## Abstract

A new scalar diffraction modeling method for simulating the readout signal
of optical disks is described. The information layer is discretized into pixels
that are grouped in specific ways to form written and unwritten areas. A set
of 2D wave functions resulting from these pixels at the detection
aperture is established. A readout signal is obtained via the assembly of
wave functions from this set according to the content under the scanning
spot. The method allows efficient simulation of jitter noise due to edge
deformation of recorded marks, which is important at high densities. It is also
capable of simulating a physically irregular mark, thereby helping to understand
and optimize the recording process.

© 2007 Optical Society of America

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### Equations (14)

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(1)
$$\mathit{I}\left({R}_{p}\right)={\displaystyle {\int}_{\text{CA}}{\left|\tilde{q}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p}\right)\right|}^{2}\mathrm{d}\mathbf{\Omega}}={\displaystyle {\int}_{\text{CA}}{\left|{\text{FT}}_{R\to \mathbf{\Omega}}\left[p\left(R-{R}_{p}\right)r\left(R\right)\right]\right|}^{2}\mathrm{d}\mathbf{\Omega}},$$
(2)
$$r\left(R\right)=1+{\displaystyle \sum _{\mathbf{k}\in \mathcal{P}}{m}_{\mathbf{k}}\delta \left(R-{R}_{k}\right)},$$
(3)
$${m}_{k}={a}_{k}\text{\hspace{0.17em}}\mathrm{exp}\left(j{\varphi}_{k}\right)-1\text{,}\phantom{\rule[-0.0ex]{0.8em}{0.0ex}}0<{a}_{k}\le 1.$$
(4)
$$\tilde{q}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p}\right)=\tilde{p}\left(\mathbf{\Omega}\mathrm{;}\text{\hspace{0.17em}}{R}_{p}\right)+{\displaystyle \sum _{\mathbf{k}\in \mathcal{P}}{m}_{\mathbf{k}}\tilde{s}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p};\text{\hspace{0.17em}}{R}_{k}\right)},$$
(5)
$$\text{\hspace{0.17em}}\tilde{p}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p}\right)={\text{FT}}_{R\to \mathbf{\Omega}}\left[p\left(R-{R}_{p}\right)\right],$$
(6)
$$\tilde{s}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p};\text{\hspace{0.17em}}{R}_{k}\right)={\text{FT}}_{R\to \mathbf{\Omega}}\left[p\left(R-{R}_{p}\right)\delta \left(R-{R}_{k}\right)\right].$$
(7)
$$\tilde{s}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{\mathbf{R}}_{p};\text{\hspace{0.17em}}{\mathbf{R}}_{k}\right)={\displaystyle \int \mathrm{exp}\left(-j2\pi \mathbf{\Omega}\mathbf{R}\right)p\left(\mathbf{R}-{\mathbf{R}}_{p}\right)\delta \left(\mathbf{R}-{\mathbf{R}}_{k}\right)\mathrm{d}\mathbf{R}=\mathrm{exp}\left(-j2\pi \mathbf{\Omega}{\mathbf{R}}_{k}\right)p\left({\mathbf{R}}_{k}-{\mathbf{R}}_{p}\right)},$$
(8)
$${N}_{\text{pix}}={\lceil \alpha \text{\hspace{0.17em}}\frac{1.22\lambda}{\text{NA}}/d\rceil}^{2},$$
(9)
$${N}_{\text{freq}}={\lfloor \frac{2\text{NA}}{\lambda}\text{\hspace{0.17em}}dL+0.5\rfloor}^{2},$$
(10)
$$\Vert \mathbf{\Omega}\Vert \le \left(\text{NA}/\lambda \right),$$
(11)
$$\tilde{c}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p};\text{\hspace{0.17em}}{R}_{\mathbf{l}}\right)={\displaystyle \sum _{k\in {\mathcal{P}}_{l}\u2033}\tilde{s}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p};\text{\hspace{0.17em}}{R}_{l}\right)}\text{,}$$
(12)
$$\tilde{w}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p};\text{\hspace{0.17em}}{R}_{i}\right)={\displaystyle \sum _{k\in {\mathcal{P}}_{i}\u2034}\tilde{s}\left(\mathbf{\Omega};\text{\hspace{0.17em}}{R}_{p};\text{\hspace{0.17em}}{R}_{k}\right)}\text{,}$$
(13)
$$r\left(\mathbf{R}\right)=1+[a\text{\hspace{0.17em}}\mathrm{exp}\left(j\varphi \right)-1][\sum _{\mathbf{i}\in \widehat{\mathcal{B}}}W(\mathbf{R}-{\mathbf{R}}_{\mathbf{i}})+\sum _{\mathbf{l}\in \widehat{\mathcal{C}}}C(\mathbf{R}-{\mathbf{R}}_{\mathbf{l}})+\sum _{\mathbf{k}\in \widehat{\mathcal{P}}}\delta (\mathbf{R}-{\mathbf{R}}_{\mathbf{k}}\left)\right]\text{,}$$
(14)
$$\text{SNR}=20\text{\hspace{0.17em}}\mathrm{log}\text{\hspace{0.17em}}\frac{{\displaystyle \sum {\left({I}_{n}-{I}_{n}*\right)}^{2}}}{{\displaystyle \sum {({I}_{n}*)}^{2}}}\text{,}$$