**3. Performance analysis**

In this section performance of DAO systems is analyzed using a numerical simulation and results for various system configurations and turbulence strengths are discussed.

#### **3.1. Numerical model**

channels of the DWFC. The corrector phase function *φDAO*(**r**) is then applied to the complex field amplitude *A*(**r**) provided by the CFS and results in compensated field

The compensated field *ADAO*(**r**) in Eq. (6) is used for synthesis of the DAO compensat‐ ed image *IDAO*(**r**). The DAO image is computed using the Fresnel approximation as

> *k* <sup>2</sup> ( <sup>|</sup>**r'**|2

where *k* is the wave number, *F* is the focal length of the digital lens and *<sup>L</sup> <sup>i</sup>* =(1 / *<sup>F</sup>* - <sup>1</sup> / *<sup>L</sup>* )-1

the distance between the digital lens plane and the image plane. The term *L* denotes the

The quality of the synthesized image *IDAO*(**r**) in Eq. (7) depends on the command vector **a** applied to the digital WFC [Eq. (5)]. Vector **a** can be considered as a parameter controlling the quality of image *IDAO*(**r**). Improving image quality in the region Ω *<sup>j</sup>* can be achieved by

(**r**)*d* **r**

*<sup>F</sup>* - <sup>|</sup>**<sup>r</sup>** - **r'**|2 *L i*

) *<sup>d</sup>***r'**|<sup>2</sup>

(**r**)*<sup>d</sup>* **<sup>r</sup>** , (8)

[see Eq. (4)]. Note that although the intensi‐

for *k* =1, …, *NDAO*, (9)

can be achieved using various numerical techniques. We con‐

, (7)

is

*ADAO*(**r**)= *A*(**r**)exp - *jφDAO*(**r**) . (6)

*ADAO*(**r**) given by

132 Adaptive Optics Progress

**Step 2: Image synthesis**

*IDAO*(**r**)=| <sup>1</sup>

*<sup>λ</sup><sup>Z</sup> ∫* -*∞*

distance between the lens and the object plane of interest.

**Step 3: Local image quality metric computation**

optimizing a sharpness metric *J*Ω<sup>j</sup>

**Step 4: Image quality metric optimization**

*ak* (*n*+1) =*ak* (*n*) + *γ* (*n*)

Optimization of metrics *J*<sup>Ω</sup> *<sup>j</sup>*

<sup>+</sup>*<sup>∞</sup>ADAO*(**r'**)exp - *<sup>j</sup>*

given by

*∫I DAO* <sup>2</sup> (**r**)*M*<sup>Ω</sup> *<sup>j</sup>*

*<sup>∫</sup><sup>I</sup> DAO* (**r**)*M*<sup>Ω</sup> *<sup>j</sup>*

ty-squared sharpness metric is commonly used, other criteria could be used to assess image

sider for example metric optimization based on the stochastic parallel gradient descent (SPGD) control algorithm [40]. In accordance with this algorithm command vector **a** update

*J*Ω *j* (**a**)=

quality such as a gradient-based metric or the Tenengrad criterion.

(**r**) is the function defining region Ω *<sup>j</sup>*

rule is given at each iteration *n* by the following procedure:

*δJ*<sup>Ω</sup> *<sup>j</sup>* (*n*) *δak* (*n*)

follows [25]:

Where *M*<sup>Ω</sup> *<sup>j</sup>*

Performance was evaluated from an ensemble of digitally-generated random complex-fields used as input optical waves to the DAO system. For each realization of the input field the complex amplitude in the DAO system pupil plane *Ain*(*r*) (see Fig. 1) was obtained using the conventional split-operator approach for simulating wave optics propagation through a vol‐ ume of atmospheric turbulence [41]. At the beginning of the propagation path (*z* =0) we used a monochromatic optical field with complex amplitude *Aprop*(**r**, *z* =0)= *Iobj* 1/2(**r**)exp *<sup>j</sup>φsurf* (**r**) , where *Iobj* (**r**) is the intensity distribution of the object be‐ ing imaged and *φsurf* (**r**) is a random phase function uniformly distributed in - *π*, *π* and *δ*correlated in space. The term *φsurf* (**r**) is used to model the "optically rough" surface of the object. The optical field complex amplitude at the end of the propagation path (*z* = *L* ) was utilized as the DAO system input field: *Ain*(**r**)= *Aprop*(**r**, *z* = *L* ). Optical inhomogeneities along the propagation path were modeled with a set of 10 thin random phase screens correspond‐ ing to the Kolmogorov turbulence power spectrum. We considered a horizontal propagation scenario so the phase screens were equally spaced along the propagation path and their im‐ pact (i.e. turbulence strength) was characterized by a constant ratio *D* /*r*0 where *D* is the di‐ ameter of the DAO system aperture and *r*0 is the characteristic Fried parameter for plane waves. By modifying ratio *D* /*r*0 one can control the strength of input field phase aberra‐ tions. In the numerical simulations, *D* /*r*0 ranged from zero (i.e. free-space propagation) to 10. Figures 3(a)-3(d) show examples of the input field intensity and phase distributions that are obtained using the technique described above for *D* /*r*<sup>0</sup> =4 [(a) and (b)] and for *D* /*r*<sup>0</sup> =8 [(c) and (d)]. Note that the phase distributions in Figs. 3(b) and 3(d) contain phase disconti‐ nuities (branch points). Images were obtained for a propagation distance *L* =0.05*L diff* where *<sup>L</sup> diff* <sup>=</sup>*k*(*<sup>D</sup>* / 2)2 is the diffractive distance, *k* =2*π* / *λ* is the wave number, and *λ* is the imaging wavelength.

The strength of the input field intensity scintillations was characterized by the apertureaveraged scintillation index *σ<sup>I</sup>* 2 given by

$$\left| \sigma\_{I} \right|^{2} = \frac{1}{S} \text{f} \left| \frac{\left\{ \int\_{I} I(\mathbf{r}) \right\}^{\*} }{\left\{ I(\mathbf{r}) \right\}^{2}} - 1 \right| d^{\text{-}2} \mathbf{r}, \tag{11}$$

**Figure 3.** Intensity (left column) and phase (right column) distributions of the computer-generated complex field *Ain*(**r**) used as input of the DAO system for *D* / *r*<sup>0</sup> =4 [(a),(b)] and *D* / *r*<sup>0</sup> =8 [(c),(d)]. Phase distributions are shown in a 2π

The quality of the DAO-compensated image *IDAO*(**r**) is assessed using a sharpness metric

Where *Idl*(**r**) is the image that would be obtained in the absence of atmospheric turbulence (i.e. diffraction-limited image). In the case of an ideal compensation the turbulence-induced

In this section we analyze results of image synthesis and compensation using the DAO ap‐ proach described in section 2 using the numerical model presented in section 3.1. In order to illustrate the effect of anisoplanatism we first consider DAO performance over an image re‐

region Ω (anisoplanatic conditions). Figure 4 shows intensity distribution *IDAO*(**r**) and cross-

that is nearly isoplanatic in size. Later we consider processing of the entire image

2(**r**)*<sup>d</sup>* **<sup>r</sup>** , (12)

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135

*<sup>J</sup>* <sup>=</sup> *<sup>∫</sup><sup>I</sup> DAO* <sup>2</sup> (**r**)*<sup>d</sup>* **<sup>r</sup>** *∫Idl*

wavefront aberrations are fully corrected by the DWFC [*φDAO*(**r**)=*φturb*(**r**)] and *J* =1.

range [between –π (black) and +π (white)].

**3.2. DAO system performance**

defined as

gion Ω *<sup>j</sup>*

where *I*(**r**)=|*Ain*(**r**)|2 and *S* is the aperture area of the DAO system. Here < > denotes aver‐ aging over an ensemble of input fields corresponding to statistically independent realiza‐ tions of the phase screens as well as the object roughness phase function *φsurf* (**r**). In the numerical simulations, ensemble averaging was performed over 100 sets of phase screens and object phases. Both intensity distributions in Figs. 3(a) and 3(c) are characterized by strong scintillations with an average scintillation index value of 1.

In the DAO system, digital wavefront compensation function *φDAO*(**r**) is computed as a weighted sum of response functions *Sk* (**r**) [see Eq. (5)]. In our numerical simulation these response functions are taken as scaled Zernike polynomials: *Sk* (**r**)=*Zk* (*Q***r**), where *Zk* (**r**) is the Zernike polynomial with index *k* and *Q* is a scaling factor. Since Zernike polynomials are defined onto the unit circle the term *Q* is chosen as *Q* =*D* / 2 so that response functions *Sk* (**r**) are defined over the aperture area of the DAO system. In the numerical analysis we used *NDAO* =36 Zernike polynomials corresponding to the first 8 Zernike modes. It should be noted that the first Zernike polynomial (piston) does not impact image quality and does not need to be included in the construction of *φDAO*(**r**). Similarly, Zernike polynomials with index *k* =2 and *k* =3 (tip and tilt) do not have an influence on image quality or its metric. However, tip-tilt wavefront aberrations in the pupil plane cause a global shift of the intensity distribution in the image plane. In or‐ der to compensate for this, image alignment is performed in our numerical simula‐ tions by mean of a conventional registration technique [42] using an ensemble average image as a reference.

Digital Adaptive Optics: Introduction and Application to Anisoplanatic Imaging http://dx.doi.org/10.5772/54108 135

**Figure 3.** Intensity (left column) and phase (right column) distributions of the computer-generated complex field *Ain*(**r**) used as input of the DAO system for *D* / *r*<sup>0</sup> =4 [(a),(b)] and *D* / *r*<sup>0</sup> =8 [(c),(d)]. Phase distributions are shown in a 2π range [between –π (black) and +π (white)].

The quality of the DAO-compensated image *IDAO*(**r**) is assessed using a sharpness metric defined as

$$J = \frac{\int \mathcal{l}\_{DAO}^2(\mathbf{r})d\mathbf{r}}{\int \mathcal{l}\_d^2(\mathbf{r})d\mathbf{r}}\,'\tag{12}$$

Where *Idl*(**r**) is the image that would be obtained in the absence of atmospheric turbulence (i.e. diffraction-limited image). In the case of an ideal compensation the turbulence-induced wavefront aberrations are fully corrected by the DWFC [*φDAO*(**r**)=*φturb*(**r**)] and *J* =1.

#### **3.2. DAO system performance**

ing to the Kolmogorov turbulence power spectrum. We considered a horizontal propagation scenario so the phase screens were equally spaced along the propagation path and their im‐ pact (i.e. turbulence strength) was characterized by a constant ratio *D* /*r*0 where *D* is the di‐ ameter of the DAO system aperture and *r*0 is the characteristic Fried parameter for plane waves. By modifying ratio *D* /*r*0 one can control the strength of input field phase aberra‐ tions. In the numerical simulations, *D* /*r*0 ranged from zero (i.e. free-space propagation) to 10. Figures 3(a)-3(d) show examples of the input field intensity and phase distributions that are obtained using the technique described above for *D* /*r*<sup>0</sup> =4 [(a) and (b)] and for *D* /*r*<sup>0</sup> =8 [(c) and (d)]. Note that the phase distributions in Figs. 3(b) and 3(d) contain phase disconti‐ nuities (branch points). Images were obtained for a propagation distance *L* =0.05*L diff*

The strength of the input field intensity scintillations was characterized by the aperture-

*<sup>I</sup>* (**r**) <sup>2</sup> - 1}*<sup>d</sup>* <sup>2</sup>

where *I*(**r**)=|*Ain*(**r**)|2 and *S* is the aperture area of the DAO system. Here < > denotes aver‐ aging over an ensemble of input fields corresponding to statistically independent realiza‐ tions of the phase screens as well as the object roughness phase function *φsurf* (**r**). In the numerical simulations, ensemble averaging was performed over 100 sets of phase screens and object phases. Both intensity distributions in Figs. 3(a) and 3(c) are characterized by

In the DAO system, digital wavefront compensation function *φDAO*(**r**) is computed as a weighted sum of response functions *Sk* (**r**) [see Eq. (5)]. In our numerical simulation these response functions are taken as scaled Zernike polynomials: *Sk* (**r**)=*Zk* (*Q***r**), where *Zk* (**r**) is the Zernike polynomial with index *k* and *Q* is a scaling factor. Since Zernike polynomials are defined onto the unit circle the term *Q* is chosen as *Q* =*D* / 2 so that response functions *Sk* (**r**) are defined over the aperture area of the DAO system. In the numerical analysis we used *NDAO* =36 Zernike polynomials corresponding to the first 8 Zernike modes. It should be noted that the first Zernike polynomial (piston) does not impact image quality and does not need to be included in the construction of *φDAO*(**r**). Similarly, Zernike polynomials with index *k* =2 and *k* =3 (tip and tilt) do not have an influence on image quality or its metric. However, tip-tilt wavefront aberrations in the pupil plane cause a global shift of the intensity distribution in the image plane. In or‐ der to compensate for this, image alignment is performed in our numerical simula‐ tions by mean of a conventional registration technique [42] using an ensemble average

is the diffractive distance, *k* =2*π* / *λ* is the wave number, and *λ* is the

**r**, (11)

where *<sup>L</sup> diff* <sup>=</sup>*k*(*<sup>D</sup>* / 2)2

134 Adaptive Optics Progress

imaging wavelength.

image as a reference.

averaged scintillation index *σ<sup>I</sup>*

2

*σI* <sup>2</sup> <sup>=</sup> <sup>1</sup>

strong scintillations with an average scintillation index value of 1.

given by

<sup>S</sup> *<sup>∫</sup>*{ *<sup>I</sup>* (**r**) <sup>2</sup>

In this section we analyze results of image synthesis and compensation using the DAO ap‐ proach described in section 2 using the numerical model presented in section 3.1. In order to illustrate the effect of anisoplanatism we first consider DAO performance over an image re‐ gion Ω *<sup>j</sup>* that is nearly isoplanatic in size. Later we consider processing of the entire image region Ω (anisoplanatic conditions). Figure 4 shows intensity distribution *IDAO*(**r**) and crosssections for an object with intensity distribution consisting of point sources arranged in a 7 by-7 array. The resulting intensity distributions hence correspond to the average DAOcompensated PSF of the system for different values of the field angle *θ*, and is showed for *D* /*r*<sup>0</sup> =4 [Figs. 4(a) and 4(b)] and for *D* /*r*<sup>0</sup> =8 [Figs. 4(c) and 4(d)]. As a result of anisoplana‐ tism the PSF is space-varying and its distribution broadens significantly as the angular sepa‐ ration *θ* with the metric region Ω *<sup>j</sup>* increases. Also, the degradation occurs more rapidly with respect to angle *θ* as turbulence strength increases [compare cross-sections in Figs. 4(b) and 4(d)]. Results were obtained by averaging the resulting images *IDAO*(**r**) for 100 realiza‐ tions of the random phase screens.

As described in section 2.4 compensation is based on the optimization of metric *J <sup>j</sup>*

cases the metric value approximately doubled during the optimization process.

**Figure 5.** Average convergence curves for metric *J <sup>j</sup>*

ject) for *D* /*r*<sup>0</sup> =4, and 123% and 33% for *D* /*r*<sup>0</sup> =8.

shown in Fig. 4 for *D* / *r*<sup>0</sup> =4 and *D* / *r*<sup>0</sup> =8.

as depicted in Fig. 6.

Ω *j*

iterative SPGD algorithm. Figure 5 shows average convergence curves for metric *J <sup>j</sup>*

function of the number of SPGD iterations performed. The two curves displayed correspond to the optimization of image regions Ω *<sup>j</sup>* shown in Figure 4 for *D* /*r*<sup>0</sup> =4 and *D* /*r*<sup>0</sup> =8. In both

Digital Adaptive Optics: Introduction and Application to Anisoplanatic Imaging

We consider now the performance of DAO systems under anisoplanatic conditions. Figures 6 and 7 display images prior and after DAO compensation for the point source object used in Figure 4 and for an USAF resolution chart respectively. Results are shown for two turbu‐ lence conditions: *D* /*r*<sup>0</sup> =4 and *D* /*r*<sup>0</sup> =8 and correspond to a full field-of-view of approxi‐ mately 10*θ*0 and 16*θ*0. In both Figures significant image quality improvements can be observed with an increase of the metric *J* of 70% (point source object) and 49% (USAF ob‐

The performance of the DAO compensation technique with respect to turbulence strength is illustrated in Fig. 8 for a ratio *D* /*r*<sup>0</sup> in the range 0;10 . Within that range the average image quality metric *J* after compensation always exceeds significantly the metric value prior processing. Image quality improvements become especially important for large *D* /*r*0. For example, for *D* /*r*<sup>0</sup> =10 the metric grew by a factor of nearly 3. Plots showed in Fig. 8 and in the remainder of the chapter as shown for the object consisting of an array of point sources

. The curves displayed correspond to optimization of image region

using an

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as a

137

**Figure 4.** Average DAO-compensated intensity distributions (left column) for an array of 7-by-7 point sources for *D* / *r*<sup>0</sup> =4 (top row) and *D* / *r*<sup>0</sup> =8 (bottom row). The column on the right depicts the average uncompensated (dotted curve) and DAO-compensated (solid curve) cross-sections of the PSF's through the center of region Ω *<sup>j</sup>* . Image com‐ pensation is based on optimizing image quality metric *J <sup>j</sup>* defined over region Ω *<sup>j</sup>* . Region Ω *<sup>j</sup>* has a diameter ωΩ of ap‐ proximately 1.2θ0 and 2θ0 for *D* / *r*<sup>0</sup> =4 and *D* / *r*<sup>0</sup> =8 respectively (see circled areas).

As described in section 2.4 compensation is based on the optimization of metric *J <sup>j</sup>* using an iterative SPGD algorithm. Figure 5 shows average convergence curves for metric *J <sup>j</sup>* as a function of the number of SPGD iterations performed. The two curves displayed correspond to the optimization of image regions Ω *<sup>j</sup>* shown in Figure 4 for *D* /*r*<sup>0</sup> =4 and *D* /*r*<sup>0</sup> =8. In both cases the metric value approximately doubled during the optimization process.

sections for an object with intensity distribution consisting of point sources arranged in a 7 by-7 array. The resulting intensity distributions hence correspond to the average DAOcompensated PSF of the system for different values of the field angle *θ*, and is showed for *D* /*r*<sup>0</sup> =4 [Figs. 4(a) and 4(b)] and for *D* /*r*<sup>0</sup> =8 [Figs. 4(c) and 4(d)]. As a result of anisoplana‐ tism the PSF is space-varying and its distribution broadens significantly as the angular sepa‐

with respect to angle *θ* as turbulence strength increases [compare cross-sections in Figs. 4(b) and 4(d)]. Results were obtained by averaging the resulting images *IDAO*(**r**) for 100 realiza‐

**Figure 4.** Average DAO-compensated intensity distributions (left column) for an array of 7-by-7 point sources for *D* / *r*<sup>0</sup> =4 (top row) and *D* / *r*<sup>0</sup> =8 (bottom row). The column on the right depicts the average uncompensated (dotted

defined over region Ω *<sup>j</sup>*

. Region Ω *<sup>j</sup>*

. Image com‐

has a diameter ωΩ of ap‐

curve) and DAO-compensated (solid curve) cross-sections of the PSF's through the center of region Ω *<sup>j</sup>*

proximately 1.2θ0 and 2θ0 for *D* / *r*<sup>0</sup> =4 and *D* / *r*<sup>0</sup> =8 respectively (see circled areas).

pensation is based on optimizing image quality metric *J <sup>j</sup>*

increases. Also, the degradation occurs more rapidly

ration *θ* with the metric region Ω *<sup>j</sup>*

136 Adaptive Optics Progress

tions of the random phase screens.

**Figure 5.** Average convergence curves for metric *J <sup>j</sup>* . The curves displayed correspond to optimization of image region Ω *j* shown in Fig. 4 for *D* / *r*<sup>0</sup> =4 and *D* / *r*<sup>0</sup> =8.

We consider now the performance of DAO systems under anisoplanatic conditions. Figures 6 and 7 display images prior and after DAO compensation for the point source object used in Figure 4 and for an USAF resolution chart respectively. Results are shown for two turbu‐ lence conditions: *D* /*r*<sup>0</sup> =4 and *D* /*r*<sup>0</sup> =8 and correspond to a full field-of-view of approxi‐ mately 10*θ*0 and 16*θ*0. In both Figures significant image quality improvements can be observed with an increase of the metric *J* of 70% (point source object) and 49% (USAF ob‐ ject) for *D* /*r*<sup>0</sup> =4, and 123% and 33% for *D* /*r*<sup>0</sup> =8.

The performance of the DAO compensation technique with respect to turbulence strength is illustrated in Fig. 8 for a ratio *D* /*r*<sup>0</sup> in the range 0;10 . Within that range the average image quality metric *J* after compensation always exceeds significantly the metric value prior processing. Image quality improvements become especially important for large *D* /*r*0. For example, for *D* /*r*<sup>0</sup> =10 the metric grew by a factor of nearly 3. Plots showed in Fig. 8 and in the remainder of the chapter as shown for the object consisting of an array of point sources as depicted in Fig. 6.

**Figure 6.** Image of an array of point sources prior and after anisoplanatic DAO compensation for *D* / *r*<sup>0</sup> =4 (top row) and *D* / *r*<sup>0</sup> =8 (bottom row).

**Figure 8.** Average image quality metric *J* as function of the turbulence strength characterized by the ratio *D* / *r*0 with

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139

As mentioned in section 1.3 anisoplanatism causes compensation approaches based on sin‐ gle phase conjugation to be effective only over a small angle of size related to the isoplanatic angle *θ*0. As a result the block-by-block processing technique used here performs differently as the size *ω*Ω of blocks Ω *<sup>j</sup>* changes. As shown in Fig. 9 DAO performance degrades noticea‐ bly as *ω*Ω increases. For example we have *J* =0.73 for *ω*<sup>Ω</sup> =1.8*θ*0 and *J* =0.44 for *ω*<sup>Ω</sup> =14*θ*0. This illustrates the efficiently of the block-by-block processing technique to mitigate the ani‐

**Figure 9.** Average image quality metric *J* as a function of the diameter ωΩ of region Ω *<sup>j</sup>*

used for metric computation.

and without DAO compensation.

soplanatic effect.

**Figure 7.** Image of an USAF resolution chart prior and after anisoplanatic DAO compensation for *D* / *r*<sup>0</sup> =4 and *D* / *r*<sup>0</sup> =8. Note that the DAO compensation process reveals image details as pointed out by the circled areas.

**Figure 8.** Average image quality metric *J* as function of the turbulence strength characterized by the ratio *D* / *r*0 with and without DAO compensation.

As mentioned in section 1.3 anisoplanatism causes compensation approaches based on sin‐ gle phase conjugation to be effective only over a small angle of size related to the isoplanatic angle *θ*0. As a result the block-by-block processing technique used here performs differently as the size *ω*Ω of blocks Ω *<sup>j</sup>* changes. As shown in Fig. 9 DAO performance degrades noticea‐ bly as *ω*Ω increases. For example we have *J* =0.73 for *ω*<sup>Ω</sup> =1.8*θ*0 and *J* =0.44 for *ω*<sup>Ω</sup> =14*θ*0. This illustrates the efficiently of the block-by-block processing technique to mitigate the ani‐ soplanatic effect.

**Figure 6.** Image of an array of point sources prior and after anisoplanatic DAO compensation for *D* / *r*<sup>0</sup> =4 (top row)

**Figure 7.** Image of an USAF resolution chart prior and after anisoplanatic DAO compensation for *D* / *r*<sup>0</sup> =4 and

*D* / *r*<sup>0</sup> =8. Note that the DAO compensation process reveals image details as pointed out by the circled areas.

and *D* / *r*<sup>0</sup> =8 (bottom row).

138 Adaptive Optics Progress

**Figure 9.** Average image quality metric *J* as a function of the diameter ωΩ of region Ω *<sup>j</sup>* used for metric computation.

Finally the influence of the number of Zernike polynomials *NDAO* compensated [see Eq. (5)] is shown in Fig. 10 for two turbulence strength levels: *D* /*r*<sup>0</sup> =4 and *D* /*r*<sup>0</sup> =8. Image quality improvements become negligible beyond a threshold for parameter *NDAO*. This threshold is in the range of 10;20 for *D* /*r*<sup>0</sup> =4 and 15;25 for *D* /*r*<sup>0</sup> =8.

tive for image synthesis and compensation under anisoplanatic scenarios. The influence of the block size on DAO performance was showed to enhance performance as the block size decreases and nears values of the isoplanatic angle. Finally, increasing the degree of DAO compensation (i.e. number of Zernike coefficients compensated) was showed to benefit per‐

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141

1 Intelligent Optics Laboratory, Institute for Systems Research, University of Maryland, Col‐

2 Intelligent Optics Laboratory, School of Engineering, University of Dayton, Dayton, Ohio,

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formance up to a threshold value which depends on the turbulence strength.

**Author details**

lege Park, Maryland, USA

USA

**References**

Mathieu Aubailly1\* and Mikhail A. Vorontsov2

\*Address all correspondence to: mathieu@umd.edu

**Figure 10.** Average image quality metric *J* as a function of the degree of DAO compensation *NDAO*.
