{"id":3743,"date":"2025-02-09T01:09:10","date_gmt":"2025-02-08T17:09:10","guid":{"rendered":"https:\/\/fredkuo.idv.tw\/wordpress\/?p=3743"},"modified":"2025-02-09T01:09:10","modified_gmt":"2025-02-08T17:09:10","slug":"how-beers-law-predict-best-color-density","status":"publish","type":"post","link":"https:\/\/fredkuo.idv.tw\/wordpress\/?p=3743","title":{"rendered":"How Beer’s Law predict “Best Color” density"},"content":{"rendered":"

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<\/p>\n

How Beer\u2019s Law predict \u201cBest Color\u201d density<\/p>\n

Beer\u2019s Law \u5982\u4f55\u9810\u6e2c \u201c\u6700\u4f73\u8272\u5f69\u201d \u6fc3\u5ea6<\/p>\n

\u6211\u7d93\u5e38\u8aac\u7684\uff0c\u5f71\u50cf\u8f38\u51fa\u63a7\u5236\u5c31\u9019\u5169\u4ef6\u4e8b\uff1a\u6eff\u7248\u8207\u4e2d\u9593\u8abf\u3002<\/p>\n

\u8981\u641e\u5b9a\u6eff\u7248\uff0c\u9760\u7684\u662f Beer\u2019s Law\uff1b\u8981\u641e\u5b9a\u4e2d\u9593\u8abf\uff0c\u9760\u7684\u662f\u66f2\u7dda\u3002\u4e0d\u7ba1\u662f PSO\u3001G7\u3001gmi\u2026\u90fd\u662f\u4e00\u6a23\u7684\u3002<\/p>\n

\u8d81\u8457\u6e96\u5099\u6559\u6750\uff0c\u4e00\u6b21\u628aBeer\u2019s Law\u8b1b\u6e05\u695a\u3002<\/p>\n

Beer\u2019s Law (or Beer Lambert’s Law)\u539f\u672c\u662f\u7528\u4f86\u8a08\u7b97\u5316\u5b78\u6eb6\u5291\u6fc3\u5ea6\u7684\u5de5\u5177\uff0c\u81f3\u65bc\u70ba\u4f55\u6703\u7528\u4f86\u9810\u6e2c\u5370\u5237\u653e\u58a8\u6fc3\u5ea6\uff0c\u6211\u7684\u539f\u59cb\u4f86\u6e90\u662fRIT Prof. Bob Chung \u7684\u4e00\u500bExcel Spreadsheet\uff0c\u770b spreadsheet \u88cf\u7684\u8a3b\u8a18\uff0c\u628a\u5b83\u7528\u4f86\u9810\u6e2c\u653e\u58a8\u6fc3\u5ea6\u770b\u4f86\u662f Prof. Franz Sigg \u7684\u624b\u7b46\uff0c\u9806\u4fbf\u63d0\u4e00\u4e0b\uff0cGCR (Gray Component Replacement) \u9019\u500b\u8a5e\u5f59\u4e5f\u662f Franz Sigg \u5b9a\u4e0b\u4f86\u4e86\u7684\u3002<\/p>\n

<\/p>\n

Fig. Beer\u2019s Law \u539f\u672c\u662f\u7528\u4f86\u8a08\u7b97\u5316\u5b78\u6eb6\u5291\u6fc3\u5ea6\u7684\u5de5\u5177\u3002A \u70ba\u5438\u6536\u7387\uff0cI0 \u70ba\u539f\u59cb\u5149\u91cf\uff0cI \u70ba\u88ab\u6eb6\u5291\u5438\u6536\u5f8c\u7684\u5149\u91cf\u3002<\/p>\n

<\/p>\n

Fig. Beer\u2019s Law \u6eb6\u5291\u5438\u6536\u7387\u793a\u610f<\/p>\n

\u81f3\u65bc\u5982\u4f55\u8f49\u5316\u70ba\u5370\u5237\u6cb9\u58a8\u6fc3\u5ea6\u7684\u63a8\u7b97\uff0cExcel \u88cf\u7528\u7684\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n

Rnm=10^(-((((-LOG(U$12))-(-LOG(U$11)))*$T14)+(-LOG(U$11))))*1<\/p>\n

\u6558\u8ff0\u5982\u4e0b\uff1a<\/p>\n

\u5149\u8b5c\u53cd\u5c04\u7387nm=10^(-((((-LOG(\u6cb9\u58a8\u5149\u8b5c\u53cd\u5c04\u7387nm))-(-LOG(\u7d19\u5f35\u5149\u8b5c\u53cd\u5c04\u7387nm)))*\u6a21\u64ec\u4fee\u6b63\u91cf)+(-LOG(\u7d19\u5f35\u5149\u8b5c\u53cd\u5c04\u7387nm))))*1<\/p>\n

\u7528\u7684\u65b9\u5f0f\u8ddf\u5316\u5b78\u7684\u6eb6\u5291\u8a08\u7b97\u4e0d\u592a\u4e00\u6a23\uff0c\u662f\u4e00\u7a2e Beer\u2019s Law \u8f49\u5316\u7684\u61c9\u7528\uff0c\u4e0d\u662f\u5b8c\u5168\u4e00\u6a23\u7684\u5957\u7528\u3002<\/p>\n

Beer\u2019s Law \u662f\u7528\u55ae\u4e00\u6ce2\u9577\u4f86\u5c0d\u5316\u5b78\u6eb6\u5291\u505a\u6fc3\u5ea6\u8a08\u7b97\uff0c\u5728\u5370\u5237\u6cb9\u58a8\u7684\u61c9\u7528\uff0c\u56e0\u5149\u8b5c\u5100\u5c0d\u6cb9\u58a8\u6a23\u672c\u4ee510nm\u9593\u9694\uff0c\u5f9e 380nm \u5230 730nm \u7e3d\u5171\u53d6\u4e86 36 \u500b\u55ae\u4e00\u6ce2\u9577\u6a23\u672c\uff0c\u5982\u6b64\uff0c\u5c31\u53ef\u4ee5\u7528 Beer\u2019s Law \u5957\u7528\u5728\u901936\u7d44\u55ae\u4e00\u5149\u8b5c\u8cc7\u6599\u3002\u6211\u5011\u5c0d\u6bcf\u4e00\u500b\u55ae\u4e00\u6ce2\u9577\u4ee5 Beer\u2019s Law \u505a\u5291\u91cf\u52a0\u6e1b\u6a21\u64ec\uff0c\u6700\u5f8c\u91cd\u7d44\u901936\u7d44\u8cc7\u6599\uff0c\u5c31\u53ef\u4ee5\u63a8\u6e2c\u51fa\u6a21\u64ec\u7684Lab\u503c\u53ca\u5176\u6fc3\u5ea6\u503c\uff1b\u7576\u627e\u5230\u8207\u76ee\u6a19Lab\u503c\u6700\u63a5\u8fd1\u7684\u90a3\u7d44\u5149\u8b5c\u503c\uff0c\u4e5f\u5c31\u53ef\u4ee5\u7b97\u5f97\u51fa\u61c9\u8a72\u653e\u7684\u6cb9\u58a8\u6fc3\u5ea6\u3002<\/p>\n

\u5be6\u969b\u7528\u6578\u64da\u4f86\u8aaa\u660e\u4e00\u4e0b\uff1a<\/p>\n

\u53d6\u4e00\u6d0b\u7d05\u58a8\u53ca\u5176\u7d19\u5f35\u6a23\u672c\u5149\u8b5c\u3002<\/p>\n

<\/p>\n

Fig. \u53d6\u4e00\u6d0b\u7d05\u58a8\u53ca\u5176\u7d19\u5f35\u5149\u8b5c<\/p>\n

\u8a08\u7b97\u51fa\u8a72\u6d0b\u7d05\u58a8Lab\u503c\u70ba\uff1a44.92, 71.86, -1.65, \u6fc3\u5ea6\u70ba1.488\uff0c \u8207Fogra39 \u6a19\u6e96\u6d0b\u7d05 Lab 48, 74, -3 \u8272\u5dee De76 3.98\u3002<\/p>\n

<\/p>\n

Fig. \u6d0b\u7d05\u58a8\u6a23\u672c\u5149\u8b5c<\/p>\n

\u6a21\u64ec\u4e00\u4e0b\u5728 430 nm \u8655\u52a01\u500b\u55ae\u5143\u5291\u91cf\uff0c\u539f\u672c 430 nm \u8655\u5149\u8b5c\u53cd\u5c04\u7387\u70ba 0.1834\uff0c\u7d19\u5f35\u5728 430nm \u8655\u7684\u53cd\u5c04\u7387\u70ba 0.7733\uff0c\u6bcf\u4e00\u500b\u5291\u91cf\u8a2d\u70ba0.015\uff0c\u5957\u5165\u516c\u5f0f\uff1a <\/p>\n

\u6a21\u64ec\u53cd\u5c04\u7387430nm=10^(-((((-LOG(0.1834))-(-LOG(0.7733)))*(1+0.015*1))+(-LOG(0.7733))))*1= 0.1795<\/p>\n

\u6a21\u64ec\u4e00\u4e0b\u5728 430 nm \u8655\u6e1b1\u500b\u55ae\u5143\u5291\u91cf\uff1a <\/p>\n

\u6a21\u64ec\u53cd\u5c04\u7387430nm=10^(-((((-LOG(0.1834))-(-LOG(0.7733)))*(1-0.015*1))+(-LOG(0.7733))))*1= 0.1874<\/p>\n

\u6a21\u64ec\u4e00\u76f4\u52a0\u523015\u500b\u55ae\u5143\u53ca\u6e1b15\u500b\u55ae\u5143\u5f97\u5230430nm\u8655\u7684\u5149\u8b5c\u6a21\u64ec\u503c\u70ba<\/p>\n

<\/p>\n

Fig. \u52a015\u500b\u55ae\u5143\u5230\u6e1b15\u500b\u55ae\u5143\u5728430nm\u8655\u7684\u5149\u8b5c\u6a21\u64ec\u503c<\/p>\n

<\/p>\n

Fig. \u5716\u8868\u986f\u793a+15\u53ca-15\u500b\u55ae\u5143\u5728430nm\u8655\u6a21\u64ec\u503c(\u56e0\u8cc7\u8a0a\u592a\u5bc6\u96c6\uff0c\u5716\u793a\u70ba\u9593\u96943\u500b\u55ae\u5143\u7684\u6578\u64da)<\/p>\n

\u4ee5+3\u55ae\u5143\u70ba\u4f8b\uff0c\u6b64\u908f\u8f2f\u63a8\u6f14\u5230\u5176\u5b83380nm~730nm\uff0c\u5f97\u5230+3\u7684\u5149\u8b5c\u6a21\u64ec\u6578\u64da\u70ba\uff1a<\/p>\n

<\/p>\n

Fig. 380nm~730nm\uff0c+3\u7684\u5149\u8b5c\u6a21\u64ec\u6578\u64da<\/p>\n

+3\u55ae\u5143\u5149\u8b5c\u6a21\u64ec\u5206\u5e03\u66f2\u7dda\u70ba\uff1a<\/p>\n

<\/p>\n

Fig. +3\u55ae\u5143\u5149\u8b5c\u6a21\u64ec\u5206\u5e03\u66f2\u7dda(\u7da0\u8272\u70ba\u539f\u59cb\u66f2\u7dda\uff0c\u7d05\u8272\u70ba+3\u6a21\u64ec\u66f2\u7dda)<\/p>\n

\u540c\u6a23\u908f\u8f2f\u884d\u751f\u5230\u6240\u6709\u7684+15\u5230-15\u55ae\u5143\uff0c\u6578\u64da\u5982\u4e0b\uff1a<\/p>\n

<\/p>\n

\u4f9d\u6b64\u6578\u64da\u53d6\u5f97\u6240\u670930\u689d\u6a21\u64ec\u5149\u8b5c\u5206\u5e03\u66f2\u7dda\u3002<\/p>\n

<\/p>\n

Fig. \u5f9e+15\u5230-15\u55ae\u5143\uff0c\u53d6\u5f9730\u689d\u6a21\u64ec\u5149\u8b5c\u5206\u5e03\u66f2\u7dda\u3002(\u56e0\u8cc7\u8a0a\u592a\u5bc6\u96c6\uff0c\u5716\u793a\u70ba\u9593\u96943\u500b\u55ae\u5143\u7684\u6578\u64da)<\/p>\n

\u5f9e\u901930\u689d\u6a21\u64ec\u5149\u8b5c\u5206\u5e03\u66f2\u7dda\u53ef\u4ee5\u53d6\u5f9730\u7d44\u76f8\u61c9\u7684 Lab\u503c\u3002\u901930\u7d44Lab\u503c\u6703\u6709\u4e00\u7d44\u6700\u63a5\u8fd1\u6211\u5011\u7684\u6a19\u6e96\u503c\uff1a48, 74, -3\u3002<\/p>\n

\u7531\u6578\u64da\u986f\u793a\uff0c\u7576\u6a21\u64ec\u6e1b2\u500b\u55ae\u5143\u6642\uff0c\u53d6\u5f97Lab\u70ba 45.47, 71.32, -2.46\uff0c\u8207\u6a19\u6e96\u503c\u5dee de76 3.721\uff0c\u6fc3\u5ea6\u70ba1.448\u3002 \u4f9d\u6b64\u904b\u7b97\u7d50\u679c\uff0c\u5f9e\u73fe\u5728\u7684\u6fc3\u5ea61.488\u964d\u5230\u6fc3\u5ea61.448\u6642\uff0c\u8272\u5dee\u53ef\u4ee5\u5f9e3.98\u964d\u52303.72\u3002<\/p>\n

<\/p>\n

Fig. \u7531\u6578\u64da\u986f\u793a\uff0c\u7576\u6a21\u64ec\u6e1b2\u500b\u55ae\u5143\u6642\uff0c\u53d6\u5f97Lab\u70ba 45.47, 71.32, -2.46\uff0c\u8207\u6a19\u6e96\u503c\u5dee de76 3.721\uff0c\u6fc3\u5ea6\u70ba1.448\u3002<\/p>\n

<\/p>\n

Fig. \u4f9d\u904b\u7b97\u7d50\u679c\uff0c\u5f9e\u73fe\u5728\u7684\u6fc3\u5ea61.488\u964d\u5230\u6fc3\u5ea61.448\u6642\uff0c\u8272\u5dee\u53ef\u4ee5\u5f9ede76 3.98\u964d\u5230 de76 3.72\u3002<\/p>\n

\u9019\u500b\u6848\u4f8b\u4fee\u6b63\u91cf\u4e26\u4e0d\u5927\uff0c\u4f46 Beer\u2019s Law \u7684\u904b\u4f5c\u908f\u8f2f\u5df2\u8db3\u4ee5\u4ea4\u4ee3\u6e05\u9664\u3002<\/p>\n

\u518d\u7c21\u55ae\u6574\u7406\u4e00\u4e0b\uff0c\u7576\u53d6\u5f97\u4e00\u500b\u6a23\u672c\u8cc7\u6599\u6642\uff0c\u4ee5Beer\u2019s Law \u5c0d\u6bcf\u4e00\u55ae\u4e00\u5149\u8b5c\u503c(380nm~730nm in 10nm intervals)\u505a\u52a0\u6e1b\u5291\u91cf\u7684\u6a21\u64ec\uff0c\u4e32\u806f\u6bcf\u55ae\u4e00\u5149\u8b5c\u7684\u6a21\u64ec\u5149\u8b5c\u503c\u5373\u53ef\u53d6\u5f97\u5176\u5149\u8b5c\u5206\u5e03\u66f2\u7dda\u9032\u800c\u8a08\u7b97\u51fa\u5176Lab\u503c\u53ca\u6fc3\u5ea6\u503c(\u6b64\u7bc4\u4f8b\u6a21\u64ec-15\u5230+15\u517130\u7d44\u6a21\u64ec\u503c)\uff0c\u5728\u773e\u591a\u7684\u6a21\u64ecLab\u503c\u4e2d\u7e3d\u6709\u4e00\u500b\u6700\u63a5\u8fd1\u6211\u5011\u7684\u76ee\u6a19Lab\uff0c\u800c\u5176\u76f8\u61c9\u6fc3\u5ea6\u5c31\u662f\u6211\u5011\u61c9\u8a72\u4e0b\u7684\u6fc3\u5ea6\u3002<\/p>\n

\u4ee5\u6b64\uff0c\u6211\u5011\u53ef\u4ee5\u7528Beer\u2019s Law\u4f86\u9810\u6e2c\u6eff\u7248\u7684\u201c\u6700\u4f73\u8272\u5f69\u201d\u6fc3\u5ea6\u503c(Best Color)\u3002<\/p>\n

<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

How Beer\u2019s Law predict \u201cBest Color\u201d density Beer\u2019s Law […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3743","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3743"}],"collection":[{"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3743"}],"version-history":[{"count":1,"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3743\/revisions"}],"predecessor-version":[{"id":3744,"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3743\/revisions\/3744"}],"wp:attachment":[{"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3743"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3743"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fredkuo.idv.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3743"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}