Numerical simulation investigations of the effects of noise and detection error in an adaptive optics system

In an adaptive optics (AO) system, noise and detection error can produce errors in the slope measurement of a Hartmann-Shack (HS) wavefront sensor and have further effects on the performance of the AO System. The noise in an AO system can be divided into the readout noise and the photon noise. The detection error in an AO system results from the discrete sampling by using number-limited CCD pixels in the HS sensor and the deadspace between the CCD pixels. A theoretical model for numerically simulating the effects of noise and detection error is presented and a corresponding computer program has been compiled, which is combined with our existing program of numerical simulation of the laser propagation in a turbulent media and an AO system in a stationary state. Taking the long-exposure Strehl ratio and the percentage relative error of the centroid slopes for each subaperture as two evaluation parameters, numerical simulation investigations of the effects of detection error (including the limited sampling density and the deadspace), readout noise and photon noise on a practical AO system have been carried out. Statistics method and formulation method are used to evaluate the effects of readout noise and photon noise in the numerical simulation. It is shown that there is no significant difference between results by using these two methods when the signal to noise ratio (SNR) is larger. However, as SNR gets smaller, the formulation method becomes less accurate than the statistics method. The numerical results are very useful for the design of a practical AO system