Measurement and Error Compensation of 3D Morphology with Precision Rotation Line Structured Light

Xiang Liu; Zhenliang Wang; Peng Yao; Yao Hou; Heyong Zhang; Dongkai Chu; Shuoshuo Qu

doi:10.3788/CJL202249.2104004

Chinese Journal of Lasers, Volume. 49, Issue 21, 2104004(2022)

Measurement and Error Compensation of 3D Morphology with Precision Rotation Line Structured Light

Xiang Liu^1,2, Zhenliang Wang³, Peng Yao^1,2、*, Yao Hou^1,2, Heyong Zhang^1,2, Dongkai Chu^1,2, and Shuoshuo Qu^1,2

¹Center for Advanced Jet Engineering Technologies, School of Mechanical Engineering, Shandong University, Jinan 250061, Shandong, China

²Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, Jinan 250061, Shandong, China

³Engine Manufacturing Company, Sinotruk Jinan Power Co., Ltd., Jinan 250220, Shandong, China

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Figures & Tables(31)

Fig. 1. Imaging principle of structured light method. (a) Imaging path of line structured light method; (b) direct-type laser triangulation method; (c) oblique-type laser triangulation method

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Fig. 2. Common measurement methods based on line laser profilometer. (a) Translation motion of laser profilometer; (b) translation motion of measured workpiece; (c) rotational motion of measured workpiece

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Fig. 3. Workpieces and machining robot in aerospace field . (a) Support bin of launch rocket; (b) grid support tube of aircraft; (c) five-degree-of-freedom hybrid machining robot

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Fig. 4. Rotation measuring device based on line laser profilometer

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Fig. 5. Schematics of rotation measurement system integrated on five-degree-of-freedom hybrid processing robot. (a) 3D model of five-degree-of-freedom hybrid machining robot; (b) integrated parts of rotation measurement system

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Fig. 6. Relative position of line structured light and rotation center of rotation stage. (a) Incomplete measurement area; (b) complete measurement area

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Fig. 7. Flow chart of eccentric error calculation program

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Fig. 8. Calculation principle of coordinate based on data measured by rotating line structured light

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Fig. 9. Tilt error between laser profilometer and rotating stage. (a) Error principle; (b) compensation principle

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Fig. 10. Line structured light rotation measurement system

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Fig. 11. Gaussian fitting image of gray value distribution when laser stripe is rotated to 125° position

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Fig. 12. Laser strip images taken by camera at different rotation stage angles. (a) 40°；(b) 125°；(c) 240°；(d) 330°

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Fig. 13. Trajectory fitting of line structured light. (a) Measurement starting point using line structured light; (b) fitted ellipse

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Fig. 14. Incomplete 3D morphology data measured without removing eccentric error

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Fig. 15. Complete 3D morphology data measured after removing eccentric error. (a) Surface morphology; (b) sectional drawing of peripheral contour; (c) leveled surface; (d) section height change along Z axis

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Fig. 16. Results after tilt error correction. (a) Surface morphology; (b) sectional profile

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Fig. 17. On-site photo and results of ceramic plate measurement with profilometer. (a) On-site photo; (b)(c) measured section profiles along different directions

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Fig. 18. Measurement results of zirconia ceramic ball. (a) Physical photograph; (b) top view; (c) section view

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Fig. 19. On-site photo of ball measurement with profilometer

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Fig. 20. Measurement results of key surface morphology. (a) Physical picture; (b) complete 3D morphology by proposed method; (c)(e)(g) enlarged images of local topography measured by proposed method; (d)(f)(h) enlarged images of local topography measured by confocal method

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Table 1. Comparison of direct-type and oblique-type laser triangulation

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Table 1. Comparison of direct-type and oblique-type laser triangulation

Critical information	Direct-type laser triangulation method	Oblique-type laser triangulation method
Satisfied condition	tan ε₂＝ε₀×tan ε₃	tan(ε₁＋ε₂)＝ε₀×tan ε₃
Formula	$H ＝ \frac{L_{1} H' sin ε_{3}}{L_{2} sin ε_{2} － H' sin (ε_{2} ＋ ε_{3})}$	$\begin{matrix} H ＝ \end{matrix} \frac{L_{1} H' sin ε_{3} cos ε_{3}}{L_{2} sin (ε_{1} ＋ ε_{2}) － H' sin (ε_{1} ＋ ε_{2} ＋ ε_{3})}$
Characteristic	High stability, wide measurement range, good flexibility, being suitable for surface with good scattering	High resolution，being suitable for smooth surface, but complicated operation and large space occupation

Table 2. Some parameters of line laser profilometer

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Table 2. Some parameters of line laser profilometer

Parameter	Content
Mounting condition	Diffuse reflection
Reference distance /mm	20
Height /mm	－2.6～＋2.6(F.S. of 5.2)
Width on near side /mm	6.5
Reference distance /mm	7
Width on far side /mm	7.5
Repeatability of height /μm	0.2
Repeatability of width /μm	2.5
Linearity of height	±0.1% F.S.
Profile data interval along X-axis /μm	10
Spot size /(μm×μm)	14×35
Wavelength /nm	405

Table 3. Some parameters of precision rotating stage

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Table 3. Some parameters of precision rotating stage

Parameter	Value
Travel range /(°)	360(continuous)
Accuracy /(″)	3
Resolution /(″)	0.01
Unidirectional repeatability /(″)	0.5
Tilt error between synchronous motion and asynchronous motion /(″)	10/3
Axial error between synchronous motion and asynchronous motion /μm	2
Radial error between synchronous motion and asynchronous motion /μm	3

Table 4. Some parameters of CMOS camera
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Table 4. Some parameters of CMOS camera
Parameter Value
Frame rate /(frame·s^－1) 9.2
Resolution /(pixel×pixel) 4000×3000
Pixel size /(μm×μm) 1.85×1.85
Image area /(mm×mm) 7.4×5.55

Table 5. Gaussian fitting function and its regression evaluation indexes

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Table 5. Gaussian fitting function and its regression evaluation indexes

Parameter	Content
Gaussian fitting function	$f (x) ＝ 262 \times exp \frac{{(x － 0.02803)}^{2}}{{0.5618}^{2}}$
Sum of squared error (SSE) /pixel²	1.304×10⁶
Root mean squard error(RMSE) /pixel	35.7424
Coefficient of determination (R²)	0.8731
Adjusted coefficient of determination ( $R_{ADJ}^{2}$ )	0.8729

Table 6. Regression evaluation indexes of Gaussian fitting for gray distribution of laser strips at different angles

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Table 6. Regression evaluation indexes of Gaussian fitting for gray distribution of laser strips at different angles

Rotation stage angle /(°)	R²	$R_{ADJ}^{2}$	Rotation stage angle /(°)	R²	$R_{ADJ}^{2}$	Rotation stage angle /(°)	R²	$R_{ADJ}^{2}$
0	0.7593	0.7590	110	0.8758	0.8756	240	0.7902	0.7900
15	0.7873	0.7870	120	0.8785	0.8783	250	0.7912	0.7910
30	0.7612	0.7610	125	0.8731	0.8729	280	0.8622	0.8620
45	0.7569	0.7566	135	0.8732	0.8730	295	0.8615	0.8612
60	0.7916	0.7914	150	0.8718	0.8715	310	0.8698	0.8696
75	0.7983	0.7981	165	0.8261	0.8259	325	0.8680	0.8677
90	0.8069	0.8066	180	0.8149	0.8147	340	0.8608	0.8605
105	0.8555	0.8553	195	0.7828	0.7826	355	0.7936	0.7933

Table 7. Regression evaluation indexes of linear fitting for laser strips at different angles by least square method

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Table 7. Regression evaluation indexes of linear fitting for laser strips at different angles by least square method

Rotation stage angle /(°)	RMSE /pixel	$R_{ADJ}^{2}$	Rotation stage angle /(°)	RMSE /pixel	$R_{ADJ}^{2}$	Rotation stage angle /(°)	RMSE /pixel	$R_{ADJ}^{2}$
0	3.0528	0.9993	110	6.4290	0.9978	240	2.6408	0.9974
15	2.7930	0.9989	120	5.6574	0.9887	250	2.7710	0.9988
30	2.5141	0.9960	125	5.2381	0.8196	280	5.2130	0.9987
45	2.3881	0.8859	135	5.5422	0.9938	295	5.5347	0.9964
60	2.7347	0.9975	150	5.6315	0.9990	310	5.3335	0.9439
75	3.2607	0.9989	165	4.1523	0.9993	325	5.4857	0.9983
90	4.3018	0.9990	180	3.1183	0.9994	340	4.5075	0.9992
105	6.0104	0.9987	195	2.4413	0.9992	355	3.3165	0.9994

Table 8. Laser stripe lengths at different angles

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Table 8. Laser stripe lengths at different angles

Rotation stage angle /(°)	Laser stripe length /pixel	Rotation stage angle /(°)	Laser stripe length /pixel	Rotation stage angle /(°)	Laser stripe length /pixel
0	1307.313	40.5	1581.133	49.5	841.056
5	1356.549	41	1592.315	50	762.510
10	1434.167	41.5	1601.187	55	692.915
15	1486.129	42	1588.588	60	644.841
20	1534.052	42.5	1591.926	65	624.454
25	1564.608	43	1581.333	70	645.113
30	1589.003	43.5	1570.801	75	695.786
35	1607.934	44	1550.96	80	733.680
35.5	1587.285	44.5	1533.769	85	804.043
36	1601.389	45	1514.985	90	904.439
36.5	1592.984	45.5	1456.267	95	991.563
37	1604.624	46	1402.323	100	1063.748
37.5	1586.348	46.5	1311.365	105	1152.653
38	1594.162	47	1248.923	335	1234.443
38.5	1602.313	47.5	1166.271	340	1304.497
39	1602.046	48	1095.006	345	1375.174
39.5	1577.002	48.5	1004.367	350	1415.386
40	1579.027	49	911.964	355	1460.802

Table 9. Fitted results of eccentric error and deflection angle

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Table 9. Fitted results of eccentric error and deflection angle

Fitted ellipse center coordinate	Eccentric error /mm	Deflection angle /(°)
(1450.6028, 1979.3201)	0.9838	140.1801
(1562.8977, 1943.8902)	0.0642	122.1208
(1562.0212, 1943.1210)	0.0398	124.9813
(1561.9853, 1943.5147)	0.0389	139.7264
(1561.0801, 1945.9902)	0.0275	143.6845
(1561.3261, 1940.6634)	0.0397	100.8764
(1562.1362, 1942.8301)	0.0334	135.6443
(1562.3614, 1942.7806)	0.0346	148.6949
(1563.0726, 1942.9401)	0.0637	127.1804

Table 10. Fitted radii of zirconia ceramic ball

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Table 10. Fitted radii of zirconia ceramic ball

Fitted radius obtained by proposed method	Fitted radius obtained by contact method	Average value
5.0011	5.0041	0.0029
5.0012	5.0033
5.0014	5.0043
5.0012	5.0043
5.0009	5.0042
5.0010	5.0037
5.0008	5.0039
5.0010	5.0041
5.0000	5.0036

Table 11. Comparison of characteristic parameters of key surface morphologies obtained by different methods
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Table 11. Comparison of characteristic parameters of key surface morphologies obtained by different methods
Characteristic parameter Proposed method Confocal method Error
Width 1 0.3371 0.3346 0.0025
Width 2 0.3682 0.3663 0.0019
Width 3 0.3585 0.3618 0.0033
Diameter 0.4633 0.4591 0.0042
Height 0.2532 0.2504 0.0028

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Xiang Liu, Zhenliang Wang, Peng Yao, Yao Hou, Heyong Zhang, Dongkai Chu, Shuoshuo Qu. Measurement and Error Compensation of 3D Morphology with Precision Rotation Line Structured Light[J]. Chinese Journal of Lasers, 2022, 49(21): 2104004

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