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摘要:
拼接镜的共相误差检测是当前科学研究的热点问题之一，基于宽波段光源的共相检测技术解决了夏克哈特曼法由于目标流量低引起的测量时间长的问题，从而提升了piston误差的检测精度和量程。然而，当前宽波段算法在实际应用中，由于复杂的环境以及相机扰动等干扰因素的存在导致获取的圆形孔径衍射图像含有一定量的噪声，从而导致相关系数值低于设定阈值，最终使该方法精度降低，甚至失效。针对这一问题，本文提出将基于深度降噪卷积神经网络（DnCNN）的算法集成到宽波段算法中，以实现对噪声干扰的控制，并保留远场图像的相位信息。首先，将使用MATLAB获得的圆孔衍射图像作为DnCNN的训练数据，然后，将不同噪声水平的图像导入到训练好的降噪模型中，即可得到降噪后的图像以及降噪前、后圆孔衍射图像的峰值信噪比和二者与清晰无噪声图像间的结构相似度。结果表明：降噪处理后的图像与理想清晰图像之间的平均结构相似度较处理之前有了明显提升，获得了理想的降噪效果，有效增强了宽波段算法在高噪声条件下的应对能力。该研究对于探索用于实际共相检测环境宽波段光源算法具有较强的理论意义和应用价值。
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关键词:
- 拼接镜 /
- piston误差 /
- 圆孔衍射 /
- 图像降噪 /
- 深度降噪卷积神经网络
Abstract:The co-phase error detection of segmented mirrors is currently a critical focus of scientific research. Co-phase detection technology based on a broad-band light source solves the problem of long measurement times caused by the Shackle-Hartmann method’s low target flow rates, thereby improving the accuracy and range of piston error detection. However, in the application of the current broad-band algorithm, the complex environment and the presence of disturbing factors such as camera perturbations cause the acquired circular aperture diffraction images to contain a certain amount of noise, which leads to a correlation coefficient value below the set threshold, reduces the accuracy of the method, and even makes it ineffective. To solve the problem, we propose a method by integrating an algorithm based on Denoising Convolutional Neural Network (DnCNN) into the broad-band algorithm in order to control the noise interference and retain the phase information of the far-field image. First, the circular hole diffraction image obtained by using MATLAB is used as the training data for DnCNN. After the training, the images with different noise levels are imported into the trained noise reduction model to obtain the denoised image as well as the peak signal-to-noise ratios of the circular hole diffraction images before and after denoising. The structural similarity between the two images and the clear and noiseless image are also obtained. The results indicate that the average structural similarity between the denoised image and the ideal clear image has significantly improved compared to the image before processing, and this achieves an ideal denoising effect, which effectively increases the ability of broad-band algorithms to cope with the effects of high noise conditions. This study has strong theoretical significance and application value for exploring the broad-band light source algorithm for applications in practical co-phase detection environments.
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Key words:
- segmented mirror /
- piston error /
- circular diffraction /
- image denoising /
- DnCNN
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图 1 子镜间的圆孔衍射示意图
Figure 1. Schematic diagram of circular aperture diffraction between submirrors
图 2 掩膜半径为r的理论圆孔衍射图
Figure 2. Theoretical diffractogram of circular aperture with mask radius r
图 4 20 dB加性高斯白噪声影响下的Corr2图像
Figure 4. Corr2 image under the influence of 20 dB additive white Gaussian noise
图 7 DnCNN训练时损失函数和学习率的变化过程
Figure 7. The change process of the loss function and learning rate during DnCNN training
图 8 当4组子镜的piston分别为−0.2 μm、0、0.2 μm、2 μm时，不同方法的降噪效果图。(a)清晰图像；(b)噪声图像；(c)使用BM3D网络降噪后的图像；(d)使用WNNM网络降噪后的图像；(e)使用DnCNN降噪后的图像
Figure 8. Plots of the noise reduction effect of different methods for Gaussian noise for four sets of submirror piston errors of −0.2, 0, 0.2, and 2 μm. (a) Clear images; (b) noisy images; (c) images after noise reduction by BM3D network; (d) images after noise reduction by WNNM network; (e) images after noise reduction by DnCNN
图 10 对于piston分别为−0.2 μm、0、0.2 μm、2 μm的4组子镜，不同方法对于泊松噪声的降噪效果图。(a)清晰图像；(b)噪声图像;(c)使用BM3D网络降噪后的图像；(d)使用DnCNN网络降噪后的图像
Figure 10. The denoising effect of different methods on Poisson noise for four sets of submirror piston errors of −0.2 μm, 0, 0.2 μm, and 2 μm (from left to right). (a) Clear images; (b) noisy images; (c) images denoised by BM3D network; (d) images denoised by DnCNN
图 13 (a)不含piston误差及(b)含piston误差的相机直采衍射图像
Figure 13. Camera direct images (a) without piston error (b) with piston error
图 14 图像增强后的降噪效果对比。(a)(c)原始含噪声图像；(b)(d)降噪后图像
Figure 14. Comparison of denoise effect after image enhancement. (a) (b) Original noise-containing images; (c) (d) images after denoising
表 1 4组具有不同piston误差的含有高斯噪声的图像降噪前、后与清晰无噪声图像之间的SSIM值
Table 1. SSIM values between images containing Gaussian noise with four sets of submirror piston errors before and after noise reduction and clear noise-free images
piston SSIM值 BM3D WNNM DnCNN −0.2 μm 0.3527 0.2049 0.9747 0 0.2680 0.1376 0.9811 0.2 μm 0.3639 0.2109 0.9762 2 μm 0.3959 0.2294 0.9810 SSIM均值 0.3451 0.1957 0.9783 
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表 2 4组子镜piston误差下，PSNR在40 ~20 dB范围内的降噪前、降噪后图像与清晰无噪声图像之间的SSIM值
Table 2. SSIM values between pre- and post-noise reduction images with four sets of submirror piston errors and clear noise-free images when PSNR in the range of 40 dB to 20 dB
piston=-0.2 μm piston=0 piston=0.2 μm piston=2 μm PSNR before after before after before after before after 20 0.2875 0.9747 0.2610 0.9811 0.2892 0.9762 0.2954 0.9810 24 0.4794 0.9766 0.4669 0.9954 0.4858 0.9785 0.4942 0.9811 28 0.6992 0.9753 0.6798 0.9962 0.7001 0.9769 0.6981 0.9824 32 0.8536 0.9739 0.8387 0.9962 0.8537 0.9738 0.8519 0.9785 36 0.9349 0.9735 0.9321 0.9965 0.9354 0.9739 0.9366 0.9761 40 0.9731 0.9726 0.9714 0.9966 0.9726 0.9728 0.9735 0.9750 AVG 0.7046 0.9744 0.6917 0.9937 0.7061 0.9754 0.7083 0.9790
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表 3 4组子镜piston误差下的含有泊松噪声的图像在降噪前、后与清晰无噪声图像之间的SSIM值
Table 3. SSIM values between images containing Poisson noise with four sets of submirror piston errors before and after noise reduction and clear noise-free image
piston=−0.2 μm piston=0 piston=0.2 μm piston=2 μm 平均值 BM3D 0.9114 0.8966 0.9334 0.9046 0.9115 DnCNN 0.9998 0.9998 0.9997 0.9998 0.9998
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表 4 4组子镜piston误差下，PSNR在30 dB至10 dB范围内的降噪前、降噪后图像与清晰无噪声图像之间的SSIM值
Table 4. SSIM values of pre- and post-noise reduction images and clear noise-free images with PSNR in the range of 30 dB to 10 dB for four sets of submirror piston errors
piston=-0.2 μm piston=0 piston=0.2 μm piston=2 μm PSNR before after before after before after before after 10 0.0726 0.9973 0.0579 0.9970 0.0761 0.9973 0.0838 0.9973 14 0.2046 0.9995 0.2032 0.9996 0.1985 0.9995 0.3131 0.9996 18 0.5811 0.9995 0.5337 0.9993 0.5453 0.9995 0.6148 0.9981 22 0.7555 0.9997 0.8255 0.9998 0.7599 0.9995 0.7926 0.9997 26 0.8767 0.9999 0.9125 0.9999 0.9406 0.9998 0.9617 0.9999 30 0.9543 0.9998 0.9781 0.9998 0.9496 0.9999 0.9307 0.9997 AVG 0.5741 0.9993 0.5852 0.9992 0.5783 0.9993 0.6161 0.9991
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