1、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 estimat
2、ion 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
3、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 fix
4、ed 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 effe
5、ctiveness 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)
6、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 curre
7、nt, 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 est
8、imated 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 thresho
9、ld 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 cen
10、ter 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
11、 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
12、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 beaco
13、n 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
14、 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
15、 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
16、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
17、this, lets take an example where the spot signal is low. For deep space optical communications that may require stars as a beacon source, the minimum signal available from 11* star with 30cm telescope is 10,000 photons with 25% system efficiency. Assuming CCD QE of 50%, this translates to 5000 elect
18、rons. In this example, the reduction of the centroid window size improves the centroid accuracy significantly if that does not truncate the signal notably. The allocated error for NEA is 1/25* of the pixel. Plots of the NEA vs. the number of pixels used in centrod estimation were shown in Figure 1.
19、The assumptions are the same fixed per pixel noise ranging f?om 5e- to 20e- with no background signal. Bias error, which can be mitigated by centroiding algorithm, is caused by non-uniform signal distribution, which include straylight and background image. This corresponds to the cases where the tel
20、escope is pointing toward the Earth or close to the Sun. Even if background subtraction were applied, there would be some bias left, especially if the threshold is below the maximum of the background signal. As Figure 1shows, even 0.1% of the peak spot value as the maximum bias value, can cause cons
21、iderable bias error if the centroid window size is large, 9x9 pixels in this example. Figure 1 Airy pattern spot used in the simulation3. Model-Based noise reduction In construction of spot models, the PSF is sampled (spatially quantized) at every INthpixel movement.This forms a spot model at the sp
22、ecific location of PSF relative to the sub-pixel positions. Beyond a certain resolution, the benefits of finer resolution are expected to diminish. In this paper, N=10 was used. Once the database of spot models is constructed, each model can be used to determine which pixels in the measured spot ima
23、ge (corrupted by noise) should be truncated. As illustrated, the rough centroid estimate is obtained using the standard (center of brightness) centroid algorithm. This centroid is used to determine which spot model should be used. If the error in the rough centroid estimate exceeds the pixel movemen
24、t determined by N, then the incorrect spot model can be selected. The effect of incorrect spot models is presented in section 4. Once the spot model is determined, the next task is to estimate the noise level present in the centroid window. There can be many ways to best estimate the noise level. In
25、 this paper, we used simple mean of four edge lines. This noise level is compared with the spot model. If the pixel value of the spot model is smaller than the noise level, the pixel position is used to truncate the pixel in the centroid window. Once this process is completed over the entire pixels
26、of both spot model and the centroid window, truncation of the noise is complete. The final task is to apply the standard centroid algorithm to the truncated centroid window to obtain the new centroid value.4. Simulation result The objective of the simulation is to show the effectiveness and robustne
27、ss of the model-based noise reduction method in centroid estimation. For this objective, three cases were investigated. These are:(a) Comparison of three centroiding algorithms (including model-based) at various noise levels given the(b) Comparison of three centroiding methods on the bias error.(c)
28、Three scenarios of using incorrect spot models were used: incorrect models at 0.1 pixel, 0.2 pixel, and total signal equivalent to 5000e-.0.3 pixel used to show the robustness of the model-based method. Three algorithms were run 100 times for a fixed noise value and the noise was increased from 10ee
29、quivalent to 100e- equivalent (Gaussian noise with 1 sigma value from 10e to 100e- equivalent). As is shown, the model-based algorithm outperforms the other two methods: standard centroid and thresholding method. The strength of the model-based method is not only the much smaller centroid error but
30、also its immunity to the noise as demonstrated in both plots. As the noise increases, the centroid error from the standard and thresholding methods also increases. However, the model-based method exhibits almost steady error. The objective of this simulation is to compare the effect of bias in the s
31、pot image on the three centroid methods. As was evident in EQ (1), even the model-based method would be affected by the presence of the background bias unless complete removal of the bias is conducted. In the simulation, bias value was selected based on the peak pixel value that is 28.5% of the tota
32、l signal. Maximum bias was varied from 0.1% to 1% of the peak pixel value.5. Conclusion A new method based on the spot model was proposed to improve centroid estimates of a point source image. The new method assumes the spot model can be used to truncate noise and bias in the measured spot, thereby
33、improving centroid estimates. Simulations were performed to demonstratethe effectiveness of the proposed method for noise and bias. Compared with the standard centroiding and the more advanced thresholding method, the model-based method turned out to be superior in accuracy. From the simulation wher
34、e the incorrect spot models were intentionally used, the effect on its performance was minimal, especially at high noise level. Since this method was intended for low SNR signal, it could prove to be essential for deep space missions, where the strong optical signal is not readily available.附录B基于降噪模
35、型的方法提高指向精度Lee S.Applied High-Power Lasers and Applications. International Society for Optics and Photonics，2002：65-71摘要：本文提出了一种提高质心精度，从而提高指向精度的新方法。精确的质心估计对于自由空间光通信来说至关重要，其中参考光源（例如恒星或上行链路信标）的光子数量受到限制。已知质心精度与SNR成比例。在CCD曝光期间各种噪声源的存在可能导致质心估计的显着劣化。噪声源包括CCD读取噪声，背景光，杂散光和CCD处理电子元件。减少噪声和背景偏差影响的最广泛使用的方法之一是阈值法
36、其在质心计算之前从质心窗中减去固定阈值。相反，这里提出的方法利用点模型来导出用于截断信号边界外的噪声的信号边界。本文的方法有效地减少了偏差和随机误差，所提出的方法的有效性通过模拟证明。关键词：指向；质心估计；光通信1. 简介 准确的质心估计是基于信标的指点系统的关键任务。最近的一项研究表明，深空光通信的质心误差（随机和偏差误差）需要小于1/20像素，而允许的总指向误差（I sigma）为1/16像素。两种重心错误，随机和偏见受到各种来源的影响。随机误差由CCD读取噪声，散粒噪声，暗电流和ADC量化噪声等噪声引起。当非均匀背景光如杂散光和地球背景图像存在时，会发生偏差错误。 降低噪声和偏差的常
37、规方法包括归一化零交叉的阈值和重心。对于阈值法，从质心窗中减去估计的阈值，这相当于执行偏置减法并消除噪声。当阈值取出大部分偏差和噪声时，该方法可以有效。然而，一般来说，简单的阈值是无效的，因为阈值取决于图像的亮度，并且可以通过阈值处理改变形成对象的像素的数量。为了避免这个问题，提出了使用过零点进行重心估计。这种方法的局限性在于，它仅适用于质心估计，并对每个像素承担相等的权重。 为了减少噪声的影响，同样的目的是建议在信号峰值周围仅使用9个像素。只有信号被限制在这个小的局部区域，这种截断简化了加速重心计算，而不影响质心精度。然而，正如所指出的那样，宽信号的截断显着地影响了质心估计的精度。因此，需要
38、仔细选择质心估计中使用的像素数，以免牺牲质心精度。本文中，我们提出使用斑点模型来确定哪些像素用于质心估计。可以从光学系统（光学系统的PSF）的表征中构建斑点模型。在质心窗口上，通常比信标光斑尺寸大几个像素，以允许信标运动，可以从斑点模型和测量的噪声水平估计束斑的近似信号边界。一旦识别边界，信号边界的像素可以设置为零，有效地消除了光束外的所有噪声和偏差。本文的结构如下。在第2节中，我们将介绍噪声对质心精度的影响。在第3节中，介绍了基于模型的降噪方法。在第4节中，给出了仿真结果。2. 噪声和偏差对中心精度的影响 CCD类型焦平面阵列上的点的质心方程（亮度中心）是已知的： (2-1) 从（2-1）可
39、以看出，随着坐标朝向边缘增加，由于较大的加权因子，靠近质心窗口边缘的噪声或偏置主导了质心误差。本文最重要的部分之一。因此，为了减少NbA，需要增加信号或者需要降低噪声。如果信号相对大于噪声，噪声的影响很小，反之亦然。为了说明这一点，让我们举一个例子，其中点信号是低的。对于可能需要恒星作为信标源的深空光通信，具有30厘米望远镜的11星的最小信号为10,000光子，系统效率为25。假定CCD QE为50，则转换为5000个电子。在该示例中，如果不明显地截断信号，则质心窗尺寸的减小显着改善了质心精度。 NEA的分配错误是像素的1/25 *。 NEA的曲线与中心估计中使用的像素数量如图1所示。假设是相
40、同的固定每像素噪声，范围5e至20e，无背景信号。 通过重心算法可以减轻偏差，是由不均匀的信号分布引起的，其中包括杂散光和背景图像。这对应于望远镜指向地球或靠近太阳的情况。即使应用背景减法，也会留下一些偏差，特别是如果阈值低于背景信号的最大值。如图2-1所示显示，即使0.1的峰值值作为最大偏置值，如果质心窗口尺寸较大，则在本例中为9X9像素，可能会引起相当大的偏差误差。图2-1仿真中使用的通风模式点3. 基于模型的降噪 在点模型的构建中，PSF在每个INth像素移动时被采样（空间量化）。这在PSF的特定位置处相对于子像素位置形成点模型。除了一定的决议之外，预期更好的解决方案的好处将会减少。在本
41、文中，使用N = 10。一旦构建了现货模型的数据库，就可以使用每个模型来确定测得的斑点图像（被噪声损坏）中哪些像素应被截断。如图所示，使用标准（亮度中心）质心算法获得粗略质心估计。该质心用于确定应使用哪个点模型。如果粗略质心估计中的误差超过像素运动由N确定，则可以选择不正确的点模型。第4节给出了不正确的点模型的影响。 一旦确定了斑点模型，下一个任务是估计质心窗口中存在的噪声水平。可以有很多方法来最佳地估计噪音水平。在本文中，我们使用四条边线的简单均值。该噪声水平与斑点模型进行比较。如果斑点模型的像素值小于噪声水平，则使用像素位置来截断质心窗口中的像素。 一旦这个过程在斑点模型和质心窗口的整个像
42、素上完成，噪声的截断就完成了。最后的任务是将标准中心算法应用于截断质心窗口以获得新的质心值。4. 仿真结果 仿真的目的是显示基于模型的降噪方法在质心估计中的有效性。为此目的，调查了3例。这些是： 1. 在给定的各种噪声水平下的三个重音算法（包括基于模型）的比较； 2.三种重心方法对偏差误差的比较； 3.使用了不正确的点模型的三种情况：0.1像素，0.2像素的不正确模型和等于5000e-.0.3像素的总信号用于显示基于模型的方法。对于固定噪声值，运行100次算法，噪声从10等于100e-当量（1西格玛值从10e到100e当量的高斯噪声）增加。如图所示，基于模型的算法优于其他两种方法：标准质心和阈
43、值法。基于模型的方法的优点不仅在于质心越小越好，而且它们对噪声的抵抗力也在两个图中都表现出来。随着噪声的增加，标准和阈值方法的质心误差也增加。然而，基于模型的方法表现出几乎稳定的误差。这次模拟的目的是比较斑点图像中的偏差对三个质心方法的影响。在公式(2-1)中显而易见的是，即使是基于模型的方法也将受背景偏差的影响，除非进行偏差的完全消除。在仿真中，基于总信号的28.5%的峰值像素值选择偏置值。最大偏差从峰值像素值的0.1%变化到1%。如预期的，基于模型的方法优于其他两个在偏置值和质心误差之间呈线性关系的方法。5. 结论本文提出了一种基于斑点模型的新方法来改善点源图像的质心估计。 新方法假定斑点
44、模型可用于截断测量点中的噪声和偏差，从而改善质心估这次，基于模型的算法在每个噪声级别运行了100次，这三种情况：第一种使用与真实点模型不同的0.1像素的不正确的斑点模型，第二种是0.2像素不同，第三个是0.3像素不同。在优选实施例中，信息获取和传输设备720的第二分支包括朝向待扫描表面传输光的LED 711，然后将其朝向透镜反射其他光学装置721并且连接到光学传感器722.光学传感器优选地将光能转换成形成更容易数字化，用于计算机操纵所得数据。 光信息优选地被转换成为与测量的光能的强度成比例的电压。 传感器可用于此目的包括但不限于电荷耦合器件（CCD）和接触式图像传感器（CIS）。 转换后光信息
45、转换为电压，ADC 723将电压转换为数字数据，依次传输到专用状态机724。目的是验证模型的鲁棒性基于方法。总体而言，性能受斑点模型的准确性影响，但是，随着噪声的增加，这种区别并不明显。还有一些对于0.2和0.3像素不同的斑点模型，可以看出改进。 这个改进是由于附加噪声增加了噪声电平，从而限制了使用的像素数量质心计算。西格玛和平均误差在像素的1/50附近计。进行模拟以证明所提出的噪声和偏差方法的有效性。与标准的重心和较高级的阈值法相比，基于模型的方法精度优于原型。有意使用不正确的光点模型的模拟中，对其性能的影响很小，特别是在高噪声水平。由于该方法适用于低信噪比信号，因此可能被证明对于深空任务至关重要，其中强光信号不容易获得。- 9 -
免费区 
