Evaluation Method for Error Calibration of Laser Tracking Measurement Systems

Fig. 7. The influence of different layout factors on the mean of uncertainty of structural error parameters. (a) Azimuth coverage; (b) pitch coverage; (c) the difference in distance between the internal and external calibration surfaces; (d) azimuth density; (e) pitch density; (f) the number of calibration surfaces; (g) azimuth center line angle; (h) pitch center line angle; (i) inner calibration surface distance

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Fig. 8. ORMS structure error calibration and evaluation experiment scene and schematic diagram. (a) Scene diagram; (b) schematic diagram

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Fig. 9. Layout of calibration points. (a) Recommended layout; (b) two transfers; (c) decrease θ_r, φ_r, n_θ, n_φ; (d) decrease n_θ, n_φ; (e) Δ_d approaches 0, decrease n_d; (f) decrease θ_r, φ_r, n_θ, n_φ, change θ_m; (f) decrease θ_r, φ_r, n_θ, n_φ, change φ_m; (f) Δ_d approaches 0, decrease n_d, increase d₀

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Table 1. Structural error parameters of laser tracking measurement system

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Table 1. Structural error parameters of laser tracking measurement system

Structural error parameter	Symbol	Ideal value	Unit
Mirror offset	r	0	mm
Beam offset	I₁，I₂	0，0	mm
Transit axis offset	e	0	mm
Mirror tilt	α₁，α₂	90，135	°
Beam axis tilt	β₁，β₂	0，0	°
Transit axis tilt	k	90	°
Circular grating error	A_x，A_y，E_x，E_y	0，0，0，0	°
Correction length	L₀		mm

Table 2. The accuracy of observations from laser tracking measurement system
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Table 2. The accuracy of observations from laser tracking measurement system
precision σ_H /（"） σ_V /（"） σ_L /μm
precision 1 1 1 1
precision 2 5 5 1
precision 3 1 1 10

Table 3. The default values of layout indicators
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Table 3. The default values of layout indicators
Indicator θ_r /（°） φ_r /（°） Δ_d /m n_θ n_φ n_d θ_m /（°） φ_m /（°） d₀ /m
Default value 90 90 2 5 5 2 0 90 1

Table 4. Reference values for layout indicators
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Table 4. Reference values for layout indicators
Indicator θ_r /（°） φ_r /（°） Δ_d /m n_θ n_φ n_d θ_m /（°） φ_m /（°） d₀ /m
Reference value >40 >30 >1 ≥3 ≥3 ≥2 ≈0 ≈90 <5

Table 5. The setting values of layout indicators in the experiment
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Table 5. The setting values of layout indicators in the experiment
Indicator θ_r /（°） φ_r /（°） Δ_d /m n_θ n_φ n_d θ_m /（°） φ_m /（°） d₀ /m
Theoretical setting value 42.1 65.2 1.3 5 5 2 -0.1 90.4 1.3

Table 6. PRMSE of ORMS
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Table 6. PRMSE of ORMS
PRMSE PRMSE_θ /（"） PRMSE_φ /（"） PRMSE_d /μm
Value 2.00 5.10 6.27

Table 7. The mean of uncertainty of structural error parameters under different layouts
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Table 7. The mean of uncertainty of structural error parameters under different layouts
Layout （a）（b）（c）（d）（e）（f）（g）（h）
Mean of $σ_{X}$ 21.90 42.37 126.12 38.57 146.03 128.54 125.76 410.96

Table 8. RMSE of evaluation points under different layouts

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Table 8. RMSE of evaluation points under different layouts

Layout	RMSE_θ /（"）	RMSE_φ /（"）	RMSE_d /μm	RMSE_xyz /mm
（a）	2.42	5.70	7.87	0.2910
（b）	2.54	6.17	8.51	0.3221
（c）	2.78	10.05	10.25	0.4653
（d）	2.44	5.91	8.19	0.3004
（e）	12.38	24.58	7.70	1.2981
（f）	2.97	10.60	12.99	0.4929
（g）	2.71	9.21	10.54	0.4322
（h）	33.47	33.34	8.83	2.2365

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Shixiong Wen, Tengfei Wu, Haochen Qu. Evaluation Method for Error Calibration of Laser Tracking Measurement Systems[J]. Laser & Optoelectronics Progress, 2025, 62(7): 0712002

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