Canada-France-Hawaii Telescope Canada-France-Hawaii Telescope
4 A few Notions about Adaptive Optics Observing with PUEO may require a fine and very elaborated strategy. The Pegasus interface of PUEO has been developed having in mind a user friendly control of the bonnette. Most adaptive optics instruments that we have had the privilege to see in operation, usually require a team of specialists to be operated. Our goal was to develop a simple interface offering a minimum of options to the user without compromising the flexibility or performance. Various on-line displays will keep the users informed of the atmospheric turbulence conditions allowing him-her to make judicious choices for his-her observing program.
We have tried to arrange all the information gathered during the engineering and commissioning runs in a somewhat organized fashion to make it more easily accessible to observers. The following table lists a few questions related to your observing program (questions you should ask yourself) and provides some answers by connecting to plots and graphs which describe the behavior of PUEO.
| Question or Run Parameter | PUEO Characteristics | Comments | -Overall Performance -Object Brightness -Reference Source Brightness -Observing Wavelength |  Strehl and FWHM expected  Strehl Attenuation  FWHM versus Wavelength | Comment | -Distance between reference and science target |  Isoplanetic patch size (FWHM)  Isoplanetic patch size (STREHL) | Comment |
| Technical Aspects | PUEO Characteristics | Comment |
| Image improvement |  Strehl improvement  FWHM improvement  Strehl versus FWHM | Comment |
| Modal Control |  Modal Gain Efficiency  Optical Gain | Comment |
| PSF | PUEO Characteristics | Comment |
| -Encircled Energy -Coherent Energy -PSF Examples |  Strehl vs 50% radius  Coherent Energy  PSF @ 2.12 micron  PSF @ 1.65 micron  PSF @ 1.2 micron | Comment |
The WFS measurements and mirror electrode voltages are recorded in so-called circular files. The file size allows these signals to be recorded for a time long-enough (a few seconds) to get good characterization of the atmosphere. The WFS error signals and commands to the bimorph mirrors provide a mean of determining the residual wavefront error, which can be linked to Ro and a reconstructed PSF.
Another useful information is the Fourier transform of the mirror modes. The electrode voltages carry a different information than the WFS signals. They are the best available approximation to the real wavefront shape. The WFS signals are error signals with respect to the correction at the previous cycle.
The electrode voltages to the bimorph mirrors represent the wavefront. One can extract the correction modes from this wavefront information. For instance, one can obtain the time evolution of the amplitude of a mode like focus or astigmatism (in the atmospheric turbulence). The Fourier transform shows the amplitude distribution of this mode versus frequency, and can give useful information about the cut-off frequency of this particular mode.
Other data of interest to the observer are the count rates on the APD's. It is important to avoid saturation (at 10E6 counts/sec). A set of neutral density filters are available to limit the number of counts in case of a very bright reference source. Unfortunately, most of the time the reference source will be very faint ! The immediate consequence of this is a few number of counts per cycle on the APD display. Our experience and simulations tend to demonstrate that it is preferable to apply adaptive corrections frequently, even if they are not the most accurate, rather than applying very accurate correction less frequently. The latter results in an accurate correction at time "to" being applied at time "to+Delta_t", when it is no more appropriate.
The object brightness and Reference source brightness should guide your choice of beamsplitter. At the time of this writing (June 1996) there are 4 beamsplitter available. The most straigtforward is for Infrared observation. In that case one uses the dichroic, and most of the visible flux goes to the wavefront sensor and most of the infrared to the science path. For the visible a decision has to be made between 3 beamsplitter. See this link for transmission curves of beamsplitters. Remember that a sacrifice in the fraction of the flux going to the science path might be a necessity if you want any image improvement. This depends whether there is an independant reference source, its brigthness, or whether the science target itself is used. If the reference source is bright (m~10) the best performance is obtained from PUEO. If the reference is fainter, the noise in the wavefront sensor starts degrading the performance.
The Strehl ratio in the first plot has corrected for static aberrations. See this section for more details about this plot. The second plot shows normalized FWHM that is the FWHM divided by the telescope resolution at that particular wavelength. The 2 regimes of diffraction limited (Ro larger than 50 cm) and at shorter wavelength (smaller Ro) the normalized FWHM increases as Ro decreases.
The strehl attenuation shows how a faint reference source degrades the strehl ratio. For brighter stars, (m /< 13) the strehl is as good as can be obtained by our AO system. The degradation is primarily due to photon noise in the wavefront sensing path. Another cause that can degrade the quality of the correction is sensing the wavefront of an extended source (galaxy nucleus) or a point source over a bright background. These causes of degradation have not been quantified.
The scatter in the plot showing FWHM versus wavelength is caused by different atmospheric conditions. The best resolution is obtained at a wavelength of 1 micron.
IsoplanetismThe very few observations obtained so far that pertains to isoplanetism indicate that the patch size is somewhat larger than first expected for a 19 modes system. However, the seeing, when this particular test was carried out, was excellent, and the patch size may be smaller for worse seeing conditions. If the observer judges that the change in PSF over its field of view is too important, he-she has the choice to decrease the number of modes used for the AO correction. This has for effect to slightly increase the Strehl (or FWHM) away from the guide source and decrease it at the position of the guide source. We still do not know of a useful "isoplanetism meter" device that would provide this crucial information to the observers. However, the Adaptive Optics page gives access to a simulation tool to evaluate quality of AO correction given a few parameter. One of them is the distance to the guide star. It has shown to give results very close to our observational experience. You can access it through this link . Another possibility is to observe a set of "Isoplanetism Standards" during your observing night. That is a set of stars with given separation. Note that if you plan to determine the scale of the detector (arcsec/pixel) you should use astrometric standards. We will make sure such a list is always at the disposal of observers.
Image ImprovementThe best image improvement or gain over what the telescope can provide without AO is at wavelength slightly longer than 1 micron or the J and H infrared bands. Strehl improvement means the strehl of the AO corrected images divided by the seeing limited strehl ratio. The maximum gain in FWHM is obtained for a Ro of approximately 40 cm (or D/Ro=9). It is worth mentioning that the maximal gain in Strehl ratio takes place at a Ro of approximately 60 cm (D/Ro=6). The decrease of the FWHM improvement toward shorter Ro is due to the inability of the system to correct for phase corrugation shorter than the inter-actuator distance. Note that at Ro=20 cm, which is approximately the typical Ro value in V band, the gain in FWHM is still 2-3. The decrease of the FWHM improvement toward large Ro is simply explained by the fact that the width of the diffraction pattern increases, whereas at the same time the width of the seeing limited image decreases.
Modal gains and Optical GainThe plot of Relative Strehl versus loop gain shows a sequence taken to evaluate teh efficiency of the mode gain optimization procedure. A period of stable Ro was chosen for these tests. The mode gain optimization procedure was used to deduce a set of gains. These mode gains were then entered manually mode by mode. Then, for each image of teh sequence, an overall gain factor was applied to the mode gains. The resulting strehl is plotted against this overall gain factor on the fiugre. This shows that the initial gains (overall gain = 1) found by the mode gain optimization procedure provide the best Strehl. In addition, it shows that the optimum is not very sharp, therefore an error on the mode gain evaluation would not have severe consequences on the performance.
Data for the plot of Strehl ratio versus optical gain has been taken mainly to insure that we were operating the system at the proper gain (the so-called optical gain is the out of focus distance in the wavefront sensing path, which is proportional to the membrane mirror amplitude of vibration). Simulations show that there is an optimal optical gain for a given D/Ro. This figure illustrates this effect. Overall, we found the the useful optical grain for close-loop operation ranges from 120 to 200 (accessible values 1 to 256) for Ro(0.5 micron) = 10 to 20 cm and more, respectively. As a preliminary result, G_opt= 8*Ro(0.5 mic) + 40. this relation can be used to find the optimal optical grain for given atmospheric conditions.
Examples of PSF'sThe coherent energy plot shows the fraction of light in the coherent diffraction core of the corrected image. This is interesting for interferometric considerations. This is however model dependant and not accurate for images with Strehl lower than 25 %. The coherent energy is computed as the image Strehl minus the Strehl ratio of the seeing limited image weighted by the fraction of light in the halo.
The PSF plots show cuts through a diameter of the profils. The solid line represents the fit (with parameters indicated in the upper right corner of the plot) with our analytical PSF model. "#act./diam." is the ratio of the telescope diameter to the distance between actuators, taken here as 4.0 (PUEO has 5 actuators over the telescope pupil). Note that this model has been developed for Shack-Hartmann systems. Only the noise behviour has been modified to better match the behavior of a curvature system. It may therefore not be completely suited for this kind of data. In any case, the fit is good, and if we assume this model apply reasonably well to curvature system, this tends to indicate that there is no other major contribution to the image than those that are consequent to the AO correction (i.e. scattered light).
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