{"id":1238,"date":"2024-10-13T19:36:45","date_gmt":"2024-10-13T10:36:45","guid":{"rendered":"https:\/\/xn--k10aa.com\/?p=1238"},"modified":"2024-10-26T12:09:54","modified_gmt":"2024-10-26T03:09:54","slug":"plt02","status":"publish","type":"post","link":"https:\/\/remoooo.com\/en\/plt02\/","title":{"rendered":"Hair Rendering Research: Wave Optics Hair Rendering - Study Notes - 2"},"content":{"rendered":"\n<p>\u58f0\u660e\uff1a\u8fd9\u7bc7\u6587\u7ae0\u4e3b\u8981\u662f\u5173\u4e8eSIG23\u5e74\u8fd9\u7bc7\u9ed1\u72d7\u6bdb\u8bba\u6587\u7684\u4e2a\u4eba\u7b14\u8bb0\u3002\u5e94\u8be5\u4e5f\u6ca1\u5565\u9605\u8bfb\u95e8\u69db\uff0c\u56e0\u4e3a\u6211\u81ea\u5df1\u4e5f\u6ca1\u6709\u5165\u95e8\u56fe\u5f62\u5b66\u3002\u516c\u5f0f\u6709\u4f46\u662f\u4e0d\u591a\u3002\u516c\u5f0ftag\u8ddf\u539f\u8bba\u6587\u4e00\u6837\u3002\u6240\u6709\u5185\u5bb9\u90fd\u662f\u6211\u778e\u6363\u9f13\u7684\uff0c\u516c\u5f0f\u5982\u679c\u6709\u7406\u89e3\u9519\u8bef\u8bf7\u591a\u591a\u6307\u6b63\uff0c\u611f\u8c22\u611f\u8c22\uff01<\/p>\n\n\n\n<p class=\"has-text-align-center\">\u539f\u6587\uff1a<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/809636731\">https:\/\/zhuanlan.zhihu.com\/p\/809636731<\/a><\/p>\n\n\n\n<p>\u5173\u952e\u8bcd\uff1a\u56fe\u5f62\u5b66\u5165\u95e8\u3001\u79bb\u7ebf\u6e32\u67d3\u3001\u57fa\u4e8e\u6ce2\u52a8\u5149\u5b66\u6e32\u67d3\u3001\u6bdb\u53d1\u6e32\u67d3<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Mengqi Xia, Bruce Walter, Christophe Hery, Olivier Maury, Eric Michielssen, and Steve Marschner, \u201cA Practical Wave Optics Reflection Model for Hair and Fur,\u201d <em>ACM Transactions on Graphics (TOG)<\/em>, vol. 42, no. 4, article 39, pp. 1-15, Jul. 2023.<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">1. Related Work<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u57fa\u4e8eRay\u7684\u7ea4\u7ef4\u6a21\u578b<\/strong> \u5728\u4eba\u7c7b\u6bdb\u53d1\u7684\u7814\u7a76\u4e2d\uff0cMarschner[2003]\u7684\u6a21\u578b\u5e7f\u6cdb\u5e94\u7528\u4e8e\u4e1a\u754c\uff0c\u901a\u8fc7\u5206\u6790\u4ecb\u7535\u5706\u67f1\u548c\u5706\u9525\u4e2d\u7684\u5149\u7ebf\u8def\u5f84\uff0c\u5c06\u6563\u5c04\u5206\u4e3aR\u3001TT\u548cTRT\u3002Zinke[2009]\u52a0\u5165\u4e86\u6f2b\u53cd\u5c04\u6210\u5206\u3002Sadeghi[2010]\u63d0\u51fa\u4e86\u827a\u672f\u5bb6\u63a7\u5236\u53c2\u6570\u5316\u65b9\u6cd5\u3002d&#8217;Eon[2014]\u548cHuang[2022]\u63d0\u51fa\u4e86\u975e\u53ef\u5206\u79bb\u7684\u8868\u5f81\u65b9\u6cd5\uff0c\u4e5f\u5c31\u662f\u8bf4\u65b9\u4f4d\u89d2\u548c\u7eb5\u5411\u89d2\u5ea6\u4e4b\u95f4\u6709\u8026\u5408\u6548\u5e94\uff0c\u4e0d\u53ef\u7b80\u5355\u5206\u79bb\u3002Chiang[2016] \u8fdb\u4e00\u6b65\u4f18\u5316\u4e86\u8be5\u6a21\u578b\uff0c\u4f7f\u5176\u9002\u7528\u4e8e\u751f\u4ea7\u7ea7\u6e32\u67d3\u3002 \u9664\u4e86\u4eba\u7c7b\u6bdb\u53d1\uff0cKhungurn\u548cMarschner[2017]\u63a2\u8ba8\u4e86\u692d\u5706\u5f62\u6bdb\u53d1\u7684\u5efa\u6a21\u3002Yan[2015, 2017]\u7814\u7a76\u4e86\u5e26\u6709\u5185\u90e8\u9ad3\u8d28\u7684\u52a8\u7269\u6bdb\u53d1\u3002Aliaga[2017]\u5c06\u6a21\u578b\u63a8\u5e7f\u81f3\u6709\u66f4\u52a0\u590d\u6742\u622a\u9762\u7684\u7eba\u7ec7\u7ea4\u7ef4\u3002<\/li>\n\n\n\n<li><strong>\u57fa\u4e8e\u6ce2\u52a8\u5149\u5b66\u7684\u7ea4\u7ef4\u6a21\u578b<\/strong> Linder[2014]\u89e3\u6790\u4e86\u5177\u6709\u5b8c\u5168\u5706\u5f62\u622a\u9762\u7684\u5706\u67f1\u7ea4\u7ef4\uff0c\u5e76\u4e14\u63a2\u8ba8\u4e86\u6563\u5c04\u884c\u4e3a\u3002Xia[2020]\u901a\u8fc7\u5728\u5177\u6709\u4efb\u610f\u622a\u9762\u7684\u5706\u67f1\u4e0a\u8fdb\u884c\u4e8c\u7ef4\u6ce2\u52a8\u6a21\u62df\uff0c\u5c55\u793a\u4e86\u4e0e\u51e0\u4f55\u5149\u5b66\u6a21\u578b\u76f8\u6bd4\u7684\u82e5\u5e72\u91cd\u8981\u5dee\u5f02\u3002\u7136\u800c\u8fd9\u4e2a\u6a21\u578b\u662f\u89c4\u5219\u7684\u5706\u5f62\uff0c\u5e76\u6ca1\u6709\u8b6c\u5982\u6bdb\u9cde\u7247\u7b49\u5fae\u89c2\u51e0\u4f55\u7ed3\u6784\u3002Benamira\u548cPattanaik[2021]\u63d0\u51fa\u4e86\u66f4\u52a0\u5feb\u901f\u7684\u6df7\u5408\u6a21\u578b\uff0c\u8fd9\u4e2a\u6a21\u578b\u4ec5\u4ec5\u5728\u524d\u5411\u6563\u5c04\u4f7f\u7528\u6ce2\u52a8\u5149\u5b66\u6c42\u89e3\uff0c\u5176\u4f59\u90e8\u4efd\u5219\u662f\u4f9d\u8d56\u51e0\u4f55\u5149\u5b66\u3002<\/li>\n\n\n\n<li><strong>\u57fa\u4e8e\u7269\u7406\u5149\u5b66\u7684\u5e73\u9762\u6a21\u578b\u6a21\u62df<\/strong> \u7269\u7406\u5149\u5b66\u5e73\u9762\u6a21\u578b\u4f7f\u7528\u7269\u7406\u5149\u5b66\u8fd1\u4f3c\u6765\u6a21\u62df\u5149\u7ebf\u5728\u63a5\u8fd1\u5e73\u9762\u3001\u53ef\u4ee5\u8868\u793a\u4e3a\u9ad8\u5ea6\u573a\u7684\u7c97\u7cd9\u8868\u9762\u4e0a\u7684\u6563\u5c04\u884c\u4e3a\uff0c\u5305\u62ec\u9ad8\u65af\u968f\u673a\u3001\u5468\u671f\u6027\u3001\u9884\u8ba1\u7b97\u548c\u5212\u75d5\u8868\u9762\u3002\u5b83\u4eec\u7ed3\u5408\u4e86Kirchhoff\u6807\u91cf\u884d\u5c04\u7406\u8bba\u548c\u8def\u5f84\u8ffd\u8e2a\u65b9\u6cd5\u6765\u5904\u7406\u6563\u5c04\u4e0e\u53cd\u5c04\uff0c\u5e76\u901a\u8fc7\u5404\u79cd\u6a21\u578b\uff08\u5982Beckmann-Kirchhoff\u548cHarvey-Shack\uff09\u8ba1\u7b97\u5149\u5728\u4e0d\u540c\u7c97\u7cd9\u8868\u9762\u4e0a\u7684\u884d\u5c04\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u6a21\u578b\u5728\u5e73\u9762\u8868\u9762\u4e0a\u6709\u6548\uff0c\u4f46\u7ea4\u7ef4\u51e0\u4f55\u7684\u5c01\u95ed\u6027\u548c\u590d\u6742\u7684\u5149\u7ebf\u4ea4\u4e92\u9700\u8981\u66f4\u590d\u6742\u7684\u5904\u7406\u65b9\u6cd5\u3002<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u7535\u78c1\u5b66<\/strong>\u3001<strong>Spickle Effect<\/strong> \u4e0e <strong>\u7a0b\u5f0f\u5316\u566a\u58f0<\/strong> \u4e0a\u4e00\u7bc7\u6587\u7ae0\u5df2\u7ecf\u63d0\u53ca\u4e86\uff0c\u8fd9\u91cc\u7565\u8fc7\u3002<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><a href=\"https:\/\/zhuanlan.zhihu.com\/p\/776529221\">https:\/\/zhuanlan.zhihu.com\/p\/776529221<\/a><\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">2. Background Research<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u6982\u8ff0<\/h3>\n\n\n\n<p>\u6bdb\u53d1\u5efa\u6a21\u662f\u57fa\u4e8e\u6bdb\u53d1\u7684\u626b\u63cf\u7535\u5b50\u663e\u5fae\u955c\uff08SEM\uff09\u56fe\u50cf\u3002\u53ef\u4ee5\u51c6\u786e\u8fd8\u539f\u6bdb\u53d1\u7684\u5fae\u89c2\u7ed3\u6784\uff0c\u4f8b\u5982\u6bdb\u9cde\u7247\u3001\u7c97\u7cd9\u5ea6\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-184-1024x504.png\" alt=\"\" class=\"wp-image-1240 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"504\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-184-1024x504.png\" alt=\"\" class=\"wp-image-1240 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-184-1024x504.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-184-300x148.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-184-768x378.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-184.png 1044w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u7528\u300cWAVE SIMULATION WITH 3D FIBER MICROGEOMETRY\u300d\u8ba1\u7b97\u7c97\u7cd9\u7ea4\u7ef4\u8868\u9762\u7684\u53cd\u5c04\u548c\u884d\u5c04\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-185-1024x774.png\" alt=\"\" class=\"wp-image-1241 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"774\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-185-1024x774.png\" alt=\"\" class=\"wp-image-1241 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-185-1024x774.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-185-300x227.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-185-768x580.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-185.png 1146w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u57fa\u7840\u4e0a\uff0c\u5f15\u5165\u4e86\u6563\u6591\u7406\u8bba\u6765\u5206\u6790\u6563\u5c04\u6a21\u5f0f\u7684\u7edf\u8ba1\u7279\u6027\u3002\u5e76\u4e14\u7528\u566a\u58f0\u6765\u63cf\u8ff0\u8fd9\u4e9b\u6563\u6591\uff0c\u5927\u5e45\u4f18\u5316\u6a21\u578b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-186.png\" alt=\"\" class=\"wp-image-1242 lazyload\"\/><noscript><img decoding=\"async\" width=\"616\" height=\"224\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-186.png\" alt=\"\" class=\"wp-image-1242 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-186.png 616w, https:\/\/remoooo.com\/wp-content\/uploads\/image-186-300x109.png 300w\" sizes=\"(max-width: 616px) 100vw, 616px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u7136\u540e\u901a\u8fc7\u4e0e\u5b9e\u9645\u6d4b\u91cf\u6570\u636e\u7684\u5bf9\u6bd4\uff0c\u63a8\u5bfc\u51fa\u5408\u7406\u7684\u7ea4\u7ef4\u53c2\u6570\uff08\u4f8b\u5982\u5c3a\u5bf8\u3001\u8868\u76ae\u89d2\u5ea6\u548c\u8868\u9762\u7c97\u7cd9\u5ea6\uff09\u3002\u6700\u540e\u96c6\u6210\u8fdb\u6e32\u67d3\u7cfb\u7edf\u4e2d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3. OVERVIEW<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 Fiber scattering models<\/h3>\n\n\n\n<p>\u8fd9\u4e2a\u6211\u7ffb\u8bd1\u6210\u7ea4\u7ef4\u6563\u5c04\u6a21\u578b\u3002\u8fd9\u4e2a\u4e1c\u897f\u63cf\u8ff0\u7684\u662f\u5355\u6839\u7ea4\u7ef4\u53d1\u751f\u76f8\u4e92\u4f5c\u7528\u3002\u8fd9\u91cc\u7684\u5173\u952e\u6838\u5fc3\u662f<strong>BCSDF\uff08\u53cc\u5411\u66f2\u7ebf\u6563\u5c04\u5206\u5e03\u51fd\u6570\uff09<\/strong>\u3002\u6709\u522b\u4e8e\u5728\u8868\u9762\u53cd\u5c04\u548c\u6298\u5c04\u4e2d\u5e38\u7528\u7684\u53cc\u5411\u6563\u5c04\u5206\u5e03\u51fd\u6570\uff08BSDF\uff09\uff0cBCSDF\u662f\u4e13\u95e8\u4e3a\u66f2\u7ebf\u5f62\u72b6\u7684\u7ea4\u7ef4\u8bbe\u8ba1\u7684\u3002\u4e0b\u9762\u8fd9\u4e2a\u516c\u5f0f\u8bb2\u7684\u662f\uff0c\u7ed9\u5b9a\u67d0\u6ce2\u957f\u7684\u5149\u7167\u5c04\u5728\u4e00\u6839\u7ea4\u7ef4\u4e0a\u65f6\uff0c\u5b83\u4ece\u67d0\u4e2a\u65b9\u5411\u5c04\u5165\u540e\uff0c\u4f1a\u4ece\u53e6\u4e00\u4e2a\u65b9\u5411\u53cd\u5c04\u6216\u900f\u5c04\u51fa\u6765\u3002<br>$$<br>L_r(\\omega_r, \\lambda) = \\int L_i(\\omega_i, \\lambda) S(\\omega_i, \\omega_r, \\lambda) \\cos \\theta_i d\\omega_i \\tag{1}<br>$$<br>\u516c\u5f0f\u5de6\u8fb9\u8868\u793a\u7ed9\u5b9a\u6ce2\u957f $\\lambda$ \uff0c<strong>\u51fa\u5c04<\/strong>\u65b9\u5411 $\\omega_r$ \u4e0b\u7684\u8f90\u5c04\u4eae\u5ea6\u3002$ L_i(\\omega_i, \\lambda)$ \u662f<strong>\u5165\u5c04<\/strong>\u65b9\u5411 $\\omega_i$ \u7684\u8f90\u5c04\u4eae\u5ea6\u3002 $S(\\omega_i, \\omega_r, \\lambda)$ \u662f\u53cc\u5411\u66f2\u7ebf\u6563\u5c04\u5206\u5e03\u51fd\u6570\uff0c\u63cf\u8ff0\u4e86\u5149\u7ebf\u5982\u4f55\u88ab\u7ea4\u7ef4\u201d\u6253\u6563\u201d\u3002$\\cos \\theta_i$ \u662f\u4e3a\u4e86\u8003\u8651\u5165\u5c04\u89d2\u5ea6\u7684\u5f71\u54cd\uff0c\u5982\u679c\u5149\u7ebf\u4ee5\u4e00\u4e2a\u5f88\u5e73\u7684\u89d2\u5ea6\u7167\u5c04\u5230\u7ea4\u7ef4\u4e0a\uff0c\u5b83\u7684\u5f71\u54cd\u4f1a\u6bd4\u5782\u76f4\u7167\u5c04\u65f6\u5c0f\u3002<\/p>\n\n\n\n<p>\u628a\u4e0a\u9762\u8fd9\u4e2a\u516c\u5f0f\u5199\u6210\u7403\u5750\u6807\uff0c\u5e76\u4e14\u628a\u6bcf\u4e00\u79cd\u4e0d\u540c\u7684\u5149\u7ebf\u4e0e\u6bdb\u53d1\u7ea4\u7ef4\u7684\u4ea4\u4e92\u5f53\u4f5c\u4e0d\u540c\u7684\u6a21\u5f0f\uff0c\u7136\u540e\u628a\u4e0d\u540c\u7684\u6563\u5c04\u9879\u7d2f\u52a0\u8d77\u6765\uff1a<br>$$<br>S(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda) = \\sum_{p=0}^{\\infty} S_p(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda)<br>\\tag{2}<br>$$<br>\u7b2c\u4e00\u6563\u5c04\u9879 $S_0$ \u63cf\u8ff0\u8868\u9762\u53cd\u5c04\uff0c\u5373\u4ee5\u524d\u7ecf\u5e38\u8bf4\u7684\u76f4\u63a5\u53cd\u5c04\u9879 $R$ \u3002\u8fd9\u4e00\u9879\u662f\u4e00\u822c\u4ee3\u8868\u4ece\u5149\u6ed1\u7ea4\u7ef4\u7684\u53cd\u5c04\u6216\u8005\u7c97\u7cd9\u7ea4\u7ef4\u8868\u9762\u53cd\u5c04\u7684\u7edf\u8ba1\u5e73\u5747\u503c\u3002\u8bba\u6587\u8fd9\u91cc\u80fd\u66f4\u52a0\u7cbe\u786e\u5730\u8ba1\u7b97\u8fd9\u4e00\u9879\u3002<\/p>\n\n\n\n<p>\u56de\u60f3\u4ee5\u524d\u7684\u6e32\u67d3\u65b9\u6cd5\uff08\u6bd4\u5982Marschner[2003]\uff09\uff0c\u901a\u5e38\u662f\u5c06\u6bcf\u4e00\u4e2a\u6563\u5c04\u6a21\u5f0f $S_p$ \u5206\u89e3\u4e3a\u4e24\u4e2a\u72ec\u7acb\u7684\u51fd\u6570\uff1alongitudinal function $M_p$ \u548canazimuthal function $N_p$ \uff0c\u8fd9\u6837\u7684\u65b9\u6cd5\u5df2\u7ecf\u88ab\u6279\u5224\u8fc7\u662f\u4e0d\u51c6\u786e\u7684\uff0c\u56e0\u6b64\u5e94\u8be5\u907f\u514d\u4f7f\u7528\u4e0b\u9762\u8fd9\u79cd\u53ef\u5206\u79bb\u7684\u8fd1\u4f3c\u65b9\u6cd5\u3002<br>$$<br>S_p(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda) = M_p(\\theta_i, \\theta_r)N_p(\\theta_i, \\phi_i, \\phi_r, \\lambda)<br>\\tag{3}<br>$$<br>\u56e0\u6b64\uff0cXIA[2023]\u91c7\u6837\u4e86\u591a\u4e2a\u7c97\u7cd9\u7ea4\u7ef4\u7684\u6563\u5c04\u53c2\u6570\u5e76\u4e14\u53d6\u5747\u503c\uff0c\u8bb0\u4e3a $S_0,avg$ \u3002 $f(\\theta_h, \\phi_h, \\lambda)$ \u662f\u566a\u58f0\u5206\u91cf\uff0c\u901a\u8fc7\u4e24\u4e2a\u534a\u7a0b\u5411\u91cf\u89d2\u5ea6\u548c\u6ce2\u957f\u6765\u8868\u793a\uff0c\u7528\u6765\u4fee\u6b63\u5f53\u524d\u7684\u7279\u5b9a\u7ea4\u7ef4\u5b9e\u4f8b\u548c\u5747\u503c\u7684\u504f\u5dee\u3002<br>$$<br>S_{0,\\text{sim}}(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda) \\approx S_{0,\\text{avg}}(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda) f(\\theta_h, \\phi_h, \\lambda)<br>\\tag{4}<br>$$<br>\u5f53\u524d\uff0c\u5b8c\u6574\u7684\u7ea4\u7ef4\u6563\u5c04\u6a21\u578b\u5982\u4e0b\u3002\u7b2c\u4e00\u9879\u8868\u793a\u7ea4\u7ef4\u8868\u9762\u7684\u53cd\u5c04\u7684\u6563\u5c04\u6a21\u5f0f\uff0c\u7ed3\u5408\u4e863D\u6ce2\u52a8\u6a21\u62df\u3002\u540e\u9762\u7684\u6c42\u548c\u9879\u662f\u5176\u4ed6\u9ad8\u9636\u7684\u6563\u5c04\u6a21\u5f0f\u4e4b\u548c\u3002<br>$$<br>S_{\\text{prac}}(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda) = S_{0,\\text{prac}}(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda) + \\sum_{p=1}^{\\infty} S_p(\\theta_i, \\theta_r, \\phi_i, \\phi_r, \\lambda)<br>\\tag{5}<br>$$<br>\u5b9e\u9645\u4e0a\uff0c\u6700\u7ec8\u7684\u6563\u5c04\u516c\u5f0f\u66f4\u4e3a\u7b80\u6d01\uff0c\u4ee5\u9002\u5e94\u6709\u66f4\u590d\u6742\u51e0\u4f55\u7ed3\u6784\u7684\u8868\u9762\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2 Speckle theory<\/h3>\n\n\n\n<p>\u6563\u6591\u7406\u8bba\uff08Speckle Theory\uff09\u63cf\u8ff0\u5149\u4e0e\u7c97\u7cd9\u8868\u9762\u76f8\u4e92\u4f5c\u7528\u65f6\u4ea7\u751f\u7684\u968f\u673a\u5149\u5f3a\u5206\u5e03\u73b0\u8c61\u3002Goodman[2007]\u516c\u5f0f\u4e2d\u7684 $A$ \u8868\u793a\u6240\u6709\u76f8\u4f4d\u5411\u91cf\u7684\u53e0\u52a0\uff0c\u5373\u7ed3\u679c\u76f8\u4f4d\u5411\u91cf\uff08Phasor\uff09\uff1a<br>$$<br>\\mathbf{A} = \\frac{1}{\\sqrt{N}} \\sum_{n=1}^{N} a_n = \\frac{1}{\\sqrt{N}} \\sum_{n=1}^{N} a_n e^{i\\phi_n}<br>$$<br>\u4e0a\u5f0f\u4e3a\u6563\u6591\u5f3a\u5ea6\u7684\u7efc\u5408\u8868\u8fbe\uff0c\u6362\u800c\u8a00\u4e4b\uff0c\u7528\u6765\u8868\u793a\u6563\u5c04\u540e\u7684\u5149\u7ebf\u5f3a\u5ea6\u3002\u4ea7\u751f\u8be5\u73b0\u8c61\u7684\u539f\u56e0\u662f\u5149\u7ebf\u4f1a\u5728\u8bb8\u591a\u5fae\u5c0f\u8868\u9762\u4e4b\u95f4\u76f8\u4e92\u53cd\u5c04\u3001\u6298\u5c04\u5e76\u76f8\u4e92\u5e72\u6d89\u3002\u5149\u7ebf\u4f20\u64ad\u53d1\u751f\u7684\u76f8\u4f4d\u5dee\u5bfc\u81f4\u660e\u6697\u4e0d\u5747\u7684\u56fe\u6848\u3002\u901a\u8fc7\u8be5\u516c\u5f0f\uff0c\u53ef\u4ee5\u7edf\u8ba1\u6027\u5730\u8ba1\u7b97\u51fa\u5149\u7ebf\u5982\u4f55\u5728\u7ea4\u7ef4\u8868\u9762\u76f8\u4e92\u5e72\u6d89\uff0c\u5f97\u5230\u6563\u6591\u56fe\u6848\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4. WAVE SIMULATION WITH 3D FIBER MICROGEOMETRY<\/h2>\n\n\n\n<p>\u5728\u6ce2\u52a8\u5149\u5b66\u6a21\u62df\u4e2d\uff0c\u5149\u770b\u4f5c\u4e00\u79cd\u7535\u78c1\u6ce2\u3002\u7531\u76f8\u4e92\u5782\u76f4\u7684\u78c1\u573a\u548c\u7535\u573a\u7ec4\u6210\u3002\u5149\u7ebf\u4e0e\u6bdb\u53d1\u7684\u76f8\u4e92\u4f5c\u7528\uff08\u5982\u6563\u5c04\uff09\u53ef\u4ee5\u8f6c\u5316\u4e3a\u5206\u6790\u7535\u78c1\u573a\u5982\u4f55\u53d7\u5230\u7269\u4f53\u7684\u5f71\u54cd\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 Wave optics<\/h3>\n\n\n\n<p>\u9996\u5148\u9700\u8981\u660e\u767d\uff0c\u5f53\u7535\u78c1\u573a\u968f\u7740\u65f6\u95f4\u5468\u671f\u53d8\u5316\u65f6\uff0c\u79f0\u8be5\u573a\u4e3a\u65f6\u5055\u573a\uff08Time-Harmonic Fields\uff09\u3002\u5728\u65f6\u8c10\u573a\u4e2d\uff0c\u7535\u573a\u548c\u78c1\u573a\u53ef\u4ee5\u901a\u8fc7\u590d\u6570\u8868\u793a\u4e3a\u76f8\u4f4d\u5411\u91cf\uff08phasors\uff09\u3002\u5de7\u5999\u7684\u662f\uff0c\u7535\u573a\u548c\u78c1\u573a\u672c\u8eab\u5c31\u662f\u76f8\u4e92\u5782\u76f4\u3002<br>$$<br>E_{\\text{inst}} = \\Re(E e^{j\\omega t}), \\quad H_{\\text{inst}} = \\Re(H e^{j\\omega t})<br>\\tag{6}<br>$$<br>\u5206\u522b\u662f\u7535\u573a\u548c\u78c1\u573a\uff0c\u53ea\u4e0d\u8fc7\u662f\u5206\u522b\u53d6\u4e86\u5b9e\u6570\u90e8\u5206\u3002\u590d\u6570\u90e8\u5206\u5305\u542b\u4e86\u573a\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u4fe1\u606f\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u8fd9\u4e24\u7ec4\u65b9\u7a0b\u662f<strong>\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4<\/strong>\u5728\u65f6\u8c10\u573a\u4e2d\u7684\u5f62\u5f0f\uff1a<br>$$<br>\\nabla \\times \\mathbf{E} = -\\mathbf{M} &#8211; j\\omega \\mu \\mathbf{H}<br>\\<br>\\nabla \\times \\mathbf{H} = \\mathbf{J} + j\\omega \\varepsilon \\mathbf{E}<br>\\tag{7}<br>$$<br>\u5176\u4e2d\uff0c $\\varepsilon$ \u662f\u4ecb\u7535\u5e38\u6570\uff08\u5f71\u54cd\u7535\u573a\uff09\uff0c $\\mu$ \u662f\u78c1\u5bfc\u7387\uff08\u5f71\u54cd\u78c1\u573a\uff09\u3002\u8fd9\u4e24\u9879\u63cf\u8ff0\u4e86\u6750\u6599\u600e\u4e48\u5f71\u54cd\u7535\u78c1\u573a\u7684\u4f20\u64ad\u3002<\/p>\n\n\n\n<p>\u5f53\u7269\u4f53\uff08\u5982\u7ea4\u7ef4\uff09\u88ab\u4e00\u675f\u5165\u5c04\u6ce2\u7167\u5c04\u65f6\uff0c\u5165\u5c04\u7535\u573a\u548c\u78c1\u573a\u5206\u522b\u7528 $\\mathbf{E}_i$ \u548c $\\mathbf{H}_i$ \u8868\u793a\u3002\u4f46\u662f\u7269\u4f53\u7684\u5b58\u5728\u6539\u53d8\u4e86\u8fd9\u4e9b\u573a\uff0c\u4f7f\u5f97\u6211\u4eec\u89c2\u5bdf\u5230\u7684\u662f<strong>\u603b\u573a<\/strong>\u3002<br>$$<br>\\mathbf{E}_1 = \\mathbf{E}_i + \\mathbf{E}_s, \\quad \\mathbf{H}_1 = \\mathbf{H}_i + \\mathbf{H}_s<br>\\tag{8}<br>$$<br>\u7b80\u800c\u8a00\u4e4b\uff0c\u603b\u573a = \u5165\u5c04\u573a + \u6563\u5c04\u573a\u3002<\/p>\n\n\n\n<p>\u5149\u80fd\u91cf\u968f\u7740\u6563\u5c04\u573a $\\mathbf{E}_s$ \u548c $\\mathbf{H}_s$ \u5411\u5916\u4f20\u64ad\uff0c\u56e0\u6b64\u8ba1\u7b97\u7ea4\u7ef4\u7684\u6563\u5c04\u51fd\u6570\u662f\u5173\u952e\u3002\u600e\u4e48\u7b97\u5462\uff1f<\/p>\n\n\n\n<p>\u5168\u6ce2\u6a21\u62df\u662f\u6700\u4e3a\u51c6\u786e\u7684\u3002\u8fdb\u884c\u5168\u6ce2\u6a21\u62df\u9700\u8981\u5c06\u7269\u4f53\u79bb\u6563\u5316\u4e3a\u7f51\u683c\uff0c\u5e76\u4e14\u9700\u8981\u9ad8\u5206\u8fa8\u7387\uff08\u4e00\u822c\u6765\u8bf4\uff0c\u6bcf\u4e2a\u6ce2\u957f\u81f3\u5c1110\u4e2a\u7f51\u683c\u5355\u5143\uff09\uff0c\u8fd9\u5bfc\u81f4\u9700\u8981\u5904\u7406<strong>\u767e\u4e07\u7ea7\u522b\u7684\u7f51\u683c\u5355\u5143<\/strong>\u3002\u5728\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4e5f\u6709\u63d0\u53ca\u3002<\/p>\n\n\n\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5373\u4fbf\u662f\u6a21\u62df\u4e00\u4e2a\u4ec5\u4ec5\u51e0\u5341\u5fae\u7c73\u957f\u7684\u77ed\u7ea4\u7ef4\u6bb5\uff0c\u4e5f\u9700\u8981\u5904\u7406\u6570\u767e\u4e07\u4e2a\u7f51\u683c\u5355\u5143\u3002<\/p>\n\n\n\n<p>\u56e0\u6b64\uff0c\u91c7\u7528 <strong>\u7269\u7406\u5149\u5b66\u8fd1\u4f3c\uff08PO\uff09<\/strong>\u3002\u5728PO\u4e2d\uff0c\u7269\u4f53\u8868\u9762\u7684\u7535\u6d41\u548c\u78c1\u6d41\uff08\u5206\u522b\u8bb0\u4f5c $J$ \u548c $M$ \uff09\u53ef\u4ee5\u770b\u4f5c\u662f\u6563\u5c04\u573a\u7684\u6b21\u7ea7\u6e90\u5934\u3002\u7535\u78c1\u6d41\u4ea7\u751f\u4e86\u4e8c\u6b21\u8f90\u5c04\uff0c\u5f62\u6210\u6563\u5c04\u6ce2\u3002PO\u5047\u8bbe\u7269\u4f53\u8868\u9762\u53ea\u4f1a\u53d1\u751f\u5355\u6b21\u53cd\u5c04\uff0c\u5ffd\u7565\u591a\u6b21\u53cd\u5c04\u548c\u590d\u6742\u7684\u884d\u5c04\u6548\u5e94\u3002\u5f97\u5230\u8868\u9762\u7684\u7535\u6d41\u548c\u78c1\u6d41\u4e4b\u540e\uff0c\u8ba1\u7b97\u4ed6\u4eec\u4ea7\u751f\u7684\u6563\u5c04\u6ce2\u3002\u901a\u8fc7\u4ece\u8868\u9762\u7535\u6d41\u548c\u78c1\u6d41\u4e2d\u63a8\u5bfc\u51fa\u8fd9\u4e9b\u8fdc\u573a\u6ce2\u7684\u6027\u8d28\u3002<\/p>\n\n\n\n<p>\u5149\u4e00\u4e2aPO\u8fd8\u4e0d\u591f\uff0c\u8fd8\u5f97\u63c9\u4e2a\u516b\u53c9\u6811\u7b97\u6cd5\u8fdb\u53bb\u52a0\u901f\u8fdc\u573a\u8ba1\u7b97\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.2 Physical Optics Approximation<\/h3>\n\n\n\n<p>\u5177\u4f53\u5730\uff0cPO\u505a\u4e86\u4e24\u4e2a\u7b80\u5316\u5047\u8bbe\uff1a\u5355\u6b21\u6563\u5c04\u4e0e\u5c40\u90e8\u5e73\u9762\u5047\u8bbe\u3002\u8fd9\u4e2a\u65b9\u6cd5\u4e5f\u8db3\u591f\u901a\u7528\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-187-1024x803.png\" alt=\"\" class=\"wp-image-1243 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"803\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-187-1024x803.png\" alt=\"\" class=\"wp-image-1243 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-187-1024x803.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-187-300x235.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-187-768x603.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-187.png 1114w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u5982\u4e0a\u56fe\uff0c\u67d0\u7269\u4f53\u8868\u9762\u91c7\u6837\u4e86\u591a\u4e2a\u70b9\uff0c\u8fd1\u4f3c\u4e3a\u5e73\u9762\u3002\u8ba1\u7b97\u5207\u5e73\u9762\u7535\u6d41\u548c\u78c1\u573a\uff0c\u8fdb\u800c\u4ea7\u751f\u4e00\u4e2a\u6563\u5c04\u573a\u3002\u901a\u8fc7\u8fd9\u4e2a\u6563\u5c04\u573a\uff0c\u8ba1\u7b97\u8fd9\u4e9b\u7535\u6d41\u548c\u78c1\u6d41\u4ea7\u751f\u7684\u8fdc\u573a\u6563\u5c04\u6ce2\u3002\u4e0e\u6b64\u540c\u65f6\uff0c\u4f7f\u7528Octree\u7ed3\u6784\u5212\u5206\u4e3a\u66f4\u5c0f\u7684\u4f53\u7d20\u3002\u6bcf\u4e2a\u53f6\u8282\u70b9\u7684\u8ba1\u7b97\u7ed3\u679c\u4f1a\u805a\u5408\u81f3\u7236\u8282\u70b9\uff0c\u5f97\u5230\u603b\u7684\u8f90\u5c04\u8d21\u732e\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Surface current calculation.<\/h4>\n\n\n\n<p>\u8868\u9762\u7535\u6d41\u3001\u78c1\u6d41\u7684\u8ba1\u7b97\u662fPO\u6a21\u62df\u4e2d\u975e\u5e38\u5173\u952e\u7684\u4e00\u6b65\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u91c7\u6837\u70b9\uff0c\u5b58\u50a8\u5176\u6cd5\u5411\u91cf $n(r{\\prime})$ \u548c\u9762\u79ef\u4fe1\u606f\u3002\u63a5\u4e0b\u6765\u518d\u6bcf\u4e2a\u5c0f\u5e73\u9762\u8ba1\u7b97\u5165\u5c04\u6ce2\u548c\u8868\u9762\u7535\u6d41\u7684\u76f8\u4e92\u4f5c\u7528\u3002<\/p>\n\n\n\n<p>\u6839\u636e\u5165\u5c04\u6ce2\u7684\u65b9\u5411 $e_i$ \u548c\u8868\u9762\u6cd5\u5411 $n(r{\\prime})$ \uff0c\u5c06\u5165\u5c04\u7535\u573a\u5206\u89e3\u4e3a\u5e73\u884c\u6781\u5316\u548c\u5782\u76f4\u6781\u5316\u5206\u91cf\u3002\u5206\u89e3\u7684\u539f\u56e0\u662f\uff0c\u5e73\u884c\u6781\u5316\u548c\u5782\u76f4\u6781\u5316\u5728\u83f2\u6d85\u5c14\u65b9\u7a0b\u4e2d\uff0c\u662f\u5b8c\u5168\u4e0d\u540c\u7684\u8868\u8fbe\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u5e73\u884c\u6781\u5316\u5206\u91cf\uff1a\u5149\u7684\u7535\u573a\u5e73\u884c\u4e8e\u5165\u5c04\u5149\u7ebf\u7684\u53cd\u5c04\u9762\u3002<br>\u5782\u76f4\u6781\u5316\u5206\u91cf\uff1a\u5149\u7684\u7535\u573a\u5782\u76f4\u4e8e\u5165\u5c04\u5149\u7ebf\u7684\u53cd\u5c04\u9762\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u56e0\u6b64\uff0c\u5f97\u5230\u5165\u5c04\u573a $E_i$ \u88ab\u5206\u89e3\u4e3a\u5e73\u884c\u6781\u5316\u7684\u5206\u91cf $E_i^p$ \u548c\u5782\u76f4\u6781\u5316\u7684\u5206\u91cf $E_i^s$ \uff0c\u957f\u8fd9\u4e2a\u6837\u5b50\uff1a $E_i = E_i^p + E_i^s$ \u3002<\/p>\n\n\n\n<p>\u53cd\u5c04\u573a $E_r$ \u88ab\u8868\u793a\u4e3a\u5e73\u884c\u6781\u5316\u548c\u5782\u76f4\u6781\u5316\u7684\u5206\u91cf\u4e4b\u548c\uff0c\u5165\u5c04\u573a\u65c1\u8fb9\u7684\u7cfb\u6570\u8868\u793a\u83f2\u6d85\u5c14\u65b9\u7a0b\u4e2d\u7684\u53cd\u5c04\uff1a<br>$$<br>E_r = E_r^p + E_r^s = F^p E_i^p + F^s E_i^s<br>\\tag{9-1}<br>$$<br>\u7136\u540e\uff0c\u603b\u7535\u573a $E_1$ \u662f\u5165\u5c04\u573a\u548c\u53cd\u5c04\u573a\u7684\u603b\u548c\uff1a<br>$$<br>E_1 = E_i + E_r<br>\\tag{9-2}<br>$$<br>\u6839\u636e\u4e2d\u5b66\u7269\u7406\uff0c\u6211\u4eec\u77e5\u9053\u7535\u4f1a\u751f\u78c1\uff0c\u78c1\u4e5f\u4f1a\u751f\u7535\u3002\u56e0\u6b64\u6709\u5982\u4e0b\u8868\u8fbe\uff1a<br>$$<br>M = -n \\times E_1,<br>J = n \\times H_1<br>\\tag{10}<br>$$<br>\u56e0\u6b64\uff0c\u6839\u636e\u5165\u5c04\u573a\u548c\u53cd\u5c04\u573a\u5c31\u53ef\u4ee5\u8ba1\u7b97\u51fa\u8868\u9762\u7684\u611f\u5e94\u7535\u6d41\u548c\u78c1\u6d41\u3002\u5f97\u5230\u7535\u6d41\u548c\u78c1\u6d41\u540e\uff0c\u8ba1\u7b97\u8fdc\u573a\u7684\u6563\u5c04\u6ce2\u3002<\/p>\n\n\n\n<p>\u5728\u7406\u8bba\u4e0a\uff0c\u5165\u5c04\u573a\u53ef\u4ee5\u662f\u4efb\u610f\u7684\u3002\u4f46\u662f\u8fd9\u91cc\u4f5c\u8005\u7528\u4e86Gaussian-windowed\u5e73\u9762\u6ce2\u3002\u8fd9\u79cd\u6ce2\u7684\u632f\u5e45\u9075\u5faa\u6b63\u6001\u5206\u5e03\uff0c\u597d\u7b97\u3002<\/p>\n\n\n\n<p>\u603b\u7ed3\u4e00\u4e0b\uff0c\u8fd9\u91cc\u5c06\u5165\u5c04\u5149\u5206\u89e3\u4e3a\u4e24\u4e2a\u5206\u91cf\uff0c\u7528\u83f2\u6d85\u5c14\u65b9\u7a0b\u7b97\u53cd\u5c04\u573a\u3002\u8fdb\u800c\u5c06\u53cd\u5c04\u573a\u4e0e\u5165\u5c04\u573a\u76f8\u52a0\uff0c\u5f97\u5230\u603b\u573a\u3002\u901a\u8fc7\u7535\/\u78c1\u573a\u4e0e\u7535\/\u78c1\u6d41\u7684\u5173\u7cfb\uff0c\u8ba1\u7b97\u8868\u9762\u7684\u611f\u5e94\u7535\/\u78c1\u6d41\u3002\u8fd9\u6837\u5c31\u53ef\u4ee5\u6a21\u62df\u7ea4\u7ef4\u7684\u6563\u5c04\u4e86\u3002<\/p>\n\n\n\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c<strong>\u8ba1\u7b97\u7ea4\u7ef4\u8868\u9762\u7684\u7535\u6d41\u548c\u78c1\u6d41<\/strong>\u7684\u786e\u53ef\u4ee5\u5f97\u5230\u5149\u7684\u6563\u5c04\u884c\u4e3a\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Far-field radiation in 3D<\/h4>\n\n\n\n<p>\u4e0a\u4e00\u8282\u901a\u8fc7\u8868\u9762\u7535\u6d41\u5f97\u5230\u8868\u9762\u7535\u6d41\u548c\u78c1\u6d41\u3002\u672c\u8282\u7528\u8fd9\u4e2a\u4fe1\u606f\u6765\u8ba1\u7b97\u8fdc\u573a\u6563\u5c04\u3002<\/p>\n\n\n\n<p>\u57fa\u4e8e<strong>\u60e0\u66f4\u65af\u539f\u7406\uff08Huygens\u2019s Principle\uff09<\/strong>\u5c06\u539f\u672c\u7684\u6563\u5c04\u95ee\u9898\u8f6c\u5316\u4e3a\u8f90\u5c04\u95ee\u9898\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u60e0\u66f4\u65af\u539f\u7406\u6307\u51fa\uff0c\u6bcf\u4e2a\u6ce2\u524d\u7684\u7535\u90fd\u53ef\u4ee5\u770b\u4f5c\u65b0\u7684\u6b21\u7ea7\u6ce2\u6e90\u3002\u4e00\u73af\u6263\u4e00\u73af\u7684\u611f\u89c9\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u6bdb\u53d1\u7ea4\u7ef4\u8868\u9762\u7684\u7535\u6d41 $J$ \u548c \u78c1\u6d41 $M$ \u88ab\u89c6\u4e3a\u5149\u7ebf\u7684\u6b21\u7ea7\u5149\u6e90\uff0c\u7136\u540e\u91cd\u65b0\u8f90\u5c04\u51fa\u6765\uff0c\u5f97\u5230\u6563\u5c04\u573a\u3002<\/p>\n\n\n\n<p><em>\u8fd9\u91cc\u5c31\u6709\u70b9\u96be\u4e86\uff0c\u6d89\u53ca\u5230\u7535\u78c1\u5b66\u4e2d\u7684\u77e9\u91cf\u6cd5\uff08Method of Moments, MoM\uff09\u3002\u8bfb\u8005\u53ef\u4ee5\u6df1\u5165\u7814\u7a76\u4e00\u4e0bGibson[2021]\u8fd9\u672c\u4e66\uff0c\u5b66\u4f1a\u4e86\u4e00\u5b9a\u8981\u597d\u597d\u6559\u6211\u3002\u4f46\u662f\u6ca1\u5173\u7cfb\uff0c\u6211\u4ece\u95eb\u8001\u5e082021\u5e74\u7684paper\u4e2d\u627e\u4e86\u4e00\u5f20\u56fe\uff0c\u4fdd\u8bc1\u4f60\u80fd\u770b\u61c2\u3002<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-188-1024x530.png\" alt=\"\" class=\"wp-image-1244 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"530\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-188-1024x530.png\" alt=\"\" class=\"wp-image-1244 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-188-1024x530.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-188-300x155.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-188-768x398.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-188-1536x796.png 1536w, https:\/\/remoooo.com\/wp-content\/uploads\/image-188.png 1842w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u56fe\u4e2d\u7684\u7ea2\u8272\u5c0f\u7403\u8868\u793a\u7684<strong>\u6b21\u7ea7\u8f90\u5c04\u6e90<\/strong>\uff0c\u5404\u81ea\u5411\u5916\u8f90\u5c04\uff0c\u7c7b\u4f3c\u4e8e\u8868\u9762\u7535\u6d41\u548c\u78c1\u6d41\u4ea7\u751f\u7684\u6b21\u7ea7\u8f90\u5c04\u6ce2\u3002<br>\u6b21\u7ea7\u8f90\u5c04\u6e90\u5411<strong>\u5404\u4e2a\u65b9\u5411\u53d1\u5c04\u7b49\u5f3a\u5ea6\u7684\u6ce2<\/strong>\uff0c\u8fd9\u4e0e\u672c\u6587\u6563\u5c04\u516c\u5f0f\u4e2d\u6bcf\u4e2a\u8868\u9762\u70b9\u5bf9\u6240\u6709\u65b9\u5411\u90fd\u6709\u6563\u5c04\u8d21\u732e\u7684\u601d\u60f3\u4e00\u81f4\u3002<br>\u56fe\u4e2d\u89c2\u5bdf\u4e86\u8ddd\u79bb\u5149\u6e90\u8fdc\u573a\u533a\u57df\uff08\u8ddd\u79bb\u4e3a $r$ \uff09\u7684\u4e00\u5c0f\u7247\u533a\u57df\uff08 $\\delta \\mathbf{r}$ \uff09\u3002\u5728<strong>\u8fdc\u573a\u533a\u57df<\/strong>\u4e2d\uff0c\u5206\u6790\u6ce2\u5728\u4e0d\u540c\u4f4d\u7f6e $\\mathbf{r}_1$ \u548c $\\mathbf{r}_2$ \u7684\u884c\u4e3a\uff0c\u5206\u522b\u6cbf\u7740 $\\hat{r}_1$ \u548c $\\hat{r}_2$ \u4e24\u4e2a\u65b9\u5411\u89c2\u5bdf\u3002\u8fd9\u4e0e\u6563\u5c04\u516c\u5f0f\u4e2d\uff0c\u5728\u8fdc\u573a\u5904\u8ba1\u7b97\u6563\u5c04\u7535\u573a\u7684\u884c\u4e3a\u975e\u5e38\u76f8\u4f3c\u3002<br>\u56fe\u4e2d\u53f3\u4fa7\u7684\u5149\u6ce2\u4f1a\u5728<strong>\u8fdc\u573a\u53e0\u52a0<\/strong>\u5f62\u6210\u590d\u6742\u7684\u5e72\u6d89\u6761\u7eb9\uff0c\u8fd9\u7c7b\u4f3c\u4e8e\u6563\u5c04\u516c\u5f0f\u4e2d\u7684\u79ef\u5206\u9879\uff0c\u5c06\u6b21\u7ea7\u8f90\u5c04\u6e90\u7684\u7535\u78c1\u6ce2\u5728\u8fdc\u5904\u53e0\u52a0\u3002<\/p>\n\n\n\n<p>\u7528\u516c\u5f0f\u5219\u8868\u793a\u4e3a\uff1a<br>$$<br>E_s(\\mathbf{r}) = j \\omega \\mu_0 \\frac{e^{-jk_0 R}}{4\\pi R} \\hat{r} \\times \\int_\\Gamma \\left[ \\hat{r} \\times \\mathbf{J}(r{\\prime}) + \\frac{1}{Z_0} \\mathbf{M}(r{\\prime}) \\right] e^{jk_0 r{\\prime} \\cdot \\hat{r}} d\\mathbf{r{\\prime}}<br>\\tag{11}<br>$$<br>\u7ed3\u5408\u56fe\u6765\u7406\u89e3\uff0c\u516c\u5f0f\u63cf\u8ff0\u7684\u662f\u6563\u5c04\u7535\u573a $E_s(\\mathbf{r})$ \u5728\u8fdc\u5904\uff08\u8fdc\u573a\uff09\u67d0\u4e00\u70b9 $\\mathbf{r}$ \u5904\u7684\u8868\u73b0\uff0c\u4e0e\u8ddd\u79bb\u5448 $1\/R$ \u5173\u7cfb\u8870\u51cf\u3002\u8fd9\u4e2a\u516c\u5f0f\u662f\u4e00\u4e2a\u4e8c\u7ef4\u590d\u6570\u5e73\u9762\uff0c\u4e5f\u5c31\u662f\u628a\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4\u7684\u89e3\u770b\u4f5c<strong>\u65f6\u8c10\u7535\u78c1\u6ce2<\/strong>\u7684\u5f62\u5f0f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-189-1024x511.png\" alt=\"\" class=\"wp-image-1245 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"511\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-189-1024x511.png\" alt=\"\" class=\"wp-image-1245 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-189-1024x511.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-189-300x150.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-189-768x383.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-189-1536x766.png 1536w, https:\/\/remoooo.com\/wp-content\/uploads\/image-189-2048x1021.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u770b\u8fd9\u4e2a\u4e0a\u5f0f\u7ed3\u6784\uff0c\u5f62\u5f0f\u4e0a\u8ddf $\\mathbf{E}(\\mathbf{r}, t) = \\mathbf{E}_0 e^{j(\\omega t &#8211; k \\cdot \\mathbf{r})}$ \u5f88\u50cf\uff0c\u53eb\u7535\u573a\u7684\u5e38\u89c1\u65f6\u8c10\u89e3\u3002<\/p>\n\n\n\n<p>\u5bf9\u5e94\u8d77\u6765\u3002 $ j \\omega \\mu_0$ \u8fd9\u865a\u6570\u9879\u63cf\u8ff0<strong>\u78c1\u573a\u5bf9\u7535\u573a\u7684\u5f71\u54cd<\/strong>\uff0c\u4e0e\u7535\u78c1\u573a\u7684\u9891\u7387 $\\omega$ \u548c\u771f\u7a7a\u4e2d\u7684\u78c1\u5bfc\u7387 $\\mu_0$ \u76f8\u5173\u3002\u5149\u6ce2\u7684\u9891\u7387\u8d8a\u9ad8\uff0c\u7535\u573a\u8d8a\u5f3a\u3002 $e^{-jk_0 R}$ \u662f\u76f8\u4f4d\u56e0\u5b50\uff0c\u8868\u793a\u5149\u6ce2\u5728\u4f20\u64ad\u4e2d\u7684\u76f8\u4f4d\u53d8\u5316\u3002\u6ce2\u6570 $k_0 = \\frac{2\\pi}{\\lambda}$ \uff0c $\\lambda$ \u662f\u7535\u78c1\u6ce2\u7684\u6ce2\u957f\u3002\u8868\u793a\u6ce2\u4f20\u64ad\u5230\u8ddd\u79bb R \u7684\u5730\u65b9\u65f6\uff0c\u7535\u573a\u7684\u76f8\u4f4d\u4f1a\u53d1\u751f\u53d8\u5316\u3002 $\\hat{r}$ \u662f\u4ece\u6563\u5c04\u7269\u4f53\u6307\u5411\u89c2\u5bdf\u70b9\u7684\u5355\u4f4d\u5411\u91cf\uff0c\u8868\u793a\u6ce2\u7684\u4f20\u64ad\u65b9\u5411\u3002\u53c9\u4e58 $\\times$ \u64cd\u4f5c\u7b26\u8868\u793a\u8ba1\u7b97\u7684\u662f\u7535\u573a\u7684\u65b9\u5411\u3002\u786e\u4fdd\u8ba1\u7b97\u51fa\u7684\u7535\u573a\u548c\u6ce2\u4f20\u64ad\u7684\u65b9\u5411\u4e00\u81f4\u3002<\/p>\n\n\n\n<p>\u79ef\u5206\u9879 $ \\int_\\Gamma \\left[ \\hat{r} \\times \\mathbf{J}(r{\\prime}) + \\frac{1}{Z_0} \\mathbf{M}(r{\\prime}) \\right] e^{jk_0 r{\\prime} \\cdot \\hat{r}} d\\mathbf{r{\\prime}} $ \u662f\u8be5\u516c\u5f0f\u7684\u6838\u5fc3\u3002\u5bf9\u7269\u4f53\u8868\u9762 $\\Gamma$ \u8fdb\u884c\u79ef\u5206\uff0c\u5f97\u5230\u6bdb\u53d1\u8868\u9762\u6bcf\u4e2a\u70b9\u5bf9\u6563\u5c04\u7535\u573a\u7684\u8d21\u732e\u3002\u6bcf\u4e2a\u70b9\u7684\u8868\u9762\u7535\u6d41\u52a0\u8868\u9762\u78c1\u6d41\u4e4b\u548c\uff0c\u518d\u70b9\u4e58\u76f8\u4f4d\u56e0\u5b50\u3002\u8fdb\u4e00\u6b65\u7684\uff0c $\\mathbf{J}(r{\\prime})$ \u662f\u8868\u9762\u7535\u6d41\u5bc6\u5ea6\uff0c $\\hat{r} \\times$ \u786e\u4fdd\u4e86\u7535\u6d41\u4ea7\u751f\u7684\u6563\u5c04\u7535\u573a\u4e0e\u6ce2\u7684\u4f20\u64ad\u65b9\u5411 $\\hat{r}$ \u6b63\u4ea4\u3002 $Z_0$ \u662f\u81ea\u7531\u7a7a\u95f4\u963b\u6297\uff08free space impedance\uff09\uff0c\u5177\u4f53\u6570\u503c $Z_0 = \\sqrt{\\frac{\\mu_0}{\\varepsilon_0}} \\approx 377 \\, \\Omega$ \uff0c\u4e2a\u4eba\u7406\u89e3\u8be5\u5e38\u6570\u662f\u771f\u7a7a\u4e2d\u7535\u573a\u548c\u78c1\u573a\u7684\u6bd4\u4f8b\u5173\u7cfb\uff0c\u7535\u573a\u548c\u78c1\u573a\u7684\u6297\u963b\u4e0d\u540c\u56e0\u6b64\u9700\u8981\u7edf\u4e00\u5c3a\u5ea6\u624d\u80fd\u7ebf\u6027\u76f8\u52a0\uff0c\u5373\u5c06\u78c1\u6d41\u89c4\u8303\u5316\u5230\u548c\u7535\u6d41\u7c7b\u4f3c\u7684\u5f62\u5f0f\u3002\u6307\u6570\u9879\u4e5f\u662f\u76f8\u4f4d\u56e0\u5b50\uff0c\u4e0d\u505a\u8fc7\u591a\u89e3\u91ca\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u7ec6\u5fc3\u7684\u8bfb\u8005\u53ef\u80fd\u53d1\u73b0\uff0c\u4e3a\u4f55\u8868\u9762\u7535\u6d41\u5bc6\u5ea6 $\\mathbf{J}(r{\\prime})$ \u6709\u53c9\u4e58 $\\hat{r} \\times \\mathbf{J}(r{\\prime})$ \uff0c\u800c\u8868\u9762\u78c1\u6d41\u5bc6\u5ea6 $\\mathbf{M}(r{\\prime})$ \u6ca1\u6709\u53c9\u4e58\u3002<\/p>\n\n\n\n<p>\u6839\u636e\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4\uff0c\u7535\u573a\u548c\u78c1\u573a\u662f\u4e92\u76f8\u6b63\u4ea4\u7684\u3002\u7535\u6d41 $\\mathbf{J}$ \u4f1a\u4ea7\u751f\u78c1\u573a\uff0c\u53d8\u5316\u7684\u78c1\u573a\u518d\u53cd\u8fc7\u6765\u4ea7\u751f\u7535\u573a\u3002<strong>\u7535\u573a\u548c\u78c1\u573a\u662f\u76f8\u4e92\u8026\u5408\u7684<\/strong>\u3002\u4f46\u662f\uff0c\u6211\u4eec\u91cd\u65b0\u770b\u770b\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4\u7684\u4e0b\u9762\u4e24\u6761\u3002<br>$$<br>\\nabla \\times \\mathbf{E} = -\\frac{\\partial \\mathbf{B}}{\\partial t}<br>\\<br>\\nabla \\times \\mathbf{B} = \\mu_0 \\mathbf{J} + \\mu_0 \\varepsilon_0 \\frac{\\partial \\mathbf{E}}{\\partial t}<br>$$<br>\u78c1\u573a\u7684\u751f\u6210\u662f\u76f4\u63a5\u901a\u8fc7\u4f4d\u79fb\u7535\u573a\u6765\u5b9e\u73b0\u7684\uff0c\u65b9\u5411\u5df2\u7ecf\u548c\u7535\u573a\u6b63\u4ea4\u3002\u800c\u7535\u573a\u7684\u4ea7\u751f\u662f\u78c1\u573a\u7684\u53d8\u5316\u7387\uff0c\u65b9\u5411\u6027\u9700\u8981\u8c03\u6574\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u6362\u4e00\u4e2a\u89d2\u5ea6\u6765\u7406\u89e3\uff0c\u79ef\u5206\u9879\u5de6\u8fb9\u63cf\u8ff0\u7684\u662f<strong>\u7535\u78c1\u573a\u5f3a\u5ea6\u968f\u8ddd\u79bb\u8870\u51cf<\/strong>\uff0c\u4e5f\u8003\u8651\u4e86\u76f8\u4f4d\u53d8\u5316\u548c\u65b9\u5411\u6027\u3002\u79ef\u5206\u9879\u63cf\u8ff0<strong>\u6bcf\u4e2a\u8868\u9762\u70b9\u7684\u7535\u78c1\u6d41\u4e0e\u76f8\u4f4d\u8d21\u732e<\/strong>\u3002<\/p>\n\n\n\n<p>\u603b\u7ed3\uff0c\u516c\u5f0f(11)\u662f\u4e00\u4e2a\u7cbe\u786e\u7684\u8868\u8fbe\uff0c\u63cf\u8ff0\u7269\u4f53\u8868\u9762\u7535\u78c1\u573a\u5982\u4f55\u5728\u8ddd\u79bb $r$ \u5904\u6563\u5c04\u3002\u5f97\u5230\u4e86\u7535\u573a\u7684\u516c\u5f0f\uff0c\u78c1\u573a\u5c31\u5f88\u5bb9\u6613\u8ba1\u7b97\u4e86\u3002<\/p>\n\n\n\n<p>\u5f53\u6563\u5c04\u8ddd\u79bb $R$ \u8db3\u591f\u5927\u65f6\uff0c\u8fdc\u573a\u7684\u7b80\u5316\u8868\u8fbe\u5f0f\u5982\u4e0b\uff0c\u53ef\u4ee5\u76f4\u63a5\u5ffd\u7565\u8fd1\u573a\u6548\u5e94\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5728\u8fdc\u573a\u4e2d\uff0c\u4f20\u64ad\u7279\u6027\u5df2\u7ecf\u8d8b\u4e8e\u7a33\u5b9a\uff0c\u56e0\u6b64\u53ef\u4ee5\u628a\u79ef\u5206\u9879\u7b80\u5316\u4e3a\u4e0e\u6563\u5c04\u65b9\u5411 $\\hat{r}$ \u76f8\u5173\u7684\u9879\uff0c\u5373 $E_s^{\\text{far}}(\\hat{r})$ \u3002<br>$$<br>E_s(r) = \\frac{e^{-jk_0 R}}{R} E_s^{\\text{far}}(\\hat{r}), \\quad H_s(r) = \\frac{e^{-jk_0 R}}{R} H_s^{\\text{far}}(\\hat{r})<br>\\tag{12}<br>$$<br>\u6b64\u5916\uff0c\u82e5\u76f4\u63a5\u8ba1\u7b97\u6bcf\u4e2a\u70b9\u7684\u8d21\u732e\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a $O(MN)$ \uff0c\u5373\u79bb\u6563\u70b9\u6570$M$ $*$ \u6563\u5c04\u65b9\u5411\u6570$N$ \u3002\u6b64\u5904\u5f15\u5165\u516b\u53c9\u6811\uff0c\u901a\u8fc7\u7a7a\u95f4\u5212\u5206\u51cf\u5c11\u8ba1\u7b97\u8868\u9762\u7684\u79bb\u6563\u70b9\u6570\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u964d\u5230\u4e86 $O(M+log(M)N)$ \u3002\u5177\u4f53\u5b9e\u73b0\u65b9\u5f0f\u57284.3\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.3 Multilevel fast Physical Optics<\/h3>\n\n\n\n<p>\u7528\u591a\u5c42\u5feb\u901f\u7269\u7406\u5149\u5b66\uff08Multilevel Fast Physical Optics, MFPO\uff09\u52a0\u901f\u8fdc\u573a\u6563\u5c04\u8ba1\u7b97\u3002<\/p>\n\n\n\n<p>Chew[2001]\u63d0\u51fa\u7684\u591a\u5c42\u5feb\u901f\u591a\u6781\u5b50\u7b97\u6cd5\uff08MLFMA\uff09\uff0c\u7528\u4e8e\u52a0\u901f\u6c42\u89e3\u7535\u78c1\u573a\u6563\u5c04\u95ee\u9898\u3002\u8fd9\u4e2a\u7b97\u6cd5\u9996\u5148\u4e3a\u4f8b\u5982\u6bdb\u53d1\u8868\u9762\u6784\u5efa\u4e00\u4e2a\u516b\u53c9\u6811\u7ed3\u6784\uff0c\u6bcf\u4e2a\u53f6\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u91c7\u6837\u70b9\u3002\u6784\u5efa\u5b8cOctree\u540e\u8ba1\u7b97\u6bcf\u4e2a\u53f6\u8282\u70b9\u7684\u8868\u9762\u7535\u6d41\u3001\u78c1\u6d41\u3002\u63a5\u7740\u4ece\u53f6\u8282\u70b9\u51fa\u53d1\u9010\u5c42\u5411\u4e0a\u7d2f\u79ef\u3002\u4ece\u539f\u672c\u7684 $O(MN)$ \u964d\u4f4e\u5230 $O(M + \\log(M)N)$ \u3002<\/p>\n\n\n\n<p>\u63a5\u7740\u4f5c\u8005\u4ecb\u7ecd\u4e86\u516b\u53c9\u6811\u52a0\u901f\u7b97\u6cd5\u7684\u4e09\u4e2a\u5173\u952e\u90e8\u5206\u3002\u9996\u5148\u662f\u8fdc\u573a\u6563\u5c04\u6838\uff08far-field scattering kernel\uff09\u3002<br>$$<br>e^{jk_0 r{\\prime} \\cdot \\hat{r}} = e^{jk_0 (r{\\prime} &#8211; c_L) \\cdot \\hat{r}} \\prod_{i=1}^{L} e^{jk_0 (c_i &#8211; c_{i-1}) \\cdot \\hat{r}}<br>\\tag{13}<br>$$<br>\u6700\u7ec8\u76ee\u6807\u662f\u8ba1\u7b97\u7269\u4f53\u8868\u9762\u6bcf\u4e2a\u70b9\u7684\u7535\u78c1\u6ce2\u5bf9\u67d0\u4e2a\u8fdc\u573a\u89c2\u5bdf\u533a\u57df\uff08\u8ddd\u79bb\u4e3a $R$ \uff0c\u65b9\u5411\u4e3a $\\hat{r}$ \uff09\u7684\u6563\u5c04\u8d21\u732e\u3002\u5177\u4f53\u662f\u6c42\u6563\u5c04\u7535\u573a $E_s(r)$ \u548c\u78c1\u573a $H_s(r)$ \uff0c\u5373\u4ece\u6bdb\u53d1\u8868\u9762\u4e0a\u7684\u6bcf\u4e2a\u70b9 $r{\\prime}$ \u53d1\u51fa\u7684\u7535\u78c1\u6ce2\u5728\u8fdc\u573a\u4e2d\u7684\u8d21\u732e\u3002\u516c\u5f0f\u7b49\u53f7\u5de6\u8fb9\u662f\u67d0\u8868\u9762\u70b9 $r{\\prime}$ \u5230\u8fdc\u573a\u89c2\u5bdf\u65b9\u5411 $\\hat{r}$ \u7684\u76f8\u4f4d\u53d8\u5316\u3002\u6700\u7ec8\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a $O(MN)$ \u3002\u4f5c\u8005\u628a\u8868\u9762\u5206\u4e3a\u4e0d\u540c\u7684\u533a\u57df\uff0c\u6bcf\u4e2a\u533a\u57df\u6307\u5b9a\u4e00\u4e2a\u53c2\u8003\u4e2d\u5fc3\u70b9\uff0c\u516c\u5f0f\u4e2d\u7684 $c_0, c_1, \u2026, c_L$ \u662f\u516b\u53c9\u6811\u4e2d\u4e0d\u540c\u5c42\u6b21\u7684\u8282\u70b9\u4e2d\u5fc3\u3002<\/p>\n\n\n\n<p>\u5149\u662f\u8fd9\u6837\u4e5f\u6ca1\u529e\u6cd5\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002\u56e0\u6b64\u9700\u8981\u5c06\u8ddd\u79bb\u8f83\u8fd1\u7684\u8868\u9762\u70b9\uff0c\u7531\u4e8e\u5b83\u4eec\u7684\u76f8\u4f4d\u53d8\u5316\u5dee\u522b\u5f88\u5c0f\uff0c\u901a\u8fc7\u516b\u53c9\u6811\u7684\u9ad8\u5c42\u8282\u70b9\u5408\u5e76\u8fd9\u4e9b\u70b9\u7684\u8d21\u732e\u3002<\/p>\n\n\n\n<p>\u8fd8\u662f\u7528\u95eb\u8001\u5e08\u8fd9\u5e45\u56fe\u6765\u89e3\u91ca\u3002\u5bf9\u4e8e\u8fdc\u573a\u7684\u67d0\u4e2a\u533a\u57df $\\delta \\mathbf{r} $ \uff0c\u9996\u5148\u8fd8\u662f\u4f1a\u7cbe\u786e\u8ba1\u7b97\u6240\u6709\u91c7\u6837\u70b9\u5bf9\u53c2\u8003\u70b9 $\\mathbf{r}$ \u7684\u8d21\u732e\u3002\u4f46\u662f\u8be5\u533a\u57df\u7684\u5176\u4ed6\u70b9\u5219\u7528\u516b\u53c9\u6811\u7684\u7236\u8282\u70b9\u8fdb\u884c\u8fd1\u4f3c\u8ba1\u7b97\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u65c1\u8fb9\u7684 $\\mathbf{r}_1$ \u548c $\\mathbf{r}_2$ \u5c31\u4e0d\u518d\u9700\u8981\u8003\u8651\u8fd9\u4e48\u591a\u7684\u91c7\u6837\u70b9\u4e86\uff0c\u800c\u662f\u76f4\u63a5\u7528\u516b\u53c9\u6811\u5f97\u5230\u7684\u603b\u8d21\u732e\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-190-1024x530.png\" alt=\"\" class=\"wp-image-1246 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"530\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-190-1024x530.png\" alt=\"\" class=\"wp-image-1246 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-190-1024x530.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-190-300x155.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-190-768x398.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-190-1536x796.png 1536w, https:\/\/remoooo.com\/wp-content\/uploads\/image-190.png 1842w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u4f5c\u8005\u5b9a\u4e49\u4e86\u4e00\u4e2a\u65b9\u5411\u96c6\uff0c\u516b\u53c9\u6811\u6bcf\u4e2a\u7236\u8282\u70b9\u90fd\u5b58\u50a8\u4e86\u5173\u4e8e\u4e0d\u540c\u65b9\u5411\u96c6\u7684\u7d2f\u79ef\u8d21\u732e\u6570\u636e\u3002\u56e0\u6b64\uff0c\u7236\u8282\u70b9\u4e0d\u4ec5\u5305\u542b\u7a7a\u95f4\u4e0a\u7684\u4fe1\u606f\uff0c\u8fd8\u5305\u542b\u591a\u4e2a\u6563\u5c04\u65b9\u5411\u4e0a\u7684\u7d2f\u79ef\u4fe1\u606f\u3002\u6700\u7ec8\u5728\u6839\u8282\u70b9\u5f97\u5230\u5b8c\u6574\u7684360\u5ea6\u6563\u5c04\u573a\u5206\u5e03\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-191-1024x154.png\" alt=\"\" class=\"wp-image-1247 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"154\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-191-1024x154.png\" alt=\"\" class=\"wp-image-1247 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-191-1024x154.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-191-300x45.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-191-768x115.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-191.png 1038w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u4ece\u6811\u7684\u7b2c\u4e8c\u5c42\u5f00\u59cb\uff0c\u4f9d\u6b21\u5411\u4e0a\u5408\u5e76\u3002\u4e0a\u91c7\u6837\u5177\u4f53\u65b9\u6cd5\u662f\u5bf9\u5b50\u8282\u70b9\u7684\u65b9\u5411\u96c6\u4e2d\u7684\u6563\u5c04\u8d21\u732e\u505a\u6b63\u5411FFT\uff0c\u63a5\u7740zero-padding\u6269\u5145\u9891\u57df\u6570\u636e\u6700\u540e\u9006\u5411FFT\u8f6c\u6362\u4e3a\u7a7a\u95f4\u57df\u3002\u6700\u7ec8\uff0c\u4f7f\u5f97\u7236\u8282\u70b9\u53ef\u4ee5\u5728\u4e0d\u540c\u65b9\u5411\u4e0a\u5f97\u5230\u66f4\u52a0\u7cbe\u786e\u7684\u6563\u5c04\u4fe1\u606f\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Performance<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u516b\u53c9\u6811\u52a0\u901f\u6548\u679c\u5f88\u597d\u3002\u4e09\u5c42\u6811\u6548\u679c\u6700\u4f73\u3002\u8d8a\u590d\u6742\u7684\u7ea4\u7ef4\u4f18\u5316\u6548\u679c\u8d8a\u597d\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-192-1024x570.png\" alt=\"\" class=\"wp-image-1248 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"570\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-192-1024x570.png\" alt=\"\" class=\"wp-image-1248 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-192-1024x570.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-192-300x167.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-192-768x428.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-192.png 1088w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Fiber microgeometry and scattering patterns<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u6bdb\u53d1\u7ea4\u7ef4\u6a2a\u622a\u9762\u4e00\u822c\u4e0d\u662f\u5b8c\u7f8e\u7684\u5706\u5f62\uff0c\u800c\u662f\u692d\u5706\u5f62\u3002\u901a\u8fc7\u692d\u5706\u7684\u4e3b\u534a\u5f84 $r_1$ \u548c\u6b21\u534a\u5f84 $r_2$ \u6765\u5b9a\u4e49\u7ea4\u7ef4\u7684\u51e0\u4f55\u53c2\u6570\u3002\u4e3a\u4e86\u6a21\u62df\u7ea4\u7ef4\u8868\u9762\u7684\u5fae\u89c2\u7c97\u7cd9\u5ea6\uff0c\u4f5c\u8005\u5728\u692d\u5706\u67f1\u4f53\u7684\u8868\u9762\u4e0a\u53e0\u52a0\u4e86\u4e00\u4e2a<strong>\u9ad8\u65af\u968f\u673a\u9ad8\u5ea6\u573a\uff08Gaussian random height field\uff09<\/strong>\uff0c\u6a21\u62df\u771f\u5b9e\u7684\u7ea4\u7ef4\u8868\u9762\u3002\u8fdb\u4e00\u6b65\u5730\uff0c\u52a0\u5165\u4e86<strong>\u89d2\u8d28\u5c42\u503e\u659c\uff08cuticle tilt\uff09<\/strong>\uff0c\u6a21\u62df\u8584\u7247\u5728\u7ea4\u7ef4\u8868\u9762\u503e\u659c\u6392\u5217\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u5bf9\u6bd4\u4f20\u7edf\u7684\u57fa\u4e8e\u5149\u7ebf\u7684\u6bdb\u53d1\u6a21\u578b\uff0c\u6ce2\u52a8\u5149\u5b66\u6a21\u62df\u53d1\u73b0\uff0c\u9664\u4e86XIA[2020]\u9884\u6d4b\u5230\u7684\u663e\u8457\u7684\u5411\u524d\u6563\u5c04\uff08forward-scattering\uff09\u73b0\u8c61\uff0c\u8fd8\u89c2\u5bdf\u5230\u4e86\u590d\u6742\u7684\u6ce2\u957f\u4f9d\u8d56\u9897\u7c92\u56fe\u6848\uff08wavelength-dependent granular patterns\uff09\u3002\u5728\u8f6c\u6362\u4e3aRGB\u989c\u8272\u65f6\uff0c\u4f1a\u751f\u6210\u4e30\u5bcc\u7684\u8272\u5f69\u6548\u679c\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-193-1024x597.png\" alt=\"\" class=\"wp-image-1249 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"597\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-193-1024x597.png\" alt=\"\" class=\"wp-image-1249 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-193-1024x597.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-193-300x175.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-193-768x448.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-193-1536x896.png 1536w, https:\/\/remoooo.com\/wp-content\/uploads\/image-193-2048x1195.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u7814\u7a76\u6307\u51fa\u4e86\u4e00\u4e9b\u4ece\u6a21\u62df\u4e2d\u89c2\u5bdf\u5230\u7684\u89c4\u5f8b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u65e0\u8bba\u5b83\u4eec\u7684\u5b9e\u9645\u4f4d\u7f6e\u5982\u4f55\uff0c\u5177\u6709\u76f8\u540c\u51e0\u4f55\u53c2\u6570\uff08\u5982\u534a\u5f84\u3001\u7c97\u7cd9\u5ea6\u3001\u89d2\u8d28\u5c42\u503e\u659c\u7b49\uff09\u7684\u7ea4\u7ef4\uff0c\u5728\u6563\u5c04\u884c\u4e3a\u4e0a\u4f1a\u751f\u6210<strong>\u76f8\u4f3c\u7684\u9897\u7c92\u56fe\u6848<\/strong>\u3002<\/li>\n\n\n\n<li>\u5982\u679c\u7ea4\u7ef4\u7684\u51e0\u4f55\u53c2\u6570\u4e0d\u540c\uff0c\u5219\u5b83\u4eec\u4f1a\u751f\u6210<strong>\u4e0d\u540c\u7edf\u8ba1\u7279\u6027\u7684\u9897\u7c92\u56fe\u6848<\/strong>\uff0c\u5373\u6563\u5c04\u6a21\u5f0f\u660e\u663e\u4e0d\u540c\u3002<\/li>\n\n\n\n<li>\u6563\u5c04\u6591\u70b9\u7684\u4f4d\u7f6e\u4f9d\u8d56\u4e8e\u5149\u7ebf\u7684\u5165\u5c04\u89d2\u5ea6\uff0c\u504f\u79fb\u7684\u65b9\u5411\u8ddf\u968f<strong>half vector<\/strong>\u65b9\u5411\u3002<\/li>\n\n\n\n<li>\u6591\u70b9\uff08speckle\uff09\u56fe\u6848\u7684\u5927\u5c0f\u968f\u5149\u6ce2\u6ce2\u957f\u7684\u589e\u52a0\u800c\u589e\u5927\u3002\u8fd9\u4e00\u73b0\u8c61\u4e0eGoodman[2007]\u7ed3\u679c\u4e00\u81f4\u3002 <\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-194.png\" alt=\"\" class=\"wp-image-1250 lazyload\"\/><noscript><img decoding=\"async\" width=\"908\" height=\"226\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-194.png\" alt=\"\" class=\"wp-image-1250 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-194.png 908w, https:\/\/remoooo.com\/wp-content\/uploads\/image-194-300x75.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-194-768x191.png 768w\" sizes=\"(max-width: 908px) 100vw, 908px\" \/><\/noscript><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">5. A PRACTICAL FIBER SCATTERING MODEL<\/h2>\n\n\n\n<p><strong>\u5b9e\u7528\u7ea4\u7ef4\u6563\u5c04\u6a21\u578b\uff08A PRACTICAL FIBER SCATTERING MODEL\uff09<\/strong>\u65e8\u5728\u89e3\u51b3\u7ea4\u7ef4\u7684\u5fae\u89c2\u51e0\u4f55\u53d8\u5316\u548c\u590d\u6742\u6563\u5c04\u884c\u4e3a\u3002<\/p>\n\n\n\n<p>\u4ee5\u524d\u7684\u7814\u7a76\u4e00\u822c\u662f\u7528Lut\u5b58\u6563\u5c04\u5206\u5e03\u51fd\u6570\uff0c\u8fd9\u79cd\u65b9\u6cd5\u7a7a\u95f4\u6d88\u8017\u5de8\u5927\uff0c\u9700\u8981\u540c\u65f6\u8bb0\u5f55\u7eb5\u5411\u548c\u65b9\u4f4d\u89d2\u6563\u5c04\u5206\u5e03\u3002<\/p>\n\n\n\n<p>\u73b0\u5728\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u4e00\u79cd<strong>\u57fa\u4e8e\u5c0f\u6ce2\u566a\u58f0\u8868\u793a<\/strong>\u7684\u7d27\u51d1\u7ea4\u7ef4\u6563\u5c04\u6a21\u578b\uff0c\u53ef\u8868\u793a\u7684\u51e0\u4f55\u590d\u6742\u5ea6\u63d0\u9ad8\u4e86\uff0c\u6563\u5c04\u6548\u679c\u66f4\u597d\u4e86\u3002<\/p>\n\n\n\n<p>\u7b80\u5355\u7684\u8bf4\uff0c\u4f5c\u8005\u60f3\u8981\u7d27\u51d1\u7684\u7edf\u8ba1\u6563\u6591\u73b0\u8c61\uff0c\u4f7f\u5176\u53ef\u4ee5\u901a\u8fc7<strong>\u5747\u503c<\/strong>\u3001<strong>\u65b9\u5dee<\/strong>\u3001<strong>\u81ea\u76f8\u5173\u51fd\u6570<\/strong>\uff08ACF\uff09\u7b49\u7edf\u8ba1\u91cf\u6765\u8868\u793a\u3002\u56e0\u6b64\u4f5c\u8005\u501f\u52a9\u4e86<strong>\u6563\u6591\u7406\u8bba\uff08Speckle Theory\uff09<\/strong>\u6765\u63cf\u8ff0\u5149\u968f\u673a\u5e72\u6d89\u6240\u4ea7\u751f\u7684\u56fe\u6837\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.1 Speckle statistics<\/h3>\n\n\n\n<p>\u8fd9\u91cc\u4f5c\u8005\u4e0a\u6765\u5c31\u63d0\u5230<strong>\u5b8c\u5168\u53d1\u5c55\u7684\u6563\u6591 (Fully Developed Speckle)<\/strong>\u8fd9\u4e2a\u6982\u5ff5\u3002\u4ee5\u4e0b\u662f\u4e2a\u4eba\u7406\u89e3\u3002\u5728\u5149\u7ebf\u7167\u5c04\u5230\u4e00\u4e2a\u7c97\u7cd9\u7684\u8868\u9762\uff08\u6bd4\u5982\u7ea4\u7ef4\/\u6bdb\u53d1\u8868\u9762\uff09\u65f6\uff0c\u8868\u9762\u4e0a\u7684\u6bcf\u4e2a\u5c0f\u533a\u57df\u90fd\u4f1a\u6563\u5c04\u5149\u7ebf\u3002\u7531\u4e8e\u8868\u9762\u7684\u5fae\u5c0f\u4e0d\u89c4\u5219\u6027\uff0c\u6563\u5c04\u7684\u5149\u7ebf\u4e4b\u95f4\u4f1a\u76f8\u4e92\u5e72\u6d89\uff0c\u4ea7\u751f\u4e00\u4e2a\u590d\u6742\u7684\u5149\u5f3a\u5206\u5e03\u3002\u8fd9\u79cd\u5206\u5e03\u8868\u73b0\u4e3a\u4e00\u7cfb\u5217<strong>\u4eae\u70b9\u548c\u6697\u70b9<\/strong>\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u6563\u6591<\/strong>\u3002\u8868\u9762\u7684\u5fae\u5c0f\u7279\u5f81\uff08\u6bd4\u5982\u7c97\u7cd9\u5ea6\uff09\u5728\u6574\u4e2a\u7167\u5c04\u533a\u57df\uff08\u76f8\u5bf9\u4e8e\u5149\u7ebf\u7684\u6ce2\u957f\u6765\u8bf4\uff09\u53d8\u5f97\u8db3\u591f\u4e0d\u89c4\u5219\uff0c\u5bfc\u81f4\u6563\u5c04\u5149\u7ebf\u5728\u5404\u4e2a\u70b9\u4e0a\u7684\u76f8\u4f4d\u548c\u5f3a\u5ea6\u662f\u968f\u673a\u7684\uff0c\u8fd9\u5c31\u662f\u6240\u8c13\u7684<strong>\u5b8c\u5168\u53d1\u5c55\u7684\u6563\u6591<\/strong>\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u65f6\u5019\uff0c\u53ef\u4ee5\u7528Goodman[2007]\u7684complex Gaussian distribution\u6765\u63cf\u8ff0Fully Developed Speckle\u3002\u5373\uff0c\u7535\u78c1\u573a\u7684\u5b9e\u90e8 $\\mathcal{R}$ \u548c\u865a\u90e8 $\\mathcal{I}$ \u5728\u7a7a\u95f4\u4e0a\u670d\u4ece\u590d\u9ad8\u65af\u5206\u5e03\uff08complex Gaussian distribution\uff09\u3002<br>$$<br>p_{\\mathcal{R},\\mathcal{I}}(\\mathcal{R}, \\mathcal{I}) = \\frac{1}{2 \\pi \\sigma^2} \\exp\\left( &#8211; \\frac{\\mathcal{R}^2 + \\mathcal{I}^2}{2\\sigma^2} \\right)<br>\\tag{14}<br>$$<br>\u573a\u7684\u5b9e\u90e8\u548c\u865a\u90e8\u662f\u72ec\u7acb\u4e14\u6b63\u6001\u5206\u5e03\u7684\u3002\u5747\u503c\u4e3a\u96f6\uff0c\u65b9\u5dee\u76f8\u540c\u3002<\/p>\n\n\n\n<p>\u7535\u78c1\u573a\u5149\u5f3a $I$ \u548c\u8be5\u5149\u5f3a\u5206\u5e03\u7684\u670d\u4ece\u6307\u6570\u5206\u5e03\uff08exponential distribution\uff09\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff1a<br>$$<br>I = \\mathcal{R}^2 + \\mathcal{I}^2 \\ p_I(I) = \\frac{1}{2\\sigma^2} \\exp\\left( -\\frac{I}{2\\sigma^2} \\right)<br>\\tag{15}<br>$$<br>\u8fd9\u4e9b\u516c\u5f0f\u6ca1\u5565\u53ef\u8bb2\u7684\uff0c\u603b\u4e4b\u6563\u6591\u573a\u5c31\u662f\u5f88\u968f\u673a\u54d2\uff01<\/p>\n\n\n\n<p>\u4f5c\u8005\u8ba9\u5149\u5f3a\u9075\u5faa\u6307\u6570\u5206\u5e03\uff0c\u786e\u4fdd\u5728\u5355\u4e2a\u65b9\u5411\u7684\u7edf\u8ba1\u7279\u6027\u3002\u5176\u6b21\uff0c\u901a\u8fc7\u7814\u7a76\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u5149\u5f3a\u7edf\u8ba1\u5173\u7cfb\uff0c\u8861\u91cf\u4e24\u4e2a\u70b9\u7684ensemble average\u3002\u8fd9\u91cc\u7528autocorrelation function (ACF)\u3002<br>$$<br>C(I_{p_1}, I_{p_2}) = \\frac{\\overline{(I_{p_1} &#8211; \\overline{I_{p_1}})(I_{p_2} &#8211; \\overline{I_{p_2}})}}{\\sigma(I_{p_1}) \\sigma(I_{p_2})}<br>\\tag{16}<br>$$<br>\u81ea\u76f8\u5173\u51fd\u6570\u7684\u503c\u4ecb\u4e8e -1 \u548c 1 \u4e4b\u95f4\uff0c<strong>\u5f53\u503c\u63a5\u8fd1 1 \u65f6<\/strong>\uff0c\u8bf4\u660e\u4e24\u4e2a\u5149\u5f3a\u7684\u6563\u5c04\u884c\u4e3a\u975e\u5e38\u76f8\u8fd1\u3002\u8fd9\u662f\u9ad8\u6548\u518d\u73b0\u7ea4\u7ef4\u6563\u5c04\u573a\u4e2d\u9897\u7c92\u7ed3\u6784\u7684\u5173\u952e\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5.2 Wavelet noise representation of the speckles<\/h3>\n\n\n\n<p>\u4f5c\u8005\u5f15\u5165\u5c0f\u6ce2\u566a\u58f0\uff08Wavelet noise\uff09\u6765\u8868\u793a\u6563\u6591\u7684\u566a\u58f0\u5206\u91cf $f(\\theta_h, \\phi_h, \\lambda)$ \u3002\u5177\u4f53\u516c\u5f0f\u5982\u4e0b\uff1a<br>$$<br>f(\\mathbf{x}) = \\sum_{b=0}^{n-1} w_b(\\mathbf{x}) I\\left(2^b g_{\\lambda}(\\mathbf{x})\\right)<br>\\tag{17}<br>$$<br>\u516c\u5f0f\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u6563\u6591\u7684\u5149\u5f3a\u5206\u89e3\u4e3a\u4e0d\u540c\u9891\u7387\u5c42\u6b21\u7684\u566a\u58f0\uff0c\u5e76\u4e14\u52a0\u6743\u7ec4\u5408\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u8c03\u6574\u4e0d\u540c\u9891\u7387\u5e26\u7684\u6743\u91cd\uff0c\u751f\u6210\u81ea\u76f8\u5173\u51fd\u6570 $ C_f(\\mathbf{x}_1, \\mathbf{x}_2)$ \u63a5\u8fd1\u4e0e\u76ee\u6807\u81ea\u76f8\u5173\u51fd\u6570\u7684\u6700\u7ec8\u566a\u58f0\u3002<\/p>\n\n\n\n<p>\u6839\u636e\u7ef4\u7eb3-\u8f9b\u94a6\u5b9a\u7406\uff08Wiener-Khinchin theorem\uff09\uff0c\u81ea\u76f8\u5173\u51fd\u6570\u53ef\u4ee5\u901a\u8fc7<strong>\u5085\u91cc\u53f6\u53d8\u6362\uff08Fourier Transform\uff09<\/strong>\u6765\u8ba1\u7b97\u3002\u5177\u4f53\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>$$<br>C_f(\\mathbf{x}_1, \\mathbf{x}2) = \\mathcal{F} \\left( \\mathcal{F}^{-1} \\left( \\sum{b=0}^{n-1} w_b I_b \\right)^2 \\right)<br>\\tag{18}<br>$$<br>\u8fd9\u8868\u793a\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u5c0f\u6ce2\u566a\u58f0\u7684\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u6765\u83b7\u5f97\u81ea\u76f8\u5173\u51fd\u6570\u3002\u81ea\u76f8\u5173\u51fd\u6570\u548c\u529f\u7387\u8c31\u5bc6\u5ea6\u51fd\u6570\u662f\u4e00\u5bf9\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u592aAmazing\u4e86\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u8fd9\u91cc\u539f\u8bba\u6587\u7ed9\u4e86\u4e00\u4e2a\u901a\u8fc7\u9891\u7387\u5e26\u52a0\u6743\u6c42\u548c\u8fd1\u4f3c\u8ba1\u7b97ACF\u7684\u8bc1\u660e\u3002<\/p>\n\n\n\n<p>\u7701\u6d41\uff1a\u901a\u8fc7\u5bf9\u566a\u58f0\u7684\u5404\u4e2a\u9891\u7387\u5e26\u8fdb\u884c\u52a0\u6743\uff0c\u53ef\u4ee5\u8fd1\u4f3c\u5f97\u5230\u6574\u4e2a\u566a\u58f0\u7684\u81ea\u76f8\u5173\u51fd\u6570\uff0c\u800c\u4e0d\u7528\u5904\u7406\u4e0d\u540c\u9891\u7387\u5e26\u4e4b\u95f4\u7684\u4ea4\u4e92\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-195-1024x851.png\" alt=\"\" class=\"wp-image-1251 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"851\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-195-1024x851.png\" alt=\"\" class=\"wp-image-1251 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-195-1024x851.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-195-300x249.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-195-768x639.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-195-1536x1277.png 1536w, https:\/\/remoooo.com\/wp-content\/uploads\/image-195.png 1792w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n<\/blockquote>\n\n\n\n<p>\u901a\u8fc7\u6700\u5c0f\u4e8c\u4e58\u6cd5\u627e\u5230\u975e\u8d1f\u6743\u91cd $v_b$ \uff0c\u4ee5\u4f7f\u5f97\u6bcf\u4e2a\u9891\u7387\u5e26\u7684\u81ea\u76f8\u5173\u51fd\u6570 $C_b(\\mathbf{x}1, \\mathbf{x}_2)$ \u7684\u52a0\u6743\u548c\u53ef\u4ee5\u903c\u8fd1\u76ee\u6807\u81ea\u76f8\u5173\u51fd\u6570 $C_t(\\mathbf{x}_1, \\mathbf{x}_2)$ \u3002 <\/p>\n\n\n\n<p>$$ C_t(\\mathbf{x}_1, \\mathbf{x}2) \\approx \\sum{b=0}^{n-1} v_b C_b(\\mathbf{x}_1, \\mathbf{x}_2) \\tag{19} $$ \u8ba1\u7b97\u5b8c\u6743\u91cd\u540e\uff0c\u8981\u786e\u4fdd\u80fd\u91cf\u5b88\u6052\u3002\u4e5f\u5c31\u662f\u8c03\u6574\u566a\u58f0\u51fd\u6570 $f(\\mathbf{x})$ \u7684\u671f\u671b\u503c $\\mathbb{E}[f(\\mathbf{x})] = 1$ \u3002 $$ \\begin{aligned} &amp; \\mathrm{E}\\left[S{\\text {avg }}\\left(\\theta_i, \\theta_r, \\phi_r, \\phi_r, \\lambda\\right) f\\left(\\theta_h, \\phi_h, \\lambda\\right)\\right] \\\\\\<br>&amp; =S_{\\text {avg }}\\left(\\theta_i, \\theta_r, \\phi_r, \\phi_r, \\lambda\\right) \\mathrm{E}[f(\\mathbf{x})] \\<br>&amp; \\approx S_{\\text {avg }}\\left(\\theta_i, \\theta_r, \\phi_r, \\phi_r, \\lambda\\right)<br>\\end{aligned}<br>\\tag{20}<br>$$<\/p>\n\n\n\n<p><br>\u867d\u7136\u6548\u679c\u597d\uff0c\u4f46\u662f\u6709\u5c40\u9650\u6027\u3002\u6bd4\u5982\u5728grazing incidence angles\u7684\u5730\u65b9\uff08\u5149\u7ebf\u51e0\u4e4e\u5e73\u884c\u8868\u9762\u7684\u60c5\u51b5\uff09\uff0c\u62df\u5408\u51c6\u786e\u6027\u4e0b\u964d\uff0c\u5bfc\u81f4\u6563\u5c04\u51c6\u786e\u5ea6\u4e0b\u964d\u3002Degeneration in the Forward Direction\u95ee\u9898\uff0c\u5f53\u5149\u7ebf\u5904\u4e8e\u6b63\u524d\u65b9\u65b9\u5411\uff08\u5149\u7ebf\u65b9\u5411\u4e0e\u8868\u9762\u6cd5\u7ebf\u4e00\u81f4\uff09\u65f6\uff0c\u534a\u5411\u91cf\u65b9\u5411\u4f1a\u9000\u5316\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">6. Validation<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">6.1 Wave simulation validation<\/h3>\n\n\n\n<p>\u8ba1\u7b97\u4e86x-y\u5e73\u9762\u4e2d\u7684\u6563\u5c04\u5f3a\u5ea6\uff0c\u5e76\u901a\u8fc73600\u4e2a\u65b9\u4f4d\u89d2 $\\phi_r$ \u8fdb\u884c\u8ba1\u7b97\uff0c\u6700\u7ec8\u5c06\u8fd9\u4e9b\u89d2\u5ea6\u5e73\u5747\u5230360\u4e2a\u65b9\u5411\u4e0a\u3002<\/p>\n\n\n\n<p>\u9996\u5148\u5bf9\u6bd4Mie\u6563\u5c04\u3002\u5728grazing angles\u4e0d\u5982Mie\u6563\u5c04\u3002\u7269\u4f53\u7684\u534a\u5f84\u76f8\u5bf9\u4e8e\u6ce2\u957f\u8f83\u5927\u65f6\uff0cPO\u8fd1\u4f3c\u66f4\u4e3a\u7cbe\u786e\u3002\u5f53\u7269\u4f53\u66f2\u7387\u8f83\u5c0f\uff0c\u5c31\u4e0d\u51c6\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-196-1020x1024.png\" alt=\"\" class=\"wp-image-1252 lazyload\"\/><noscript><img decoding=\"async\" width=\"1020\" height=\"1024\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-196-1020x1024.png\" alt=\"\" class=\"wp-image-1252 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-196-1020x1024.png 1020w, https:\/\/remoooo.com\/wp-content\/uploads\/image-196-300x300.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-196-150x150.png 150w, https:\/\/remoooo.com\/wp-content\/uploads\/image-196-768x771.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-196.png 1148w\" sizes=\"(max-width: 1020px) 100vw, 1020px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u7136\u540e\u5bf9\u6bd4BEM\u3002\u6a21\u62df\u4e00\u4e2a\u5c0f\u692d\u7403\u4f53\u7684\u6ce2\u6563\u5c04\u3002BEM\u7528\u4e86\u4e09\u4e2a\u5c0f\u65f6\uff0cPO\u82b1\u4e86\u4e24\u79d2\u3002<\/p>\n\n\n\n<p>\u6700\u540e\u5bf9\u6bd42D BEM\u3002\u7528\u4e00\u7ef4\u9ad8\u65af\u9ad8\u5ea6\u573a\uff081D Gaussian height fields\uff09\u5305\u88f9\u5728\u5706\u5f62\u548c\u692d\u5706\u5f62\u7684\u6a2a\u622a\u9762\u4e0a\u3002PO\u5b8c\u80dc\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.2 Measurement<\/h3>\n\n\n\n<p>\u4f7f\u7528\u4e86\u6ce2\u957f\u4e3a 633nm \u7684 HeNe \u6fc0\u5149\u5668\uff0c\u5149\u675f\u7684\u5149\u6591\u5927\u5c0f\u4e3a <strong>0.7mm\uff08\u6cbf\u7740\u5934\u53d1\u7684\u957f\u5ea6\u65b9\u5411\uff09\u00d7 3mm\uff08\u5782\u76f4\u4e8e\u5934\u53d1\u65b9\u5411\uff09<\/strong>\u3002\u6fc0\u5149\u901a\u8fc7\u4e00\u4e2a\u5c0f\u5b54\u7167\u5c04\u5728\u4eba\u7c7b\u5934\u53d1\u6837\u672c\u7684\u4e00\u4e2a\u5c0f\u533a\u57df\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-197-779x1024.png\" alt=\"\" class=\"wp-image-1253 lazyload\"\/><noscript><img decoding=\"async\" width=\"779\" height=\"1024\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-197-779x1024.png\" alt=\"\" class=\"wp-image-1253 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-197-779x1024.png 779w, https:\/\/remoooo.com\/wp-content\/uploads\/image-197-228x300.png 228w, https:\/\/remoooo.com\/wp-content\/uploads\/image-197-768x1010.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-197.png 1156w\" sizes=\"(max-width: 779px) 100vw, 779px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u603b\u4e4b\u5c31\u662f\u6548\u679c\u597d\uff01<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6.3 Noise representation validation<\/h3>\n\n\n\n<p>\u4e00\u4e2a\u5b57\uff0c\u597d\uff01<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">7. Rendering<\/h2>\n\n\n\n<p>\u6574\u5408\u8fdbPBRT-v3\u3002\u539f\u672c\u7684\u57fa\u4e8e\u5149\u7ebf\u7684\u6a21\u578b\u8bb0\u4f5c $S_{\\text{ray}}$ \uff0c\u800c\u884d\u5c04\u6a21\u578b\u8bb0\u4f5c $S_{\\text{diffract}}$ \u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u884d\u5c04\uff0c\u8fd9\u91cc\u8fd1\u4f3c\u4e3a\u5355\u7f1d\u884d\u5c04\uff0c\u800c\u7f1d\u7684\u5bbd\u5ea6\u7b49\u4e8e\u5706\u67f1\u4f53\uff08\u7ea4\u7ef4\uff09\u7684\u76f4\u5f84\u3002<br>$$<br>f_{\\text{diffract}}(\\theta_i, \\phi_d, a) = a \\cos \\theta_i \\cdot \\text{sinc}^2(a \\cos \\theta_i \\sin \\phi_d)<br>\\tag{22}<br>$$<br>\u8fd9\u79cd\u884d\u5c04\u6a21\u578b\u88ab\u7528\u6765\u548c\u7eb5\u5411\u51fd\u6570\u7ed3\u5408\uff0c\u5f97\u5230\u4e00\u4e2a\u5b8c\u6574\u7684<strong>\u53cc\u5411\u66f2\u9762\u6563\u5c04\u5206\u5e03\u51fd\u6570\uff08BCSDF\uff09<\/strong>\u3002\u5c06\u884d\u5c04\u56e0\u5b50\u4ee5 $50 \\times 50 \\times 200$ \u7684\u8868\u683c\u5f62\u5f0f\u8fdb\u884c\u9884\u8ba1\u7b97\u3002\u5e76\u4f7f\u7528\u540c\u6837\u5927\u5c0f\u7684\u8868\u683c\u8fdb\u884c\u91cd\u8981\u6027\u91c7\u6837\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-198-1024x610.png\" alt=\"\" class=\"wp-image-1254 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"610\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-198-1024x610.png\" alt=\"\" class=\"wp-image-1254 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-198-1024x610.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-198-300x179.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-198-768x457.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-198.png 1122w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u6d88\u5149\u622a\u9762\u53ef\u4ee5\u7b80\u5355\u7406\u89e3\u4e3a\u5149\u4e0e\u7269\u4f53\u76f8\u4e92\u4f5c\u7528\u7684\u201c\u6709\u6548\u9762\u79ef\u201d\u3002 \u7ea4\u7ef4\u7684\u6d88\u5149\u622a\u9762\u4f1a\u6bd4\u5b83\u7684\u5b9e\u9645\u51e0\u4f55\u622a\u9762\u5927\u3002\u6d88\u5149\u622a\u9762\u4f1a\u63a5\u8fd1\u4e8e\u51e0\u4f55\u622a\u9762\u7684\u4e24\u500d\u3002\u5149\u5728\u7ea4\u7ef4\u4e0a\u65e2\u53d1\u751f\u53cd\u5c04\u4e5f\u53d1\u751f\u884d\u5c04\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u628a\u603b\u80fd\u91cf\u5206\u914d\u7ed9\u8fd9\u4e24\u79cd\u73b0\u8c61\u3002\u6839\u636e\u7ecf\u9a8c\uff0c\u53ef\u4ee5\u628a\u4e00\u534a\u7684\u80fd\u91cf\u7528\u4e8e\u884d\u5c04\uff0c\u53e6\u4e00\u534a\u7528\u4e8e\u53cd\u5c04\u3002<br>$$<br>S_{\\text{diffract}}(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) = \\frac{1}{2} \\left[S_{\\text{ray}}(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) + f_{\\text{diffract}}(\\theta_i, \\phi_d, D\/\\lambda)\\right]<br>\\tag{23}<br>$$<br>\u901a\u8fc7\u91cd\u8981\u6027\u91c7\u6837\uff0c\u516c\u5e73\u5730\u8003\u8651\u5149\u7684\u53cd\u5c04\u548c\u884d\u5c04\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u6700\u7ec8\u7684\u63cf\u8ff0\u5149\u6563\u5c04\u73b0\u8c61\u7684\u6e32\u67d3\u516c\u5f0f\uff0c\u5f62\u5f0f\u6574\u5f97\u633a\u597d\uff1a<br>$$<br>S_{0,\\text{prac}}(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) = S_{0,\\text{avg}}(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) f(\\theta_h, \\phi_h, \\lambda)\\ \\\\<br>= \\frac{1}{2} \\left[ S_{\\text{ray}}(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) + f_{\\text{diffract}}(\\theta_i, \\phi_d, D\/\\lambda) \\right] f(\\theta_h, \\phi_h, \\lambda)\\<br>\\tag{24}<br>$$<br><strong>\u53cd\u5c04+\u884d\u5c04+\u566a\u58f0<\/strong>\u3002\u566a\u58f0\u51fd\u6570 $f(\\theta_h, \\phi_h, \\lambda)$ \u5728\u6700\u540e\uff0c\u4f7f\u5f97\u6563\u5c04\u7684\u5149\u7ebf\u4e0d\u5728\u96c6\u4e2d\u5728\u5c11\u6570\u65b9\u5411\u3002<\/p>\n\n\n\n<p>\u91cd\u70b9\u770b\u8fd9\u4e2a\u90e8\u5206\uff1a<br>$$<br>S_{0,\\text{prac}}(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) = S_{0,\\text{avg}}(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) f(\\theta_h, \\phi_h, \\lambda)<br>$$<br>$S_{0,\\text{avg}}$ \u8868\u793a\u6bdb\u53d1\u8868\u9762\u5e73\u5747\u53cd\u5c04\/\u6298\u5c04\u548c\u884d\u5c04\u7684\u884c\u4e3a\uff0c\u8fd9\u662f\u901a\u8fc7\u9884\u5904\u7406\uff08BSDF\u8868\u683c\uff09\u8ba1\u7b97\u5f97\u5230\u7684\u3002<\/p>\n\n\n\n<p>\u63a5\u4e0b\u6765\u8bb2\u8bb2\u5982\u4f55\u4ecePO\u63d0\u53d6BCSDF\u3002<\/p>\n\n\n\n<p>\u901a\u8fc7\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u5f97\u5230\u6563\u5c04\u7684\u7535\u573a\u548c\u78c1\u573a\uff08$E_s^{\\text{far}}$ \u548c $H_s^{\\text{far}}$\uff09\u3002<\/p>\n\n\n\n<p>\u63a5\u7740\u7528\u5761\u5370\u5ef7\u77e2\u91cf\uff08Poynting vector\uff09\u8ba1\u7b97\u80fd\u91cf\u6d41\u3002\u76f8\u5f53\u4e8e\u8ba1\u7b97\u5149\u7684\u5f3a\u5ea6\u3002<\/p>\n\n\n\n<p><br>$$<br>\\langle S \\rangle = \\frac{1}{2} \\text{Re}(E \\times H^) \\tag{25} <br>$$<\/p>\n\n\n\n<p><em>\u4e3a\u4e86\u5c06\u6a21\u62df\u7ed3\u679c\u7528\u4e8e\u6e32\u67d3\uff0c\u5c06\u6563\u5c04\u5f3a\u5ea6\u4e0e\u5165\u5c04\u529f\u7387\u5173\u8054\u8d77\u6765\u3002\u6563\u5c04\u5f3a\u5ea6\u7684\u8ba1\u7b97\u516c\u5f0f\uff0c\u5176\u4e2d $R^2$ \u662f\u8fdc\u573a\u7403\u9762\u9762\u79ef\uff1a <\/em><\/p>\n\n\n\n<p>$$<br>I_s(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) = \\langle S(\\mathbf{r}) \\rangle \\cdot \\hat{n} R^2 \\tag{26} <br>$$ <\/p>\n\n\n\n<p>\u6563\u5c04\u529f\u7387 $P_s$ \u548c\u5438\u6536\u529f\u7387 $P_a$ \u5206\u522b\u901a\u8fc7\u79ef\u5206\u6563\u5c04\u5149\u548c\u5438\u6536\u5149\u7684\u5f3a\u5ea6\u6765\u8ba1\u7b97\u3002 <\/p>\n\n\n\n<p>$$<br>P_s = \\int_{\\Omega} I_s(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) \\, d\\omega \\tag{27}<br>$$ <\/p>\n\n\n\n<p>\u5bf9\u4e8e\u5438\u6536\u529f\u7387 $P_a$ \uff0c\u901a\u8fc7\u8868\u9762\u4e0a\u7684\u5761\u5370\u5ef7\u77e2\u91cf\u79ef\u5206\u8ba1\u7b97\u3002 <\/p>\n\n\n\n<p>$$<br>\\begin{aligned}<br>P_a &amp; =\\int_{\\Gamma} \\frac{1}{2} \\operatorname{Re}\\left(\\mathbf{E}1 \\times \\mathbf{H}_1^{}\\right) \\cdot \\hat{\\mathbf{n}}_1(A) d A \\ &amp; = \\\\<br>\\int{\\Gamma} \\frac{1}{2} \\operatorname{Re}\\left(\\mathbf{J}^{} \\times \\mathbf{M}\\right) \\cdot \\hat{\\mathbf{n}}_1(s) d s<br>\\end{aligned}<br>\\tag{28}<br>$$<\/p>\n\n\n\n<p><br>\u6700\u7ec8\uff0cBCSDF\u641e\u51fa\u6765\u4e86\u3002<br><\/p>\n\n\n\n<p>$$<br>S(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda) = \\frac{I_s(\\theta_i, \\phi_i, \\theta_r, \\phi_r, \\lambda)}{|P_a &#8211; P_s|}<br>\\tag{30}<br>$$<br><\/p>\n\n\n\n<p>\u6700\u540e\u7528\u4e86\u4e00\u4e2a5D\u7684\u8868\u683c\u3002<\/p>\n\n\n\n<p>1D \u7ef4\u5ea6\u63cf\u8ff0\u6ce2\u957f\u3002<br>2D \u63cf\u8ff0\u5165\u5c04\u5149\u7684\u65b9\u5411\u3002<br>2D \u63cf\u8ff0\u51fa\u5c04\u5149\u7684\u65b9\u5411\u3002<\/p>\n\n\n\n<p>\u53ef\u4ee5\u901a\u8fc7\u6563\u5c04\u7684\u8bb0\u5fc6\u6548\u5e94\u51cf\u5c11\u5b58\u50a8\u9700\u6c42\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-199.png\" alt=\"\" class=\"wp-image-1255 lazyload\"\/><noscript><img decoding=\"async\" width=\"972\" height=\"516\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-199.png\" alt=\"\" class=\"wp-image-1255 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-199.png 972w, https:\/\/remoooo.com\/wp-content\/uploads\/image-199-300x159.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-199-768x408.png 768w\" sizes=\"(max-width: 972px) 100vw, 972px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u6e32\u67d3\u65f6\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u5165\u5c04\u5149\u65b9\u5411\uff0c\u67e5\u8be2\u76f8\u90bb\u7684\u8868\u683c\u6570\u636e\uff0c\u5e94\u7528\u76f8\u5e94\u7684\u89d2\u5ea6\u504f\u79fb\uff08\u8bb0\u5fc6\u6548\u5e94\u4e2d\u7684\u89d2\u5ea6\u504f\u79fb\u91cf\uff09\u3002<\/p>\n\n\n\n<p>\u6700\u7ec8\u4f7f\u7528\u7684\u8868\u683c\u5927\u5c0f\u4e3a $25 \\times 32 \\times 72 \\times 180 \\times 360$ \uff0c\u975e\u5e38\u5927\uff0c\u7ea615GB\u7684\u5185\u5b58\u9700\u6c42\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-200-1024x307.png\" alt=\"\" class=\"wp-image-1256 lazyload\"\/><noscript><img decoding=\"async\" width=\"1024\" height=\"307\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-200-1024x307.png\" alt=\"\" class=\"wp-image-1256 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-200-1024x307.png 1024w, https:\/\/remoooo.com\/wp-content\/uploads\/image-200-300x90.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-200-768x230.png 768w, https:\/\/remoooo.com\/wp-content\/uploads\/image-200-1536x460.png 1536w, https:\/\/remoooo.com\/wp-content\/uploads\/image-200.png 1968w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">8. Result<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-201.png\" alt=\"\" class=\"wp-image-1257 lazyload\"\/><noscript><img decoding=\"async\" width=\"908\" height=\"898\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-201.png\" alt=\"\" class=\"wp-image-1257 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-201.png 908w, https:\/\/remoooo.com\/wp-content\/uploads\/image-201-300x297.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-201-768x760.png 768w\" sizes=\"(max-width: 908px) 100vw, 908px\" \/><\/noscript><\/figure>\n\n\n\n<p>\u4e0eXIA[2020]\u76f8\u6bd4\uff0c\u65b0\u6a21\u578b\u66f4\u52a0\u9c9c\u8273\u3002\u8272\u5f69\u5149\u6591\uff08colorful glints\uff09\u66f4\u597d\u3002\u4f53\u73b0\u591a\u79cd\u6ce2\u957f\u5bf9\u6bdb\u53d1\u4ea7\u751f\u7684\u5149\u6591\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-202.png\" alt=\"\" class=\"wp-image-1258 lazyload\"\/><noscript><img decoding=\"async\" width=\"962\" height=\"704\" src=\"https:\/\/\u80a5\u80a5.com\/wp-content\/uploads\/image-202.png\" alt=\"\" class=\"wp-image-1258 lazyload\" srcset=\"https:\/\/remoooo.com\/wp-content\/uploads\/image-202.png 962w, https:\/\/remoooo.com\/wp-content\/uploads\/image-202-300x220.png 300w, https:\/\/remoooo.com\/wp-content\/uploads\/image-202-768x562.png 768w\" sizes=\"(max-width: 962px) 100vw, 962px\" \/><\/noscript><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">9. DISCUSSION AND CONCLUSION<\/h2>\n\n\n\n<p>\u7b2c\u4e00\u7bc7\u80fd\u591f\u5b9e\u9645\u5e94\u7528\u7684 3D \u6ce2\u52a8\u5149\u5b66\u7ea4\u7ef4\u6563\u5c04\u6a21\u578b\u3002<\/p>\n\n\n\n<p>\u80fd\u591f\u751f\u6210\u5149\u5b66\u6563\u5c04\u4e2d\u5e38\u89c1\u7684\u7ec6\u5fae\u5149\u6591\uff08speckle patterns\uff09\u3002<\/p>\n\n\n\n<p>\u867d\u7136 3D \u6a21\u62df\u7684\u7cbe\u5ea6\u5f88\u9ad8\uff0c\u4f46\u5b83\u7684\u5185\u5b58\u5360\u7528\u548c\u8ba1\u7b97\u6210\u672c\u975e\u5e38\u5927\u3002\u63d0\u51fa\u4e86\u566a\u58f0\u5b9e\u7528\u6a21\u578b\uff0c\u901a\u8fc7\u6355\u6349\u7ea4\u7ef4\u6563\u5c04\u5149\u6591\u7684\u7edf\u8ba1\u7279\u6027\uff08\u5982\u81ea\u76f8\u5173\u51fd\u6570\uff09\uff0c\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002<\/p>\n\n\n\n<p>\u76ee\u524d\u8be5\u6a21\u578b\u4e3b\u8981\u7528\u4e8e\u7b2c\u4e00\u9636\u53cd\u5c04\u6a21\u5f0f\u7684\u6a21\u62df\u3002\u672a\u6765\u53ef\u4ee5\u6269\u5c55\u5230\u66f4\u9ad8\u9636\u7684\u6563\u5c04\u6a21\u5f0f\u3002<\/p>\n\n\n\n<p>\u9ad8\u9636\u6a21\u5f0f\u65f6\u53ef\u80fd\u9700\u8981\u8fdb\u4e00\u6b65\u5f00\u53d1\u65b0\u6280\u672f\u6765\u9884\u6d4b\u6216\u6d4b\u91cf\u9ad8\u9636\u6a21\u5f0f\u7684\u7edf\u8ba1\u7279\u6027\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u58f0\u660e\uff1a\u8fd9\u7bc7\u6587\u7ae0\u4e3b\u8981\u662f\u5173\u4e8eSIG23\u5e74\u8fd9\u7bc7\u9ed1\u72d7\u6bdb\u8bba\u6587\u7684\u4e2a\u4eba\u7b14\u8bb0\u3002\u5e94\u8be5\u4e5f\u6ca1\u5565\u9605\u8bfb\u95e8\u69db\uff0c\u56e0\u4e3a\u6211\u81ea\u5df1\u4e5f\u6ca1\u6709\u5165\u95e8\u56fe\u5f62\u5b66\u3002 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1240,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[53],"tags":[56,57,58],"class_list":["post-1238","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tech","tag-cg","tag-hair-rendering","tag-wave-optics"],"_links":{"self":[{"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/posts\/1238","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/comments?post=1238"}],"version-history":[{"count":19,"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/posts\/1238\/revisions"}],"predecessor-version":[{"id":1970,"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/posts\/1238\/revisions\/1970"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/media\/1240"}],"wp:attachment":[{"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/media?parent=1238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/categories?post=1238"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/remoooo.com\/en\/wp-json\/wp\/v2\/tags?post=1238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}