## Abstract

A major problem of optical microscopes is their small depth-of-field (DOF), which hinders automation of micro object manipulation using visual feedback. Wavefront coding, a well-known method for extending DOF, is not suitable for direct application to micro object manipulation systems based on visual feedback owing to its expensive computational cost and due to a trade-off between the DOF and the image resolution properties. To solve such inherent problems, a flexible DOF imaging system using a spatial light modulator in the pupil plane is proposed. Especially, the trade-off relationship is quantitatively analyzed by experiments. Experimental results show that,
for low criterion resolution, the DOF increases as the strength of the mask increases, while such a trend was not found for high criterion resolution. With high criterion resolution, the DOF decreases as the mask strength increases when high-resolution images are required. The results obtained can be used effectively to find the optimum mask strength given the desired image resolution.

© 2007 Optical Society of America

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### Equations (7)

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(1)
$$p\left({x}_{p},{y}_{p}\right)=\{\begin{array}{c}\mathrm{exp}\left[\mathit{i}\alpha \left({{{\displaystyle x}}_{p}}^{3}+{{{\displaystyle y}}_{p}}^{3}\right)\right]\\ 0\hfill \end{array}\text{, \hspace{1em}}\begin{array}{c}\text{for \hspace{0.17em}}\left|{x}_{p}\right|\le 1,\left|{y}_{p}\right|\le 1\\ \text{}\end{array}\mathrm{.}$$
(2)
$$M\left(u,\psi \right)=\{\begin{array}{cc}{\left(\frac{\pi}{12\left|\alpha u\right|}\right)}^{1/2}\text{\hspace{0.17em} \hspace{0.17em}exp}\left(i\text{\hspace{0.17em}}\frac{\alpha {u}^{3}}{4}\right)& \left|\alpha \right|\gg 20\text{\hspace{1em}}u\ne 0\\ 1\hfill & \text{\hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em} \hspace{0.17em}}u=0\end{array}\text{,}$$
(3)
$$F\left(\mu ,v\right)=\left[\frac{1}{H\left(\mu ,v\right)}\text{\hspace{0.17em}}\frac{{\left|H\left(\mu ,v\right)\right|}^{2}}{{\left|H\left(\mu ,v\right)\right|}^{2}+K}\right]G\left(\mu ,v\right)\text{,}$$
(4)
$$\{\begin{array}{c}H\left(\mu ,v\right)=\mathcal{F}\left\{h\left({x}_{i},{y}_{i}\right)\right\}\\ G\left(\mu ,v\right)=\mathcal{F}\left\{g\left({x}_{i},{y}_{i}\right)\right\}\\ F\left(\mu ,v\right)=\mathcal{F}\left\{f\left({x}_{i},{y}_{i}\right)\right\}\end{array}\text{,}$$
(5)
$$J\left(v\right)=c\text{\hspace{0.17em} exp}\left[-i\left({\varphi}_{o}+\beta \left(v\right)\right)\right]\times \left(\begin{array}{cc}f\left(v\right)-ig\left(v\right)& -h\left(v\right)-ij\left(v\right)\\ h\left(v\right)-ij\left(v\right)& f\left(v\right)+ig\left(v\right)\end{array}\right)$$
(6)
$$\left(\begin{array}{c}{x}_{\text{out}}\\ {y}_{\text{out}}\end{array}\right)=P\left({\theta}_{A}\right)JP\left({\theta}_{P}\right)\left(\begin{array}{c}{x}_{\text{in}}\\ {y}_{\text{in}}\end{array}\right)\text{,}$$
(7)
$$\text{Contrast \hspace{0.17em} Modulation}=\frac{{I}_{\text{max}}-{I}_{\text{min}}}{{I}_{\text{max}}+{I}_{\text{min}}}\text{.}$$