**1. Introduction**

Minimizing the aberrations is the basic concern of all the optical system designers. For this purpose, a large amount of work has been carried out and plenty of literature can be found on the subject. Until the last twenty years, the large majority of the optical design was relat‐ ed to "static" optical systems, where several opto-mechanical parameters, such as refractive index, shape, curvatures, etc. are slowly time dependent. In these systems, simple mecha‐ nisms can be adopted to change the relative position of one or more optical elements (for example, the secondary mirror of many astronomical telescopes), or slightly modify their shape and curvature (as in some synchrotron beamlines, where some optical surfaces are mechanically bent) to compensate defocusing. In the last years, a new type of optical sys‐ tems, that we may call "dynamical", have heavily occupied the interest of optical designers, opening the possibility of working also in situations where the system environment varies rather quickly with time, either in a controlled or not-controlled way. For this class of optical systems adaptive optics (AO) with a closed loop control system has to be implemented. The correction of dynamical systems was predicted by Babcock in the 1953 [1] and, then, the first prototypes were realized in the early 70s with the purpose of satellite surveillance and launching high power laser beams trough the atmosphere [2]. The most known scientific ap‐ plications of closed loop correction by means of AO is the acquisition of astronomical im‐ ages in ground-based telescopes [3] and *in-vivo* imaging of cone photoreceptor mosaic by AO enhanced Fundus Cameras [4]. In astronomy, to remove the so called "seeing effect", the star light twinkling due to local dynamic variations of the atmospheric density in the air column above the telescope, it is necessary to have the real time knowledge of the wavefront of the observed object. This can be realized, for instance, by means of a Shack-Hartmann wavefront sensing device coupled to a dedicated fast algorithm which returns the mathe‐ matical description of the wavefront aberration, typically through a Zernike series decompo‐

© 2013 Bonora et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Bonora et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

sition [5]. Then, this information is suitably coded and passed to an AO, as a fast deformable mirror located along the optical path, that adapts its shape to compensate the time depend‐ ent aberrations. Similarly in vision science [6, 7] or retinal imaging [8-15], static and dynamic aberrations created by variation in shape of eye refractive elements and eye movements are measured by wavefront sensor, usually Schack-Hartmann and corrected by wavefront cor‐ rector, in most cases a deformable mirror. Other applications which make use of AO sys‐ tems are for example: free space optical communication systems [16, 17], microscopy [18-20] or beam shaping in laser applications [21]. It is, however, rather obvious that not all AO ap‐ plications have similar needs, and in particular that in some cases systems simpler than the astronomical ones can be realized. For example, in some cases there is no need to have the real time information about the aberrated wavefront: either because the aberration variation is slow [22] or because there is a specific phase which remains for a limited amount of time, as for example when correcting low order ocular aberrations "eyeglass prescription"for pa‐ tient in ophthalmic diagnostics, or in optical devices in which the environmental conditions are not initially defined but the system remains stable in time [23-25]. In all these cases it can be convenient to have a simpler AO system, able to correct only the slow variations of the wavefront aberrations.

explain in detail the genetic algorithm and the ant colonies optimization process, while pro‐

Devices and Techniques for Sensorless Adaptive Optics

http://dx.doi.org/10.5772/53550

45

The image-based algorithms will be explained in section 3, together with a few examples of recently reported successful applications in optical experiments. New devices useful to gen‐

A genetic algorithm [30] searches the solution of a problem by simulating the evolution process. Starting from a population of possible solutions, it saves some of the strongest ele‐ ments, that are the only ones selected to survive, and, thus, are able to reproduce themselves giving rise to the next generations. In general, the inferior individuals can survive and re‐

This strategy allows solving a large class of problems without any initial hypothesis or pre‐ liminary knowledge. Its effectiveness was demonstrated in many experimental setups, as

The initial population is chosen randomly in the whole set of possible solutions. The selec‐ tion function can be either probabilistic or deterministic. In the probabilistic case, the stron‐ gest elements have more chances of being selected and of reproducing to the next

The reproduction function creates new individuals from the old population. There are two

*CrossOver* functions: they mix the genes of the two parents by slightly modifying them and

generation. This decreases the possibility of falling in a "local" maximum solution.

The main steps of a genetic algorithm are depicted in Table 1 and in Fig. 1.

viding a few examples of their application in optical experimental setups.

erate the bias aberrations will also be presented.

**2.1. Genetic algorithm**

produce with a smaller probability.

will be discussed in the following paragraphs.

**Table 1.** Main steps required by a genetic algorithm.

kinds of functions: crossover and mutations.

by obtaining two sons.

**2. Stochastic algorithms for sensorless correction**

In the above mentioned cases the wavefront correction can be operated with a strong re‐ duction in the hardware complexity, in particular by using a sensorless approach. Sever‐ al techniques have been developed which use these simpler AO systems. They are generally based on the optimization of some merit function that depends on the optical system under consideration.

The algorithms for the sensorless correction can be divided into two main classes: the stochastic and the image-based ones. In the first class, the system is optimized starting from a random set and, then, applying an iterative selection of the best solutions. These algorithms have the advantage of not requiring any preliminary information about the system but they take a lot of time for converging. Many algorithms using this approach have been written and exploited successfully in different fields. Among them the most popular are: genetic algorithms [18, 26, 24], simulated annealing [13], simplex or ant col‐ onies [27]. These approaches have the drawback of requiring a rather long computation time, or many iterations before converging, taking up to several minutes before reaching the desired system optimization.

Other sensorless techniques can be realized by analyzing some specific known feature, ei‐ ther intrinsic to the system or artificially introduced. An example of the latter case can be found in [28-29]. With respect to classical AO systems, the sensorless approach offers the ad‐ vantage of not needing the wavefront sensor: this reduces the cost of the instrument and avoids all the problems related to maintaining the performance of such a device once instal‐ led and aligned. However, the absence of the wavefront sensor implies also some limita‐ tions, for instance, a much longer time before reaching an optimal image quality, or a final image not perfectly optimized. Clearly, the required final result and the available resources are the key elements driving the choice towards one system or another. In section 2, we will explain in detail the genetic algorithm and the ant colonies optimization process, while pro‐ viding a few examples of their application in optical experimental setups.

The image-based algorithms will be explained in section 3, together with a few examples of recently reported successful applications in optical experiments. New devices useful to gen‐ erate the bias aberrations will also be presented.
