Fig. 4.

The golden section search algorithm for automatic focus tuning. $z_1$ and $z_2$ are the two initial boundaries of the search region. Two extra intensities ($I\left(z_3\right) \mathrm{and} I(z_4)$) at the golden ratio distance from the initial boundaries are then calculated based on the intensities at the two boundaries. The search region is narrowed down by comparing$I\left(z_2\right)$ and $I(z_4)$. The boundaries of the search region are updated according to the values at $z_3$ and $z_4$ . The values of $z_3$ and $z_4$ are then the replaced by the values of $z_3^{\prime }$ and $z_4^{\prime }$ accordingly. This process is repeated until the difference between $I\left(z_2\right)$ and $I(z_4)$ is smaller than a pre-defined threshold.