**3. Image based algorithms**

shortest path is a parabolic function, which is represented by the red line. Fig. 5 (top) shows the initial random pheromone distribution, while Fig. 5 (bottom) shows the pheromone dis‐

**Figure 5.** Implementation of an ant colony strategy for the optimization of a deformable mirror with 32 actuators and 8 bit control. The red curve represents the shortest (optimized) path. The top panel shows the initial random phero‐

The quality of an optical wavefront plays an important role in Spontaneous Down Conver‐ sion (SPDC) process. As demonstrated by [31] the use of a deformable mirror can enhance the generation of photon pairs acting on the wavefront before the generation takes place in the nonlinear crystal. In that system the optimization was carried out by the use of an elec‐

In the experiment, the pump beam is reflected by the DM to a BBO type-I nonlinear crystal. Then, the degenerate SPDC photons at 808 nm are selected and measured by a high efficien‐ cy SPADs (Single Photon Avalanche Diode). Since the wavefront has a strong effect on the downconverted light, it can strongly affect the coupling in the fibers of the SPAD detectors. The feedback for the algorithm imposed the condition of photon coincidences. It was dem‐ onstrated in the experiment that the coincidences rate was increased by about 20% when the optimization algorithm was applied. The algorithm used about 80 ants and the convergence

mone distribution while the bottom panel shows the pheromone at the end of the selection process.

trostatic DM (PAN, Adaptica srl) and the application of the ant colonies algorithm.

tribution at the end of the optimization process.

50 Adaptive Optics Progress

*2.2.1. Application example: Quantum optics*

took place in about 800 iterations.

Although the stochastic optimization algorithms have been demonstrated to represent im‐ portant tools for optical experiments, new techniques, which demonstrated to be more effec‐ tive, have recently been introduced. The use of a modal approach, based on the application of bias aberrations and of a suitable metrics, sorted out some of the limitations of the search algorithms, such as the long convergence time and the need of a training for the determina‐ tion of the algorithm parameters. This new approach demonstrated to be effective both in visual optics and in laser optimization, as described later in this section. The arbitrary gener‐ ation of aberrations can be achieved through the use of deformable mirrors, either thanks to a preliminary calibration of them or through the design of a suitable new class of wavefront correctors [32].
