◆波長(スペクトル)ＲＧＢ変換プログラムコード

光の波長（スペクトル）からRGB値を導く簡易プログラムです。

この方法は◆2色型色覚の画像表現法；色覚シミュレータ でスペクトル図をビットマップデータとして得るために使っています。

参考までに波長を選択しRGBを得るUIを付けたものを下に載せます。スライダーまたは 波長数値入力で波長を指定するとRGB値、XYZ値と色が表示されます。
なお、RGBテーブル生成時のガンマ補正値を変更可能としています。R,G,Bそれぞれ 別々に設定することができます。代表値を変更するとR,G,Bに同じ値が設定されます、

 定数テーブルと関数

10nm毎のテーブルを作成し、中間は線形補完しています。
下に載せた関数はAS3用ですが、他の言語への転用は難しくないはずです。
引数はnm単位の波長で380≦λ≦780,戻り値はR,G,Bそれぞれ0.0≦v≦1.0の浮動少数値です。

var rgbTable:Array = [
    { L:380 ,R:0.06076 ,G:0.00000 ,B:0.11058 }
   ,{ L:390 ,R:0.08700 ,G:0.00000 ,B:0.16790 }
   ,{ L:400 ,R:0.13772 ,G:0.00000 ,B:0.26354 }
   ,{ L:410 ,R:0.20707 ,G:0.00000 ,B:0.39852 }
   ,{ L:420 ,R:0.31129 ,G:0.00000 ,B:0.60684 }
   ,{ L:430 ,R:0.39930 ,G:0.00000 ,B:0.80505 }
   ,{ L:440 ,R:0.40542 ,G:0.00000 ,B:0.87684 }
   ,{ L:450 ,R:0.34444 ,G:0.00000 ,B:0.88080 }
   ,{ L:460 ,R:0.11139 ,G:0.00000 ,B:0.86037 }
   ,{ L:470 ,R:0.00000 ,G:0.15233 ,B:0.77928 }
   ,{ L:480 ,R:0.00000 ,G:0.38550 ,B:0.65217 }
   ,{ L:490 ,R:0.00000 ,G:0.49412 ,B:0.51919 }
   ,{ L:500 ,R:0.00000 ,G:0.59271 ,B:0.40008 }
   ,{ L:510 ,R:0.00000 ,G:0.69549 ,B:0.25749 }
   ,{ L:520 ,R:0.00000 ,G:0.77773 ,B:0.00000 }
   ,{ L:530 ,R:0.00000 ,G:0.81692 ,B:0.00000 }
   ,{ L:540 ,R:0.00000 ,G:0.82625 ,B:0.00000 }
   ,{ L:550 ,R:0.00000 ,G:0.81204 ,B:0.00000 }
   ,{ L:560 ,R:0.47369 ,G:0.77626 ,B:0.00000 }
   ,{ L:570 ,R:0.70174 ,G:0.71523 ,B:0.00000 }
   ,{ L:580 ,R:0.84922 ,G:0.62468 ,B:0.00000 }
   ,{ L:590 ,R:0.94726 ,G:0.49713 ,B:0.00000 }
   ,{ L:600 ,R:0.99803 ,G:0.31072 ,B:0.00000 }
   ,{ L:610 ,R:1.00000 ,G:0.00000 ,B:0.00000 }
   ,{ L:620 ,R:0.95520 ,G:0.00000 ,B:0.00000 }
   ,{ L:630 ,R:0.86620 ,G:0.00000 ,B:0.00000 }
   ,{ L:640 ,R:0.76170 ,G:0.00000 ,B:0.00000 }
   ,{ L:650 ,R:0.64495 ,G:0.00000 ,B:0.00000 }
   ,{ L:660 ,R:0.52857 ,G:0.00000 ,B:0.00000 }
   ,{ L:670 ,R:0.41817 ,G:0.00000 ,B:0.00000 }
   ,{ L:680 ,R:0.33202 ,G:0.00000 ,B:0.00000 }
   ,{ L:690 ,R:0.25409 ,G:0.00000 ,B:0.00000 }
   ,{ L:700 ,R:0.19695 ,G:0.00000 ,B:0.00000 }
   ,{ L:710 ,R:0.15326 ,G:0.00000 ,B:0.00000 }
   ,{ L:720 ,R:0.11902 ,G:0.00000 ,B:0.00000 }
   ,{ L:730 ,R:0.09063 ,G:0.00000 ,B:0.00000 }
   ,{ L:740 ,R:0.06898 ,G:0.00000 ,B:0.00000 }
   ,{ L:750 ,R:0.05150 ,G:0.00000 ,B:0.00000 }
   ,{ L:760 ,R:0.04264 ,G:0.00000 ,B:0.00000 }
   ,{ L:770 ,R:0.03666 ,G:0.00000 ,B:0.00794 }
   ,{ L:780 ,R:0.00000 ,G:0.00000 ,B:0.00000 }
   ];
var wlenStep:Number = 10;
var wlenMin:Number  = 380;
var wlenMax:Number  = 780
function wlen2rgb(wlen:Number):Object{
   wlen               = Math.max(wlenMin,wlen);
   wlen               = Math.min(wlenMax,wlen);
   var widx:int       = (wlen-wlenMin)/wlenStep;
   var wlenSub:Number = (wlen-wlenMin)-(widx*wlenStep);
   var ret            = new Object();
   ret.R              = rgbTable[widx].R;
   ret.G              = rgbTable[widx].G;
   ret.B              = rgbTable[widx].B;
   if( wlenSub==0 ) return ret;
   var rate:Number    = wlenSub/wlenStep;
   ret.R  += (rgbTable[widx+1].R-rgbTable[widx].R)*rate;
   ret.G  += (rgbTable[widx+1].G-rgbTable[widx].G)*rate;
   ret.B  += (rgbTable[widx+1].B-rgbTable[widx].B)*rate;
   return ret;
   }

 テーブルのグラフ表示

波長ごとのRGB感度を示します。

このグラフは、RGBテーブルをExcelに読ませてグラフ化したものです。
プログラムはガンマ補正値が1/2.7で、このテーブルは1/2.2であり、 差はありますが、見た目としてグラフに大きな差はありません。

L,R,G,B   
380,0.03215,0.00000,0.06704
390,0.04994,0.00000,0.11193
400,0.08777,0.00000,0.19463
410,0.14477,0.00000,0.32333
420,0.23877,0.00000,0.54172
430,0.32410,0.00000,0.76634
440,0.33021,0.00000,0.85104
450,0.27034,0.00000,0.85575
460,0.06765,0.00000,0.83146
470,0.00000,0.09932,0.73634
480,0.00000,0.31041,0.59180
490,0.00000,0.42097,0.44733
500,0.00000,0.52628,0.32488
510,0.00000,0.64040,0.18917
520,0.00000,0.73454,0.00000
530,0.00000,0.78022,0.00000
540,0.00000,0.79118,0.00000
550,0.00000,0.77451,0.00000
560,0.39971,0.73284,0.00000
570,0.64746,0.66278,0.00000
580,0.81826,0.56132,0.00000
590,0.93567,0.42412,0.00000
600,0.99758,0.23823,0.00000
610,1.00000,0.00000,0.00000
620,0.94530,0.00000,0.00000
630,0.83838,0.00000,0.00000
640,0.71600,0.00000,0.00000
650,0.58376,0.00000,0.00000
660,0.45727,0.00000,0.00000
670,0.34301,0.00000,0.00000
680,0.25843,0.00000,0.00000
690,0.18611,0.00000,0.00000
700,0.13614,0.00000,0.00000
710,0.10007,0.00000,0.00000
720,0.07337,0.00000,0.00000
730,0.05252,0.00000,0.00000
740,0.03756,0.00000,0.00000
750,0.02624,0.00000,0.00000
760,0.02081,0.00000,0.00000
770,0.01729,0.00000,0.00264
780,0.00000,0.00000,0.00000

 RGBで画像化する例

AS3で画像に出す例を載せます。冒頭のスペクトル図はこのプログラムで出したものです。

..上記のプログラムに加えて..
var bmd:BitmapData= new BitmapData(390,100,false,0x00000000);
var bm:Bitmap     = new Bitmap(bmd);
addChild(bm);
var posx:int      = 0;
for(var wlen:int=380;wlen<730;++wlen){
   var rgb:Object = wlen2rgb(wlen);
   var r:uint     = rgb.R*255;
   var g:uint     = rgb.G*255;
   var b:uint     = rgb.B*255;
   var color:uint = (r<<16)+(g<<8)+b;  
   bmd.fillRect(new Rectangle(++posx+20,35,1,30),color);
   }

 テーブルを作成するプログラム

波長/RGB変換テーブルは、 波長から三刺激値（XYZ値）を得、それをRGBに 変換したものです。
三刺激値のテーブルは理科年表から得ました。
今回ガンマ補正を（1/2.7）乗 の形で行ってあります。この値は少し調整が必要かもしれません。
RGBテーブル作成とその利用を別プログラムとしてありますが、 もちろん、初期化と利用の形の単一プログラムとしてもかまいません。

// 理科年表
//   測光と測色
//   単色光の色度座標と等エネルギー単色放射の三刺激値
// から３刺激値 Lは波長nm
var triStimulusVals:Array = [
    {L:380, X:0.0014, Y:0.0000, Z:0.0065}
   ,{L:390, X:0.0042, Y:0.0001, Z:0.0201}
   ,{L:400, X:0.0143, Y:0.0004, Z:0.0679} // 紫..

   ,{L:410, X:0.0435, Y:0.0012, Z:0.2074}
   ,{L:420, X:0.1344, Y:0.0040, Z:0.6456}
   ,{L:430, X:0.2839, Y:0.0116, Z:1.3856}
   ,{L:440, X:0.3483, Y:0.0230, Z:1.7471} // 青..
   ,{L:450, X:0.3362, Y:0.0380, Z:1.7721}

   ,{L:460, X:0.2908, Y:0.0600, Z:1.6692}
   ,{L:470, X:0.1954, Y:0.0910, Z:1.2876}
   ,{L:480, X:0.0956, Y:0.1390, Z:0.8130}
   ,{L:490, X:0.0320, Y:0.2080, Z:0.4652}
   ,{L:500, X:0.0049, Y:0.3230, Z:0.2720}  // 緑..

   ,{L:510, X:0.0093, Y:0.5030, Z:0.1582}
   ,{L:520, X:0.0633, Y:0.7100, Z:0.0782}
   ,{L:530, X:0.1655, Y:0.8620, Z:0.0422}
   ,{L:540, X:0.2904, Y:0.9540, Z:0.0203}
   ,{L:550, X:0.4334, Y:0.9950, Z:0.0087}

   ,{L:560, X:0.5945, Y:0.9950, Z:0.0039}
   ,{L:570, X:0.7621, Y:0.9520, Z:0.0021}  // 黄..
   ,{L:580, X:0.9163, Y:0.8700, Z:0.0017}
   ,{L:590, X:1.0263, Y:0.7570, Z:0.0011}
   ,{L:600, X:1.0622, Y:0.6310, Z:0.0008}

   ,{L:610, X:1.0026, Y:0.5030, Z:0.0003}  // 赤..
   ,{L:620, X:0.8544, Y:0.3810, Z:0.0002}
   ,{L:630, X:0.6424, Y:0.2650, Z:0.0000}
   ,{L:640, X:0.4479, Y:0.1750, Z:0.0000}
   ,{L:650, X:0.2835, Y:0.1070, Z:0.0000}

   ,{L:660, X:0.1649, Y:0.0610, Z:0.0000}
   ,{L:670, X:0.0874, Y:0.0320, Z:0.0000}
   ,{L:680, X:0.0468, Y:0.0170, Z:0.0000}
   ,{L:690, X:0.0227, Y:0.0082, Z:0.0000}
   ,{L:700, X:0.0114, Y:0.0041, Z:0.0000}

   ,{L:710, X:0.0058, Y:0.0021, Z:0.0000}
   ,{L:720, X:0.0029, Y:0.0010, Z:0.0000}
   ,{L:730, X:0.0014, Y:0.0005, Z:0.0000}
   ,{L:740, X:0.0007, Y:0.0003, Z:0.0000}
   ,{L:750, X:0.0003, Y:0.0001, Z:0.0000}

   ,{L:760, X:0.0002, Y:0.0001, Z:0.0000}
   ,{L:770, X:0.0001, Y:0.0000, Z:0.0000}
   ,{L:780, X:0.0000, Y:0.0000, Z:0.0000}
   ];
// XYZからRGB作成
function xyz2rgb(elm:Object):Object{
   var ret:Object = new Object;
   ret.L =  elm.L;
   ret.R =  3.5064*elm.X - 1.7400*elm.Y - 0.5441*elm.Z;
   ret.G = -1.0690*elm.X + 1.9777*elm.Y + 0.0352*elm.Z;
   ret.B =  0.0563*elm.X - 0.1970*elm.Y + 1.0511*elm.Z;
   return ret;
   }
// 三刺激テーブルからRGBテーブルを作成
function createRGBtable_0(tbl:Array):Array{
   var array:Array= new Array();
   for each(var elm:Object in tbl){
      array.push(xyz2rgb(elm));
      }
   return array;
   }
// ガンマ補正と正規化を行う
function gammaCorrection(tbl:Array,gammaFactor:Number){
   var max:Number=0;
   for(var idx:int=0;idx<tbl.length;++idx){
      tbl[idx].R= Math.pow(Math.max(0,tbl[idx].R),gammaFactor);
      tbl[idx].G= Math.pow(Math.max(0,tbl[idx].G),gammaFactor);
      tbl[idx].B= Math.pow(Math.max(0,tbl[idx].B),gammaFactor);
      max= Math.max(max,tbl[idx].R);
      max= Math.max(max,tbl[idx].G);
      max= Math.max(max,tbl[idx].B);
      }
   for(idx=0;idx<tbl.length;++idx){
      tbl[idx].R /= max;
      tbl[idx].G /= max;
      tbl[idx].B /= max;
      }
   }
// テーブル生成
function createRGBtable():Array{
   var rgbTable:Array= createRGBtable_0(triStimulusVals);
   gammaCorrection(rgbTable,1/2.7);
   return rgbTable;
   }
// RGBテーブルダンプ
function dumpRGB(tbl:Array){
   trace("var rgbTable:Array = [");
   var dlmt:String=" ";
   for each(var elm:Object in tbl){
      trace("   "+dlmt+"{ L:"+elm.L
           +" ,R:"+elm.R.toFixed(5)+" ,G:"+elm.G.toFixed(5)
           +" ,B:"+elm.B.toFixed(5)+" }");
      dlmt=",";
      }
   trace("   ];");
   trace("var wlenStep:int = "+(tbl[2].L-tbl[1].L)+";");
   trace("var wlenMin:int  = "+tbl[0].L+";");
   trace("var wlenMax:int  = "+tbl[tbl.length-1].L+";");
   }
var rgbTable:Array= createRGBtable();
dumpRGB(rgbTable);

 XYZテーブル

三刺激値のグラフを載せます。

小さな値が見づらくＸとＹの広がりが分からないので、対数軸にしたグラフも載せます。

L,X,Y,Z
380,0.0014,0.0000,0.0065
390,0.0042,0.0001,0.0201
400,0.0143,0.0004,0.0679
410,0.0435,0.0012,0.2074
420,0.1344,0.0040,0.6456
430,0.2839,0.0116,1.3856
440,0.3483,0.0230,1.7471
450,0.3362,0.0380,1.7721
460,0.2908,0.0600,1.6692
470,0.1954,0.0910,1.2876
480,0.0956,0.1390,0.8130
490,0.0320,0.2080,0.4652
500,0.0049,0.3230,0.2720
510,0.0093,0.5030,0.1582
520,0.0633,0.7100,0.0782
530,0.1655,0.8620,0.0422
540,0.2904,0.9540,0.0203
550,0.4334,0.9950,0.0087
560,0.5945,0.9950,0.0039
570,0.7621,0.9520,0.0021
580,0.9163,0.8700,0.0017
590,1.0263,0.7570,0.0011
600,1.0622,0.6310,0.0008
610,1.0026,0.5030,0.0003
620,0.8544,0.3810,0.0002
630,0.6424,0.2650,0.0000
640,0.4479,0.1750,0.0000
650,0.2835,0.1070,0.0000
660,0.1649,0.0610,0.0000
670,0.0874,0.0320,0.0000
680,0.0468,0.0170,0.0000
690,0.0227,0.0082,0.0000
700,0.0114,0.0041,0.0000
710,0.0058,0.0021,0.0000
720,0.0029,0.0010,0.0000
730,0.0014,0.0005,0.0000
740,0.0007,0.0003,0.0000
750,0.0003,0.0001,0.0000
760,0.0002,0.0001,0.0000
770,0.0001,0.0000,0.0000
780,0.0000,0.0000,0.0000

 ＃＃＃

(2009/6/16) ExcelによるRGB感度図を追加。プログラムを表示/非表示とした。

(2009/6/21) XYZ図に対数軸版追加

(2011/6/25) 波長、ガンマ補正値を指定するUI付きプログラムを追加

(2011/7/2) XYZ値（３刺激値）も表示するようにした

(2011/11/18) ガンマ補正値を2.2から2.7に変更