复杂印刷电路板表面相位保真条纹超分辨三维测量方法

吴福培; 胡聪; 韩强; 叶玮琳

doi:10.37188/CO.2026-0061

复杂印刷电路板表面相位保真条纹超分辨三维测量方法

doi: 10.37188/CO.2026-0061

cstr: 32171.14.CO.2026-0061

吴福培^1, ,,
胡聪^{1, 2,},
韩强¹,
叶玮琳¹

1.
汕头大学工学院机械工程系, 广东汕头 515063
2.
广东弘景光电科技股份有限公司, 广东中山 528400

基金项目: 国家自然科学基金（No. 61573233）；广东省自然科学基金（No. 2021A1515010661）；广东省普通高校创新团队资助项目（No. 2020KCXTD012）

详细信息

作者简介:
吴福培（1980—），男，广西玉林人，博士，教授， 2009年于华南理工大学机械工程专业获得博士学位，现就职于汕头大学机械工程系，主要研究方向为自动光学检测和3D测量。 E-mail：fpwu@stu.edu.cn

胡　聪（1997—），男，湖北荆州人，硕士，工程师，2026年于汕头大学机械专业获得硕士学位，现就职于广东弘景光电科技股份有限公司，担任软件研发工程师。研究方向：结构光三维测量。E-mail：1193809355@qq.com

中图分类号: TP394.1
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出版历程
- 网络出版日期: 2026-08-05

Phase-preserving fringe super-resolution for three-dimensional measurement of complex printed circuit board surfaces

WU Fu-pei^{1
, ,},
HU Cong^{1, 2
,},
HAN Qiang¹,
YEEWEI-LIN¹

1.
Department of Mechanical Engineering, College of Engineering, Shantou University, Shantou 515063, Guangdong, China
2.
Guangdong Hongjing Optoelectronic Technology Inc., Zhongshan, Guangdong 528400

Funds: Supported by National Natural Science Foundation of China (No. 61573233); National Natural Science Found-ation of Guangdong, China (No. 2021A1515010661); the Guangdong Provincial University Innovation TeamProject (No. 2020KCXTD012)

More Information

Corresponding author: fpwu@stu.edu.cn

摘要

摘要:
目的
针对复杂反光印刷电路板（printed circuit board，PCB）表面条纹测量中统一图像插值易破坏条纹正弦性、弯曲条纹条件下插值方向与局部等相位线不一致以及低调制度区域误差易扩散的问题，提出一种测量导向的相位保真条纹超分辨重采样方法。
方法
该方法在图像灰度域完成条纹超分辨，但利用相位域解算得到的载波强度指数、局部调制度和多频包裹相位作为物理约束。首先，利用归一化载波强度指数对条纹脊线、谷线及过渡区域进行结构解耦，并结合脊谷距离与局部调制度构建联合权重；随后，基于多频相移信息估计二维条纹对齐位移场，经局部相关细化与二维总变差正则化后，将原始条纹映射至条纹对齐域并实施方向性插值；最后，依据位移场梯度与局部相位变化率构建平坦区陡变区自适应融合策略，实现面向相位保真的条纹重采样与三维测量。
结果
在3 mm、6 mm 和9 mm 量块实验中，所提方法将平均绝对误差由 0.0290 mm 降至 0.0208 mm，均方根误差由0.0428 mm 降至 0.0295 mm；在 PCB 引脚区域和晶振封装区域中，所提方法均改善了相位连续性和三维重建稳定性。以引脚区域为例，与图像双三次插值相比，所提方法将平均绝对误差由 0.1753 mm降至0.0254 mm，降幅约为 85.5%。
结论
实验结果表明，该方法在当前 PCB 引脚区域和晶振封装局部结构中能够提高条纹重采样后的相位一致性和点云采样密度，并降低局部重建误差。
- 三维测量 /
- 条纹结构光 /
- 相位保真 /
- 印刷电路板 /
- 超分辨 /
- 自适应融合
Abstract:
Objective: This study addresses fringe-based three-dimensional measurement of local structures on complex reflective printed circuit boards. Uniform image interpolation may distort sinusoidal fringes. Curved fringes may also cause a mismatch between the interpolation direction and local iso-phase lines. Low-modulation regions may further amplify phase errors.Methods: A measurement-oriented phase-preserving fringe super-resolution resampling method is proposed. The super-resolution operation is performed in the gray-image domain. Phase-domain quantities are used as physical constraints. First, a normalized carrier intensity index is used to decouple fringe ridges, valleys, and transition regions. Ridge-valley distance and local modulation are then combined to construct a joint weight. Next, a two-dimensional fringe-alignment displacement field is estimated from multi-frequency phase-shifting data. The field is refined by local correlation and two-dimensional total-variation regularization. The original fringe images are then mapped into an aligned domain for directional interpolation. Finally, a flat/steep-region adaptive fusion strategy is constructed using the displacement-field gradient and local phase variation rate.Results: In the 3 mm, 6 mm, and 9 mm gauge-block experiments, the proposed method reduced the mean absolute error from 0.0290 mm to 0.0208 mm. It also reduced the root mean square error from 0.0428 mm to 0.0295 mm. In the high-reflective PCB pin region and the crystal oscillator package region, the proposed method improved phase continuity and three-dimensional reconstruction stability. In the pin region, compared with image-domain bicubic interpolation, the proposed method reduced the mean absolute error from 0.1753 mm to 0.0254 mm, corresponding to a reduction of about 85.5%. The error standard deviation was reduced to 0.0126 mm.Conclusion:The proposed method improves phase consistency after fringe resampling, increases point-cloud sampling density, and reduces local reconstruction errors in the selected PCB regions. This super-resolution process should be interpreted as sampling-grid densification and interpolation-induced phase-error reduction, rather than as exceeding the true lateral resolution limited by the optical system. The current conclusions are limited to the tested PCB local ROIs and imaging conditions.
- three-dimensional measurement /
- fringe structured light /
- phase preservation /
- printed circuit board /
- super-resolution /
- adaptive fusion

HTML全文

图 1 三维重建流程括号中标明各模块的主要操作域

Figure 1. Flow chart of the proposed 3D reconstruction framework. The terms in parentheses indicate the main operation domain of each module

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图 2 调制条纹图像

Figure 2. Fringe pattern image

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图 3 自适应插值流程图

Figure 3. Adaptive interpolation flowchart

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图 4 实验平台。((a)结构光系统示意图;(b)实验平台实物图)

Figure 4. Experimental setup. ((a) Structured light system; (b) photograph of the experimental platform)

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图 5 3mm标准量块的表面平面度剖面对比

Figure 5. Comparison of surface flatness profiles for a 3mm gauge block

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图 6 PCB表面重建效果对比（(a)原始条纹图像(b)点云超分辨前后对比）

Figure 6. Comparison of PCB surface reconstruction results: (a) original fringe image; (b) point cloud before and after super-resolution

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图 7 引脚区域与晶振封装区域的原始图像及相位结果对比。左列为高密度引脚区域，右列为晶振封装区域。（a）原始图像；（b）原始相位结果；（c）所提方法处理后的相位结果。

Figure 7. Comparison of original images and phase results in the pin region and crystal oscillator package region. The left column shows the high-density pin region, and the right column shows the crystal oscillator package region. (a) Original images; (b) original phase results; (c) phase results obtained by the proposed method.

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图 8 引脚区域与晶振封装区域的多方法三维重建结果对比。左列为高密度引脚区域，右列为晶振封装区域。（a）原始重建结果；（b）图像双三次插值结果；（c）基于深度学习的图像超分辨结果；（d）相位双三次插值结果；（e）所提方法的重建结果。

Figure 8. Comparison of 3D reconstruction results obtained by different methods in the pin region and crystal oscillator package region. The left column shows the high-density pin region, and the right column shows the crystal oscillator package region. (a) Original reconstruction; (b) image bicubic interpolation; (c) deep-learning-based image super-resolution; (d) phase bicubic interpolation ; (e) proposed method.

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图 9 复杂PCB引脚表面的重建质量综合评估（a）高度截图轮廓对比（b）绝对重建误差分布

Figure 9. Comprehensive evaluation of reconstruction quality on a complex PCB pin surface: (a) height profile comparison; (b) absolute reconstruction error distribution

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图 10 不同方法在 PCB 局部 ROI 内的绝对误差累积分布曲线

Figure 10. Cumulative distribution curves of absolute errors for different methods within the PCB local ROI.

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图 11 相位域保真性能的局部对比。

Figure 11. Local comparison of phase-domain fidelity performance.

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图 12 沿图11中标记剖面线提取的包裹相位曲线对比。

Figure 12. Comparison of wrapped-phase curves extracted along the marked profile line in Fig. 11.

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表 1 不同方法主导计算代价对比

Table 1. Comparison of dominant computational costs among different methods

方法	时间复杂度	空间复杂度	依赖
双三次插值	O(R·C·t²)	O(R·C·t²)	CPU
样条插值	O(R·C·t²)	O(R·C·t²)	CPU
本文方法	O((N+F+$ {I}_{TV} $)·R·C + R·C·t²)	O(R·C·t² + R·C)	CPU
深度学习	O(k·R·C·t²), $ \mathrm{k}\gg 1 $	O(Model size + R·C·t²)	GPU; 需预训练模型

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表 6 主要误差指标的95%置信区间

Table 6. 95% confidence intervals of the main error metrics

实验场景	方法	>指标	均值 ± SD/mm	95% CI/mm
标准量块	原始重建	MAE	0.0290 ± 0.0021	[0.0275, 0.0305]
	本文方法	MAE	0.0208 ± 0.0015	[0.0197, 0.0219]
	原始重建	RMSE	0.0428 ± 0.0037	[0.0402, 0.0454]
	本文方法	RMSE	0.0295 ± 0.0026	[0.0276, 0.0314]
引脚	图像双三次	MAE	0.1753 ± 0.0120	[0.1667, 0.1839]
	深度学习	MAE	0.1721 ± 0.0140	[0.1621, 0.1821]
	相位双三次	MAE	0.0485 ± 0.0040	[0.0456, 0.0514]
	本文方法	MAE	0.0254 ± 0.0021	[0.0239, 0.0269]
	本文方法	RMSE	0.0298 ± 0.0026	[0.0279, 0.0317]
	本文方法	MaxAE	0.0820 ± 0.0110	[0.0741, 0.0899]
晶振	图像双三次	MAE	0.1626 ± 0.0105	[0.1551, 0.1701]
	深度学习	MAE	0.1667 ± 0.0120	[0.1581, 0.1753]
	相位双三次	MAE	0.0675 ± 0.0055	[0.0636, 0.0714]
	本文方法	MAE	0.0221 ± 0.0018	[0.0208, 0.0234]
	本文方法	RMSE	0.0347 ± 0.0030	[0.0326, 0.0368]
	本文方法	MaxAE	0.0950 ± 0.0120	[0.0864,0.1036]

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表 2 不同分辨率下测量结果对比

Table 2. Comparison of measurement results under different resolutions

量块	超分辨前		超分辨后
	MAE/mm	RMSE/mm	MAE/mm	RMSE/mm
3mm	0.0253 ± 0.0018	0.0361 ± 0.0032	0.0212 ± 0.0015**	0.0226 ± 0.0020**
6mm	0.0272 ± 0.0020	0.0479 ± 0.0041	0.0164 ± 0.0012**	0.0332 ± 0.0030**
9mm	0.0345 ± 0.0026	0.0443 ± 0.0038	0.0249 ± 0.0019**	0.0326 ± 0.0028**
平均	0.0290 ± 0.0021	0.0428 ± 0.0037	0.0208 ± 0.0015	0.0295 ± 0.0026

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表 3 不同方法测量结果对比

Table 3. Comparison of measurement results by different methods

方法	RMSE/mm	Planarity Error/mm	平均耗时/s
图像双三次	0.0497 ± 0.0038**	0.0128 ± 0.0011**	0.064 ± 0.004
深度学习	0.0482 ± 0.0042**	0.0095 ± 0.0009**	2.684 ± 0.100
相位双三次	0.0286 ± 0.0023**	0.0078 ± 0.0007**	0.071 ± 0.005
所提方法（无几何校正）	0.0395 ± 0.0030**	0.0051 ± 0.0005*	0.184 ± 0.012
所提方法（无权重融合）	0.0291 ± 0.0024**	0.0073 ± 0.0007**	0.263 ± 0.016
所提方法	0.0226 ± 0.0018	0.0046 ± 0.0004	0.342 ± 0.020

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表 4 引脚区域与晶振封装区域不同方法的重建误差对比

Table 4. Reconstruction errors of different methods in the pin region and crystal oscillator package region

区域	方法	MAE/mm	RMSE/mm	STD/mm	MaxAE/mm	Planarity Error/mm	平均耗时/s
引脚	图像双三次	0.1753 ± 0.0120**	0.2057 ± 0.0160**	0.0951 ± 0.0085**	0.560 ± 0.060**	0.0201 ± 0.0020**	0.066 ± 0.005
	深度学习	0.1721 ± 0.0140**	0.2184 ± 0.0180**	0.0758 ± 0.0070**	0.590 ± 0.065**	0.0185 ± 0.0018**	3.126 ± 0.130
	相位双三次	0.0485 ± 0.0040**	0.0552 ± 0.0048**	0.0483 ± 0.0042**	0.150 ± 0.020**	0.0123 ± 0.0013**	0.074 ± 0.005
	本文方法	0.0254 ± 0.0021	0.0298 ± 0.0026	0.0126 ± 0.0014	0.082 ± 0.011	0.0081 ± 0.0008	0.349 ± 0.020
晶振	图像双三次	0.1626 ± 0.0105**	0.2416 ± 0.0170**	0.1180 ± 0.0100**	0.610 ± 0.070**	0.0220 ± 0.0020**	0.068 ± 0.005
	深度学习	0.1667 ± 0.0120**	0.2447 ± 0.0185**	0.1260 ± 0.0110**	0.630 ± 0.075**	0.0292 ± 0.0025**	3.184 ± 0.135
	相位双三次	0.0675 ± 0.0055**	0.1332 ± 0.0120**	0.0815 ± 0.0075**	0.310 ± 0.040**	0.0180 ± 0.0016	0.079 ± 0.006
	本文方法	0.0221 ± 0.0018	0.0347 ± 0.0030	0.0158 ± 0.0016	0.095 ± 0.012	0.0176 ± 0.0014	0.361 ± 0.022

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表 5 不同方法在相位域中的定量比较

Table 5. Quantitative comparison of different methods in the phase domain

方法	phase MAE / rad	phase RMSE / rad	相位误差 STD / rad	结果说明
图像双三次	0.092	0.124	0.083	边缘附近易出现局部振荡与周期性扰动
相位双三次	0.050	0.074	0.054	可减弱相位扰动，但边缘存在过平滑
本文方法	0.028	0.037	0.025	平坦区与边缘区均与参考结果保持较高一致性

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表 7 PCB 引脚区域不同图像扰动条件下的鲁棒性分析

Table 7. Robustness analysis under different image perturbation conditions in the PCB pin region

扰动类型	条件	图像双三次 MAE/mm	相位双三次 MAE/mm	本文方法 MAE/mm	图像双三次 RMSE/mm	相位双三次 RMSE/mm	本文方法 RMSE/mm
无扰动	Baseline	0.1753 ± 0.0120	0.0485 ± 0.0040	0.0254 ± 0.0021	0.2057 ± 0.0160	0.0552 ± 0.0048	0.0298 ± 0.0026
高斯噪声	σ = 0.01	0.1846 ± 0.0134	0.0506 ± 0.0044	0.0262 ± 0.0024	0.2162 ± 0.0176	0.0574 ± 0.0052	0.0307 ± 0.0029
	σ = 0.02	0.1978 ± 0.0152	0.0539 ± 0.0049	0.0274 ± 0.0028	0.2315 ± 0.0195	0.0612 ± 0.0059	0.0321 ± 0.0032
	σ = 0.04	0.2265 ± 0.0196	0.0618 ± 0.0058	0.0301 ± 0.0034	0.2648 ± 0.0240	0.0699 ± 0.0068	0.0351 ± 0.0040
曝光扰动	α = 0.7	0.2072 ± 0.0165	0.0556 ± 0.0051	0.0279 ± 0.0029	0.2436 ± 0.0210	0.0637 ± 0.0060	0.0329 ± 0.0034
	α = 1.3	0.1991 ± 0.0158	0.0542 ± 0.0048	0.0275 ± 0.0028	0.2338 ± 0.0202	0.0621 ± 0.0058	0.0324 ± 0.0033
	α = 1.5	0.2348 ± 0.0215	0.0639 ± 0.0063	0.0309 ± 0.0036	0.2764 ± 0.0265	0.0728 ± 0.0075	0.0362 ± 0.0042

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