KK关系计算方法.docx

KK关系计算方法.docx

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KK关系计算方法

KK关系计算方法

使用软件：

Mathematice6.0

计算数据：

反射光谱

计算目标：

折射率、消光系数（复折射率）、介电常数（实部、虚部）、吸收系数

计算步骤：

　步

第一步不做任何处理的原始数据拟合

1数据处理

把反射谱中的一一对应的数据点做如下形式：

{x1,y1},{x2,y2},…{xn,yn}

这一步可用Excel完成，如图所示：

复制需要拟合的数据到mathematice中。

先打开“未做任何处理的200-2500的原始数据拟合.nb”。

以我的数据为例，我只取了其中200－800nm数据。

需要说明的文字我用红字标出。

如图所示：

f={{200,9.28083},{204,10.67989},{208,10.68956},{212,11.35133},{216,11.94466},{220,11.97739},{224,12.44642},{228,12.79128},{232,13.17627},{236,13.33227},{240,13.64892},{244,14.02046},{248,14.1844},{252,14.43982},{256,14.59005},{260,14.93265},{264,15.08296},{268,15.44994},{272,15.63906},{276,15.83285},{280,16.0089},{284,16.18497},{288,16.4413},{292,16.5467},{296,16.80329},{300,17.0636},{304,17.37439},{308,17.24754},{312,17.53314},{316,17.54477},{320,17.88985},{324,18.20747},{328,18.15253},{332,18.29901},{336,18.48072},{340,18.63027},{344,18.68853},{348,18.93796},{352,18.87828},{356,18.97925},{360,19.07318},{364,19.20597},{368,19.46847},{372,19.4527},{376,19.63037},{380,19.45939},{384,19.54249},{388,19.50909},{392,19.71648},{396,19.72745},{400,19.86541},{404,19.88394},{408,19.94855},{412,19.99085},{416,20.10268},{420,20.17271},{424,20.24376},{428,20.28775},{432,20.33652},{436,20.36746},{440,20.45098},{444,20.51344},{448,20.56255},{452,20.61329},{456,20.59809},{460,20.61791},{464,20.712},{468,20.75117},{472,20.80953},{476,20.84951},{480,20.91447},{484,21.04063},{488,21.0387},{492,21.05206},{496,21.08511},{500,21.08685},{504,21.14488},{508,21.14559},{512,21.17371},{516,21.2372},{520,21.27362},{524,21.31675},{528,21.37},{532,21.39788},{536,21.45977},{540,21.49712},{544,21.54286},{548,21.58125},{552,21.63051},{556,21.68476},{560,21.71518},{564,21.74266},{568,21.77074},{572,21.79919},{576,21.8478},{580,21.87746},{584,21.91433},{588,21.96476},{592,21.95952},{596,21.99251},{600,22.01649},{604,22.06857},{608,22.05836},{612,22.10567},{616,22.13445},{620,22.11847},{624,22.16107},{628,22.18187},{632,22.21075},{636,22.22322},{640,22.21166},{644,22.26408},{648,22.26516},{652,22.27371},{656,22.28789},{660,22.33599},{664,22.33009},{668,22.35576},{672,22.37441},{676,22.38908},{680,22.4118},{684,22.43644},{688,22.39334},{692,22.45349},{696,22.45548},{700,22.46142},{704,22.50477},{708,22.50623},{712,22.51435},{716,22.56872},{720,22.56509},{724,22.57602},{728,22.59907},{732,22.6267},{736,22.63849},{740,22.69148},{744,22.6825},{748,22.70658},{752,22.73869},{756,22.79487},{760,22.8029},{764,22.835},{768,22.86978},{772,22.87246},{776,22.93132},{780,22.98215},{784,22.99017},{788,23.03298},{792,23.06776},{796,23.10254},{800,23.12929}}（f为定义的一个变量，值为原始数据。

你使用时，只需覆盖我原来的数据就行）

F=FindFit[f,

Table[Tu,{u,-10,10}],x]（表示寻找一个多项式来拟合数据，求和号上下为正负10，表明，从负10次方，到正10次方。

这里只要改变需要拟合的次数就行，即改多少次方就行了。

）

/.F（这一个命令可以不管它，但必须保持与上一命令相同的次数）

p=ListPlot[f]（这个命令的意思是将原始数据以点的形式画出）

Plot[

/.F,{x,200,800}]（这个命令的意思是在指定区间内画出拟合的函数的图形。

区间为（200,800），可改动，但最好与你的原始数据区间相同，本例中采用200－800nm。

）

Show[%,p]（这个命令是将原始数据与拟合曲线画在一起，用以判断拟合效果如何）

（以下为输出结果）

{{200,9.28083},{204,10.6799},{208,10.6896},{212,11.3513},{216,11.9447},{220,11.9774},{224,12.4464},{228,12.7913},{232,13.1763},{236,13.3323},{240,13.6489},{244,14.0205},{248,14.1844},{252,14.4398},{256,14.5901},{260,14.9327},{264,15.083},{268,15.4499},{272,15.6391},{276,15.8329},{280,16.0089},{284,16.185},{288,16.4413},{292,16.5467},{296,16.8033},{300,17.0636},{304,17.3744},{308,17.2475},{312,17.5331},{316,17.5448},{320,17.8899},{324,18.2075},{328,18.1525},{332,18.299},{336,18.4807},{340,18.6303},{344,18.6885},{348,18.938},{352,18.8783},{356,18.9793},{360,19.0732},{364,19.206},{368,19.4685},{372,19.4527},{376,19.6304},{380,19.4594},{384,19.5425},{388,19.5091},{392,19.7165},{396,19.7275},{400,19.8654},{404,19.8839},{408,19.9486},{412,19.9909},{416,20.1027},{420,20.1727},{424,20.2438},{428,20.2878},{432,20.3365},{436,20.3675},{440,20.451},{444,20.5134},{448,20.5626},{452,20.6133},{456,20.5981},{460,20.6179},{464,20.712},{468,20.7512},{472,20.8095},{476,20.8495},{480,20.9145},{484,21.0406},{488,21.0387},{492,21.0521},{496,21.0851},{500,21.0869},{504,21.1449},{508,21.1456},{512,21.1737},{516,21.2372},{520,21.2736},{524,21.3168},{528,21.37},{532,21.3979},{536,21.4598},{540,21.4971},{544,21.5429},{548,21.5813},{552,21.6305},{556,21.6848},{560,21.7152},{564,21.7427},{568,21.7707},{572,21.7992},{576,21.8478},{580,21.8775},{584,21.9143},{588,21.9648},{592,21.9595},{596,21.9925},{600,22.0165},{604,22.0686},{608,22.0584},{612,22.1057},{616,22.1345},{620,22.1185},{624,22.1611},{628,22.1819},{632,22.2108},{636,22.2232},{640,22.2117},{644,22.2641},{648,22.2652},{652,22.2737},{656,22.2879},{660,22.336},{664,22.3301},{668,22.3558},{672,22.3744},{676,22.3891},{680,22.4118},{684,22.4364},{688,22.3933},{692,22.4535},{696,22.4555},{700,22.4614},{704,22.5048},{708,22.5062},{712,22.5144},{716,22.5687},{720,22.5651},{724,22.576},{728,22.5991},{732,22.6267},{736,22.6385},{740,22.6915},{744,22.6825},{748,22.7066},{752,22.7387},{756,22.7949},{760,22.8029},{764,22.835},{768,22.8698},{772,22.8725},{776,22.9313},{780,22.9822},{784,22.9902},{788,23.033},{792,23.0678},{796,23.1025},{800,23.1293}}（原始数据输出，可以不管这个结果）

{T-10-1.26756_1031,T-95.27225_1029,T-8-9.89949_1027,T-71.10041_1026,T-6-7.92496_1023,T-53.73215_1021,T-4-1.02308_1019,T-33.39511_1015,T-21.08241_1014,T-1-5.4828_1011,T01.52085_109,T1-2.6332_106,T22370.82,T31.04202,T4-0.00721988,T50.00001255,T6-1.31978_10-8,T79.22389_10-12,T8-4.22857_10-15,T91.1615_10-18,T10-1.45878_10-22}（多项式相应的系数，可以不管这个结果）

1.52085_109-1.26756_1031/x10+5.27225_1029/x9-9.89949_1027/x8+1.10041_1026/x7-7.92496_1023/x6+3.73215_1021/x5-1.02308_1019/x4+3.39511_1015/x3+1.08241_1014/x2-5.4828_1011/x-2.6332_106x+2370.82x2+1.04202x3-0.00721988x4+0.00001255x5-1.31978_10-8x6+9.22389_10-12x7-4.22857_10-15x8+1.1615_10-18x9-1.45878_10-22x10（拟合函数表达式，在word里，可能看不清楚，请看我的原程序）

以下为第二次操作：

a=Table[1.5208520266172135`*^9-1.2675581804893597`*^31/x10+5.27224820518729`*^29/x9-9.899490662109208`*^27/x8+1.1004074726951989`*^26/x7-7.924963241331437`*^23/x6+3.7321468261159687`*^21/x5-1.023076110480841`*^19/x4+3.395110161290293`*^15/x3+1.0824109439997714`*^14/x2-5.482795964973215`*^11/x-2.633201540205769`*^6x+2370.817263501473`x2+1.0420215704202724`x3-0.007219884471347927`x4+0.000012550049332281336`x5-1.3197768147930983`*^-8x6+9.223889143423574`*^-12x7-4.22856898484929`*^-15x8+1.161504051032442`*^-18x9-1.4587766069643154`*^-22x10,{x,200,800,1}]（此命令的作用是将拟合出来的函数数值化）

{9.30477,9.79019,10.1304,10.3698,10.5415,10.6697,10.7718,10.86,10.9424,11.0243,11.1087,11.1972,11.2902,11.3874,11.4882,11.5916,11.6966,11.8022,11.9075,12.0117,12.1141,12.2141,12.3114,12.4056,12.4968,12.5848,12.6697,12.7516,12.8307,12.9072,12.9814,13.0535,13.1239,13.1927,13.2602,13.3267,13.3924,13.4574,13.522,13.5863,13.6505,13.7145,13.7785,13.8426,13.9067,13.971,14.0353,14.0997,14.1642,14.2287,14.2931,14.3575,14.4218,14.4858,14.5496,14.6132,14.6764,14.7392,14.8015,14.8634,14.9248,14.9856,15.0458,15.1054,15.1644,15.2227,15.2805,15.3375,15.394,15.4498,15.505,15.5596,15.6136,15.667,15.7199,15.7723,15.8242,15.8756,15.9266,15.9772,16.0275,16.0773,16.1269,16.1762,16.2252,16.2739,16.3225,16.3708,16.419,16.467,16.5149,16.5626,16.6103,16.6578,16.7052,16.7525,16.7998,16.8469,16.8939,16.9409,16.9877,17.0344,17.081,17.1275,17.1738,17.22,17.266,17.3118,17.3574,17.4028,17.4479,17.4929,17.5375,17.5819,17.6259,17.6697,17.713,17.7561,17.7987,17.841,17.8828,17.9243,17.9653,18.0058,18.0458,18.0854,18.1245,18.1631,18.2011,18.2387,18.2757,18.3121,18.348,18.3834,18.4182,18.4524,18.4861,18.5192,18.5518,18.5838,18.6152,18.6461,18.6764,18.7062,18.7355,18.7642,18.7924,18.82,18.8472,18.8739,18.9,18.9257,18.9509,18.9756,18.9999,19.0238,19.0473,19.0703,19.0929,19.1152,19.137,19.1586,19.1797,19.2006,19.2211,19.2413,19.2612,19.2809,19.3002,19.3194,19.3382,19.3569,19.3753,19.3935,19.4116,19.4294,19.4471,19.4646,19.482,19.4992,19.5163,19.5333,19.5501,19.5669,19.5835,19.6001,19.6166,19.633,19.6493,19.6655,19.6817,19.6979,19.714,19.73,19.746,19.7619,19.7778,19.7937,19.8095,19.8253,19.8411,19.8569,19.8726,19.8883,19.9039,19.9195,19.9351,19.9507,19.9662,19.9817,19.9972,20.0126,20.028,20.0434,20.0587,20.074,20.0893,20.1045,20.1196,20.1347,20.1498,20.1648,20.1797,20.1946,20.2094,20.2242,20.2388,20.2535,20.268,20.2825,20.2969,20.3112,20.3255,20.3396,20.3537,20.3677,20.3816,20.3955,20.4092,20.4228,20.4364,20.4499,20.4632,20.4765,20.4897,20.5027,20.5157,20.5286,20.5414,20.554,20.5666,20.5791,20.5915,20.6038,20.616,20.6281,20.6401,20.652,20.6638,20.6755,20.6872,20.6987,20.7102,20.7215,20.7328,20.744,20.7551,20.7662,20.7771,20.788,20.7988,20.8096,20.8202,20.8308,20.8414,20.8519,20.8623,20.8726,20.883,20.8932,20.9034,20.9136,20.9237,20.9338,20.9438,20.9538,20.9638,20.9737,20.9836,20.9935,21.0034,21.0132,21.023,21.0328,21.0426,21.0524,21.0621,21.0719,21.0816,21.0914,21.1011,21.1108,21.1206,21.1303,21.1401,21.1498,21.1596,21.1693,21.1791,21.1889,21.1986,21.2084,21.2182,21.2281,21.2379,21.2477,21.2576,21.2675,21.2774,21.2873,21.2972,21.3071,21.3171,21.327,21.337,21.347,21.357,21.367,21.377,21.3871,21.3971,21.4072,21.4172,21.4273,21.4374,21.4474,21.4575,21.4676,21.4777,21.4877,21.4978,21.5079,21.5179,21.528,21.538,21.548,21.558,21.568,21.578,21.588,21.5979,21.6078,21.6177,21.6276,21.6374,21.6472,21.6569,21.6667,21.6764,21.686,21.6956,21.7052,21.7147,21.7242,21.7336,21.743,21.7523,21.7615,21.7707,21.7799,21.789,21.798,21.807,21.8158,21.8247,21.8334,21.8421,21.8507,21.8593,21.8678,21.8761,21.8845,21.8927,21.9009,21.909,21.917,21.9249,21.9327,21.9405,21.9482,21.9558,21.9633,21.9707,21.9781,21.9853,21.9925,21.9996,22.0066,22.0135,22.0203,22.0271,22.0338,22.0403,22.0468,22.0532,22.0596,22.0658,22.072,22.0781,22.0841,22.09,22.0959,22.1017,22.1074,22.113,22.1185,22.124,22.1294,22.1348,22.14,22.1452,22.1504,22.1554,22.1604,22.1654,22.1703,22.1751,22.1799,22.1846,22.1893,22.1939,22.1984,22.203,22.2074,22.2118,22.2162,22.2206,22.2249,22.2291,22.2333,22.2375,22.2417,22.2458,22.2499,22.254,22.258,22.262,22.266,22.27,22.274,22.2779,22.2818,22.2857,22.2896,22.2935,22.2974,22.3013,22.3051,22.309,22.3128,22.3167,22.3205,22.3243