Simple understanding of white light interferometry (with matlab simulation code)

White light interferometry is a special interferometry technique that uses white light with a certain spectral width instead of monochromatic light as the interference light source for measurement. According to the characteristics of short coherence length and very obvious coherence peak of white light interference signal, the interference signal is obtained by vertical scanning interferometry.
If two lasers of the same frequency interfere to form an interference fringe, the interference fringe is regarded as a "laser pair", and the white light interference signal can be understood as being composed of countless "laser pairs".

Since white light contains a wide spectrum component, that is, it is composed of many sine waves with continuous but unequal frequencies, and the frequency of the "laser pair" is also different. When the optical path difference is zero, the phase is the same, and the superposition result has a maximum value, that is, coherence peak .
With the gradual increase of the optical path difference, the phase is gradually dispersed, and the interference light intensity is gradually flattened, and the contrast is also reduced, and finally tends to zero. Moreover, the envelope curve of the white light interference signal conforms to the Gaussian distribution, which also shows that the white light interference signal is a Gaussian signal curve modulated sinusoidally.
references:

1. A Survey of White Light Interferometric Vertical Scanning Measurement Algorithms

2. Full-field heterodyne white light interferometry technique

3. Algorithm Research Based on Full Field Heterodyne White Light Interferometry

    具体代码如下所示：
   

clc;clear;
close all;

z = linspace(-5e-6,5e-6,2e3);    % 干涉信号坐标
h = 0;                           % 干涉位置
lamda = 1550e-9;                 % 光源中心波长
d_lamda = 25e-8;                 % 光谱宽度
lc = lamda^2/d_lamda;            % 相干长度
gz = exp(-((z-h)*2*pi/lc).^2);   % 高斯包络曲线
cz = cos(4*pi/lamda*(z-h));      % 正弦调制
I = 3*gz.*cz+3;                  % 白光干涉信号
figure,plot(z,I,'k');
hold on,plot(z,3*gz+3.1,'r','linewidth',2);
xlabel('Interfemetry Label(mm)','FontSize',12);
ylabel('Light Intensity(cd)','FontSize',12);
title('Signal Gauss Envelope Curve','FontSize',12);

cz1 = cos(4.1*pi/lamda*(z-h));      % 正弦调制
cz2 = cos(4.2*pi/lamda*(z-h));      % 正弦调制
cz3 = cos(4.3*pi/lamda*(z-h));      % 正弦调制
cz4 = cos(4.4*pi/lamda*(z-h));      % 正弦调制
cz5 = cos(4.5*pi/lamda*(z-h));      % 正弦调制

plot(z,cz);
plot(z,cz1);
plot(z,cz2);
plot(z,cz3);
plot(z,cz4);
plot(z,cz5);
legend('白光干涉信号','包络曲线','激光对1','激光对2','激光对3','激光对4','激光对5','激光对6');