**2. Digital adaptive optics**

### **2.1. General approach**

**1.2. Limitations of conventional adaptive optics**

ceed the rate of aberration changes.

compensation.

126 Adaptive Optics Progress

profile *Cn*

2

**1.3. Anisoplanatism**

Performance of AO systems is limited by a number of factors among which wavefront cor‐ rectors performance have a strong impact. First, WFC's have a limited number of degreesof-freedom. For example, the number of control channels of a deformable mirror seldom exceeds a few tens across its aperture. This limitation affects the spatial scale of the wave‐ front features the WFC can compensate and prevents the system from mitigating high-order aberrations (i.e. aberrations with small spatial features). This constrain is especially critical for optical systems with aperture diameter *D*≫*r* 0, where *r* 0 is the Fried parameter [4]. An‐ other restrictive feature of WFC's is the limited amplitude of the wavefront phase they can compensate. This limitation prevents in parts conventional AO systems to be effective under strong (deep) turbulence conditions, which are typical for optical systems operating over long and/or near-horizontal (slant) atmospheric propagation paths. Finally, the limited tem‐ poral response of WFC's may prevent them from providing compensation at rates that ex‐

Although technological developments have been providing WFC's with higher spatial reso‐ lution, increased dynamical range and bandwidth, an effect known as anisoplanatism which is reviewed briefly in the next section remains a fundamental limitation for adaptive optics

Conventional AO systems typically require a reference beam (guide star) that is used to probe the atmospheric turbulence and provide an optical signal to the WFS [5]. However, the light arising from different directions within the scene does not experience the same at‐ mospheric turbulence aberrations (propagation through volume turbulence) [6]. This causes AO performance to vary spatially across the field-of-view (FOV) with best image quality achieved for directions near the reference beam and over a small angular subtense in the or‐ der of the isoplanatic angle *θ*<sup>0</sup> [7]. The isoplanatic angle depends on the turbulence strength

*λ* 6/5

where *θz* is the Zenith angle of observation and *λ* is the wavelength [4]. Even under condi‐ tions of weak turbulence *θ*0 is usually small and remains in the order of a few microradians to a few tens of microradians. The isoplanatic angle is especially narrow for near-ground

natism degrades the performance of AO systems as the angular separation *θ* (known as

A number of techniques have been developed to mitigate the effect of anisoplanatism such as using multiple WFS's and WFC's located in optical conjugates of planes at various distan‐

*dz* 3/5 , (1)

<sup>2</sup> values). Anisopla‐

(*z*) where *z* is the altitude, and is given by

*<sup>θ</sup>*<sup>0</sup> <sup>=</sup> 58.1 <sup>×</sup> <sup>10</sup>-3

and near-horizontal propagation paths (i.e. high and nearly constant *Cn*

field angle) between the reference beam and points on the object increases [8].

(sec *θ<sup>z</sup>* )8/3*∫* 0 *<sup>L</sup> Cn* 2(*z*)*z* 5/3 The notional schematic in Figure 1 shows the sequential steps required for obtaining a com‐ pensated image using the digital adaptive optics approach. Two major steps of the process are as follow:
