多频外差法

公式推导：

• https://github.com/SHU-FLYMAN/PhaseShift/network
• https://zhuanlan.zhihu.com/p/533450290
• https://www.doc88.com/p-1806015065983.html

代码

clc;
close all;
clear;


%% [1] 参数设置
width   = 1024;         % 投影仪的图像宽度
heigth  = 768;          % 投影仪的图像高度
freq    = [70,64,59];   % 宽度方向有多少个周期
T       = width./freq;  % 条纹周期(一个正弦周期下的像素个数)
M       = length(freq); % 频率个数
A       = 128;          % 背景强度
B       = 127;          % 调制强度
N       = 4;            % 相移步数

save_stripes = true;    % 是否保存条纹图
stripes_folder = 'stripes';

%% [2] 条纹生成
stripes = cell(M,N);
if(save_stripes)
    mkdir(stripes_folder);
end
for i=1:M
    for j=1:N
        % 生成图像
        temp = zeros(heigth,width);
        for col = 1:width
            phi = 2*pi*col/T(i);
            delta_phi = 2*pi*(j-1)/N;
            temp(:,col) = A + B*cos(phi + delta_phi);
        end
        stripes{i,j} = temp;
        % 保存图像
        if(save_stripes)
            save_path = [stripes_folder,'/',int2str(i),'_',int2str(j),'.png'];
            imwrite(mat2gray(stripes{i,j}),save_path);
        end
    end
end

%% [3] 包裹相位(相位主值)
wrapped_phase = cell(M,1);
for i = 1:M
    sin_sum = 0;
    cos_sum = 0;
    for j = 1: N
        Ik = stripes{i, j};
        sin_sum = sin_sum + Ik * sin(2 * (j - 1) * pi / N);
        cos_sum = cos_sum + Ik * cos(2 * (j - 1) * pi / N);
    end
    temp  = -atan2(sin_sum, cos_sum);
    wrapped_phase{i,1} = temp;
    % 保存图像
    if(save_stripes)
        save_path = [stripes_folder,'/',int2str(i),'_相位主值.png'];
        imwrite(mat2gray(wrapped_phase{i,1}),save_path);
    end
end

%% [4] 绝对相位(多频外差法进行相位展开)
unwrapped_phase = wrapped_phase;
unwrapped_phase_name = cell(M,1);
for i=1:M
    unwrapped_phase_name{i,1} = int2str(i);
end
% 倒二叉树外差计算
for i=M-1:-1:1
    for j=1:i
        phi1 = unwrapped_phase{j,1};
        phi2 = unwrapped_phase{j+1,1};
        mask = phi1 > phi2;
        pha12 = (phi1 - phi2) .* mask + (2 * pi - (phi2 - phi1)) .* (1 - mask);
        unwrapped_phase{j,1} = pha12;
        % 保存图像
        if(save_stripes)
            phase_name = [unwrapped_phase_name{j,1},'_',unwrapped_phase_name{j+1,1}];
            unwrapped_phase_name{j,1} = phase_name;
            save_path = [stripes_folder,'/',phase_name,'_外差.png'];
            imwrite(mat2gray(unwrapped_phase{j,1}),save_path);
        end
    end
end

输出结果