MATLAB实现光学三维重构中时间相位展开算法

一、算法原理与流程

1. 时间相位展开核心原理

\(ϕ_{abs}=ϕ_{wrapped}+2πk\)

• 多频外差法：通过不同频率条纹的相位差计算绝对相位阶次
• 三频序列：选择高频\(（f_₁）\)、中频\(（f_₂）\)、低频\(（f_₃）\)条纹，满足\(f_2/f_1≈f_1/f_3\)（如70/64/59）

2. 算法流程

1. 条纹投影：依次投射4步相移条纹（0°,90°,180°,270°）
2. 相位解调：计算包裹相位主值\(ϕ_wrapped\)
3. 多频外差：通过频率差计算绝对相位阶次
4. 三维重建：相位-高度映射生成三维点云

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二、MATLAB核心代码实现

1. 条纹生成与投影

function fringe = generate_fringe(size, freq, phase_shift)
    [X,Y] = meshgrid(1:size);
    fringe = 0.5 + 0.5*cos(2*pi*freq*X + phase_shift);
end

% 参数设置
N = 512;        % 图像分辨率
frequencies = ; % 三频序列
phase_steps = [0, pi/2, pi, 3*pi/2](@ref); % 四步相移

% 生成四步相移条纹组
fringe_set = cell(length(frequencies), length(phase_steps));
for i = 1:length(frequencies)
    for j = 1:length(phase_steps)
        fringe_set{i,j} = generate_fringe(N, frequencies(i), phase_steps(j));
    end
end

2. 相位解调（四步相移法）

function phase = phase_demodulation(fringe_set)
    % 四步相移公式
    I1 = fringe_set{1,1}; I2 = fringe_set{1,2};
    I3 = fringe_set{1,3}; I4 = fringe_set{1,4};
    
    phase = atan2((I4-I2), (I1-I3));
    phase(phase < 0) = phase(phase < 0) + 2*pi; % 映射到[0,2π]
end

3. 多频外差相位展开

function absolute_phase = phase_unwrapping(wrapped_phase, frequencies)
    % 频率序列处理
    T = 1./frequencies;
    T12 = (T(1)*T(2))/(T(2)-T(1));
    T23 = (T(2)*T(3))/(T(3)-T(2));
    T123 = (T12*T23)/(T23-T12);
    
    % 相位差计算
    delta_phi12 = wrapped_phase(:,:,1) - wrapped_phase(:,:,2);
    delta_phi23 = wrapped_phase(:,:,2) - wrapped_phase(:,:,3);
    
    % 阶次计算
    Ox12 = round((delta_phi12 * T123 / T12 - delta_phi12) / (2*pi));
    Ox23 = round((delta_phi23 * T123 / T23 - delta_phi23) / (2*pi));
    
    % 绝对相位展开
    absolute_phase = wrapped_phase(:,:,1) + 2*pi*(Ox12 + Ox23);
end

4. 三维重建模块

function [X,Y,Z] = reconstruct_3d(phase, camera_params)
    % 相位-高度映射
    [rows,cols] = size(phase);
    [X,Y] = meshgrid(1:cols,1:rows);
    
    % 相机参数标定（示例值）
    baseline = 0.1;    % 基线距离(m)
    focal_length = 0.05; % 焦距(m)
    
    % 高度计算
    Z = baseline * tan(phase * focal_length / (2*pi));
    X = (X - cols/2) * pixel_size * Z / baseline;
    Y = (Y - rows/2) * pixel_size * Z / baseline;
end

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三、仿真流程

%% 参数设置
img_size = ;
pixel_size = 0.005; % 像素尺寸(mm)

%% 1. 生成投影条纹
[fringe_set] = generate_fringe_set(img_size, );

%% 2. 采集变形条纹（模拟）
deformed_fringe = apply_deformation(fringe_set(:,:,1), height_map);

%% 3. 相位解调
wrapped_phase = phase_demodulation(deformed_fringe);

%% 4. 相位展开
absolute_phase = phase_unwrapping(wrapped_phase, );

%% 5. 三维重建
camera_params = struct('baseline',0.1, 'focal_length',0.05);
[X,Y,Z] = reconstruct_3d(absolute_phase, camera_params);

%% 6. 可视化
figure;
surf(X,Y,Z, 'EdgeColor','none');
colormap(jet);
shading interp;
xlabel('X (mm)'); ylabel('Y (mm)'); zlabel('Z (mm)');

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四、优化

1. 噪声抑制

% 中值滤波去噪
denoised_phase = medfilt2(wrapped_phase, );

% 自适应滤波
window_size = 5;
local_var = stdfilt(denoised_phase, ones(window_size))/mean2(denoised_phase);
denoised_phase = wdenoise(denoised_phase, 3, 'Wavelet','db4');

2. 相位误差补偿

% 相位跳变检测
[rows,cols] = size(absolute_phase);
error_mask = zeros(rows,cols);
for i = 2:rows-1
    for j = 2:cols-1
        if abs(absolute_phase(i,j) - absolute_phase(i+1,j)) > 3*pi
            error_mask(i,j) = 1;
        end
    end
end

% 区域生长校正
clean_phase = region_growing(absolute_phase, error_mask);

3. 加速计算

% GPU加速
gpu_fringe = gpuArray(fringe_set);
gpu_phase = gpuArray(wrapped_phase);
absolute_phase = phase_unwrapping(gpu_phase, frequencies);

参考代码 基于MATLAB光学三维重构中的时间相位展开算法 www.youwenfan.com/contentcnl/79227.html

五、应用

1. 动态物体测量

% 高速相机动态采集
for t = 1:frame_num
    fringe = project_dynamic_fringe(t);
    deformed = capture_deformed_fringe();
    phase(:,:,t) = phase_demodulation(deformed);
end

% 时序相位展开
absolute_phase = temporal_unwrapping(phase);

2. 复杂曲面重建

% 多频融合算法
high_freq = 120; low_freq = 40;
multi_freq_phase = combine_frequencies(high_freq, low_freq);
absolute_phase = multi_freq_unwrapping(multi_freq_phase);