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Journals >Laser & Optoelectronics Progress >Volume 60 >Issue 3 >Page 0312016 > Article

Laser & Optoelectronics Progress
Vol. 60, Issue 3, 0312016 (2023)

Laser Interferometer Technology and Instruments for Sub-Nanometer and Picometer Displacement Measurements

Xionglei Lin^1,2, Xiaobo Su^1,2, Jianing Wang^1,2, Yunke Sun^1,2, and Pengcheng Hu^1,2,*

Author Affiliations

¹Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, Heilongjiang, China

²Key Laboratory of Ultra-Precision Intelligent Instrumentation, Ministry of Industry and Information Technology, Harbin 150080, Heilongjiang, China

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DOI: 10.3788/LOP230440 Cite this Article Set citation alerts

Xionglei Lin, Xiaobo Su, Jianing Wang, Yunke Sun, Pengcheng Hu. Laser Interferometer Technology and Instruments for Sub-Nanometer and Picometer Displacement Measurements[J]. Laser & Optoelectronics Progress, 2023, 60(3): 0312016 Copy Citation Text

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Principle of homodyne laser interference measurement

Fig. 1. Principle of homodyne laser interference measurement

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Principle of heterodyne laser interference measurement

Fig. 2. Principle of heterodyne laser interference measurement

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Fig. 3. HIT HUE displacement measurement system

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Fig. 4. Keysight 55280B displacement measurement system^［12］

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Fig. 5. Zygo ZMI displacement measurement system^［13］

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Fig. 6. SIOS SP displacement measurement system^［14］

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Fig. 7. Renishaw RLE displacement measurement system^［15］

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Fig. 8. Schematic of the offset locked thermal frequency stabilization principle

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Fig. 9. Periodic nonlinearity error mechanism in homodyne and heterodyne interferometers. (a) Lissajous figure of the three errors and multi-order ghost reflection; (b) spectral distribution of the multi-order ghost reflection and dual-frequency aliasing

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Fig. 10. Multi-order ghost reflection

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Fig. 11. Structure of fully symmetrical optical path^［27］

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Fig. 12. Schematic of measurement principle of double quadrature phase-locked algorithm^[36-37]

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Error source	Error model	Traditional interferometer	Sub-nanometer and petermeter interferometer
Laser frequency stability	$L_{m a x} \cdot Δ v_{0} / v_{0}$	$L_{m a x} \times 10^{- 8}$	$L_{m a x} \times 10^{- 9}$
Laser frequency accuracy	$L_{D} \cdot Δ v_{0} / v_{0}$	$L_{D} \times 10^{- 9}$	$L_{D} \times 10^{- 9}$
Dual-frequency laser frequency stability	$L_{C} \cdot Δ f_{0} / f_{0}$	$L_{C} \times 10^{- 11}$	$L_{C} \times 10^{- 11}$
Phase measurement error	$Δ φ$	$2 π / 512 - 2 π / 1024$	$2 π / 1024 - 2 π / 4096$
Periodic nonlinearity error		$\geq 10 n m$	$\leq 1 n m$
Air refractive index error	$L_{m a x} \cdot Δ n / n$	$L_{m a x} \times (10^{- 9} - 10^{- 8})$	≈0@vacuum
Thermal drift error of optical prism group	$D E_{T} \cdot Δ T$	$\geq 50 n m / ℃ \times Δ T$	$\leq 20 n m / ℃ \times Δ T$
Abbe error	$L_{m a x} \cdot θ$	$\approx 0$	$\approx 0$
Cosine error	$L_{m a x} \cdot s i n^{2} β / 2$	$L_{m a x} \times 10^{- 10}$	$L_{m a x} \times 10^{- 10}$
Dead-path error	$L_{D} \cdot Δ n / n$	$L_{D} \times 10^{- 9}$	≈0
Dynamic measurement error	$Δ τ \cdot v$	$(10^{- 7} - 10^{- 6}) \times v$	$(10^{- 8} - 10^{- 9}) \times v$

Table 1. Typical error term of the laser interferometer

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Xionglei Lin, Xiaobo Su, Jianing Wang, Yunke Sun, Pengcheng Hu. Laser Interferometer Technology and Instruments for Sub-Nanometer and Picometer Displacement Measurements[J]. Laser & Optoelectronics Progress, 2023, 60(3): 0312016

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