## Abstract

In the past, aligning the counterpropagating beams in our 3D real-time generalized phase contrast (GPC) trapping system has been a task requiring moderate skills and prior experience with optical instrumentation. A ray transfer matrix analysis and computer-controlled actuation of mirrors, objective, and sample stage has made this process user friendly. The alignment procedure can now be done in a very short time with just a few drag-and-drop tasks in the user-interface. The future inclusion of an image recognition algorithm will allow the alignment process to be executed completely without any user interaction. An automated sample loading tray with a loading precision of a few microns has also been added to simplify the switching of samples under study. These enhancements have significantly reduced the level of skill and experience required to operate the system, thus making the GPC-based micromanipulation system more accessible to people with little or no technical expertise in optics.

© 2007 Optical Society of America

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### Equations (5)

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(1)
$$\left(\begin{array}{cc}1& {f}_{2}\\ 0& 1\end{array}\right)\left(\begin{array}{cc}1& 0\\ -\frac{1}{{f}_{2}}& 1\end{array}\right)\left(\begin{array}{cc}1& {f}_{1}+{f}_{2}\\ 0& 1\end{array}\right)\left(\begin{array}{cc}1& 0\\ -\frac{1}{{f}_{1}}& 1\end{array}\right)\left(\begin{array}{cc}1& {f}_{1}-a\\ 0& 1\end{array}\right)\left(\begin{array}{c}0\\ \theta \end{array}\right)=\left(\begin{array}{c}\frac{{\mathrm{af}}_{2\theta}}{{f}_{1}}\\ -\frac{{f}_{1\theta}}{{f}_{2}}\end{array}\right)$$
(2)
$$\left(\begin{array}{cc}1& {f}_{2}\\ 0& 1\end{array}\right)\left(\begin{array}{cc}1& 0\\ -\frac{1}{{f}_{2}}& 1\end{array}\right)\left(\begin{array}{cc}1& s+{f}_{2}\\ 0& 1\end{array}\right)\left(\begin{array}{c}0\\ \phi \end{array}\right)=\left(\begin{array}{c}{f}_{2}\phi \\ -\frac{s\phi}{{f}_{2}}\end{array}\right)$$
(3)
$$\left(\begin{array}{c}x\\ \psi \end{array}\right)=\left(\begin{array}{c}\frac{a{f}_{2}\theta}{{f}_{1}}\\ -\frac{{f}_{1}\theta \phantom{\rule{.2em}{0ex}}}{{f}_{2}}\end{array}\right)+\left(\begin{array}{c}{f}_{2}\phi \\ -\frac{s\phi}{{f}_{2}}\end{array}\right)$$
(4)
$$\theta \left(x\right)=\frac{-\mathrm{sx}{f}_{1}}{{f}_{2}\left({f}_{1}^{2}-\mathrm{sa}\right)},\phi \left(x\right)=\frac{{f}_{1}^{2}x}{{f}_{2}\left({f}_{1}^{2}-\mathrm{sa}\right)}$$
(5)
$$\theta \left(\psi \right)=\frac{\psi {f}_{2}{f}_{1}}{{f}_{1}^{2}+\mathrm{sa}},\phi \left(\psi \right)=\frac{\mathrm{a\psi}{f}_{2}}{{f}_{1}^{2}+\mathrm{sa}}$$