附录APointing Accuracy Improvement using Model-Based Noise Reduction MethodLee S.Applied High-Power Lasers and Applications. International Society for Optics and Photonics，2002：65-71Abstract：A new method for improving centroid accuracy, thereby pointing accuracy, is proposed. Accurate centroid estimation is critical for free-space optical communications where the number of photons from the reference optical sources such as stars or an uplink beacon is limited. It is known that the centroid accuracy is proportional to the SNR. Presence of various noise sources during the exposure of CCD can lead to significant degradation of the centroid estimation. The noise sources include CCD read noise, background light, stray light, and CCD processing electronics. One of the most widely used methods to reduce the effects of the noise and background bias is the thresholding method, which subtracts a fixed threshold from the centroid window before centroid computation. The approach presented here, instead, utilizes the spot model to derive the signal boundary that is used to truncate the noise outside the signal boundary. This process effectively reduces both the bias and the random error. The effectiveness of the proposed method is demonstrated through simulations.Keywords：pointing, centroid estimation, optical communications1. Introduction Accurate centroid estimation is a critical task for a beacon based pointing system. A recent study shows that the centroid error (random and bias error) for deep space optical communications needs to be less than1/20thpixel whereas the total pointing error allowed (I sigma) is 1/16th pixel. Two types of centroid errors, random and bias, are affected by various sources. A random error is caused by noises such as CCD read noise, shot noise, dark current, and ADC quantization noise. A bias error occurs when non-uniform background light such as straylight and Earth background image exists. Conventional methods to reduce the noise and bias include the thresholding and centroiding of the normalized zero-crossings. For the thresholding method, an estimated threshold is subtracted from the centroid window, which equivalently performs a bias subtraction and eliminates the noise. This method can be effective when the threshold value takes out most of the bias and the noise. However, a simple threshold,in general, is not effective since the threshold value is dependent on the brightness of the image and the number of pixels forming the object may be altered by the thresholding process. To avoid this problem, the use of zero-crossings for centroid estimation was proposed. The limitation of this approach is that it is only applicable to the center of mass estimation and assumes equal weighting on every pixel. For the same objective of reducing the effects of noise, there were suggestions to use only nine pixels around the signal peak. This truncation simplifies and speeds up the centroid calculation without affecting the centroid accuracy only if the signal is limited to this small local region. As was indicated in, however, the truncation of the wide signal considerably affects the accuracy of centroid estimation. Therefore, the number of pixels used in centroid estimations needs to be carefully selected so as not to sacrifice the centroid accuracy. In this paper, we propose to use a spot model to determine which pixels are used for centroid estimation. A spot model can be constructed from the characterization of optical systems (PSF of optical system). On the centroid window, which is usually several pixels larger than beacon spot size to allow beacon motion, the approximate signal boundary of a beam spot can be estimated from the spot model and the measured noise level. Once the boundary is identified, the pixels to the signal boundary can be set to zero, effectively eliminating all the noise and bias outside the beam spot.The organization of the paper is as follows. In section 2, we will present the effects of noise on centroid accuracy. In section 3, the model-based noise reduction method is presented. In section 4, simulation results are presented.2. Effect of noise and bias on centroid accuracy The equations for centroids (center of brightness) for spots on CCD type of focal plane arrays is well known: (1) From Eq.(l), it is clear that the noise or bias closer to the edges of the centroid window dominates the centroid error due to larger weighting factor as coordinates increases toward the edges. This is one of the most important motivations of this paper. Therefore, either the signal needs to be increased or ne noise needs to be decreased in order to reduce the NbA. lhis implies that the effect of the noise is small if the signal is relatively larger than the noise and vice versa. To illustrate this, lets take an example where the spot signal is low. For deep space optical communications that may require stars as a beacon source, t