Abstract

We demonstrate a small angle measurement setup enabled by the double-grating configuration, where the multiple diffractions are used to magnify the deflection angle of the optical beam. Such small angle measurement setup has characteristics of high sensitivity and compact size. The use of two unparallel blazed gratings with a special included angle can realize multiple diffractions for the incident light, leading to the realization of deflection angle amplification. Experimental results verify that small angle can be accurately characterized and the angular resolution of measurement can be improved more than 40 times by inserting the double-grating configuration into the conventional auto-collimation angle measurement setup. Therefore, the micro-radian angle can be accurately measured with our proposed compact characterization setup.

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

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References

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  1. P. R. Yoder, E. R. Schlesinger, and J. L. Chickvary, “Active annular-beam laser autocollimator system,” Appl. Opt. 14(8), 1890–1895 (1975).
    [Crossref] [PubMed]
  2. S. S. Nukala, S. S. Gorthi, and K. R. Lolla, “Novel composite coded pattern for small angle measurement using imaging method,” Proc. SPIE 6289, 62891D (2006).
    [Crossref]
  3. T. Suzuki, T. Endo, and O. Sasaki, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45(4), 043604 (2006).
    [Crossref]
  4. S. Rasouli and M. T. Tavassoly, “Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere,” Opt. Lett. 33(9), 980–982 (2008).
    [Crossref] [PubMed]
  5. P. S. Huang, S. Kiyono, and O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31(28), 6047–6055 (1992).
    [Crossref] [PubMed]
  6. W. Zhou and L. Cai, “Interferometer for small-angle measurement based on total internal reflection,” Appl. Opt. 37(25), 5957–5963 (1998).
    [Crossref] [PubMed]
  7. 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]
  8. F. Cheng and K. C. Fan, “High-resolution Angle Measurement based on Michelson Interferometry,” Phys. Procedia 19, 3–8 (2011).
    [Crossref]
  9. M. Ikram and G. Hussain, “Michelson interferometer for precision angle measurement,” Appl. Opt. 38(1), 113–120 (1999).
    [Crossref] [PubMed]
  10. Y. Wu, H. Cheng, and Y. Wen, “High-precision rotation angle measurement method based on a lensless digital holographic microscope,” Appl. Opt. 57(1), 112–118 (2018).
    [Crossref] [PubMed]
  11. H. L. Hsieh, J. Y. Lee, L. Y. Chen, and Y. Yang, “Development of an angular displacement measurement technique through birefringence heterodyne interferometry,” Opt. Express 24(7), 6802–6813 (2016).
    [Crossref] [PubMed]
  12. Y. Pavan Kumar, S. Chatterjee, and S. S. Negi, “Small roll angle measurement using lateral shearing cyclic path polarization interferometry,” Appl. Opt. 55(5), 979–983 (2016).
    [Crossref] [PubMed]
  13. K. Zhu, B. Guo, Y. Lu, S. Zhang, and Y. Tan, “Single-spot two-dimensional displacement measurement based on self-mixing interferometry,” Optica 4(7), 729–735 (2017).
    [Crossref]
  14. C. Wang, X. Fan, Y. Guo, H. Gui, H. Wang, J. Liu, B. Yu, and L. Lu, “Full-circle range and microradian resolution angle measurement using the orthogonal mirror self-mixing interferometry,” Opt. Express 26(8), 10371–10381 (2018).
    [Crossref] [PubMed]
  15. 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]
  16. O. Kafri and J. Krasinski, “High-sensitivity moire deflectometry using a telescope,” Appl. Opt. 24(17), 2746–2748 (1985).
    [Crossref] [PubMed]
  17. S. Rasouli, “Use of a moiré deflectometer on a telescope for atmospheric turbulence measurements,” Opt. Lett. 35(9), 1470–1472 (2010).
    [Crossref] [PubMed]
  18. S. Rasouli and M. Ghorbani, “Nonlinear refractive index measuring using a double-grating interferometer in pump–probe configuration and Fourier transform analysis,” J. Opt. 14(3), 35203 (2012).
    [Crossref]
  19. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
    [Crossref]
  20. M. Born and E. Wolf, Principles of Optics (Cambridge University, Cambridge, 1999), Chap. 8.

2018 (2)

2017 (1)

2016 (2)

2014 (1)

2012 (1)

S. Rasouli and M. Ghorbani, “Nonlinear refractive index measuring using a double-grating interferometer in pump–probe configuration and Fourier transform analysis,” J. Opt. 14(3), 35203 (2012).
[Crossref]

2011 (1)

F. Cheng and K. C. Fan, “High-resolution Angle Measurement based on Michelson Interferometry,” Phys. Procedia 19, 3–8 (2011).
[Crossref]

2010 (2)

2008 (1)

2006 (2)

S. S. Nukala, S. S. Gorthi, and K. R. Lolla, “Novel composite coded pattern for small angle measurement using imaging method,” Proc. SPIE 6289, 62891D (2006).
[Crossref]

T. Suzuki, T. Endo, and O. Sasaki, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45(4), 043604 (2006).
[Crossref]

1999 (1)

1998 (1)

1992 (1)

1985 (2)

O. Kafri and J. Krasinski, “High-sensitivity moire deflectometry using a telescope,” Appl. Opt. 24(17), 2746–2748 (1985).
[Crossref] [PubMed]

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

1975 (1)

Cai, L.

Chatterjee, S.

Chen, L. Y.

Cheng, F.

F. Cheng and K. C. Fan, “High-resolution Angle Measurement based on Michelson Interferometry,” Phys. Procedia 19, 3–8 (2011).
[Crossref]

Cheng, H.

Chickvary, J. L.

Endo, T.

T. Suzuki, T. Endo, and O. Sasaki, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45(4), 043604 (2006).
[Crossref]

Fan, K. C.

F. Cheng and K. C. Fan, “High-resolution Angle Measurement based on Michelson Interferometry,” Phys. Procedia 19, 3–8 (2011).
[Crossref]

Fan, X.

Ghorbani, M.

S. Rasouli and M. Ghorbani, “Nonlinear refractive index measuring using a double-grating interferometer in pump–probe configuration and Fourier transform analysis,” J. Opt. 14(3), 35203 (2012).
[Crossref]

Gorthi, S. S.

S. S. Nukala, S. S. Gorthi, and K. R. Lolla, “Novel composite coded pattern for small angle measurement using imaging method,” Proc. SPIE 6289, 62891D (2006).
[Crossref]

Gui, H.

Guo, B.

Guo, Y.

Hsieh, H. L.

Huang, P. S.

Hussain, G.

Ikram, M.

Kafri, O.

Kamada, O.

Kiyono, S.

Krasinski, J.

Lee, J. Y.

Liao, Y. C.

Lin, J. Y.

Lin, S. T.

Lin, Z. F.

Liu, J.

Lolla, K. R.

S. S. Nukala, S. S. Gorthi, and K. R. Lolla, “Novel composite coded pattern for small angle measurement using imaging method,” Proc. SPIE 6289, 62891D (2006).
[Crossref]

Lu, L.

Lu, Y.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

Negi, S. S.

Nukala, S. S.

S. S. Nukala, S. S. Gorthi, and K. R. Lolla, “Novel composite coded pattern for small angle measurement using imaging method,” Proc. SPIE 6289, 62891D (2006).
[Crossref]

Pavan Kumar, Y.

Rasouli, S.

Sasaki, O.

T. Suzuki, T. Endo, and O. Sasaki, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45(4), 043604 (2006).
[Crossref]

Schlesinger, E. R.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

Suzuki, T.

T. Suzuki, T. Endo, and O. Sasaki, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45(4), 043604 (2006).
[Crossref]

Tan, Y.

Tavassoly, M. T.

Wang, C.

Wang, H.

Wen, Y.

Wu, Y.

Yang, Y.

Yeh, S. L.

Yoder, P. R.

Yu, B.

Zhang, S.

Zhou, W.

Zhu, K.

Appl. Opt. (8)

J. Opt. (1)

S. Rasouli and M. Ghorbani, “Nonlinear refractive index measuring using a double-grating interferometer in pump–probe configuration and Fourier transform analysis,” J. Opt. 14(3), 35203 (2012).
[Crossref]

Opt. Commun. (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

Opt. Eng. (1)

T. Suzuki, T. Endo, and O. Sasaki, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45(4), 043604 (2006).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optica (1)

Phys. Procedia (1)

F. Cheng and K. C. Fan, “High-resolution Angle Measurement based on Michelson Interferometry,” Phys. Procedia 19, 3–8 (2011).
[Crossref]

Proc. SPIE (1)

S. S. Nukala, S. S. Gorthi, and K. R. Lolla, “Novel composite coded pattern for small angle measurement using imaging method,” Proc. SPIE 6289, 62891D (2006).
[Crossref]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University, Cambridge, 1999), Chap. 8.

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Figures (4)

Fig. 1
Fig. 1 Principle of small angle magnification with the double-grating configuration.
Fig. 2
Fig. 2 Schematic diagram of the experimental setup with the double-grating configuration.
Fig. 3
Fig. 3 Simulation and experimental result of the dependence of emergent angle on the incident angle, and the dependence of angle magnification on the incident angle.
Fig. 4
Fig. 4 Experimental results and measurement error by using the double-grating configuration.

Tables (1)

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Table 1 Parameter of gratings, lenses, and image devices

Equations (5)

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sinθsini=m λ d ,m=0,±1,±2,
M= dθ di = cosi cosθ
M i c = d θ Nc d i 1c = cos i N cos θ N cos i N1 cos θ N1 cos i 2 cos θ 2 cos i 1 cos θ 1 = ( cos i 1c cos θ 1c cos i 2c cos θ 2c ) N/2
α= θ 1c i 2c = θ 1c i 1c =arcsin(sin i 1c +m λ d ) i 1c
{ θ n =arcsin( sin i n +m λ d ) i n+1 = θ n α

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