Abstract

High sensitivity of collimation testing equipment is desirable where collimated beams are used for precise and accurate measurements. Precision in the setting of collimation depends on the sensitivity of the testing equipment. In the present work, sensitivity to beam collimation of the recently reported holographic shearing interferometer (HSI) [J. Opt. 20, 055603 (2018) [CrossRef]  ] is measured and compared with sensitivities of other collimation testing techniques based on the wedge plate shearing interferometer and the Talbot shearing interferometer. For a test beam of diameter 25 mm from an He–Ne laser and displacement of the collimating lens by 1 mm from the collimation position, the Talbot shearing interferometer shows a rotation of interference fringes from the horizontal direction by 2°, the wedge plate shearing interferometer shows 20°, and the HSI shows 25°. Sensitivity is also presented in terms of measured slopes of phase maps of the recorded interferograms for a 1 mm displacement of the collimating lens and is obtained as 0.98 mrad, 15 mrad, and 19 mrad corresponding to the Talbot shearing interferometer, the wedge plate shearing interferometer, and HSI, respectively. The effect of decollimation of the laser beam on the interference fringes of diffraction of the Lloyd mirror interferometer is also demonstrated. Theoretical concepts and experimental results are presented and discussed for the above-mentioned beam collimation testing techniques.

© 2020 Optical Society of America

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References

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  1. J. Zhu, S. Hu, P. Zhou, and J. Yu, “Experimental study of Talbot imaging moiré-based lithography alignment method,” Opt. Laser Eng. 58, 54–59 (2014).
    [Crossref]
  2. J. W. de Menezes, A. Thesing, C. Valsecchi, L. E. G. Armas, and A. G. Brolo, “Improving the performance of gold nanohole array biosensors by controlling the optical collimation conditions,” Appl. Opt. 54, 6502–6507 (2015).
    [Crossref]
  3. D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik (Stuttgart) 123, 1469–1473 (2012).
    [Crossref]
  4. R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
    [Crossref]
  5. J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
    [Crossref]
  6. R. Kumar, “Diffraction Lloyd mirror interferometer,” J. Opt. 39, 90–101 (2010).
    [Crossref]
  7. R. Kumar, “Straight, conic and circular fringes in single interferogram,” Eur. J. Phys. 36, 025019 (2015).
    [Crossref]
  8. D. Malacara, Optical Shop Testing (Wiley, 2007).
  9. M. V. R. K. Murty, “The use of a single plane parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964).
    [Crossref]
  10. R. S. Sirohi and M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
    [Crossref]
  11. Y. W. Lee, H. M. Cho, and I. W. Lee, “Half-aperture shearing interferometer for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
    [Crossref]
  12. Y. Wang, H. Zhai, S. Jutamulia, and G. Mu, “Collimation test of a corrected laser diode beam using lateral shearing interferometer,” Opt. Commun. 274, 412–416 (2007).
    [Crossref]
  13. J. Dhanotia and S. Prakash, “Collimation testing using wedge plate lateral shearing interferometry and Fourier fringe analysis,” Opt. Laser Eng. 49, 1025–1031 (2011).
    [Crossref]
  14. K. V. Sriram and M. P. Kothiyal, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
    [Crossref]
  15. S. Prakash, S. Rana, S. Prakash, and O. Sasaki, “Automated collimation testing using a temporal phase shifting technique in Talbot interferometry,” Appl. Opt. 47, 5938–5943 (2008).
    [Crossref]
  16. J. Dhanotia and S. Prakash, “Automated collimation testing by incorporating the Fourier transform method in Talbot interferometry,” Appl. Opt. 50, 1446–1452 (2011).
    [Crossref]
  17. N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
    [Crossref]
  18. I. A. Lyavshuk and A. M. Lyalikov, “Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry,” Opt. Spectrosc. 96, 154–159 (2004).
    [Crossref]
  19. J. Yun and B. Wang, “Collimation testing of laser beam with holographic optical elements,” Precis. Eng. 36, 158–161 (2012).
    [Crossref]
  20. R. Kumar, R. Dubey, S. K. Debnath, and D. P. Chhachhia, “High contrast laser beam collimation testing using two proximately placed holographic optical elements,” J. Opt. 20, 055603 (2018).
    [Crossref]
  21. R. P. Shukla, D. C. Udupa, and N. C. Das, “A note on a set of wedge plates for laser beam collimation testing,” J. Opt. 32, 79–85 (2003).
    [Crossref]
  22. R. S. Sirohi and F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, 1999).
  23. C. A. Walker, Handbook of Moiré Measurement (Institute of Physics, 2003).
  24. R. Kumar and A. K. Aggarwal, “Interferometric moiré pattern encoded security holograms with concealed phase object,” Opt. Commun. 279, 120–123 (2007).
    [Crossref]
  25. A. R. Ganesan and P. Venkateswarlu, “Laser beam collimation using Talbot interferometry,” Appl. Opt. 32, 2918–2920 (1993).
    [Crossref]
  26. Y. Nakano, K. Murata, A. R. Ganesan, and P. Venkateswarlu, “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
    [Crossref]
  27. W. Zhaoyang, D. Fulong, and J. Xiaolin, “High resolution, high sensitivity moire method,” Acta Mech. Sin. 15, 176–181 (1999).
    [Crossref]
  28. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  29. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).
  30. R. Dubey and R. Kumar, “Collimation testing of laser beams having different diameters using compact holographic lateral shearing interferometer,” Opt. Eng. 59, 102404 (2020).
    [Crossref]
  31. J. Choi, G. M. Perera, M. D. Aggarwal, R. P. Shukla, and M. V. Mantravadi, “Wedge-plate shearing interferometers for collimation testing: use of a moiré technique,” Appl. Opt. 34, 3628–3638 (1995).
    [Crossref]

2020 (1)

R. Dubey and R. Kumar, “Collimation testing of laser beams having different diameters using compact holographic lateral shearing interferometer,” Opt. Eng. 59, 102404 (2020).
[Crossref]

2018 (1)

R. Kumar, R. Dubey, S. K. Debnath, and D. P. Chhachhia, “High contrast laser beam collimation testing using two proximately placed holographic optical elements,” J. Opt. 20, 055603 (2018).
[Crossref]

2015 (2)

2014 (2)

J. Zhu, S. Hu, P. Zhou, and J. Yu, “Experimental study of Talbot imaging moiré-based lithography alignment method,” Opt. Laser Eng. 58, 54–59 (2014).
[Crossref]

N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
[Crossref]

2013 (1)

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

2012 (2)

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik (Stuttgart) 123, 1469–1473 (2012).
[Crossref]

J. Yun and B. Wang, “Collimation testing of laser beam with holographic optical elements,” Precis. Eng. 36, 158–161 (2012).
[Crossref]

2011 (2)

J. Dhanotia and S. Prakash, “Automated collimation testing by incorporating the Fourier transform method in Talbot interferometry,” Appl. Opt. 50, 1446–1452 (2011).
[Crossref]

J. Dhanotia and S. Prakash, “Collimation testing using wedge plate lateral shearing interferometry and Fourier fringe analysis,” Opt. Laser Eng. 49, 1025–1031 (2011).
[Crossref]

2010 (1)

R. Kumar, “Diffraction Lloyd mirror interferometer,” J. Opt. 39, 90–101 (2010).
[Crossref]

2008 (2)

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
[Crossref]

S. Prakash, S. Rana, S. Prakash, and O. Sasaki, “Automated collimation testing using a temporal phase shifting technique in Talbot interferometry,” Appl. Opt. 47, 5938–5943 (2008).
[Crossref]

2007 (2)

Y. Wang, H. Zhai, S. Jutamulia, and G. Mu, “Collimation test of a corrected laser diode beam using lateral shearing interferometer,” Opt. Commun. 274, 412–416 (2007).
[Crossref]

R. Kumar and A. K. Aggarwal, “Interferometric moiré pattern encoded security holograms with concealed phase object,” Opt. Commun. 279, 120–123 (2007).
[Crossref]

2004 (1)

I. A. Lyavshuk and A. M. Lyalikov, “Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry,” Opt. Spectrosc. 96, 154–159 (2004).
[Crossref]

2003 (1)

R. P. Shukla, D. C. Udupa, and N. C. Das, “A note on a set of wedge plates for laser beam collimation testing,” J. Opt. 32, 79–85 (2003).
[Crossref]

1999 (1)

W. Zhaoyang, D. Fulong, and J. Xiaolin, “High resolution, high sensitivity moire method,” Acta Mech. Sin. 15, 176–181 (1999).
[Crossref]

1995 (1)

1993 (3)

A. R. Ganesan and P. Venkateswarlu, “Laser beam collimation using Talbot interferometry,” Appl. Opt. 32, 2918–2920 (1993).
[Crossref]

Y. W. Lee, H. M. Cho, and I. W. Lee, “Half-aperture shearing interferometer for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[Crossref]

K. V. Sriram and M. P. Kothiyal, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[Crossref]

1987 (1)

1985 (1)

1982 (1)

1964 (1)

Abdelsalam, D. G.

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik (Stuttgart) 123, 1469–1473 (2012).
[Crossref]

Aggarwal, A. K.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
[Crossref]

R. Kumar and A. K. Aggarwal, “Interferometric moiré pattern encoded security holograms with concealed phase object,” Opt. Commun. 279, 120–123 (2007).
[Crossref]

Aggarwal, M. D.

Armas, L. E. G.

Baek, B. J.

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik (Stuttgart) 123, 1469–1473 (2012).
[Crossref]

Brolo, A. G.

Chau, F. S.

R. S. Sirohi and F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, 1999).

Chhachhia, D. P.

R. Kumar, R. Dubey, S. K. Debnath, and D. P. Chhachhia, “High contrast laser beam collimation testing using two proximately placed holographic optical elements,” J. Opt. 20, 055603 (2018).
[Crossref]

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
[Crossref]

Cho, H. M.

Y. W. Lee, H. M. Cho, and I. W. Lee, “Half-aperture shearing interferometer for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[Crossref]

Choi, J.

Das, N. C.

R. P. Shukla, D. C. Udupa, and N. C. Das, “A note on a set of wedge plates for laser beam collimation testing,” J. Opt. 32, 79–85 (2003).
[Crossref]

de Menezes, J. W.

Debnath, S. K.

R. Kumar, R. Dubey, S. K. Debnath, and D. P. Chhachhia, “High contrast laser beam collimation testing using two proximately placed holographic optical elements,” J. Opt. 20, 055603 (2018).
[Crossref]

Dhanotia, J.

J. Dhanotia and S. Prakash, “Collimation testing using wedge plate lateral shearing interferometry and Fourier fringe analysis,” Opt. Laser Eng. 49, 1025–1031 (2011).
[Crossref]

J. Dhanotia and S. Prakash, “Automated collimation testing by incorporating the Fourier transform method in Talbot interferometry,” Appl. Opt. 50, 1446–1452 (2011).
[Crossref]

Dubey, R.

R. Dubey and R. Kumar, “Collimation testing of laser beams having different diameters using compact holographic lateral shearing interferometer,” Opt. Eng. 59, 102404 (2020).
[Crossref]

R. Kumar, R. Dubey, S. K. Debnath, and D. P. Chhachhia, “High contrast laser beam collimation testing using two proximately placed holographic optical elements,” J. Opt. 20, 055603 (2018).
[Crossref]

Fulong, D.

W. Zhaoyang, D. Fulong, and J. Xiaolin, “High resolution, high sensitivity moire method,” Acta Mech. Sin. 15, 176–181 (1999).
[Crossref]

Ganesan, A. R.

He, Y.

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Hu, S.

J. Zhu, S. Hu, P. Zhou, and J. Yu, “Experimental study of Talbot imaging moiré-based lithography alignment method,” Opt. Laser Eng. 58, 54–59 (2014).
[Crossref]

N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
[Crossref]

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Ina, H.

Jiang, W.

N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
[Crossref]

Jutamulia, S.

Y. Wang, H. Zhai, S. Jutamulia, and G. Mu, “Collimation test of a corrected laser diode beam using lateral shearing interferometer,” Opt. Commun. 274, 412–416 (2007).
[Crossref]

Kaura, S. K.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
[Crossref]

Kim, D.

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik (Stuttgart) 123, 1469–1473 (2012).
[Crossref]

Kobayashi, S.

Kothiyal, M. P.

K. V. Sriram and M. P. Kothiyal, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[Crossref]

R. S. Sirohi and M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
[Crossref]

Kumar, R.

R. Dubey and R. Kumar, “Collimation testing of laser beams having different diameters using compact holographic lateral shearing interferometer,” Opt. Eng. 59, 102404 (2020).
[Crossref]

R. Kumar, R. Dubey, S. K. Debnath, and D. P. Chhachhia, “High contrast laser beam collimation testing using two proximately placed holographic optical elements,” J. Opt. 20, 055603 (2018).
[Crossref]

R. Kumar, “Straight, conic and circular fringes in single interferogram,” Eur. J. Phys. 36, 025019 (2015).
[Crossref]

R. Kumar, “Diffraction Lloyd mirror interferometer,” J. Opt. 39, 90–101 (2010).
[Crossref]

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
[Crossref]

R. Kumar and A. K. Aggarwal, “Interferometric moiré pattern encoded security holograms with concealed phase object,” Opt. Commun. 279, 120–123 (2007).
[Crossref]

Lee, I. W.

Y. W. Lee, H. M. Cho, and I. W. Lee, “Half-aperture shearing interferometer for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[Crossref]

Lee, Y. W.

Y. W. Lee, H. M. Cho, and I. W. Lee, “Half-aperture shearing interferometer for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[Crossref]

Li, L.

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Lyalikov, A. M.

I. A. Lyavshuk and A. M. Lyalikov, “Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry,” Opt. Spectrosc. 96, 154–159 (2004).
[Crossref]

Lyavshuk, I. A.

I. A. Lyavshuk and A. M. Lyalikov, “Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry,” Opt. Spectrosc. 96, 154–159 (2004).
[Crossref]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).

Mantravadi, M. V.

Mohan, D.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
[Crossref]

Mu, G.

Y. Wang, H. Zhai, S. Jutamulia, and G. Mu, “Collimation test of a corrected laser diode beam using lateral shearing interferometer,” Opt. Commun. 274, 412–416 (2007).
[Crossref]

Murata, K.

Murty, M. V. R. K.

Nakano, Y.

Perera, G. M.

Prakash, S.

Rana, S.

Sasaki, O.

Servín, M.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).

Shukla, R. P.

Sirohi, R. S.

R. S. Sirohi and M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
[Crossref]

R. S. Sirohi and F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, 1999).

Sriram, K. V.

K. V. Sriram and M. P. Kothiyal, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[Crossref]

Takeda, M.

Tang, Y.

N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
[Crossref]

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Thesing, A.

Udupa, D. C.

R. P. Shukla, D. C. Udupa, and N. C. Das, “A note on a set of wedge plates for laser beam collimation testing,” J. Opt. 32, 79–85 (2003).
[Crossref]

Valsecchi, C.

Venkateswarlu, P.

Walker, C. A.

C. A. Walker, Handbook of Moiré Measurement (Institute of Physics, 2003).

Wang, B.

J. Yun and B. Wang, “Collimation testing of laser beam with holographic optical elements,” Precis. Eng. 36, 158–161 (2012).
[Crossref]

Wang, N.

N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
[Crossref]

Wang, Y.

Y. Wang, H. Zhai, S. Jutamulia, and G. Mu, “Collimation test of a corrected laser diode beam using lateral shearing interferometer,” Opt. Commun. 274, 412–416 (2007).
[Crossref]

Xiaolin, J.

W. Zhaoyang, D. Fulong, and J. Xiaolin, “High resolution, high sensitivity moire method,” Acta Mech. Sin. 15, 176–181 (1999).
[Crossref]

Xu, F.

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Yan, W.

N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
[Crossref]

Yu, J.

J. Zhu, S. Hu, P. Zhou, and J. Yu, “Experimental study of Talbot imaging moiré-based lithography alignment method,” Opt. Laser Eng. 58, 54–59 (2014).
[Crossref]

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Yun, J.

J. Yun and B. Wang, “Collimation testing of laser beam with holographic optical elements,” Precis. Eng. 36, 158–161 (2012).
[Crossref]

Zhai, H.

Y. Wang, H. Zhai, S. Jutamulia, and G. Mu, “Collimation test of a corrected laser diode beam using lateral shearing interferometer,” Opt. Commun. 274, 412–416 (2007).
[Crossref]

Zhaoyang, W.

W. Zhaoyang, D. Fulong, and J. Xiaolin, “High resolution, high sensitivity moire method,” Acta Mech. Sin. 15, 176–181 (1999).
[Crossref]

Zhou, P.

J. Zhu, S. Hu, P. Zhou, and J. Yu, “Experimental study of Talbot imaging moiré-based lithography alignment method,” Opt. Laser Eng. 58, 54–59 (2014).
[Crossref]

Zhou, S.

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Zhu, J.

J. Zhu, S. Hu, P. Zhou, and J. Yu, “Experimental study of Talbot imaging moiré-based lithography alignment method,” Opt. Laser Eng. 58, 54–59 (2014).
[Crossref]

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

Acta Mech. Sin. (1)

W. Zhaoyang, D. Fulong, and J. Xiaolin, “High resolution, high sensitivity moire method,” Acta Mech. Sin. 15, 176–181 (1999).
[Crossref]

Appl. Opt. (8)

Eur. J. Phys. (1)

R. Kumar, “Straight, conic and circular fringes in single interferogram,” Eur. J. Phys. 36, 025019 (2015).
[Crossref]

IEEE Photon. J. (1)

N. Wang, Y. Tang, W. Jiang, W. Yan, and S. Hu, “Collimation sensing with differential grating and Talbot interferometry,” IEEE Photon. J. 6, 6100210 (2014).
[Crossref]

J. Opt. (3)

R. Kumar, “Diffraction Lloyd mirror interferometer,” J. Opt. 39, 90–101 (2010).
[Crossref]

R. Kumar, R. Dubey, S. K. Debnath, and D. P. Chhachhia, “High contrast laser beam collimation testing using two proximately placed holographic optical elements,” J. Opt. 20, 055603 (2018).
[Crossref]

R. P. Shukla, D. C. Udupa, and N. C. Das, “A note on a set of wedge plates for laser beam collimation testing,” J. Opt. 32, 79–85 (2003).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

R. Kumar and A. K. Aggarwal, “Interferometric moiré pattern encoded security holograms with concealed phase object,” Opt. Commun. 279, 120–123 (2007).
[Crossref]

Y. Wang, H. Zhai, S. Jutamulia, and G. Mu, “Collimation test of a corrected laser diode beam using lateral shearing interferometer,” Opt. Commun. 274, 412–416 (2007).
[Crossref]

Opt. Eng. (3)

K. V. Sriram and M. P. Kothiyal, “Self-referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1993).
[Crossref]

Y. W. Lee, H. M. Cho, and I. W. Lee, “Half-aperture shearing interferometer for collimation testing,” Opt. Eng. 32, 2837–2840 (1993).
[Crossref]

R. Dubey and R. Kumar, “Collimation testing of laser beams having different diameters using compact holographic lateral shearing interferometer,” Opt. Eng. 59, 102404 (2020).
[Crossref]

Opt. Laser Eng. (3)

J. Zhu, S. Hu, P. Zhou, and J. Yu, “Experimental study of Talbot imaging moiré-based lithography alignment method,” Opt. Laser Eng. 58, 54–59 (2014).
[Crossref]

J. Zhu, S. Hu, J. Yu, Y. Tang, F. Xu, Y. He, S. Zhou, and L. Li, “Influence of tilt moiré fringe on alignment accuracy in proximity lithography,” Opt. Laser Eng. 51, 371–381 (2013).
[Crossref]

J. Dhanotia and S. Prakash, “Collimation testing using wedge plate lateral shearing interferometry and Fourier fringe analysis,” Opt. Laser Eng. 49, 1025–1031 (2011).
[Crossref]

Opt. Spectrosc. (1)

I. A. Lyavshuk and A. M. Lyalikov, “Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry,” Opt. Spectrosc. 96, 154–159 (2004).
[Crossref]

Optik (Stuttgart) (1)

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik (Stuttgart) 123, 1469–1473 (2012).
[Crossref]

Pramana J. Phys. (1)

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different Schlieren diffracting elements,” Pramana J. Phys. 70, 121–129 (2008).
[Crossref]

Precis. Eng. (1)

J. Yun and B. Wang, “Collimation testing of laser beam with holographic optical elements,” Precis. Eng. 36, 158–161 (2012).
[Crossref]

Other (4)

D. Malacara, Optical Shop Testing (Wiley, 2007).

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Taylor & Francis, 2005).

R. S. Sirohi and F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, 1999).

C. A. Walker, Handbook of Moiré Measurement (Institute of Physics, 2003).

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Figures (11)

Fig. 1.
Fig. 1. Scheme of experimental setup for collimation testing using HSI; laser, He–Ne, ${\lambda} = 632.8\;{\rm nm} $; SF, spatial filter assembly; CL, collimating lens; and ${{\rm H}_ {1}}$, ${{\rm H}_ {2}}$, HOEs.
Fig. 2.
Fig. 2. (a)–(g) Interferograms corresponding to defocusing values of ${\Delta f} = - 2\;{\rm mm} $, ${-}1\;{\rm mm} $, ${-}0.5\;{\rm mm} $, 0 mm, 0.5 mm, 1 mm, and 2 mm; (h)–(n) are corresponding unwrapped phase surface plots of recorded interferograms; and (o)–(u) are corresponding linear phase plots for the recorded interferograms using the HSI.
Fig. 3.
Fig. 3. Scheme of experimental setup for collimation testing using the wedge plate shearing interferometer; laser, He–Ne, ${\lambda} = 632.8\;{\rm nm} $; SF, spatial filter assembly; CL, collimating lens; WP; wedge plate.
Fig. 4.
Fig. 4. (a)–(g) Interferograms corresponding to defocusing values ${\Delta f} = - 2\;{\rm mm} $, ${-}1\;{\rm mm} $, ${-}0.5\;{\rm mm} $, 0 mm, 0.5 mm, 1 mm, and 2 mm; (h)–(n) are corresponding unwrapped phase surface plots of recorded interferograms; and (o)–(u) are the corresponding linear phase plots for the recorded interferograms using the wedge plate shearing interferometer.
Fig. 5.
Fig. 5. Scheme of the experimental setup for collimation testing using the Talbot shearing interferometer; laser, He–Ne, ${\lambda} = 632.8\;{\rm nm} $; SF, spatial filter assembly; CL, collimating lens; and ${\rm G }_ {1}$, ${\rm G}_2$, gratings separated by first Talbot distance of 12.6 cm; ${\rm L}_1$ is the focusing lens, ${\rm A}$ is the aperture, and ${\rm L}_2$ is the collimating lens.
Fig. 6.
Fig. 6. (a)–(g) Interferograms corresponding to defocusing values of ${\Delta f} = - 2\;{\rm mm} $, ${-}1\;{\rm mm} $, ${-}0.5\;{\rm mm} $, 0 mm, 0.5 mm, 1 mm, and 2 mm; (h)–(n) are corresponding unwrapped phase surface plots; and (o)–(u) are the corresponding linear phase plots for the recorded interferograms using the Talbot shearing interferometer.
Fig. 7.
Fig. 7. Scheme of experimental setup of DLMI; laser, He–Ne, ${\lambda} = 632.8\;{\rm nm} $; SF, spatial filter assembly; ${\rm L}_1$, ${\rm L}_3$, collimating lenses; ${\rm L}_2$, focusing lens; ${\rm S}$ is the source of diffracted and undiffracted light, and ${\rm S}^{\prime}$ is its virtual image created by the Lloyd’s mirror M; dotted lines represent the diffracted light, while solid lines represent the undiffracted light.
Fig. 8.
Fig. 8. Interferograms obtained with DLMI for (a) collimated beam, (b) diverging beam with ${\Delta f} = 10\; {\unicode{x00B5}{\rm m}}$, (c) diverging beam with ${\Delta f} = 20\; {\unicode{x00B5}{\rm m}}$.
Fig. 9.
Fig. 9. Linear phase maps corresponding to interferograms obtained with DLMI. (a) Collimated beam; (b) diverging beam for ${\Delta f} = 10\; {\unicode{x00B5}{\rm m}}$; (c) diverging beam for ${\Delta f} = 20\; {\unicode{x00B5}{\rm m}}$.
Fig. 10.
Fig. 10. Intensity profiles corresponding to interferograms obtained with DLMI. (a) Collimated beam; (b) diverging beam for ${\Delta f} = 10\; {\unicode{x00B5}{\rm m}}$; (c) diverging beam for ${\Delta f} = 20\; {\unicode{x00B5}{\rm m}}$.
Fig. 11.
Fig. 11. Variation in slope of interference fringes with different amounts of defocusing using the three techniques, i.e., HSI (small diamonds), wedge plate shearing interferometer (squares), and Talbot shearing interferometer (triangles).

Tables (1)

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Table 1. Comparative Analysis of the Three Collimation Testing Techniques for a Collimated Test Beam

Equations (8)

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T ( x , y ) = A 1 A 2 R 0 exp [ i ( φ 1 φ 2 k x sin θ ) + i k ( x 2 + y 2 2 R ) ] + A 1 A 2 R 0 exp [ ( ( x + Δ x ) 2 + y 2 2 R ) i ( φ 1 φ 2 k x sin θ ) + i k ( ( x + Δ x ) 2 + y 2 2 R ) + i k α y + i k d ] ,
x Δ x R + α y + d = m .
sin ξ = Δ x K λ R ,
K = λ δ = λ 2 α n 2 sin 2 i ,
Z = 2 β p 2 λ ,
K = p 2 sin γ 2 ,
α = N λ 2 D n 2 sin 2 i ,
δ l = f 2 λ 10. Δ x ( D Δ x ) .

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