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Local adaptive threshold segmentation method for subapture spots of Shack-Hartmann sensor
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摘要:
夏克-哈特曼传感器的质心偏移估计精度受噪声的影响非常大，在传统质心法(CoG)中尤为突出，因而阈值的选取十分重要。本文提出了一种基于统计排序的局部自适应阈值分割方法，并与传统的全局阈值法进行对比，发现自适应的局部阈值能够更加有效地分割出阵列光斑，从而减小背景噪声对质心估计的影响，降低波面复原误差。本文通过静态相差的测量实验，从质心偏移估计的精度和波前复原精度两个方面进行分析，验证了该方法的有效性。另外，本文发现自适应阈值结合灰度加权的质心提取方法，是对传统质心法的较好改进，可以有效提高峰值信噪比大约10~40的光斑质心提取精度。
Abstract:The accuracy of centroid estimation for Shcak-Hartmann wavefront sensor is highly dependent on noise, especially for the centre of gravity (CoG) method. Therefore, threshold selection is very important. This paper proposes a local adaptive threshold segmentation method based on statistical rank, which can reduce the influence of uneven background noise and decrease the wavefront reconstruction error more effectively, comparing with the traditional global threshold method. An experiment measuring static aberration was conducted, the accuracy of centroid estimation and wavefront reconstruction both testify the effectiveness of this method. Besides, we found that combing the local adaptive threshold method and intensity weighted centroiding (IWC) method can improve the performance of traditional centre of gravity method. It achieves higher centroiding accuracy under SNRp between 10~40 conditions.
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Key words:
- Shack-Hartmann sensor /
- point source spots /
- local adaptive threshold /
- centroiding /
- centre of gravity
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Overview: The accuracy of centroid estimation for Shcak-Hartmann wavefront sensor is highly dependent on noise, especially for the centre of gravity (CoG) method. Therefore, threshold selection is very important. A globally estimated threshold using the best threshold method (mean of noise plus three times of its standard deviation) ignores the difference between subaptures, thus causing large centroiding estimation error for subaptures with higher noise level. Therefore we propose an adaptive threshold segmentation method based on statistical rank, which can reduce the influence of background noise effectively. The pixels within a subapture is ranked by their intensities at first. The mean and standard deviation of the subapture noise is estimated using the last certain numbers of pixels. The number of pixels used for noise estimation is determined by estimating the size of Shack-Hartmann spots, which is related to the focal length, the wavelength, the diameter of micro lens and the size of pixel.
An experiment measuring static aberration was conducted, the accuracy of centroid estimation and wavefront reconstruction both testify the effectiveness of this method. Different from theoretical simulations, the ideal position of a spot is unknown in real experiments. However we have two ways to evaluate the accuracy of centroiding methods. Firtly, the actual postion of a certain subapture is constant for static aberrations, and the variation of centroiding for a subapture within multiple frames can be calculated and used as a criteria. Another is that we calculate the center of a spot under high signal-to-noise ratio (SNR) as the ideal position, which can be used to estimate the errors under low SNR conditions. Since the intensity of a subapture increases with the exposure time, we controlled the signal-to-noise ratio by adjusting the exposure time of the camera, which was set as 10 ms, 5 ms, 2 ms and 1 ms. Furthermore, the wavefront reconstruction errors (PV and RMS) had been calculated and displayed within this paper.
We also found that combing adaptive threshold method with intensity weighted centroiding (IWC) method can improve the performance of traditional centre of gravity method. It achieves higher centroiding accuracy under low SNR conditions (10 < SNRp < 40), comparing with the traditional method. Although several methods have been proposed to improve the CoG method, such as using Gaussian weighting function or window, the center of the weighting function or the window is difficult to define at first. However, IWC method can avoid this problem by simply using the intensities of the spot itself and the choice of parameter is much more flexible and easy.
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图 3 经过不同阈值处理的光斑阵列图。(a)全局阈值Tn1；(b)全局阈值Tn3；(c)局部自适应阈值
Figure 3. Spot array pattern obtained by different thresholding methods. (a) Gloabal thresholding Tn1; (b) Gloabal thresholding Tn3; (c) Local adaptive thresholding
图 4 静态相差测量实验光路图
Figure 4. The light path schematic of static aberration measuring experiment
图 6 采用不同阈值方法时的复原误差。(a)全局阈值Tn1；(b)全局阈值Tn3；(c)局部自适应阈值
Figure 6. Wavefront reconstruction error using different threshold methods. (a) Gloabal thresholding Tn1; (b) Gloabal thresholding Tn3; (c) Local adaptive thresholding
图 7 不同信噪比下参数q与质心测量起伏的关系
Figure 7. Relationship between q and deviation of centroiding error under different SNR levels
表 1 靶面不同区域噪声分布的统计参数
Table 1. Statistical parameters of noise at different target surface regions
信噪比等级 四角 中心 间隙 靶面上最高信噪比 衰减片 曝光时间/ms μn1 σn1 Tn1 μn2 σn2 Tn2 μn3 σn3 Tn3 lp SNRp L1 1 10 100.9 4.1 114 109.4 6.4 129 120.4 9.8 150 4566 465 L2 1 5 99.4 3.8 111 103.3 5.0 119 108.8 6.4 128 2238 349 L3 1 2 98.8 3.1 109 99.9 4.1 113 102.1 4.6 116 882 191 L4 1 1 98.2 3.0 108 98.9 3.5 110 100.0 3.9 112 481 123 L5 2 10 98.5 3.4 109 98.8 3.7 110 99.3 4.4 113 307 69 L6 2 5 98.1 3.4 109 98.6 3.5 110 99.0 4.1 112 153 37 L7 2 2 98.2 3.2 108 98.2 3.1 108 98.5 3.2 109 67 20 
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表 2 三种阈值方法在不同曝光时间下的质心起伏误差
Table 2. Diviation of CEE under different exposure time using three thresholding methods
阈值方法 10 ms 5 ms 2 ms 1ms RMS-σx RMS-σy RMS-σx RMS-σy RMS-σx RMS-σy RMS-σx RMS-σy Tn1 0.024 0.022 0.034 0.031 0.049 0.044 0.064 0.059 Tn3 0.021 0.019 0.031 0.026 0.044 0.038 0.059 0.053 自适应阈值 0.019 0.016 0.029 0.023 0.041 0.035 0.056 0.050
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表 3 三种阈值方法的质心偏移估计误差对比
Table 3. Comparison of the CEE using three thresholding methods
阈值方法 5 ms 2 ms 1ms ΔxCEE ΔyCEE ΔxCEE ΔyCEE ΔxCEE ΔyCEE Tn1 0.121 0.106 0.099 0.072 0.095 0.068 Tn3 0.066 0.042 0.074 0.046 0.082 0.057 自适应阈值 0.047 0.030 0.061 0.043 0.076 0.054
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