## Abstract

Methods of geometrical optics are used in deriving a simple expression for the focus error signal in terms of the parameters of an astigmatic system. The extent of validity of this result is then examined by comparison with diffraction calculations. Diffraction analysis also permits the study of push–pull tracking error signal from pregrooved disk surfaces.

© 1987 Optical Society of America

Full Article |

PDF Article
### Equations (7)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$d=\frac{2{f}_{1}{f}_{2}}{{f}_{1}+{f}_{2}},$$
(2)
$$\text{FES}=\frac{{h}^{2}-{w}^{2}}{{h}^{2}+{w}^{2}}$$
(3)
$$FES=\frac{2\alpha \left(1-\beta \Delta \right)\Delta}{1-2\beta \Delta +\left({\alpha}^{2}+{\beta}^{2}\right){\Delta}^{2}}.$$
(4)
$$\frac{d}{d\Delta}FES=\frac{2\alpha \left[1-2\beta \Delta -\left({\alpha}^{2}-{\beta}^{2}\right){\Delta}^{2}\right]}{{\left[1-2\beta \Delta +\left({\alpha}^{2}-{\beta}^{2}\right){\Delta}^{2}\right]}^{2}}.$$
(5)
$$\begin{array}{cc}{\Delta}_{n}=\frac{\beta \phantom{\rule{0.2em}{0ex}}+2\alpha \phantom{\rule{0.2em}{0ex}}cos\phantom{\rule{0.1em}{0ex}}\left(\left\{2n\pi \phantom{\rule{0.2em}{0ex}}+\phantom{\rule{0.2em}{0ex}}arccos\phantom{\rule{0.1em}{0ex}}\left[2\alpha \beta /\left({\alpha}^{2}\phantom{\rule{0.2em}{0ex}}+\phantom{\rule{0.2em}{0ex}}{\beta}^{2}\right)\right]\right\}/3\right)}{{\beta}^{2}-{\alpha}^{2}};& n=0,1,2.\end{array}$$
(6)
$$\text{FES}=\frac{\left({Q}_{1}+{Q}_{3}\right)-\left({Q}_{2}+{Q}_{4}\right)}{{Q}_{1}+{Q}_{2}+{Q}_{3}+{Q}_{4}},$$
(7)
$$\text{TES}=\frac{\left({Q}_{1}+{Q}_{2}\right)-\left({Q}_{3}+{Q}_{4}\right)}{{Q}_{1}+{Q}_{2}+{Q}_{3}+{Q}_{4}}.$$