5 Example

We have built a 61-element adaptive optical system at the 1.2 m telescope of the Yunnan Observatory (Jiang et al. 1998) for astronomical observations in the visible range. It consists of a 61-element deformable mirror, a Shack-Hartmann wavefront sensor with 8^*8 subapertures and a digital wavefront processor. The detector of the Shack-Hartmann wavefront sensor is an intensified CCD with frame rate of 838 Hz. The effective diameter of the system is 1.06 m and the time delay is 2.8 T (T is the sampling period of the system). Figure 5 shows the experimental results of the measurement noise of WFS for the measured photoelectrons and its fitting curve. The measurement noise may be expressed as

$$\sigma_{\rm fn}=3.25/\sqrt{P}\quad (\lambda_0)$$ (40)

where P is the photoelectrons detected by WFS per subaperture and per frame.

Figure 5: The measured wavefront noise r.m.s. value vs. photoelectrons per subaperture and per frame.

For this system, Fig. 6 presents the optimum short-exposure imaging observation wavelength and the corresponding image resolution as a function of the measured photoelectrons for the closed-loop bandwidth of 30 Hz, 60 Hz and 120 Hz respectively. During the computation, the anisoplanatic error is not considered and the following atmospheric parameters according to the statistial values at this site are taken: $r_0(\lambda_0)=12.5$ cm, $f_{\rm G}(\lambda_0)=42$ Hz.

Figure 6: Optimum observing wavelength and the corresponding image resolution as a function of photoelectrons per subaperture and per frame for different closed-loop bandwidths.

It can be seen from Fig. 6 that for the reference beacon with high brightness, the larger the closed-loop bandwidth, the shorter the optimum imaging observation wavelength is, and the higher the corresponding resolution. For the reference beacon with low brightness, the reverse is true. This is due to the fact that the uncompensated turbulence-induced error, decreasing with the increasing closed-loop bandwidth, dominates over the total wavefront residual error in contrast with the closed-loop noise error, which is proportional to the closed-loop bandwidth, induced by the measurement error of the wavefront detector for the reference beacon with high brightness. For the reference beacon with low brightness, the closed-loop noise error is larger than the uncompensated turbulence-induced error. In this case, the wider the closed-loop bandwidth, the larger the total wavefront residual error.