Abstract

A novel encoder with dual displacement resolution is developed by integrating a multiple-grating-scale holographic displacement sensor and a heterodyne interferometer. With suitable arrangement of the measurement system, two effective grating pitches (0.41 μm and 10.62 μm) can be obtained and the theoretical sensitivities of them are 0.9 °/nm and 0.036 °/nm. Meanwhile, the best resolution of the proposed method can be estimated of 0.3 pm and 7.4 pm, respectively. Furthermore, displacement errors of the proposed method can be better than 0.2% for 1 mm displacement measurement. The experimental results showed that the proposed encoder provided high sensitivity, high resolution, and well against environmental disturbance.

© 2017 Optical Society of America

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References

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  1. W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).
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    [PubMed]
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    [PubMed]
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    [PubMed]
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    [PubMed]
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  18. S. Olyaee, T. H. Yoon, and S. Hamedi, “Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer,” IET Optoelectron. 3, 215–224 (2009).
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    [PubMed]
  23. C. C. Hsu, S. Y. Chen, and Y. C. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50(12), 1689–1693 (2012).
  24. P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

2016 (2)

2015 (3)

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

S. Agarwal and C. Shakher, “In-plane displacement measurement by using circular grating Talbot interferometer,” Opt. Lasers Eng. 75, 63–71 (2015).

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).

2013 (3)

2012 (1)

C. C. Hsu, S. Y. Chen, and Y. C. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50(12), 1689–1693 (2012).

2010 (2)

P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

A. Kimura, W. Gao, Y. Arai, and Z. Lijiang, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng. 34, 145–155 (2010).

2009 (1)

S. Olyaee, T. H. Yoon, and S. Hamedi, “Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer,” IET Optoelectron. 3, 215–224 (2009).

2008 (1)

C. F. Kao, S. H. Lu, H. M. Shen, and K. C. Fan, “Diffractive laser encoder with a grating in Littrow configuration,” J. Appl. Phys. 47, 1833–1837 (2008).

2005 (1)

J. Otsuka, S. Ichikawa, T. Masuda, and K. Suzuki, “Development of a small ultraprecision positioning device with 5 nm resolution,” Meas. Sci. Technol. 16, 2186–2192 (2005).

2002 (1)

J. H. Chen, D. C. Su, and J. C. Su, “Shrinkage and refractive-index shift-corrected volume holograms for optical interconnectors,” Appl. Phys. Lett. 81, 1378–1389 (2002).

1999 (2)

1998 (1)

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).

1997 (1)

1970 (1)

Agarwal, S.

S. Agarwal and C. Shakher, “In-plane displacement measurement by using circular grating Talbot interferometer,” Opt. Lasers Eng. 75, 63–71 (2015).

Arai, Y.

A. Kimura, W. Gao, Y. Arai, and Z. Lijiang, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng. 34, 145–155 (2010).

Bojhkov, B.

Bosse, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Chen, J. H.

J. H. Chen, D. C. Su, and J. C. Su, “Shrinkage and refractive-index shift-corrected volume holograms for optical interconnectors,” Appl. Phys. Lett. 81, 1378–1389 (2002).

Chen, S. Y.

C. C. Hsu, S. Y. Chen, and Y. C. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50(12), 1689–1693 (2012).

Chen, W.

Chen, Y. C.

C. C. Hsu, S. Y. Chen, and Y. C. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50(12), 1689–1693 (2012).

Chen, Y. L.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Chen, Y. Z.

Cheng, C. C.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).

Chiu, M. H.

Clarkson, P.

P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).

Deslattes, R. D.

Estler, W. T.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Esward, T. J.

P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

Fan, K. C.

C. F. Kao, S. H. Lu, H. M. Shen, and K. C. Fan, “Diffractive laser encoder with a grating in Littrow configuration,” J. Appl. Phys. 47, 1833–1837 (2008).

Gao, W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

A. Kimura, W. Gao, Y. Arai, and Z. Lijiang, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng. 34, 145–155 (2010).

Haitjema, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Hamedi, S.

S. Olyaee, T. H. Yoon, and S. Hamedi, “Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer,” IET Optoelectron. 3, 215–224 (2009).

Harris, P. M.

P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

Hsieh, H. L.

Hsu, C. C.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).

C. C. Hsu, Y. Y. Sung, Z. R. Lin, and M. C. Kao, “Prototype of a compact displacement sensor with a holographic diffraction grating,” Opt. Laser Technol. 48, 200–205 (2013).

C. C. Hsu, S. Y. Chen, and Y. C. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50(12), 1689–1693 (2012).

Ichikawa, S.

J. Otsuka, S. Ichikawa, T. Masuda, and K. Suzuki, “Development of a small ultraprecision positioning device with 5 nm resolution,” Meas. Sci. Technol. 16, 2186–2192 (2005).

Jiang, G. A.

Kao, C. F.

C. F. Kao, S. H. Lu, H. M. Shen, and K. C. Fan, “Diffractive laser encoder with a grating in Littrow configuration,” J. Appl. Phys. 47, 1833–1837 (2008).

Kao, M. C.

C. C. Hsu, Y. Y. Sung, Z. R. Lin, and M. C. Kao, “Prototype of a compact displacement sensor with a holographic diffraction grating,” Opt. Laser Technol. 48, 200–205 (2013).

Kim, S. W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Kimura, A.

A. Kimura, W. Gao, Y. Arai, and Z. Lijiang, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng. 34, 145–155 (2010).

Knapp, W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Kunzmann, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Lawall, J.

Lee, J. Y.

Li, X.

Liao, C. H.

Lijiang, Z.

A. Kimura, W. Gao, Y. Arai, and Z. Lijiang, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng. 34, 145–155 (2010).

Lin, Z. R.

C. C. Hsu, Y. Y. Sung, Z. R. Lin, and M. C. Kao, “Prototype of a compact displacement sensor with a holographic diffraction grating,” Opt. Laser Technol. 48, 200–205 (2013).

Lu, S. H.

C. F. Kao, S. H. Lu, H. M. Shen, and K. C. Fan, “Diffractive laser encoder with a grating in Littrow configuration,” J. Appl. Phys. 47, 1833–1837 (2008).

Lu, X. D.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Mao, X.

Masuda, T.

J. Otsuka, S. Ichikawa, T. Masuda, and K. Suzuki, “Development of a small ultraprecision positioning device with 5 nm resolution,” Meas. Sci. Technol. 16, 2186–2192 (2005).

Meng, C. T.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).

Nevièvre, M.

Ni, K.

Olyaee, S.

S. Olyaee, T. H. Yoon, and S. Hamedi, “Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer,” IET Optoelectron. 3, 215–224 (2009).

Otsuka, J.

J. Otsuka, S. Ichikawa, T. Masuda, and K. Suzuki, “Development of a small ultraprecision positioning device with 5 nm resolution,” Meas. Sci. Technol. 16, 2186–2192 (2005).

Popov, E.

Shakher, C.

S. Agarwal and C. Shakher, “In-plane displacement measurement by using circular grating Talbot interferometer,” Opt. Lasers Eng. 75, 63–71 (2015).

Shen, H. M.

C. F. Kao, S. H. Lu, H. M. Shen, and K. C. Fan, “Diffractive laser encoder with a grating in Littrow configuration,” J. Appl. Phys. 47, 1833–1837 (2008).

Smith, A. A.

P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

Smith, I. M.

P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

Stevenson, W. H.

Su, D. C.

J. H. Chen, D. C. Su, and J. C. Su, “Shrinkage and refractive-index shift-corrected volume holograms for optical interconnectors,” Appl. Phys. Lett. 81, 1378–1389 (2002).

M. H. Chiu, J. Y. Lee, and D. C. Su, “Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry,” Appl. Opt. 36(13), 2936–2939 (1997).
[PubMed]

Su, J. C.

J. H. Chen, D. C. Su, and J. C. Su, “Shrinkage and refractive-index shift-corrected volume holograms for optical interconnectors,” Appl. Phys. Lett. 81, 1378–1389 (2002).

Sung, Y. Y.

C. C. Hsu, Y. Y. Sung, Z. R. Lin, and M. C. Kao, “Prototype of a compact displacement sensor with a holographic diffraction grating,” Opt. Laser Technol. 48, 200–205 (2013).

Suzuki, K.

J. Otsuka, S. Ichikawa, T. Masuda, and K. Suzuki, “Development of a small ultraprecision positioning device with 5 nm resolution,” Meas. Sci. Technol. 16, 2186–2192 (2005).

Tonchev, S.

Tsonev, L.

Wang, H.

Wang, X.

Weckenmann, A.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

Wu, C. C.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).

C. C. Wu, Y. Z. Chen, and C. H. Liao, “Common-path laser planar encoder,” Opt. Express 21(16), 18872–18883 (2013).
[PubMed]

Wu, C. M.

Xiao, X.

Yoon, T. H.

S. Olyaee, T. H. Yoon, and S. Hamedi, “Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer,” IET Optoelectron. 3, 215–224 (2009).

Zeng, L.

Zhou, Q.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

J. H. Chen, D. C. Su, and J. C. Su, “Shrinkage and refractive-index shift-corrected volume holograms for optical interconnectors,” Appl. Phys. Lett. 81, 1378–1389 (2002).

CIRP Ann Manuf. Technol. (1)

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann Manuf. Technol. 64, 773–796 (2015).

IET Optoelectron. (1)

S. Olyaee, T. H. Yoon, and S. Hamedi, “Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer,” IET Optoelectron. 3, 215–224 (2009).

J. Appl. Phys. (1)

C. F. Kao, S. H. Lu, H. M. Shen, and K. C. Fan, “Diffractive laser encoder with a grating in Littrow configuration,” J. Appl. Phys. 47, 1833–1837 (2008).

Meas. Sci. Technol. (3)

J. Otsuka, S. Ichikawa, T. Masuda, and K. Suzuki, “Development of a small ultraprecision positioning device with 5 nm resolution,” Meas. Sci. Technol. 16, 2186–2192 (2005).

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9, 1024–1030 (1998).

P. Clarkson, T. J. Esward, P. M. Harris, A. A. Smith, and I. M. Smith, “Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems,” Meas. Sci. Technol. 21, 045106 (2010).

Opt. Eng. (1)

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).

Opt. Express (4)

Opt. Laser Technol. (1)

C. C. Hsu, Y. Y. Sung, Z. R. Lin, and M. C. Kao, “Prototype of a compact displacement sensor with a holographic diffraction grating,” Opt. Laser Technol. 48, 200–205 (2013).

Opt. Lasers Eng. (2)

S. Agarwal and C. Shakher, “In-plane displacement measurement by using circular grating Talbot interferometer,” Opt. Lasers Eng. 75, 63–71 (2015).

C. C. Hsu, S. Y. Chen, and Y. C. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50(12), 1689–1693 (2012).

Precis. Eng. (1)

A. Kimura, W. Gao, Y. Arai, and Z. Lijiang, “Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness,” Precis. Eng. 34, 145–155 (2010).

Other (4)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 1.

C. Lin, S. Yan, C. Wei, G. Wang, and P. Zou, “Optimized design and error analysis of optical system for heterodyne grating interferometry,” in Proceedings of SPIE (SPIE 2013) 9046, 90460C (2013).

NPL lock-in amplifier software simulation tool, http://www.npl.co.uk/server.php?show=ConWebDoc.2644

Stanford Research System Co, “Model SR 850 DSP Lock-in amplifier user’s guide,” http://www.thinksrs.com/downloads/PDFs/Manuals/SR850m.pdf .

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Figures (13)

Fig. 1
Fig. 1 Schematics of the dual displacement resolution encoder. (a) Schematic diagram; (b) photograph of the proposed encoder.
Fig. 2
Fig. 2 Theoretical simulation of the EGP of various combination of grating pitches. (a) dEGP1; (b) dEGP2.
Fig. 3
Fig. 3 Theoretical simulation of the sensitivity and displacement error under various EGP. (a) sensitivity; (b) displacement error.
Fig. 4
Fig. 4 Physical arrangement of the HDS. (a) schematic figure; (b) photograph of HDS.
Fig. 5
Fig. 5 Effective grating pitch measurement. (a) dEGP1; (b) dEGP2.
Fig. 6
Fig. 6 Stability comparison between the proposed encoder and HPI. (a) phase variation of the proposed encoder under various EGP; (b) displacement variation comparison; (c) enlargement of the black square region in (b).
Fig. 7
Fig. 7 Long travel range measurement results. (a) 10 μm; (b) 100 μm; (c) 1000 μm.
Fig. 8
Fig. 8 Short travel range measurement results. (a) 65 nm step type movement; (b) 15 nm step type movement; (c) 15 nm sinusoidal type movement; (d) 15 nm triangular type movement.
Fig. 9
Fig. 9 The theoretical simulation of nonlinearity periodic error of the proposed method.
Fig. 10
Fig. 10 Uniformity of holographic grating. (a) Optical configuration; (b) results of G1; (c) results of G2 (or G3).
Fig. 11
Fig. 11 Compensation of the effective grating pitch error. (a) full-scale investigation of EGP1 and EGP2; (b) enlargement of black square region in (a).
Fig. 12
Fig. 12 Displacement error analysis of various effective grating pitch. (a) dEGP1; (b) dEGP2.
Fig. 13
Fig. 13 Resolution of the proposed method.

Tables (1)

Tables Icon

Table 1 Error source of the proposed method

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

I 1 1 2 [ 1+cos( ωt2 ϕ G1 ) ],
I 2 1 2 [ 1+cos( ωt+2 ϕ G1 ) ].
I 3 2{ 1+cos[ ωt( ϕ G3 +2 ϕ G1 ϕ G2 ) ] },
I 4 2{ 1+cos[ ωt+( ϕ G3 +2 ϕ G1 ϕ G2 ) ] },
ϕ Gi =m 2πS d gi , ( i=1, 2, and 3;m=1 or 2 )
S EGP1 = Φ 12 d EGP1 2π ,
S EGP2 = Φ 34 d EGP2 2π ,
d EGP1 = d G1 4 ,
d EGP2 = d G1 d G2 d G3 4 d G2 d G3 d G1 d G2 d G1 d G3 .
| Δ S EGP1 |= d EGP1 8π | Δ Φ 1 |+ Φ 12 d EGP1 | Δ d EGP1 |,
| Δ S EGP2 |= d EGP2 8π | Δ Φ 2 |+ Φ 34 d EGP2 | Δ d EGP2 |,
R EGP1 = Δ φ EGP1 8π d EGP1 ,
R EGP2 = Δ φ EGP2 8π d EGP2 ,

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