{\left({k}_{x}Q{\mathrm{\Lambda}}_{0}/4\mathrm{\pi}\right)}^{2}+{\left(\mathrm{\alpha}/2\right)}^{2}\right]}^{1/2}}{{\left[{\left({k}_{x}Q{\mathrm{\Lambda}}_{0}/4\mathrm{\pi}\right)}^{2}+{\left(\mathrm{\alpha}/2\right)}^{2}\right]}^{1/2}},$$
(3)
$${E}_{1}\left(x,y\right)=\left({A}_{1}+{B}_{1}\partial /\partial x\right)t\left(x,y\right),$$
(4)
$${E}_{2}\left(x,y\right)=\left({A}_{2}+{B}_{2}\partial /\partial y\right){E}_{1}\left(x,y\right)\approx {B}_{1}{B}_{2}{\partial}^{2}/\partial y\partial x\left[t\left(x,y\right)\right],$$