Canada-France-Hawaii Telescope Canada-France-Hawaii Telescope
2 Performance and Limitation Mauna Kea is famous for its excellent atmospheric seeing. Click here to view histograms of the image quality at CFHT. This plot shows the evolution of seeing at CFHT. This histogram shows the image quality of FOCAM (direct imager) and HRCam (fast tip-tilt correction) for 1990 and 1991. Note that image quality means: the size of stellar images on our imagers. Therefore, it includes atmospheric seeing, dome and mirror seeing, telescope and instrument aberrations and guiding errors.
The following plot shows a compilation of Ro for the 2 first PUEO engineering runs. The fitted curve is a log normal distribution with a sigma of 0.14 and a mean of 17.5 cm.
Recent observations (1995) taken by F. Roddier's group with their adaptive optics system at CFH revealed the following Ro behavior. On this plot the crosses represent the value of Ro, there is an average line going through the points. The other full line is the dome air temperature, and the dotted line the primary mirror temperature. This plot illustrates a good correlation between Ro and mirror induced seeing.
The Tip-Tilt mirror and electronic control have been built by the Observatoire de Paris Meudon (P. Gigan) subcontracted by Laserdot (now CILAS). The tip-tilt mirror performs superbly; here are a few numbers:
Small amplitude bandwidth (-3dB): 947 Hz x axis
Small amplitude bandwidth (-3dB): 902 Hz y axis
Mirror Stroke, at the mirror: +/- 200 arcsec
Mirror Stroke, on the sky: +/- 4.0 arcsec
Mirror RMS Jitter, at the mirror: 0.4 arcsec
Mirror RMS Jitter, on the sky: 0.008 arcsec
The fast tip-tilt correction mode does more than just tip-tilt. The real-time computer cpu is totally dedicated to tip-tilt measurement and applies corrections on the deformable mirror. All other modes are also active, but at a low bandwidth, insuring correction of the quasi-static telescope aberrations.
By far the simpler and most effective, the Automatic correction mode should satisfy all AO observers. This mode regularly tests (5 minutes intervals) for the efficiency of correction for all mirror modes. If the result of this test is negative, the gain is reduced for this particular mode, allowing a better time average to be determined. During the March engineering run of the AO bonnette, a test was carried out on a 12 magnitude star. First all mode were "ON" with a constant gain of 1 (the overall system gain is obviously smaller than that). Then on the same object we activated the automatic gain adjustment. In the latter case, the wavefront standard deviations were reduced by 35%. This observation mode should satisfy most users and we strongly encourage them to adopt it.
Here are a series of plot describing the performance that can be expected of PUEO. This first plot shows the strehl ratio that can be obtained versus Ro. Ro varies with wavelength, so that the wavelength dependance of the strehl ratio is taken into account by considering a Ro for a given wavelength. The solid line is the theoretical seeing limited strehl ratio (this is atmospheric only and does not include telescope tracking errors or static aberrations). The dotted line is a fit computed using an analytical model developed by F.R. The performance described by these data corresponds to approximately 6 corrected Zernikes corrected perfectly. PUEO has 19 electrodes, thereforem 18 actual correction modes (piston is not used). The difference between 19 and 6 comes from spatial aliasing noise (even on bright stars, we estimated the noise to be around 3 to 8 rd**2 at 0.5 micron) and uncompensated errors such as telescope high order aberrations, uncompensated (high freqency) telescope jitter, etc.
This plot shows the normalized FWHM versus Ro. The normalized FWHM is the image FWHM divided by the telescope resolution (lambda/D) at the image wavelength. Two regimes with a very clear cut-off are demonstrated by this figure: the image is diffraction limited (in term of FWHM), that is its nomalized FWHM is approximately 1, down to Ro=50 cm. At shorter wavelength, the FWHM increases rapidly as Ro decreases. By comparing this figure with the previous one, it can be seen that FWHM of the order of lambda/D are obtained for Strehl value down to approximately 20 %. A PSF model was used to fit the data points.
This figure is somewhat redundant with the previous one. It shows the direct relation between FWHM and wavelength. The dashed curve shows the FWHM of seeing limited images for a Ro(0.5 micron) = 17 cm. which was roughly the median seeing during the run.
The only occasion where one might not wish the full mode correction is when there are strong constraints on the size of field of view and homogeneity of the PSF. The effect of correcting many or all modes, is that the isoplanetic patch is very small. This means there is a small patch (for 19 modes it can be as small as ~10 arcsec) where the PSF is greatly improved and is essentially constant. As one considers a larger field of view, the AO correction will not be as efficient, and the PSF larger in size, and overall large variations of the PSF will be seen in the field of view. Therefore, in order to obtain a intermediate spatial resolution and homogeneous PSF, an observer might want to correct only a few modes. This option is also offered. The higher order modes are then corrected at very low bandwidth. The user selects the higher order mode to be corrected. All lower order modes are then corrected. Note that one cannot select a random choice of modes to correct.
This figure shows the variation of PSF FWHM versus the distance from the reference source. In this particular case the seeing was excellent. Ro was 26, 31 and 36 cm for the B, I and V band respectively. These data were obtained using a 11.7 mag. reference star. The typical isoplanetic patch sizes versus the number of modes corrected depends also on the atmospheric conditions (Ro) and will be investigated in more details during the third commissionning run this coming June.
We quote a limiting magnitude for full correction of 15 for the reference star. However, the situation is more complex than this; the FWHM and strehl ratio depend on the particular wavelength, the magnitude of the reference source, and the angular distance from the science target. This is a more complete view of the problem. A full simulation has been setup by one of us (F.R.) to allow observers a better planning of their observing run. This feature is available on the WWW and can be reach through the AO Web Page under the topic: "Predicted Performance" or through this link .
Results obtained during the first 2 engineering runs correspond well with the predictions of the simulation program mentioned above. However, The following plots show results obtained at the telescope. This graph shows the strehl attenuation as the number of photon for wavefront sensing decreases. This other graph shows a similar relation where the number of photon has been converted in reference star magnitude. The number of photons must be divided by 19 to find the signal per aperture, and multiplied my 1000 to find the count rate per second.All values of strehl on these graphs have been divided by the expected strehl ratio for the given Ro. Therefore, the attenuation is 1.0 (or no attenuation) for bright stars. At low flux, one sees the Strehl drops due to photon noise in the measurements. This attenuation should be chromatic (the propagation of the noise on the phase is constant in microns square, translating into an error at a given wavelength that grows as the square of the wavelength in square radian). The solid and dotted curves are ad-hoc fits, respectively
Strehl attenuation = exp(-(30./Nphoton**0.8))
Strehl attenuation = exp(-(30./Nphoton**0.8)*(1.25/2.23)**2)
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