## Abstract

In a previous paper [J. S. Dam *et al*, Opt. Express **15**,
1923 (2007)] we demonstrated computerized “drag-and-drop” optical
alignment of a counter-propagating multi-beam based micromanipulation system. By
inclusion of image analysis, we report here on the extension of this work to
accommodate a completely automated beam-alignment process. Additionally, to maintain
a cost-effective and technically less demanding system architecture, we also report
on a computer-guided manual alignment procedure. In the manual version, the computer
analyzes the initial misalignment and the required compensations for each mirror in
the system are calculated. Subsequently, the user is guided in adjusting the mirrors
exactly by the requisite amount. This way, all mirrors only need to be moved once.
The image analysis utilized in both calibration schemes employs a fitting algorithm
to determine the position of beam-center with sub-pixel accuracy, thereby providing
“better than human” alignment.

© 2007 Optical Society of America

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### Equations (3)

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(1)
$$\left(\begin{array}{c}{\Delta x}_{A}\\ {\Delta y}_{A}\\ {\Delta u}_{A}\\ {\Delta v}_{A}\end{array}\right)=\left(\begin{array}{c}{x}_{A\phantom{\rule{.2em}{0ex}}\mathrm{displaced}}\\ {y}_{A\phantom{\rule{.2em}{0ex}}\mathrm{displaced}}\\ {u}_{A\phantom{\rule{.2em}{0ex}}\mathrm{displaced}}\\ {v}_{A\phantom{\rule{.2em}{0ex}}\mathrm{displaced}}\end{array}\right)-\left(\begin{array}{c}{x}_{\mathrm{initial}}\\ {y}_{\mathrm{initial}}\\ {u}_{\mathrm{initial}}\\ {v}_{\mathrm{initial}}\end{array}\right)$$
(2)
$$a\left(\begin{array}{c}{\Delta x}_{A}\\ {\Delta y}_{A}\\ {\Delta u}_{A}\\ {\Delta v}_{A}\\ \\ \\ \end{array}\right)+b\left(\begin{array}{c}{\Delta x}_{B}\\ {\Delta y}_{B}\\ {\Delta u}_{B}\\ {\Delta v}_{B}\\ \\ \\ \end{array}\right)+c\left(\begin{array}{c}{\Delta x}_{C}\\ {\Delta y}_{C}\\ {\Delta u}_{C}\\ {\Delta v}_{C}\\ \\ \\ \end{array}\right)+d\left(\begin{array}{c}{\Delta x}_{D}\\ {\Delta y}_{D}\\ {\Delta u}_{D}\\ {\Delta v}_{D}\\ \\ \\ \end{array}\right)=\left(\begin{array}{c}\Delta x\\ \Delta y\\ \Delta u\\ \Delta v\end{array}\right)$$
(3)
$$\left(\begin{array}{c}\Delta \tilde{u}\\ \Delta \tilde{v}\end{array}\right)=a\left(\begin{array}{c}{\Delta u}_{A}\\ {\Delta v}_{A}\end{array}\right)+b\left(\begin{array}{c}{\Delta u}_{B}\\ {\Delta v}_{B}\end{array}\right)=\left(\begin{array}{c}\Delta u\\ \Delta v\end{array}\right)-c\left(\begin{array}{c}{\Delta u}_{c}\\ {\Delta v}_{c}\end{array}\right)-d\left(\begin{array}{c}{\Delta u}_{c}\\ {\Delta v}_{c}\end{array}\right)$$