Research On Algorithms Of Hartmann Wave-front Sensing Operated With Faint Object

Adaptive Optics(AO) technology has been widely used in large ground-based telescopes to compensate the wavefront distortion induced by atmospheric turbulence. The performance of wavefront correction is directly affected by the wavefront sensing accuracy. The algorithms of Hartmann wavefront sensing operated with faint object used in liquid crystal AO system(LCAOS) are studied in this paper.As the most important performance criterion, the centroid detecting accuracy determines the detection ability of Shack-Hartmann wave-front sensor(SHWFS). The centroid detecting accuracy is severely affected by photon noise when the faint objects are detected. The photon noise is mixed up with the signal, and in the small enough area, the photon signal has little change, while the photon noise has wide variance. Considering this feature, we propose the averged weighed center of gravity(AWCoG) algorithm which is based on the local averged technique and weighting technique to supress the influence of photon noise. Comparing with the charditional CoG algorithm, the centroid detecting error is decreased from 0.142??and?0.181??to 0.112??and 0.145?,and are both reduced by 20%,when the photon number per subaperture is 100(5.5 magnitude) and Fried length is 10 cm and 5cm,respectively.Zernike polynomials are not the optimal set of basis functions for modal atmospheric compensation, since their decompensation coefficients are statistically dependent. Using the K-L polynomials with independent coefficients can improve the accuracy of wavefront reconstruction. For a SHWFS with 20×20, when the Fried length r0=d=10cm and the centroid error is 0.1?, the wavefront sensing error is reduced from ???????to???????, and is reduced by 18%. The optimal reconstruction mode number will be change if the observing consition is changed, and too much or too little will increase the reconstruction error. The differential image motion(DIM) method is proposed to estimate the Fired length and centroid error simultaneously, and then the optimal mode number can be obtained. Considering the turbulence ergodic and calculation, the key parameters of this method are set as 1 subaperture seperation, sampling time 5000 ms and sampling time interval 50 ms. Using the Fried length and centroid error estimated by the DIM method, the wavefront sensing error can be minimized even the centroid error reaches 0.25??The LCAOS uses the SHWFS to detect the tip-tilt(TT) aberrations and saves the separated TT sensor, which simplifies the AOS and enhances light energy efficiency. The small spot method which uses the average of centroid biases of all valid spots as TT signals has high accuracy but small dynamic range, while the big spot method which used the centroid bias of all spots as TT signals has dynamic range as large as the whole CCD panel but low accuracy. To accurately correct the large amplitudes TT aberrations induced by the poor telescope tracking, the method based on grid meshing and template matching is proposed. The algorithm has the same dynamic range with big spot method, and same accuracy with small spot method. Even at a given condition with r0 of 5cm and the average flux of 100 photons per sub-aperture(5.5 magnitude), the ultimate measurement accuracy of TT is about 0.07″(peak-to-valley value).In conclusion, the research on Hartmann Wavefront detection algorithms operated with faint object not only improved the the performance of LCAOS, but also made the system work well under more extreme observation conditions.