Abstract

The measuring probe integrated with multiple fiber point-diffraction sources can be applied to measure both the three-dimensional coordinates and highly accurate point-diffraction wavefront. The probe determines the achievable measurement accuracy of fiber point-diffraction interferometer (PDI), in which the fiber exit end plane is required to be parallel with the detector plane. The probe misalignment due to fabrication error could introduce significant measurement error. A high-precision method is proposed to calibrate the probe misalignment in fiber PDI, including the central positioning based on phase difference and tilt adjustment based on Zernike polynomials fitting. Both numerical simulation and experiments have been carried out to demonstrate the feasibility and accuracy of the proposed probe misalignment calibration method. The proposed method provides a feasible way to address the processing uncertainty on measuring probe in fiber PDI, and enables high-precision geometry alignment and misalignment calibration in the interferometric testing systems with case of no imaging lens.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (1)

N. Voznesenskiy, M. Voznesenskaia, and D. Jha, “Testing high accuracy optics using the phase shifting point diffraction interferometer,” Proc. SPIE 10829, 1082902 (2018).
[Crossref]

2017 (3)

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

2016 (1)

2015 (1)

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

2014 (1)

2013 (2)

2012 (1)

T. Wei, D. Liu, C. Tian, L. Zhang, and Y. Y. Yang, “New interferometric method to locate aspheric in the partial null aspheric testing system,” Proc. SPIE 8417, 84173E (2012).
[Crossref]

2011 (1)

2007 (1)

2006 (1)

2003 (1)

S. W. Kim and B. C. Kim, “Point-diffraction interferometer for 3-D profile measurement of rough surfaces,” Proc. SPIE 5191, 200–207 (2003).
[Crossref]

2002 (2)

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

J. Schmit and A. Olszak, “High-precision shape measurement by white-light interferometry with real-time scanner error correction,” Appl. Opt. 41(28), 5943–5950 (2002).
[Crossref]

Chen, C.

Chen, X.

Chu, J.

de Groot, P.

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

Fukuda, Y.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

Gong, Z. D.

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

Jha, D.

N. Voznesenskiy, M. Voznesenskaia, and D. Jha, “Testing high accuracy optics using the phase shifting point diffraction interferometer,” Proc. SPIE 10829, 1082902 (2018).
[Crossref]

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

Kim, B. C.

S. W. Kim and B. C. Kim, “Point-diffraction interferometer for 3-D profile measurement of rough surfaces,” Proc. SPIE 5191, 200–207 (2003).
[Crossref]

Kim, S. W.

S. W. Kim and B. C. Kim, “Point-diffraction interferometer for 3-D profile measurement of rough surfaces,” Proc. SPIE 5191, 200–207 (2003).
[Crossref]

Kim, S.-W.

Kong, M.

Kujawinska, M.

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

Lee, Y.-W.

Li, W.

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

D. Wang, Y. Xu, R. Liang, M. Kong, J. Zhao, B. Zhang, and W. Li, “High-precision method for submicron-aperture fiber point-diffraction wavefront measurement,” Opt. Express 24(7), 7079–7090 (2016).
[Crossref]

Liang, R.

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

D. Wang, Y. Xu, R. Liang, M. Kong, J. Zhao, B. Zhang, and W. Li, “High-precision method for submicron-aperture fiber point-diffraction wavefront measurement,” Opt. Express 24(7), 7079–7090 (2016).
[Crossref]

Liang, R. G.

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

Liu, D.

L. Zhang, D. Liu, T. Shi, Y. Yang, and Y. Shen, “Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing,” Appl. Opt. 52(35), 8501–8511 (2013).
[Crossref]

T. Wei, D. Liu, C. Tian, L. Zhang, and Y. Y. Yang, “New interferometric method to locate aspheric in the partial null aspheric testing system,” Proc. SPIE 8417, 84173E (2012).
[Crossref]

Lizewski, K.

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

Mo, L.

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

Nishiyama, I.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

Okazaki, S.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

Olszak, A.

Ota, K.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

Otaki, K.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

Ottevaere, H.

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

Rhee, H.-G.

Schmit, J.

Shen, Y.

Shi, T.

Tian, C.

T. Wei, D. Liu, C. Tian, L. Zhang, and Y. Y. Yang, “New interferometric method to locate aspheric in the partial null aspheric testing system,” Proc. SPIE 8417, 84173E (2012).
[Crossref]

Trusiak, M.

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

Voznesenskaia, M.

N. Voznesenskiy, M. Voznesenskaia, and D. Jha, “Testing high accuracy optics using the phase shifting point diffraction interferometer,” Proc. SPIE 10829, 1082902 (2018).
[Crossref]

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

Voznesenskiy, N.

N. Voznesenskiy, M. Voznesenskaia, and D. Jha, “Testing high accuracy optics using the phase shifting point diffraction interferometer,” Proc. SPIE 10829, 1082902 (2018).
[Crossref]

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

Wang, D.

Wang, D. D.

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

Wang, F.

Wang, Z.

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

Wang, Z. C.

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

Wei, T.

T. Wei, D. Liu, C. Tian, L. Zhang, and Y. Y. Yang, “New interferometric method to locate aspheric in the partial null aspheric testing system,” Proc. SPIE 8417, 84173E (2012).
[Crossref]

Wyant, J. C.

Xu, P.

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

Xu, Y.

Yamamoto, T.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

Yang, Y.

Yang, Y. Y.

T. Wei, D. Liu, C. Tian, L. Zhang, and Y. Y. Yang, “New interferometric method to locate aspheric in the partial null aspheric testing system,” Proc. SPIE 8417, 84173E (2012).
[Crossref]

Zhang, B.

Zhang, L.

L. Zhang, D. Liu, T. Shi, Y. Yang, and Y. Shen, “Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing,” Appl. Opt. 52(35), 8501–8511 (2013).
[Crossref]

T. Wei, D. Liu, C. Tian, L. Zhang, and Y. Y. Yang, “New interferometric method to locate aspheric in the partial null aspheric testing system,” Proc. SPIE 8417, 84173E (2012).
[Crossref]

Zhao, J.

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

D. Wang, Y. Xu, R. Liang, M. Kong, J. Zhao, B. Zhang, and W. Li, “High-precision method for submicron-aperture fiber point-diffraction wavefront measurement,” Opt. Express 24(7), 7079–7090 (2016).
[Crossref]

D. Wang, X. Chen, Y. Xu, F. Wang, M. Kong, J. Zhao, and B. Zhang, “High-NA fiber point-diffraction interferometer for three-dimensional coordinate measurement,” Opt. Express 22(21), 25550–25559 (2014).
[Crossref]

Zhao, J. F.

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

Zhuo, Y.

Adv. Opt. Photonics (1)

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

Appl. Opt. (4)

J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. (1)

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 20(1), 295–300 (2002).
[Crossref]

Opt. Express (4)

Optik (1)

Z. C. Wang, D. D. Wang, Z. D. Gong, P. Xu, R. G. Liang, J. F. Zhao, and W. Li, “Measurement of absolute displacement based on dual-path submicron-aperture fiber point-diffraction interferometer,” Optik 140, 802–811 (2017).
[Crossref]

Proc. SPIE (5)

D. Wang, Z. Wang, R. Liang, M. Kong, J. Zhao, J. Zhao, L. Mo, and W. Li, “Fast searching measurement of absolute displacement based on submicron-aperture fiber point-diffraction interferometer,” Proc. SPIE 10329, 1032937 (2017).
[Crossref]

T. Wei, D. Liu, C. Tian, L. Zhang, and Y. Y. Yang, “New interferometric method to locate aspheric in the partial null aspheric testing system,” Proc. SPIE 8417, 84173E (2012).
[Crossref]

N. Voznesenskiy, M. Voznesenskaia, D. Jha, H. Ottevaere, M. Kujawińska, M. Trusiak, and K. Liżewski, “Revealing features of different optical shaping technologies by a point diffraction interferometer,” Proc. SPIE 10329, 103293X (2017).
[Crossref]

S. W. Kim and B. C. Kim, “Point-diffraction interferometer for 3-D profile measurement of rough surfaces,” Proc. SPIE 5191, 200–207 (2003).
[Crossref]

N. Voznesenskiy, M. Voznesenskaia, and D. Jha, “Testing high accuracy optics using the phase shifting point diffraction interferometer,” Proc. SPIE 10829, 1082902 (2018).
[Crossref]

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Figures (12)

Fig. 1.
Fig. 1. Schematic diagram of fiber PDI system.
Fig. 2.
Fig. 2. Probe misalignment based on spot distribution in (a) ideal case and (b) actual case.
Fig. 3.
Fig. 3. Probe misalignment calibration based on spot-distribution method in experiment. (a) Spot distribution on fringe pattern, (b) actual probe orientation after calibration.
Fig. 4.
Fig. 4. Schematic diagram of central positioning. Probe end face (a) before and (b) after central positioning.
Fig. 5.
Fig. 5. Procedure for the proposed probe misalignment calibration method.
Fig. 6.
Fig. 6. Measurement error for displacement and shearing wavefront due to probe misalignment in simulation. (a) Measurement error for the displacement in x- and z-axes, (b) measurement error for shearing wavefront with removal of coordinate-reconstruction-based geometrical aberrations.
Fig. 7.
Fig. 7. Central positioning in simulation. Phase difference corresponding to translation in (a) x and (b) y directions.
Fig. 8.
Fig. 8. Tilt adjustment in simulation. (a) Tilt coefficients corresponding to various adjusting angles, (b) residual probe tilt angle due to central positioning error.
Fig. 9.
Fig. 9. Central positioning in experiment. Phase difference corresponding to translation in (a) x and (b) y directions.
Fig. 10.
Fig. 10. Change of Zernike tilt coefficients with adjusting angle of probe in experiment: (a) x-tilt term corresponding to x-tilt adjustment, (b) y-tilt term corresponding to y-tilt adjustment.
Fig. 11.
Fig. 11. Displacement measurement error in experiment. Measurement error for the displacement in (a) x-, (b) y- and (c) z-axes.
Fig. 12.
Fig. 12. Measurement results of shearing wavefront with fiber PDI. Measured shearing wavefront with removal of coordinate-reconstruction-based geometrical aberrations (a) before and (b) after probe misalignment calibration.

Tables (1)

Tables Icon

Table 1. Experimental results for displacement measurement about probe misalignment calibration

Equations (9)

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{ φ ( x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x , y , z ) = 2 π λ [ R 1 ( x 1 , y 1 , z 1 ; x , y , z ) R 2 ( x 2 , y 2 , z 2 ; x , y , z ) ] φ ( x 1 , y 1 , z 2 ; x 2 , y 2 , z 2 ; x , y , z ) = 2 π λ [ R 1 ( x 1 , y 1 , z 1 ; x , y , z ) R 2 ( x 2 , y 2 , z 2 ; x , y , z ) ] ,
{ [ S 1 ( x c , y c + d cos α , z c + d sin α ) ,   S 2 ( x c , y c d cos α , z c d sin α ) ] [ S 1 ( x c , y c d cos α , z c d sin α ) ,   S 2 ( x c , y c + d cos α , z c + d sin α ) ] ,
Δ φ ( x , y , z ) = Δ φ ( x , y , z ) .
φ ( x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x , y , z ) = φ ( x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x , y , z ) .
{ Δ φ x = φ ( x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x , y , z ) φ ( x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x , y , z ) Δ φ y = φ ( x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x , y , z ) φ ( x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x , y , z ) .
O P D = z c 1 + ( r / r z c z c ) 2 + ( d / d z c z c ) 2 + 2 d sin α / 2 d sin α z c z c 2 d r cos α sin θ / 2 d r cos α sin θ z c 2 z c 2 z c 1 + ( r / r z c z c ) 2 + ( d / d z c z c ) 2 2 d sin α / 2 d sin α z c z c + 2 d r cos α sin θ / 2 d r cos α sin θ z c 2 z c 2 ,
O P D = z c [ ζ 2 ζ 1 ζ 2 / ζ 1 ζ 2 2 2 + ζ 2 ( 3 ζ 1 2 + ζ 2 2 ) / ζ 2 ( 3 ζ 1 2 + ζ 2 2 ) 8 8 5 ζ 1 ζ 2 ( ζ 1 2 + ζ 2 2 ) / 5 ζ 1 ζ 2 ( ζ 1 2 + ζ 2 2 ) 16 16 ] ,
O P D a 0 Z 0 + a 2 Z 2 .
a 2 = 2 t d cos α ( 1 + t / t 8 8 + t 2 / t 2 3 3 3 t 4 / 3 t 4 16 16 + d 2 / d 2 2 z c 2 z c t 2 d 2 / t 2 d 2 2 z c 2 2 z c 2 + 15 t 4 d 2 / 15 t 4 d 2 32 z c 2 32 z c 2 ) t d 3 cos α / t d 3 cos α z c 2 z c 2 ( 3 sin 2 α + t 2 cos 2 α / t 2 cos 2 α 2 2 5 t 2 sin 2 α 15 t 4 cos 2 α / 15 t 4 cos 2 α 16 16 ) .