**3. Recent laboratory tests**

**2.5. Performance Estimation**

6

µm and 1.25 µm wavelengths, respectively.

edge [21]. Therefore, the fitting error variance *σ fit*

and 0.13 radian2

variance can be calculated approximately as *<sup>σ</sup>* <sup>2</sup> <sup>≈</sup>*<sup>σ</sup> fit*

and 0.38 radian2

0.65 µm and 1.25 µm wavelengths, respectively.

length as *r*0∝*λ*

32 Adaptive Optics Progress

given as

*σtem*

*σtem*

2 is 0.44 radian2

iance of 0.90 radian2

As an example, the AO performance estimation will only focus on the Kitt Peak 1.6-meter McMP that has a large aperture size. The estimated performance should be better for other telescope with a smaller aperture size or a site with a better seeing condition. The Fried pa‐ rameter *r*<sup>0</sup> is equal to ~ 5 cm at 0.5 µm for the daytime median seeing conditions at Kitt Peak, which is available almost every week for a clear sky. The seeing *r*<sup>0</sup> is scalable with wave‐

A DM surface with a finite actuator number cannot exactly match the wave-front patterns of the atmospheric turbulence. For an atmospheric wave-front with Kolmogorov spectrum, the fitting error variance of a DM with finite actuator number is derived by Hudgin [20] and is

> 2 5/3 <sup>0</sup> (/) *fit s*

where *rs* and *r*0 are the spaces between two actuators and the Fried parameter, respectively. *κ* is the fitting parameter. Since there are 12 actuators across the DM aperture that is conju‐ gated onto the 1.0-meter effective telescope aperture (see Section 4) although McMP has a 1.6-meter aperture, *rs* is equal to 83 mm. An extensive analysis of the fitting error showed that *κ* =0.349 was applicable for many influence functions that are not constrained at the

The temporal error of the wave-front correction is determined by the Greenwood frequency and the bandwidth of the AO system. The Greenwood frequency can be calculated as 0.43*v* /*r*<sup>0</sup> [22], where *v* is the average wind speed. At McMP, when wind speed reaches 20 m/s, the telescope will be closed and observations will not take place. We assume that the AO system will operate with an average wind speed of 8.0 m/s. This results in a Greenwood frequency of 49 Hz and 23 Hz at the 0.65 µm and 1.25 µm wavelengths, respectively. The wave-front variance due to the temporal error of the correction can be calculated as

<sup>2</sup> =( *<sup>f</sup> <sup>G</sup>* / *<sup>f</sup> BW* )5/3 , where *<sup>f</sup> <sup>G</sup>* is the Greenwood frequency and *<sup>f</sup> BW* is the bandwidth of the AO system. Since the AO closed-loop bandwidth is 80 Hz, the temporal wave-front variance

Read out noise is not a problem for solar wave-front sensing since plenty of photons are available for the wave-front sensing [10]. The corrected wave-front variance is the sum of all the error contributors. If only the fitting and temporal errors are considered, the wave-front

The overall performance of an AO system can be evaluated in terms of the Strehl ratio,

<sup>2</sup> <sup>+</sup> *<sup>σ</sup>tem*

 k

s

5 for Kolmogorov turbulence, and it reaches 70 mm and 150 mm at the 0.65

= *r r* (11)

and 0.25 radians2

<sup>2</sup> . This results in a wave-front var‐

at the

2 is 0.46 radians2

at the 0.65 µm and 1.25 µm wavelengths, respectively.

at the 0.65 µm and 1.25 µm wavelengths, respectively.

The PSAO was first built in CSUN laboratory in 2009, with an OKO 37-actuator DM for soft‐ ware development and test purpose. In 2010, the DM was upgraded with the current BMC 140-actuator model. A cross target illuminated by a white-light fiber bundle is used for the 2-dimensional object test. A 32-actuator DM from Edmund Optics is used to generate a realtime wave-front aberration at a desired frequency, which is subsequently fed into the AO system, so that the AO performance can be evaluated in real-time. The whole optics of PSAO is built on a 900mm x 600mm optical breadboard as shown in the Figure 5, and can be easily carried to any solar observatory.

**Figure 2.** Graphic WFS interfaces for AO calibration with a point source (left) and for real-time correction with a cross target (right).

The AO software consists of two parts. The first part is used for the AO calibration, while the second part is the code for AO real-time correction. In principle, the calibration only needs to be done once a time, provided that the hardware has not been realigned. In the cali‐ bration, a single-mode fiber is served as a point source. Any possible incoming wave-front error will be filtered out by the single-mode fiber, and only the fundamental mode can prop‐ agate through the fiber. The output wave-front can be viewed as a perfect wave for the cali‐ bration. In the calibration, the fiber is switched into the optical path on the telescope focal plane just before the lens L1 (see Figure 1). In AO real-time correction, the fiber is switched out the optical path, and an extended target (a cross herein), including the wave-front error generated by the 32-element Edmund Optics DM, is allowed to input into the AO for test‐ ing. A lenslet array with 8.7-mm focal length is used for the WFS. Figure 2 shows the WFS interfaces in the AO calibration with a point source (Figure 2 left) and in real-time correction with a cross target (Figure 2 right): there are 69 effective WFS sub-apertures arranged in the 9x9-lenslet grid configuration and wave-front correction up to 65 modes of Zernike polyno‐ mials can be chosen. Please note that in this test, there is no central obstruction on the pupil, although our software can be used with a telescope with central obstruction.

The AO system was also tested with a 2-dimensional extended target with the same proce‐ dure for the point-source target. In this test, a cross was printed on a transmission film and was used as a 2-dimensional target. A fiber bundle light source located immediately behind the cross target was used to illuminate it, so that the image of the fibers was almost overlap‐ ped on the cross target, except for a slight defocus between them. Figure 4 shows the origi‐ nal cross-target image (left) without aberration applied, as well as the AO-off (center) and AO-on (right) images with the aberration applied, respectively. Please note that the image of the cross target and background small fibers is seriously blurred by the wave-front error ap‐ plied (center image). Compared the left and right images, however, it is clear that the AO recovers the original image perfectly, indicating that the AO's performance is excellent. In fact, our AO system can recover the original wave-front that is associated with the original

A Solar Adaptive Optics System http://dx.doi.org/10.5772/ 52834 35

The PSAO's small size makes it can be easily brought to any observatory for science obser‐ vations. Since 2010, we have carried out observations at two different sites. To demonstrate the AO's feasibility, an initial on-site observation was conducted by using the 0.61-m solar telescope at the San Fernando Observatory, California State University Northridge. This so‐ lar telescope is a three-aspheric mirror system with a central obstruction area of 14%, and a focal ratio of f/20. Because of the poor seeing conditions at the San Fernando Observatory, WFS with 9x9 sub-apertures (exception those in regions of the four-corners and the central obstruction) was used. The best observational results were acquired in October 2011. Using a sunspot as a target, the AO system was able to lock on the sunspot for wave-front sensing and provides high-resolution images at the wavelength of 0.75 µm [24], which indicates that our PSAO is able to provide wave-front correction at a site with a poor seeing condition.

After the successful observations on the San Fernando Observatory, we continued to test this system with the 1.6-m McMP. The McMP is located at the Kitt Peak, and is operated by the National Solar Observatory. It is one of the largest solar telescopes and is accessible to the solar community around the world. The medium seeing at the Kitt Peak is better than that at the SFO, but is still poor with a Fried parameter of ~ 5 cm at median seeing condition. The poor seeing condition at the Kitt Peak is a great challenge for an adaptive optics system. There are no AO available for routine observations with the McMP, although a prototype with 36 actuator DM was developed many years ago [25]. McMP is an off-axis telescope without central obstruction. The solar image is formed on a rotational station at f/54, where our PSAO can be conveniently placed for observations. Figure 5 shows the PSAO loaded on the McMP rota‐ tion station for an observation, in which the small size of the AO system is clearly referred. The non-common optical path error between the WFS and the science camera, which the WFS

During the latest observations in May 2012, the PSAO delivered excellent performance in the visible with the McMP. Solar images were captured at 0.6-µm visible wavelength. Figure 6

cannot measure, was calibrated by an approach we proposed recently [23].

image with accuracy up to 1/1000 wave-length in the visible [23].

**4. Recent on-site observations**

**Figure 3.** Point-source images: original image without aberration applied (left), with aberration applied and AO off (center), with aberration applied and AO on (right). 9x9 lenslets (without those on the four corners) are used for wavefront sensing, and 25 Zernike modes are corrected.

The PSAO had achieved excellent corrections in the test with a point source target. Figure 3 shows the original point-source image (left) without aberration applied, as well as the AOoff (center) and AO-on (right) images with the aberration applied, respectively. In this test, the wave-front error was introduced by the 32-actuator Edmund Optics DM in real-time, in which the wave-front is variable as a sinusoidal function with a frequency up to 80Hz. The central image of the distorted point-spread function shows that the wave-front error ap‐ plied is significantly large, while the right image clearly demonstrates that the AO system can recover the diffraction-limited image. The AO system demonstrated good results in differ‐ ent situations:


**Figure 4.** Cross-target images: original image without aberration applied (left), with aberration applied and AO off (center), with aberration applied and AO on (right). 9x9 lenslets (without those on the four corners) are used for wavefront sensing, and 25 Zernike modes are corrected.

The AO system was also tested with a 2-dimensional extended target with the same proce‐ dure for the point-source target. In this test, a cross was printed on a transmission film and was used as a 2-dimensional target. A fiber bundle light source located immediately behind the cross target was used to illuminate it, so that the image of the fibers was almost overlap‐ ped on the cross target, except for a slight defocus between them. Figure 4 shows the origi‐ nal cross-target image (left) without aberration applied, as well as the AO-off (center) and AO-on (right) images with the aberration applied, respectively. Please note that the image of the cross target and background small fibers is seriously blurred by the wave-front error ap‐ plied (center image). Compared the left and right images, however, it is clear that the AO recovers the original image perfectly, indicating that the AO's performance is excellent. In fact, our AO system can recover the original wave-front that is associated with the original image with accuracy up to 1/1000 wave-length in the visible [23].
