Abstract

An angular displacement measurement sensor with high resolution for large range measurement is presented. The design concept of the proposed method is based on the birefringence effect and phase detection of heterodyne interferometry. High system symmetry and simple operation can be easily achieved by employing an innovative sandwich optical design for the angular sensor. To evaluate the feasibility and performance of the proposed method, several experiments were performed. The experimental results demonstrate that our angular displacement measurement sensor can achieve a measurement range greater than 26°. Considering the high-frequency noise, the measurement resolution of the system is approximately 1.2° × 10−4. Because of the common-path arrangement, our proposed method can provide superior immunity against environmental disturbances.

© 2016 Optical Society of America

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References

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2015 (3)

Z. He, J. Fu, L. Zhang, and X. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

S. Zhao, H. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

L. Y. Chen, J. Y. Lee, H. S. Chang, and Y. Yang, “Development of an angular displacement measurement by birefringence heterodyne interferometry,” Smart Sci. 3(4), 188–192 (2015).

2014 (2)

J. Y. Lin and Y. C. Liao, “Small-angle measurement with highly sensitive total-internal-reflection heterodyne interferometer,” Appl. Opt. 53(9), 1903–1908 (2014).
[Crossref] [PubMed]

D. Jucius, I. Grybas, V. Grigaliūnas, M. Mikolajūnas, and A. Lazauskas, “UV imprint fabrication of polymeric scales for optical rotary encoders,” Opt. Laser Technol. 56, 107–113 (2014).
[Crossref]

2013 (1)

2012 (1)

Y. Liu, C. Kuang, and Y. Ku, “Small angle measurement method based on the total internal multi-reflection,” Opt. Laser Technol. 44(5), 1346–1350 (2012).
[Crossref]

2011 (3)

2010 (2)

S. T. Lin, S. L. Yeh, and Z. F. Lin, “Angular probe based on using Fabry-Perot etalon and scanning technique,” Opt. Express 18(3), 1794–1800 (2010).
[Crossref] [PubMed]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

2008 (2)

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

2007 (4)

S. T. Lin, K. T. Lin, and W. J. Syu, “Angular interferometer using calcite prism and rotating analyzer,” Opt. Commun. 277(2), 251–255 (2007).
[Crossref]

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280(1), 1–9 (2007).
[Crossref]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).
[Crossref]

C. H. Hsieh, C. C. Tsai, H. C. Wei, L. P. Yu, J. S. Wu, and C. Chou, “Determination of retardation parameters of multiple-order wave plate using a phase-sensitive heterodyne ellipsometer,” Appl. Opt. 46(23), 5944–5950 (2007).
[Crossref] [PubMed]

2006 (1)

1998 (1)

1975 (1)

Bellon, L.

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280(1), 1–9 (2007).
[Crossref]

Brockmeyer, E.

K. D. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed optics: 3D printing of embedded optical elements for interactive devices,” in Proceedings of the 25th annual ACM Symposium on User Interface Software and Technology (ACM, 2012), 589–598.
[Crossref]

Cai, L.

Chang, H. S.

L. Y. Chen, J. Y. Lee, H. S. Chang, and Y. Yang, “Development of an angular displacement measurement by birefringence heterodyne interferometry,” Smart Sci. 3(4), 188–192 (2015).

Chang, R. S.

Chen, H. Y.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).
[Crossref]

Chen, J. C.

H. L. Hsieh, J. C. Chen, G. Lerondel, and J. Y. Lee, “Two-dimensional displacement measurement by quasi-common-optical-path heterodyne grating interferometer,” Opt. Express 19(10), 9770–9782 (2011).
[Crossref] [PubMed]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

Chen, L. Y.

L. Y. Chen, J. Y. Lee, H. S. Chang, and Y. Yang, “Development of an angular displacement measurement by birefringence heterodyne interferometry,” Smart Sci. 3(4), 188–192 (2015).

Chickvary, J. L.

Chiu, M. H.

Chou, C.

Delbressine, F.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

Deturche, R.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

Fu, J.

Z. He, J. Fu, L. Zhang, and X. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Grigaliunas, V.

D. Jucius, I. Grybas, V. Grigaliūnas, M. Mikolajūnas, and A. Lazauskas, “UV imprint fabrication of polymeric scales for optical rotary encoders,” Opt. Laser Technol. 56, 107–113 (2014).
[Crossref]

Grybas, I.

D. Jucius, I. Grybas, V. Grigaliūnas, M. Mikolajūnas, and A. Lazauskas, “UV imprint fabrication of polymeric scales for optical rotary encoders,” Opt. Laser Technol. 56, 107–113 (2014).
[Crossref]

Gundlach, J. H.

Hagedorn, C. A.

Haitjema, H.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

He, Z.

Z. He, J. Fu, L. Zhang, and X. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Hsieh, C. H.

Hsieh, H. L.

H. L. Hsieh, J. C. Chen, G. Lerondel, and J. Y. Lee, “Two-dimensional displacement measurement by quasi-common-optical-path heterodyne grating interferometer,” Opt. Express 19(10), 9770–9782 (2011).
[Crossref] [PubMed]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

Hsu, C. C.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).
[Crossref]

Hudson, S. E.

K. D. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed optics: 3D printing of embedded optical elements for interactive devices,” in Proceedings of the 25th annual ACM Symposium on User Interface Software and Technology (ACM, 2012), 589–598.
[Crossref]

Jiang, G. A.

Jucius, D.

D. Jucius, I. Grybas, V. Grigaliūnas, M. Mikolajūnas, and A. Lazauskas, “UV imprint fabrication of polymeric scales for optical rotary encoders,” Opt. Laser Technol. 56, 107–113 (2014).
[Crossref]

Knapp, W.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

Ku, Y.

Y. Liu, C. Kuang, and Y. Ku, “Small angle measurement method based on the total internal multi-reflection,” Opt. Laser Technol. 44(5), 1346–1350 (2012).
[Crossref]

Kuang, C.

Y. Liu, C. Kuang, and Y. Ku, “Small angle measurement method based on the total internal multi-reflection,” Opt. Laser Technol. 44(5), 1346–1350 (2012).
[Crossref]

Lai, C. W.

Lazauskas, A.

D. Jucius, I. Grybas, V. Grigaliūnas, M. Mikolajūnas, and A. Lazauskas, “UV imprint fabrication of polymeric scales for optical rotary encoders,” Opt. Laser Technol. 56, 107–113 (2014).
[Crossref]

Lee, J. Y.

L. Y. Chen, J. Y. Lee, H. S. Chang, and Y. Yang, “Development of an angular displacement measurement by birefringence heterodyne interferometry,” Smart Sci. 3(4), 188–192 (2015).

J. Y. Lee and G. A. Jiang, “Displacement measurement using a wavelength-phase-shifting grating interferometer,” Opt. Express 21(21), 25553–25564 (2013).
[Crossref] [PubMed]

H. L. Hsieh, J. C. Chen, G. Lerondel, and J. Y. Lee, “Two-dimensional displacement measurement by quasi-common-optical-path heterodyne grating interferometer,” Opt. Express 19(10), 9770–9782 (2011).
[Crossref] [PubMed]

J. Y. Lee and S. K. Tsai, “Measurement of refractive index variation of liquids by surface plasmon resonance and wavelength-modulated heterodyne interferometry,” Opt. Commun. 284(4), 925–929 (2011).
[Crossref]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).
[Crossref]

Lerondel, G.

H. L. Hsieh, J. C. Chen, G. Lerondel, and J. Y. Lee, “Two-dimensional displacement measurement by quasi-common-optical-path heterodyne grating interferometer,” Opt. Express 19(10), 9770–9782 (2011).
[Crossref] [PubMed]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

Li, Y.

S. Zhao, H. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

Li, Z.

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

Liao, Y. C.

Lin, J. Y.

Lin, K. T.

S. T. Lin, K. T. Lin, and W. J. Syu, “Angular interferometer using calcite prism and rotating analyzer,” Opt. Commun. 277(2), 251–255 (2007).
[Crossref]

Lin, S. T.

S. T. Lin, S. L. Yeh, and Z. F. Lin, “Angular probe based on using Fabry-Perot etalon and scanning technique,” Opt. Express 18(3), 1794–1800 (2010).
[Crossref] [PubMed]

S. T. Lin, K. T. Lin, and W. J. Syu, “Angular interferometer using calcite prism and rotating analyzer,” Opt. Commun. 277(2), 251–255 (2007).
[Crossref]

Lin, Z. F.

Liu, Y.

Y. Liu, C. Kuang, and Y. Ku, “Small angle measurement method based on the total internal multi-reflection,” Opt. Laser Technol. 44(5), 1346–1350 (2012).
[Crossref]

Mikolajunas, M.

D. Jucius, I. Grybas, V. Grigaliūnas, M. Mikolajūnas, and A. Lazauskas, “UV imprint fabrication of polymeric scales for optical rotary encoders,” Opt. Laser Technol. 56, 107–113 (2014).
[Crossref]

Paolino, P.

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280(1), 1–9 (2007).
[Crossref]

Poupyrev, I.

K. D. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed optics: 3D printing of embedded optical elements for interactive devices,” in Proceedings of the 25th annual ACM Symposium on User Interface Software and Technology (ACM, 2012), 589–598.
[Crossref]

Schlamminger, S.

Schlesinger, E. R.

Schmitt, R.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

Schwenke, H.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

Syu, W. J.

S. T. Lin, K. T. Lin, and W. J. Syu, “Angular interferometer using calcite prism and rotating analyzer,” Opt. Commun. 277(2), 251–255 (2007).
[Crossref]

Tsai, C. C.

Tsai, S. K.

J. Y. Lee and S. K. Tsai, “Measurement of refractive index variation of liquids by surface plasmon resonance and wavelength-modulated heterodyne interferometry,” Opt. Commun. 284(4), 925–929 (2011).
[Crossref]

Turner, M. D.

Wang, S. F.

Wang, X.

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

Weckenmann, A.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

Wei, H.

S. Zhao, H. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

Wei, H. C.

Willis, K. D. D.

K. D. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed optics: 3D printing of embedded optical elements for interactive devices,” in Proceedings of the 25th annual ACM Symposium on User Interface Software and Technology (ACM, 2012), 589–598.
[Crossref]

Wu, C. C.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).
[Crossref]

Wu, J. S.

Wu, W. T.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

Yang, Y.

L. Y. Chen, J. Y. Lee, H. S. Chang, and Y. Yang, “Development of an angular displacement measurement by birefringence heterodyne interferometry,” Smart Sci. 3(4), 188–192 (2015).

Yao, X.

Z. He, J. Fu, L. Zhang, and X. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Yeh, S. L.

Yoder, P. R.

Yu, L. P.

Zhang, L.

Z. He, J. Fu, L. Zhang, and X. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Zhao, S.

S. Zhao, H. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

Zheng, D.

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

Zhou, W.

Appl. Opt. (5)

CIRP Ann. Manuf. Technol. (1)

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. Manuf. Technol. 57(2), 660–675 (2008).
[Crossref]

Int. J. Mach. Tools Manuf. (1)

Z. He, J. Fu, L. Zhang, and X. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Meas. Sci. Technol. (1)

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).
[Crossref]

Opt. Commun. (3)

S. T. Lin, K. T. Lin, and W. J. Syu, “Angular interferometer using calcite prism and rotating analyzer,” Opt. Commun. 277(2), 251–255 (2007).
[Crossref]

P. Paolino and L. Bellon, “Single beam interferometric angle measurement,” Opt. Commun. 280(1), 1–9 (2007).
[Crossref]

J. Y. Lee and S. K. Tsai, “Measurement of refractive index variation of liquids by surface plasmon resonance and wavelength-modulated heterodyne interferometry,” Opt. Commun. 284(4), 925–929 (2011).
[Crossref]

Opt. Eng. (1)

S. Zhao, H. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (3)

Y. Liu, C. Kuang, and Y. Ku, “Small angle measurement method based on the total internal multi-reflection,” Opt. Laser Technol. 44(5), 1346–1350 (2012).
[Crossref]

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

D. Jucius, I. Grybas, V. Grigaliūnas, M. Mikolajūnas, and A. Lazauskas, “UV imprint fabrication of polymeric scales for optical rotary encoders,” Opt. Laser Technol. 56, 107–113 (2014).
[Crossref]

Opt. Lett. (1)

Sens. Actuators A Phys. (1)

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).
[Crossref]

Smart Sci. (1)

L. Y. Chen, J. Y. Lee, H. S. Chang, and Y. Yang, “Development of an angular displacement measurement by birefringence heterodyne interferometry,” Smart Sci. 3(4), 188–192 (2015).

Other (4)

A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley, 2003).

K. D. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed optics: 3D printing of embedded optical elements for interactive devices,” in Proceedings of the 25th annual ACM Symposium on User Interface Software and Technology (ACM, 2012), 589–598.
[Crossref]

S. O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice Hall, 2001).

Mikhail Polyanskiy, RefractiveIndex.INFO website, http://refractiveindex.info/?shelf=glass&book=SCHOTT-F&page=F2

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Figures (10)

Fig. 1
Fig. 1

(a) A linearly polarized light beam passes through a birefringent crystal with an incident angle of θi. (b) Relationship between the phase difference (δx, δy) and the incident angle θi with different surrounding refractive indices np. The slope variation in the interval (−5° < θi < 5°) was approximately 30 °/°.

Fig. 2
Fig. 2

Schematic diagram of the angular sensor

Fig. 3
Fig. 3

Relationship between the phase difference and incident angle (θ) with different refractive indices (np) of the equilateral triangle prism.

Fig. 4
Fig. 4

Schematic diagram of the angular displacement measurement configuration.

Fig. 5
Fig. 5

Phase–angle (δxθ) characteristic curve.

Fig. 6
Fig. 6

Measurement results for large angular displacement.

Fig. 7
Fig. 7

Experiment result of repeatability test.

Fig. 8
Fig. 8

Stability test.

Fig. 9
Fig. 9

Limitation of the measurement speed test.

Fig. 10
Fig. 10

Relative error.

Equations (9)

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δ x = 2πd λ [ n o 2 n p 2 sin 2 θ i n e 2 n p 2 sin 2 θ i ],
δ y = 2πd λ [ n o 2 n p 2 sin 2 θ i n e 2 ( n e n p sin θ i / n o ) 2 ],
θ i =α+ sin 1 ( sinθ / n p )
δ x = 2πd λ [ n o 2 n p 2 sin 2 ( α+ sin 1 ( sinθ/ n p ) ) n e 2 n p 2 sin 2 ( α+ sin 1 ( sinθ/ n p ) ) ].
AS=[ exp( i δ x /2 ) 0 0 exp( i δ x /2 ) ].
E 0 =[ exp( iωt /2 ) exp( iωt /2 ) ].
I r = | A N r ( 45 ) E 0 | 2 =1+cos(ωt),
I t = | A N t ( 45 )AS E 0 | 2 =1+cos( ωt+ δ x ).
δ( φ )= 2πd λ [ n e 2 ( n p sinθ) 2 co s 2 φ ( n e n p n o sinθ) 2 sin 2 φ n o 2 ( n p sinθ) 2 ].

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