## Abstract

The requirements and limitations on the use of a volume holographic
element for the simultaneous optical stamping of multilayer data into a
three-dimensional (3D) bit-oriented material that exhibits a
suitable sensitivity threshold are investigated. The expected
performance of such a holographic stamping element is examined through
a model of the coherent noise effects that result from the interference
of the many data layers with one another. We show that higher
signal-to-noise values may be achieved through the use of semicoherent
light during the readout of the hologram. The main limitations to
this technique arise from the bandwidth requirements on the holographic
element, the degree of nonlinearity required of the bit-oriented media,
and the tolerance requirements for the optical exposure levels. As
a demonstration of the concept, a two-layer stamping element is
fabricated and used to simultaneously stamp two layers of data into a
3D dye-doped photopolymer storage medium.

© 2000 Optical Society of America

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### Equations (9)

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(1)
$${p}_{\mathrm{signal}}\left(I\right)=\left\{\begin{array}{ll}\left(\frac{1}{2{\mathrm{\sigma}}^{2}}\right)exp\left(-\frac{I+{s}^{2}}{2{\mathrm{\sigma}}^{2}}\right){I}_{0}\left(\frac{s\sqrt{I}}{{\mathrm{\sigma}}^{2}}\right)& \mathrm{for}I\ge 0\\ 0& \mathrm{for}I0\end{array}\right.,$$
(2)
$${p}_{\mathrm{background}}\left(I\right)=\left\{\begin{array}{ll}\left(\frac{1}{2{\mathrm{\sigma}}^{2}}\right)exp\left(-\frac{I}{2{\mathrm{\sigma}}^{2}}\right)& \mathrm{for}I\ge 0\\ 0& \mathrm{for}I0\end{array}\right.,$$
(3)
$${M}_{\mathrm{signal}}\left(\mathrm{\omega}\right)=\mathcal{F}\left\{{p}_{\mathrm{signal}}\left(I\right)\right\}=\frac{jexp\left(-\frac{{s}^{2}\mathrm{\omega}}{j+2{\mathrm{\sigma}}^{2}\mathrm{\omega}}\right)}{j+2{\mathrm{\sigma}}^{2}\mathrm{\omega}}.$$
(4)
$${M}_{\mathrm{background}}\left(\mathrm{\omega}\right)=\frac{1}{1-2j\mathrm{\omega}{\mathrm{\sigma}}^{2}}.$$
(5)
$${p}_{\mathrm{on}}\left(I\right)={\mathcal{F}}^{-1}\left\{{M}_{\mathrm{signal}}{\left(\mathrm{\omega}\right)}^{m}\right\},$$
(6)
$${p}_{\mathrm{off}}\left(I\right)={\mathcal{F}}^{-1}\left\{{M}_{\mathrm{background}}{\left(\mathrm{\omega}\right)}^{m}\right\}.$$
(7)
$$\mathrm{SNR}=\frac{{\overline{I}}_{1}-{\overline{I}}_{0}}{{\left(\mathrm{\sigma}_{1}{}^{2}+\mathrm{\sigma}_{0}{}^{2}\right)}^{1/2}},$$
(8)
$${p}_{\mathrm{on}}\left(I\right)={\mathcal{F}}^{-1}\left\{{M}_{\mathrm{background}}{\left(\mathrm{\omega}\right)}^{m\left(n-1\right)}exp{\left(j\mathrm{\omega}{s}^{2}\right)}^{m}\right\}.$$
(9)
$${p}_{\mathrm{off}}\left(I\right)={\mathcal{F}}^{-1}\left\{{M}_{\mathrm{background}}{\left(\mathrm{\omega}\right)}^{m\left(n-1\right)}\right\}.$$