## Abstract

Although widely recognized as a promising candidate for the next generation of data storage devices, holographic data storage systems (HDSS) incur adverse effects such as noise, misalignment, and aberration. Therefore, based on the structural similarity (SSIM) concept, this work presents a more accurate locating approach than the gray level weighting method (GLWM). Three case studies demonstrate the effectiveness of the proposed approach. Case 1 focuses on achieving a high performance of a Fourier lens in HDSS, Cases 2 and 3 replace the Fourier lens with a normal lens to decrease the quality of the HDSS, and Case 3 demonstrates the feasibility of a defocus system in the worst-case scenario. Moreover, the bit error rate (BER) is evaluated in several average matrices extended from the located position. Experimental results demonstrate that the proposed SSIM method renders a more accurate centering and a lower BER, lower BER of 2 dB than those of the GLWM in Cases 1 and 2, and BER of 1.5 dB in Case 3.

© 2012 Optical Society of America

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### Equations (12)

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(1)
$$\text{SSIM}(r,t)=\frac{(2{\mu}_{r}{\mu}_{t}+{C}_{1})}{({\mu}_{r}^{2}+{\mu}_{t}^{2}+{C}_{1})}\times \frac{(2{\sigma}_{\mathrm{rt}}+{C}_{2})}{({\sigma}_{r}^{2}+{\sigma}_{t}^{2}+{C}_{2})},$$
(2)
$$\text{BER}={p}_{0}\times p(1|0)+{p}_{1}\times p(0|1),$$
(3)
$$\text{SNR}=\frac{{\mu}_{0}+{\mu}_{1}}{{({\sigma}_{0}^{2}+{\sigma}_{1}^{2})}^{1/2}},$$
(4)
$${\sigma}_{t}^{2}=[{a}_{t0}({\sigma}_{t0}^{2}+{\mu}_{t0}^{2})+{a}_{t1}({\sigma}_{t1}^{2}+{\mu}_{t1}^{2})]-{[{a}_{t0}{\mu}_{t0}+{a}_{t1}{\mu}_{t1}]}^{2}={a}_{t0}({\sigma}_{t0}^{2}+{\mu}_{t0}^{2}-{a}_{t0}{\mu}_{t0}^{2})+{a}_{t1}({\sigma}_{t1}^{2}+{\mu}_{t1}^{2}-{a}_{t1}{\mu}_{t1}^{2})-2{a}_{t0}{\mu}_{t0}{a}_{t1}{\mu}_{t1},$$
(5)
$${\sigma}_{r}^{2}={a}_{r0}({\sigma}_{r0}^{2}+{\mu}_{r0}^{2}-{a}_{r0}{\mu}_{r0}^{2})+{a}_{r1}({\sigma}_{r1}^{2}+{\mu}_{r1}^{2}-{a}_{r1}{\mu}_{r1}^{2})-2{a}_{r0}{\mu}_{r0}{a}_{r1}{\mu}_{r1},$$
(6)
$${\sigma}_{\mathrm{rt}}=\frac{1}{(N-1)}\sum _{x,y=1}^{N}({\text{Gray}}_{r}(x,y)-{\mu}_{r})\times ({\text{Gray}}_{t}(x,y)-{\mu}_{t})\phantom{\rule{0ex}{0ex}}=\frac{1}{(N-1)}\sum _{x,y=1}^{N}{\text{Gray}}_{r}(x,y)\times {\text{Gray}}_{t}(x,y)-N{\mu}_{r}{\mu}_{t},$$
(7)
$${\mu}_{r}=\frac{1}{{N}^{2}}\sum _{i,j=1}^{N}{\text{Gray}}_{r}(i,j),$$
(8)
$${\mu}_{t}=\frac{1}{{N}^{2}}\sum _{i,j=1}^{N}{\text{Gray}}_{t}(i,j),$$
(9)
$${\sigma}_{t}^{2}=\frac{1}{{(N-1)}^{2}}\sum _{i,j=1}^{N}{[{\text{Gray}}_{t}(i,j)-{\mu}_{t}]}^{2},$$
(10)
$${\sigma}_{r}^{2}=\frac{1}{{(N-1)}^{2}}\sum _{i,j=1}^{N}{[{\text{Gray}}_{r}(i,j)-{\mu}_{r}]}^{2},$$
(11)
$${\sigma}_{\mathrm{rt}}=\frac{1}{N-1}\sum _{i,j=1}^{N}[{\text{Gray}}_{r}(i,j)-{\mu}_{r}]\times [{\text{Gray}}_{t}(i,j)-{\mu}_{t}],$$
(12)
$$\frac{\partial \text{SSIM}}{\partial {\mu}_{r}}=\frac{{B}^{\prime}A-{A}^{\prime}B}{{[({\mu}_{t}^{2}+{\mu}_{r}^{2}+{C}_{1})({\sigma}_{t}^{2}+{\sigma}_{r}^{2}+{C}_{2})]}^{2}},A=(2{\mu}_{t}{\mu}_{r}+{C}_{1})(2{\sigma}_{tr}+{C}_{2}),B=({\mu}_{t}^{2}+{\mu}_{r}^{2}+{C}_{1})({\sigma}_{t}^{2}+{\sigma}_{r}^{2}+{C}_{2}),{A}^{\prime}=2{\mu}_{t}(2{\sigma}_{\mathrm{tr}}+{C}_{2})+(2{\mu}_{t}{\mu}_{r}+{C}_{1})[\frac{2}{N-1}\sum _{x,y=1}^{N}-({\text{Gray}}_{t}(x,y)-{\mu}_{t})],{B}^{\prime}=2{\mu}_{r}({\sigma}_{t}^{2}+{\sigma}_{r}^{2}+{C}_{2})+({\mu}_{t}^{2}+{\mu}_{r}^{2}+{C}_{1})[\frac{2}{{(N-1)}^{2}}\sum _{x,y=1}^{N}-({\text{Gray}}_{r}(x,y)-{\mu}_{r})],$$