Thermal imaging palette

Question

Since the early days of thermal imaging, infrared cameras often use a distinctive palette that runs from black through blue, magenta, orange, yellow to bright white. This palette is often called Iron, or Ironbow.

Here is a typical false color visualization of an image taken with a forward looking infrared camera (source: Wikipedia).

"Termografia kot" by Lcamtuf - a typical false color infrared

On a specialized infrared imagery forum I've found a post from 2005 with a discrete palette that seems to be close to what I am looking for.

A discrete FLIR palette of unknown origin

However as with the rainbow palette it would be nice to have a concise analytical expression that defines the palette.

To those who have used GNUPLOT this palette might look familiar as the default PM3D palette runs black-blue-magenta-orange-yellow.

GNUPLOT PM3D palette

This palette has a concise definition

r = Math.round(255*Math.sqrt(x)); 
g = Math.round(255*Math.pow(x,3)); 
b = Math.round(255*(Math.sin(2 * Math.PI * x)>=0?
                   Math.sin(2 * Math.PI * x) : 0 ));

However it is not quite how the other palette looks. A bit too brownish to my taste. Any additional information on the origins or an analytical expression for the palette used in FLIR cameras would help.

I have created a JSFiddle to play with different palettes.

Answer 1

These palettes are arbitrary and is mainly used to improve contrast depending of type of image you're having. The values can therefor be pure custom set.

As IR does not capture any colors (as it is outside the color range) the returned luminance value is simply mapped to what creates best contrast, in particular in regards to edges and shapes.

The iron palette has 5-7 key colors which are then interpolated (red can be made fine-tuning the mixing between yellow and magenta). The exact values and positions can be set any way you like, here is an example:

var ctx = document.querySelector("canvas").getContext("2d");
var gr = ctx.createLinearGradient(0, 0, 600, 0);
var keys = ["white", "gold", "#c07", "#20008c", "black"];

// add color stops to gradient:
for(var i = 0, key; key = keys[i]; i++) {
  gr.addColorStop(i / (keys.length-1), key);
}

ctx.fillStyle = gr;
ctx.fillRect(0, 0, 600, 20);

<canvas width=600></canvas>

Answer 2

It is unlikely that you'll find a formula for the color palette. So you should use a color array.

Here is FLIR's Iron palette (from here), and its colors in an array:

var iron_palette = ["#00000a","#000014","#00001e","#000025","#00002a","#00002e","#000032","#000036","#00003a","#00003e","#000042","#000046","#00004a","#00004f","#000052","#010055","#010057","#020059","#02005c","#03005e","#040061","#040063","#050065","#060067","#070069","#08006b","#09006e","#0a0070","#0b0073","#0c0074","#0d0075","#0d0076","#0e0077","#100078","#120079","#13007b","#15007c","#17007d","#19007e","#1b0080","#1c0081","#1e0083","#200084","#220085","#240086","#260087","#280089","#2a0089","#2c008a","#2e008b","#30008c","#32008d","#34008e","#36008e","#38008f","#390090","#3b0091","#3c0092","#3e0093","#3f0093","#410094","#420095","#440095","#450096","#470096","#490096","#4a0096","#4c0097","#4e0097","#4f0097","#510097","#520098","#540098","#560098","#580099","#5a0099","#5c0099","#5d009a","#5f009a","#61009b","#63009b","#64009b","#66009b","#68009b","#6a009b","#6c009c","#6d009c","#6f009c","#70009c","#71009d","#73009d","#75009d","#77009d","#78009d","#7a009d","#7c009d","#7e009d","#7f009d","#81009d","#83009d","#84009d","#86009d","#87009d","#89009d","#8a009d","#8b009d","#8d009d","#8f009c","#91009c","#93009c","#95009c","#96009b","#98009b","#99009b","#9b009b","#9c009b","#9d009b","#9f009b","#a0009b","#a2009b","#a3009b","#a4009b","#a6009a","#a7009a","#a8009a","#a90099","#aa0099","#ab0099","#ad0099","#ae0198","#af0198","#b00198","#b00198","#b10197","#b20197","#b30196","#b40296","#b50295","#b60295","#b70395","#b80395","#b90495","#ba0495","#ba0494","#bb0593","#bc0593","#bd0593","#be0692","#bf0692","#bf0692","#c00791","#c00791","#c10890","#c10990","#c20a8f","#c30a8e","#c30b8e","#c40c8d","#c50c8c","#c60d8b","#c60e8a","#c70f89","#c81088","#c91187","#ca1286","#ca1385","#cb1385","#cb1484","#cc1582","#cd1681","#ce1780","#ce187e","#cf187c","#cf197b","#d01a79","#d11b78","#d11c76","#d21c75","#d21d74","#d31e72","#d32071","#d4216f","#d4226e","#d5236b","#d52469","#d62567","#d72665","#d82764","#d82862","#d92a60","#da2b5e","#da2c5c","#db2e5a","#db2f57","#dc2f54","#dd3051","#dd314e","#de324a","#de3347","#df3444","#df3541","#df363d","#e0373a","#e03837","#e03933","#e13a30","#e23b2d","#e23c2a","#e33d26","#e33e23","#e43f20","#e4411d","#e4421c","#e5431b","#e54419","#e54518","#e64616","#e74715","#e74814","#e74913","#e84a12","#e84c10","#e84c0f","#e94d0e","#e94d0d","#ea4e0c","#ea4f0c","#eb500b","#eb510a","#eb520a","#eb5309","#ec5409","#ec5608","#ec5708","#ec5808","#ed5907","#ed5a07","#ed5b06","#ee5c06","#ee5c05","#ee5d05","#ee5e05","#ef5f04","#ef6004","#ef6104","#ef6204","#f06303","#f06403","#f06503","#f16603","#f16603","#f16703","#f16803","#f16902","#f16a02","#f16b02","#f16b02","#f26c01","#f26d01","#f26e01","#f36f01","#f37001","#f37101","#f37201","#f47300","#f47400","#f47500","#f47600","#f47700","#f47800","#f47a00","#f57b00","#f57c00","#f57e00","#f57f00","#f68000","#f68100","#f68200","#f78300","#f78400","#f78500","#f78600","#f88700","#f88800","#f88800","#f88900","#f88a00","#f88b00","#f88c00","#f98d00","#f98d00","#f98e00","#f98f00","#f99000","#f99100","#f99200","#f99300","#fa9400","#fa9500","#fa9600","#fb9800","#fb9900","#fb9a00","#fb9c00","#fc9d00","#fc9f00","#fca000","#fca100","#fda200","#fda300","#fda400","#fda600","#fda700","#fda800","#fdaa00","#fdab00","#fdac00","#fdad00","#fdae00","#feaf00","#feb000","#feb100","#feb200","#feb300","#feb400","#feb500","#feb600","#feb800","#feb900","#feb900","#feba00","#febb00","#febc00","#febd00","#febe00","#fec000","#fec100","#fec200","#fec300","#fec400","#fec500","#fec600","#fec700","#fec800","#fec901","#feca01","#feca01","#fecb01","#fecc02","#fecd02","#fece03","#fecf04","#fecf04","#fed005","#fed106","#fed308","#fed409","#fed50a","#fed60a","#fed70b","#fed80c","#fed90d","#ffda0e","#ffda0e","#ffdb10","#ffdc12","#ffdc14","#ffdd16","#ffde19","#ffde1b","#ffdf1e","#ffe020","#ffe122","#ffe224","#ffe226","#ffe328","#ffe42b","#ffe42e","#ffe531","#ffe635","#ffe638","#ffe73c","#ffe83f","#ffe943","#ffea46","#ffeb49","#ffeb4d","#ffec50","#ffed54","#ffee57","#ffee5b","#ffee5f","#ffef63","#ffef67","#fff06a","#fff06e","#fff172","#fff177","#fff17b","#fff280","#fff285","#fff28a","#fff38e","#fff492","#fff496","#fff49a","#fff59e","#fff5a2","#fff5a6","#fff6aa","#fff6af","#fff7b3","#fff7b6","#fff8ba","#fff8bd","#fff8c1","#fff8c4","#fff9c7","#fff9ca","#fff9cd","#fffad1","#fffad4","#fffbd8","#fffcdb","#fffcdf","#fffde2","#fffde5","#fffde8","#fffeeb","#fffeee","#fffef1","#fffef4","#fffff6"];