## Abstract

The elliptical beam of a laser diode is collected by a circular aperture
decentered with respect to the beam. The fractional optical power collected is
calculated and measured as a function of the decentered distance, beam size,
and aperture size. The calculation results agree well with the measurement
results. An application example of the results is
described.

© 1997 Optical Society of America

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### Equations (3)

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(1)
$$I\left(x,y\right)={I}_{0}exp\left(-2\frac{{x}^{2}}{w_{x}{}^{2}}-2\frac{{y}^{2}}{w_{y}{}^{2}}\right),$$
(2)
$${P}_{t}={\int}_{-\infty}^{\infty}{\int}_{-\infty}^{\infty}I\left(x,y\right)\mathit{dxdy}=\frac{\mathrm{\pi}{w}_{x}{w}_{y}{I}_{0}}{2}.$$
(3)
$$\frac{P}{{P}_{t}}=\frac{2}{\mathrm{\pi}{w}_{x}{w}_{y}}{\int}_{x={x}_{0}-a}^{x={x}_{0}+a}{\int}_{y={y}_{0}-\sqrt{{a}^{2}-{\left(x-{x}_{0}\right)}^{2}}}^{y={y}_{0}+\sqrt{{a}^{2}-{\left(x-{x}_{0}\right)}^{2}}}\times exp\left(-2\frac{{x}^{2}}{w_{x}{}^{2}}-2\frac{{y}^{2}}{w_{y}{}^{2}}\right)\mathit{dxdy},$$