Calibration Method for an Omnidirectional Industrial Laser Projection System Integrating a Dual-axis Turntable

Lili GUO; Zhenhuan HAN; Xuezhu LIN; Lijuan LI

doi:10.3788/gzxb20255403.0312005

Acta Photonica Sinica, Volume. 54, Issue 3, 0312005(2025)

Calibration Method for an Omnidirectional Industrial Laser Projection System Integrating a Dual-axis Turntable

Lili GUO^1,2、*, Zhenhuan HAN¹, Xuezhu LIN^1,2, and Lijuan LI^1,2

¹Key Laboratory of Optical Control and Optical Information Transmission Technology，Ministry of Education，School of Optoelectronic Engineering，Changchun University of Science and Technology，Changchun 130022，China

²Zhongshan Institute of Changchun University of Science and Technology，Zhongshan 528437，China

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Fig. 1. Schematic diagram of the construction and composition of an omnidirectional industrial laser 3D projection positioning system

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Fig. 2. Calibration diagram of system construction parameters

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Fig. 3. Physical model schematic of the internal dual-axis galvanometer of the omnidirectional laser 3D projection system

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Fig. 4. Schematic diagram of external parameter calibration of the system

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Fig. 5. System external parameter solution flow chart

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Fig. 6. Validation of the algorithm's capability to find the global optimum

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Fig. 7. Arrangement of cooperative target points and diagram of each coordinate system

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Fig. 8. The RMS change obtained by solving 100 times

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Fig. 9. Schematic diagram of system construction parameter calibration experiment

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Fig. 10. System projection image with dual-axis turntable at a horizontal angle of 0°

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Fig. 11. System projection image with dual-axis turntable at a horizontal angle of 60°

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Fig. 12. System projection image with dual-axis turntable at a horizontal angle of -60°

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Table 1. Spatial coordinates of cooperation target points in the coordinate system of the projected object and the rotation angles of the projector and dual-axis turntable

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Table 1. Spatial coordinates of cooperation target points in the coordinate system of the projected object and the rotation angles of the projector and dual-axis turntable

Target point	$H / (°)$	$V / (°)$	$λ / (°)$	$θ / (°)$	$(x, y, z) / m m$
$P_{1}$	10.462	1.891	60	5	（-5 208.487，-1 267.252，-2 282.100）
$P_{2}$	-21.756	25.498	60	5	（-5 835.524，-1 822.268，-5 509.313）
$P_{3}$	18.315	1.018	0	0	（-422.782，-2 617.716，195.642）
$P_{4}$	-3.556	20.712	0	0	（-1 268.345，-795.012，-1 225.202）
$P_{5}$	3.141	8.240	-60	5	（-6 709.501，-4 952.846，-6 159.055）
$P_{6}$	-18.636	23.730	-60	5	（-5 428.234，-6 075.249，-7 575.773）

Table 2. Theoretical and calculated coordinates of cooperation target points in the coordinate system of the laser 3D projection system and calculation errors

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Table 2. Theoretical and calculated coordinates of cooperation target points in the coordinate system of the laser 3D projection system and calculation errors

Target point	Theoretical coordinates $(x, y, z) / m m$	Calculated coordinates $(x, y, z) / m m$	$Δ S_{i} / m m$
$P_{1}$	（861.923，153.841，4 659.330）	（861.923，153.841，4 659.330）	$3.859 \times 10^{- 7}$
$P_{2}$	（-1 870.127，2 014.693，4 224.300）	（-1 870.127，2 014.693，4 224.300）	$8.627 \times 10^{- 7}$
$P_{3}$	（1 492.868，80.038，4 503.384）	（1 492.868，80.038，4 503.384）	$2.274 \times 10^{- 6}$
$P_{4}$	（-308.199，1 751.949，4 633.373）	（-308.199，1 751.949，4 633.373）	$1.222 \times 10^{- 6}$
$P_{5}$	（259.473，676.767，4 673.580）	（259.473，676.767，4 673.580）	$1.616 \times 10^{- 7}$
$P_{6}$	（-1 560.643，1 859.896，4 230.966）	（-1 560.643，1 859.896，4 230.966）	$9.066 \times 10^{- 7}$

Table 3. Absolute deviation between experimental calibration results and system calculation results
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Table 3. Absolute deviation between experimental calibration results and system calculation results
Rotation angle $ε ({}_{M}^{P}R) / (\times 10^{- 4})$ $ε ({}_{M}^{P}T) / m m$
$R_{Y} = 30 °, R_{X} = 5 °$ 2.036 523 0.023
$R_{Y} = 60 °, R_{X} = 10 °$ 1.769 524 0.025
$R_{Y} = - 30 °, R_{X} = - 5 °$ 1.802 263 0.023
$R_{Y} = - 60 °, R_{X} = - 10 °$ 1.959 517 0.024

Table 4. Coordinates of cooperative target points in the projected object coordinate system and the rotation angles of the dual-axis turntable during calibration

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Table 4. Coordinates of cooperative target points in the projected object coordinate system and the rotation angles of the dual-axis turntable during calibration

Target point	$(x, y, z) / m m$	$λ / (^{\circ})$
$P_{1}$	（619.042，36.293，-710.251）	-60
$P_{2}$	（1 201.371，455.893，-550.784）	-60
$P_{3}$	（1 753.281，-8.983，564.823）	0
$P_{4}$	（2 081.659，373.228，1 100.193）	0
$P_{5}$	（2 945.984，-229.788，2 621.741）	60
$P_{6}$	（2 725.147，134.262，3 221.365）	60

Table 5. The calculation error of the cooperative target point in the experiment

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Table 5. The calculation error of the cooperative target point in the experiment

Target point	Theoretical coordinates $(x, y, z) / m m$	Calculated coordinates $(x, y, z) / m m$	$Δ S_{i} / m m$
$P_{1}$	（406.297，121.855，-2 253.734）	（406.222，122.041，-2 253.785）	0.207
$P_{2}$	（-14.566，704.580，-2 099.112）	（-14.525，704.580，-2 098.903）	0.213
$P_{3}$	（390.329，-474.979，-1 529.962）	（390.272，-475.083，-1 530.133）	0.208
$P_{4}$	（-31.598，127.095，-1 534.682）	（-31.419，127.277，-1 534.578）	0.275
$P_{5}$	（407.142，-605.675，-2 380.946）	（406.982，-605.693，-2 381.159）	0.267
$P_{6}$	（-6.137，-0.951，-2 446.966）	（-6.211，-8.493，-2 447.205）	0.270

Table 6. Comparison of the calibration accuracy between smart laser 3D projection method and the calibration method in this article
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Table 6. Comparison of the calibration accuracy between smart laser 3D projection method and the calibration method in this article
Method Error of projection/mm
Smart laser 3D projection method^［14］ 0.4
Calibration method in this article 0.3

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Lili GUO, Zhenhuan HAN, Xuezhu LIN, Lijuan LI. Calibration Method for an Omnidirectional Industrial Laser Projection System Integrating a Dual-axis Turntable[J]. Acta Photonica Sinica, 2025, 54(3): 0312005

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Aug. 2, 2024

Accepted: Oct. 2, 2024

Published Online: Apr. 22, 2025

The Author Email: Lili GUO (custlily@163.com)

DOI:10.3788/gzxb20255403.0312005

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Spatial coordinates of cooperation target points in the coordinate system of the projected object and the rotation angles of the projector and dual-axis turntable

Table 1. Spatial coordinates of cooperation target points in the coordinate system of the projected object and the rotation angles of the projector and dual-axis turntable

Table 2. Theoretical and calculated coordinates of cooperation target points in the coordinate system of the laser 3D projection system and calculation errors

Table 2. Theoretical and calculated coordinates of cooperation target points in the coordinate system of the laser 3D projection system and calculation errors

Table 3. Absolute deviation between experimental calibration results and system calculation results

Table 3. Absolute deviation between experimental calibration results and system calculation results

Table 4. Coordinates of cooperative target points in the projected object coordinate system and the rotation angles of the dual-axis turntable during calibration

Table 4. Coordinates of cooperative target points in the projected object coordinate system and the rotation angles of the dual-axis turntable during calibration

Table 5. The calculation error of the cooperative target point in the experiment

Table 5. The calculation error of the cooperative target point in the experiment

Table 6. Comparison of the calibration accuracy between smart laser 3D projection method and the calibration method in this article

Table 6. Comparison of the calibration accuracy between smart laser 3D projection method and the calibration method in this article