Study On Testing And System Optimization For Adaptive Optics

Adaptive optics(AO) is a technique which is capable of measuring and compensating wavefront distortions in real time. AO is very useful in the fields of astronomical imaging, controlling of laser beam, retina imaging, free-space laser communication, high-resolution imaging with a microscopy and space optics. Although AO has succeeded in many applications, the AO technique also needs improving in some fields, such as the non-common path aberrations(NCPA) correction and the control strategy. It is very important for the measurement, analysis and improvement of the performance of AO systems to research on the testing technique and system optimization. Both the testing technique and the system optimization include many subjects; in this paper, four subjects, i.e. the testing method of the wavefront processor(WFP), the testing method of the performance of the AO system, the method of NCPA correction by using a WFP, and the evaluation and improvement on the closed-loop stability of an AO system based on the zonal wavefront reconstruction, are selected to be the researching themes. Then, studies are conducted as follows.1. At the beginning, the theory of AO and the composition of AO systems are introduced, respectively. Then, the reconstruction algorithms of AO system are summed and analyzed. Subsequently, the error sources of AO systems are introduced and the methods of suppressing the errors are analyzed. Finally, a fast algorithm for Zernike polynomials which is based on discrete Fourier transform(DFT) is derived and implemented.2. Focusing on the issue that the FPGA-based WFP suffers from the difficulty in hardware debugging, as a result of the inaccessibility of intermediate results, a method of software test of WFP is proposed and implemented. This method can facilitate hardware debugging of WFP, also can avoid unnecessary damages to the precise wavefront corrector caused by incorrect output of WFP during hardware debugging, First, an analysis on the function, composition and working flow of WFP is made, and accordingly, the steps of software test are determined. Subsequently, tests of working modes and systematic parameters of WFP are designed by means of comparing the returning data from WFP with the sending data. Further tests of wavefront gradients computation, wavefront reconstruction and wavefront control are developed by comparing the values simulated by the software with those uploaded by WFP. Finally, this method is adopted in tests of a 97-element WFP, and it is shown that the efficiency of hardware debugging is improved considerably. The WFP which passes the above tests works well, and root of mean square(RMS) and peak to valley(PV) of the residual aberrations of the experimental adaptive optics system are 0.034 wavelengths and 0.392 wavelengths, respectively, after continuous correction, which proves the effectiveness of this method.3. Focusing on the issue that the FPGA-based WFP suffers from the difficulty in the NCPA correction, a method for correcting NCPA is presented, which is very suitable for wavefront processors in forms of FPGA. First, causes of NCPA are analyzed and NCPA examination with phase diversity is discussed. Then, according to the working process of wavefront processors, an algorithm which converts NCPA to reference spot shifts of the wavefront sensor is deduced, and a software module in main controller computer is programmed for implementing this algorithm. Finally, an experiment with a light source as a target is conducted in the optical path of a telescope. Experiment results show that energy concentration of the target image is increased by 17.6% approximately after NCPA correction with this method. The experiment proves that this method is capable of NCPA correction for adaptive optics system.4. According to the requirements of testing the performance of an experimental AO system, a performance measurement method is designed and validated by experiments. In this article, a method for measuring the performance of the AO system is designed and validated by experiments. The Strehl ratio(SR) which is based on the target images is used to evaluate the performance quantitatively because it relates to the effect of AO correction directly. In the calculation of the SR, to avoid energy scaling in the diffraction-limited point spread function, an algorithm based on the integral of the optical transfer function is adopted. Then, a 97-element AO system is established to validate this method, and a white-light fiber source is used as a point-like target. To simulate the practical conditions which influence the effects of the AO system, targets of different brightness are simulated in terms of different signal-to-noise ratios(SNR) of the Shack-Hartmann wavefront sensor(SH-WFS), and atmospheric turbulence is simulated in terms of the Fried’s coherence length and the Greenwood’s frequency. Finally, two experiments are conducted in which the SR of different simulated conditions are measured. The results of the experiments show that for a moderate SNR of SH-WFS the experimenting AO system is capable of closed-loop wavefront correction when the Fried’s coherence length is larger than 5cm and the Greenwood’s frequency is lower than 60 Hz. The results also show that the performance of AO is susceptible to the SNR of SH-WFS. The experiments validates the effectiveness of this method.5. Focusing on the issue that the closed-loop control stability of an AO system based on zonal wavefront reconstruction is worse than that based on modal method, investigations on the closed-loop control stability are conducted by using the Lyapunov approach. As an direct metric of the control stability, the error propagator includes the effects of both the integral gain and the influence matrix and is effective for control-stability evaluation. An experimental 97-element AO system is developed for the control-stability investigation, and the Southwell sensor-actuator configuration rather than the Fried geometry is adopted so as to suppress the potential waffle mode. Because filtering out small singular values of the influence matrix can be used to improve the control stability, the effect of the influence matrix and the effect of the integral gain are considered as a whole by using the error propagator. Then, the control stability of the AO system is evaluated for varying the integral gains and the number of filtered-out singular values. Afterwards, an analysis of the evaluations of the error propagator is made, and a conclusion can be drawn that the control stability can be improved by filtering out more singular values of the influence matrix when the integral gain is high. In other words, the error propagator is useful for trading off the bandwidth error and the fitting error of AO systems in a control-stability approach. Finally, a performance measurement of the experimental AO system is conducted when 13 smaller singular values of the influence matrix are filtered out, and the results show that filtering out a small fraction of the singular values has a minor influence on the performance of this AO system.