Abstract

Recently, Fresnel diffraction from phase steps with parallel plates has been studied in detail, and the subject has led to many interesting metrological applications. In this report we formulate Fresnel diffraction from a physical step with arbitrarily oriented plates in reflection mode. We simulate the diffraction patterns for different orientations of the plates and develop the required procedure for determining the involved angles by analysis of the diffraction pattern. In the experimental part of the report we arrange a setup to form diffraction patterns in different orientations of the step plates and test the derived formulations. Also, we briefly review the application potentials of the subject.

© 2017 Optical Society of America

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References

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  1. M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from a step in reflection and transmission modes,” Proc. SPIE 3749, 560–561 (1999).
    [Crossref]
  2. M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from step in reflection and transmission,” Iranian J. Phys. 2, 237–246 (2001).
  3. M. T. Tavassoly, A. Darudi, H. R. Khalesifard, and M. R. Sadat Hossaini, “Applications of Fresnel diffraction from phase objects,” Proc. SPIE 4399, 98–106 (2001).
    [Crossref]
  4. M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
    [Crossref]
  5. M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
    [Crossref]
  6. M. Amiri and M. T. Tavassoly, “Spectral anomalies near phase singularities in reflection at Brewster’s angle and colored castastrophes,” Opt. Lett. 33, 1863–1865 (2008).
    [Crossref]
  7. M. T. Tavassoly, M. Dashtdar, and M. Amiri, “Spectral modification by diffraction and scattering,” Proc. SPIE 7388, 738806 (2009).
    [Crossref]
  8. M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
    [Crossref]
  9. R. Aalipour and M. T. Tavassoly, “Phase singularity in the diffracted field from Fresnel’s double mirror,” Opt. Commun. 294, 13–16 (2013).
    [Crossref]
  10. R. Aalipour, “Calculation of Fresnel diffraction from 1D phase step by discrete Fourier transform,” Opt. Commun. 382, 651–655 (2017).
    [Crossref]
  11. W.-K. Lee, P. Cloetens, and M. Schlenker, “Dispersion corrections of the copper K edge measured by Fresnel diffraction,” Acta Cryst. A60, 58–63 (2004).
    [Crossref]
  12. M. T. Tavassoly, I. M. Haghighi, and K. Hassani, “Application of Fresnel diffraction from a phase step to the measurement of film thickness,” Appl. Opt. 48, 5497–5501 (2009).
    [Crossref]
  13. Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).
  14. K. Hassani, M. Ashrafganjoie, and M. T. Tavassoly, “Application of white light Fresnel diffractometry to film thickness measurement,” Appl. Opt. 55, 1803–1807 (2016).
    [Crossref]
  15. A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
    [Crossref]
  16. A. Sabatyan and M. T. Tavassoly, “Determination of refractive indices of liquids by Fresnel diffraction,” Opt. Laser Technol. 41, 892–896 (2009).
    [Crossref]
  17. M. T. Tavassoly and A. Saber, “Optical refractometry based on Fresnel diffraction from a phase wedge,” Opt. Lett. 35, 3679–3681 (2010).
    [Crossref]
  18. M. T. Tavassoly, S. R. Hosseini, A. M. Fard, and R. R. Naraghi, “Applications of Fresnel diffraction from the edge of a transparent plate in transmission,” Appl. Opt. 51, 7170–7175 (2012).
    [Crossref]
  19. M. T. Tavassoly, R. R. Naraghi, A. Nahal, and K. Hassani, “High precision refractometry based on Fresnel diffraction from phase plates,” Opt. Lett. 37, 1493–1495 (2012).
    [Crossref]
  20. C. W. Gayer, D. Hemmers, C. Stelzmann, and G. Pretzler, “Direct measurement of the x-ray refractive index by Fresnel diffraction at a transparent edge,” Opt. Lett. 38, 1563–1565 (2013).
    [Crossref]
  21. M. Jafari Siavashani, M. T. Tavassoly, E. Ahadi Akhlaghi, and S. R. Hosseini, “Measuring refractive index and thickness of transparent thin films using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1473–1476.
  22. M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
    [Crossref]
  23. A. A. Khorshad, K. Hassani, and M. T. Tavassoly, “Nanometer displacement measurement using Fresnel diffraction,” Appl. Opt. 51, 5066–5072 (2012).
    [Crossref]
  24. E. V. Basisty and V. A. Komotskii, “Experimental investigation of laser beam diffraction on phase step and its practical applications,” Electron. Lett. 50, 693–695 (2014).
    [Crossref]
  25. S. R. Hosseini and M. Tavassoly, “The application of a phase step diffractometer in wavemetry,” J. Opt. 17, 035605 (2015).
    [Crossref]
  26. A. Saber and M. T. Tavassoly, “Measuring of diffusion coefficient of liquids using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1053–1056.
  27. M. Amiri, M. T. Tavassoly, H. Dolatkhah, and Z. Alirezaei, “Tunable spectral shifts and spectral switches by controllable phase modulation,” Opt. Express 18, 25089–25101 (2010).
    [Crossref]
  28. S. R. Hosseini and M. T. Tavassoly, “Investigation of correlation properties of light fields by Fresnel diffraction from a step,” in 11th International Conference on Correlation Optics (International Society for Optics and Photonics, 2013), pp. 906607.
  29. A. Mahmoudi, “Application of Fresnel diffraction from phase steps to measurement of etching rate of transparent materials,” Appl. Opt. 54, 7993–7996 (2015).
    [Crossref]
  30. M. Dashtdar and S. M. Hosseini-Saber, “Focal length measurement based on Fresnel diffraction from a phase plate,” Appl. Opt. 55, 7434–7437 (2016).
    [Crossref]

2017 (1)

R. Aalipour, “Calculation of Fresnel diffraction from 1D phase step by discrete Fourier transform,” Opt. Commun. 382, 651–655 (2017).
[Crossref]

2016 (2)

2015 (4)

A. Mahmoudi, “Application of Fresnel diffraction from phase steps to measurement of etching rate of transparent materials,” Appl. Opt. 54, 7993–7996 (2015).
[Crossref]

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

S. R. Hosseini and M. Tavassoly, “The application of a phase step diffractometer in wavemetry,” J. Opt. 17, 035605 (2015).
[Crossref]

Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).

2014 (1)

E. V. Basisty and V. A. Komotskii, “Experimental investigation of laser beam diffraction on phase step and its practical applications,” Electron. Lett. 50, 693–695 (2014).
[Crossref]

2013 (2)

C. W. Gayer, D. Hemmers, C. Stelzmann, and G. Pretzler, “Direct measurement of the x-ray refractive index by Fresnel diffraction at a transparent edge,” Opt. Lett. 38, 1563–1565 (2013).
[Crossref]

R. Aalipour and M. T. Tavassoly, “Phase singularity in the diffracted field from Fresnel’s double mirror,” Opt. Commun. 294, 13–16 (2013).
[Crossref]

2012 (3)

2010 (2)

2009 (4)

M. T. Tavassoly, I. M. Haghighi, and K. Hassani, “Application of Fresnel diffraction from a phase step to the measurement of film thickness,” Appl. Opt. 48, 5497–5501 (2009).
[Crossref]

A. Sabatyan and M. T. Tavassoly, “Determination of refractive indices of liquids by Fresnel diffraction,” Opt. Laser Technol. 41, 892–896 (2009).
[Crossref]

M. T. Tavassoly, M. Dashtdar, and M. Amiri, “Spectral modification by diffraction and scattering,” Proc. SPIE 7388, 738806 (2009).
[Crossref]

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
[Crossref]

2008 (1)

2007 (2)

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
[Crossref]

A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
[Crossref]

2005 (1)

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[Crossref]

2004 (1)

W.-K. Lee, P. Cloetens, and M. Schlenker, “Dispersion corrections of the copper K edge measured by Fresnel diffraction,” Acta Cryst. A60, 58–63 (2004).
[Crossref]

2001 (2)

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from step in reflection and transmission,” Iranian J. Phys. 2, 237–246 (2001).

M. T. Tavassoly, A. Darudi, H. R. Khalesifard, and M. R. Sadat Hossaini, “Applications of Fresnel diffraction from phase objects,” Proc. SPIE 4399, 98–106 (2001).
[Crossref]

1999 (1)

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from a step in reflection and transmission modes,” Proc. SPIE 3749, 560–561 (1999).
[Crossref]

Aalipour, R.

R. Aalipour, “Calculation of Fresnel diffraction from 1D phase step by discrete Fourier transform,” Opt. Commun. 382, 651–655 (2017).
[Crossref]

R. Aalipour and M. T. Tavassoly, “Phase singularity in the diffracted field from Fresnel’s double mirror,” Opt. Commun. 294, 13–16 (2013).
[Crossref]

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
[Crossref]

Ahadi Akhlaghi, E.

M. Jafari Siavashani, M. T. Tavassoly, E. Ahadi Akhlaghi, and S. R. Hosseini, “Measuring refractive index and thickness of transparent thin films using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1473–1476.

Alirezaei, Z.

Amiri, M.

M. Amiri, M. T. Tavassoly, H. Dolatkhah, and Z. Alirezaei, “Tunable spectral shifts and spectral switches by controllable phase modulation,” Opt. Express 18, 25089–25101 (2010).
[Crossref]

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
[Crossref]

M. T. Tavassoly, M. Dashtdar, and M. Amiri, “Spectral modification by diffraction and scattering,” Proc. SPIE 7388, 738806 (2009).
[Crossref]

M. Amiri and M. T. Tavassoly, “Spectral anomalies near phase singularities in reflection at Brewster’s angle and colored castastrophes,” Opt. Lett. 33, 1863–1865 (2008).
[Crossref]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
[Crossref]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[Crossref]

Ashrafganjoie, M.

Basisty, E. V.

E. V. Basisty and V. A. Komotskii, “Experimental investigation of laser beam diffraction on phase step and its practical applications,” Electron. Lett. 50, 693–695 (2014).
[Crossref]

Beygi, M. G.

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

Cloetens, P.

W.-K. Lee, P. Cloetens, and M. Schlenker, “Dispersion corrections of the copper K edge measured by Fresnel diffraction,” Acta Cryst. A60, 58–63 (2004).
[Crossref]

Darudi, A.

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
[Crossref]

M. T. Tavassoly, A. Darudi, H. R. Khalesifard, and M. R. Sadat Hossaini, “Applications of Fresnel diffraction from phase objects,” Proc. SPIE 4399, 98–106 (2001).
[Crossref]

Dashtdar, M.

M. Dashtdar and S. M. Hosseini-Saber, “Focal length measurement based on Fresnel diffraction from a phase plate,” Appl. Opt. 55, 7434–7437 (2016).
[Crossref]

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

M. T. Tavassoly, M. Dashtdar, and M. Amiri, “Spectral modification by diffraction and scattering,” Proc. SPIE 7388, 738806 (2009).
[Crossref]

Dolatkhah, H.

Fard, A. M.

Ganjkhani, Y.

Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).

Gayer, C. W.

Haghighi, I. M.

Hassani, K.

Hemmers, D.

Hosseini, S. R.

S. R. Hosseini and M. Tavassoly, “The application of a phase step diffractometer in wavemetry,” J. Opt. 17, 035605 (2015).
[Crossref]

Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).

M. T. Tavassoly, S. R. Hosseini, A. M. Fard, and R. R. Naraghi, “Applications of Fresnel diffraction from the edge of a transparent plate in transmission,” Appl. Opt. 51, 7170–7175 (2012).
[Crossref]

S. R. Hosseini and M. T. Tavassoly, “Investigation of correlation properties of light fields by Fresnel diffraction from a step,” in 11th International Conference on Correlation Optics (International Society for Optics and Photonics, 2013), pp. 906607.

M. Jafari Siavashani, M. T. Tavassoly, E. Ahadi Akhlaghi, and S. R. Hosseini, “Measuring refractive index and thickness of transparent thin films using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1473–1476.

Hosseini-Saber, S. M.

Jafari Siavashani, M.

Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).

M. Jafari Siavashani, M. T. Tavassoly, E. Ahadi Akhlaghi, and S. R. Hosseini, “Measuring refractive index and thickness of transparent thin films using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1473–1476.

Karimi, E.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[Crossref]

Karimzadeh, R.

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

Khalesifard, H. R.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[Crossref]

M. T. Tavassoly, A. Darudi, H. R. Khalesifard, and M. R. Sadat Hossaini, “Applications of Fresnel diffraction from phase objects,” Proc. SPIE 4399, 98–106 (2001).
[Crossref]

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from step in reflection and transmission,” Iranian J. Phys. 2, 237–246 (2001).

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from a step in reflection and transmission modes,” Proc. SPIE 3749, 560–561 (1999).
[Crossref]

Khorshad, A. A.

Komotskii, V. A.

E. V. Basisty and V. A. Komotskii, “Experimental investigation of laser beam diffraction on phase step and its practical applications,” Electron. Lett. 50, 693–695 (2014).
[Crossref]

Koohian, A.

Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).

Lee, W.-K.

W.-K. Lee, P. Cloetens, and M. Schlenker, “Dispersion corrections of the copper K edge measured by Fresnel diffraction,” Acta Cryst. A60, 58–63 (2004).
[Crossref]

Mahmoudi, A.

Moradi, A.-R.

Nahal, A.

Naraghi, R. R.

Pretzler, G.

Sabatyan, A.

A. Sabatyan and M. T. Tavassoly, “Determination of refractive indices of liquids by Fresnel diffraction,” Opt. Laser Technol. 41, 892–896 (2009).
[Crossref]

A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
[Crossref]

Saber, A.

M. T. Tavassoly and A. Saber, “Optical refractometry based on Fresnel diffraction from a phase wedge,” Opt. Lett. 35, 3679–3681 (2010).
[Crossref]

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
[Crossref]

A. Saber and M. T. Tavassoly, “Measuring of diffusion coefficient of liquids using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1053–1056.

Sadat Hossaini, M. R.

M. T. Tavassoly, A. Darudi, H. R. Khalesifard, and M. R. Sadat Hossaini, “Applications of Fresnel diffraction from phase objects,” Proc. SPIE 4399, 98–106 (2001).
[Crossref]

Sahlol-bai, H.

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from step in reflection and transmission,” Iranian J. Phys. 2, 237–246 (2001).

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from a step in reflection and transmission modes,” Proc. SPIE 3749, 560–561 (1999).
[Crossref]

Salehi, M.

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from step in reflection and transmission,” Iranian J. Phys. 2, 237–246 (2001).

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from a step in reflection and transmission modes,” Proc. SPIE 3749, 560–561 (1999).
[Crossref]

Schlenker, M.

W.-K. Lee, P. Cloetens, and M. Schlenker, “Dispersion corrections of the copper K edge measured by Fresnel diffraction,” Acta Cryst. A60, 58–63 (2004).
[Crossref]

Stelzmann, C.

Tavassoly, M.

S. R. Hosseini and M. Tavassoly, “The application of a phase step diffractometer in wavemetry,” J. Opt. 17, 035605 (2015).
[Crossref]

Tavassoly, M. T.

K. Hassani, M. Ashrafganjoie, and M. T. Tavassoly, “Application of white light Fresnel diffractometry to film thickness measurement,” Appl. Opt. 55, 1803–1807 (2016).
[Crossref]

Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).

R. Aalipour and M. T. Tavassoly, “Phase singularity in the diffracted field from Fresnel’s double mirror,” Opt. Commun. 294, 13–16 (2013).
[Crossref]

M. T. Tavassoly, R. R. Naraghi, A. Nahal, and K. Hassani, “High precision refractometry based on Fresnel diffraction from phase plates,” Opt. Lett. 37, 1493–1495 (2012).
[Crossref]

A. A. Khorshad, K. Hassani, and M. T. Tavassoly, “Nanometer displacement measurement using Fresnel diffraction,” Appl. Opt. 51, 5066–5072 (2012).
[Crossref]

M. T. Tavassoly, S. R. Hosseini, A. M. Fard, and R. R. Naraghi, “Applications of Fresnel diffraction from the edge of a transparent plate in transmission,” Appl. Opt. 51, 7170–7175 (2012).
[Crossref]

M. Amiri, M. T. Tavassoly, H. Dolatkhah, and Z. Alirezaei, “Tunable spectral shifts and spectral switches by controllable phase modulation,” Opt. Express 18, 25089–25101 (2010).
[Crossref]

M. T. Tavassoly and A. Saber, “Optical refractometry based on Fresnel diffraction from a phase wedge,” Opt. Lett. 35, 3679–3681 (2010).
[Crossref]

M. T. Tavassoly, I. M. Haghighi, and K. Hassani, “Application of Fresnel diffraction from a phase step to the measurement of film thickness,” Appl. Opt. 48, 5497–5501 (2009).
[Crossref]

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
[Crossref]

A. Sabatyan and M. T. Tavassoly, “Determination of refractive indices of liquids by Fresnel diffraction,” Opt. Laser Technol. 41, 892–896 (2009).
[Crossref]

M. T. Tavassoly, M. Dashtdar, and M. Amiri, “Spectral modification by diffraction and scattering,” Proc. SPIE 7388, 738806 (2009).
[Crossref]

M. Amiri and M. T. Tavassoly, “Spectral anomalies near phase singularities in reflection at Brewster’s angle and colored castastrophes,” Opt. Lett. 33, 1863–1865 (2008).
[Crossref]

A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
[Crossref]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
[Crossref]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[Crossref]

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from step in reflection and transmission,” Iranian J. Phys. 2, 237–246 (2001).

M. T. Tavassoly, A. Darudi, H. R. Khalesifard, and M. R. Sadat Hossaini, “Applications of Fresnel diffraction from phase objects,” Proc. SPIE 4399, 98–106 (2001).
[Crossref]

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from a step in reflection and transmission modes,” Proc. SPIE 3749, 560–561 (1999).
[Crossref]

M. Jafari Siavashani, M. T. Tavassoly, E. Ahadi Akhlaghi, and S. R. Hosseini, “Measuring refractive index and thickness of transparent thin films using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1473–1476.

A. Saber and M. T. Tavassoly, “Measuring of diffusion coefficient of liquids using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1053–1056.

S. R. Hosseini and M. T. Tavassoly, “Investigation of correlation properties of light fields by Fresnel diffraction from a step,” in 11th International Conference on Correlation Optics (International Society for Optics and Photonics, 2013), pp. 906607.

Acta Cryst. (1)

W.-K. Lee, P. Cloetens, and M. Schlenker, “Dispersion corrections of the copper K edge measured by Fresnel diffraction,” Acta Cryst. A60, 58–63 (2004).
[Crossref]

Appl. Opt. (6)

Electron. Lett. (1)

E. V. Basisty and V. A. Komotskii, “Experimental investigation of laser beam diffraction on phase step and its practical applications,” Electron. Lett. 50, 693–695 (2014).
[Crossref]

Iranian J. Phys. (1)

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from step in reflection and transmission,” Iranian J. Phys. 2, 237–246 (2001).

J. Opt. (1)

S. R. Hosseini and M. Tavassoly, “The application of a phase step diffractometer in wavemetry,” J. Opt. 17, 035605 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (4)

R. Aalipour and M. T. Tavassoly, “Phase singularity in the diffracted field from Fresnel’s double mirror,” Opt. Commun. 294, 13–16 (2013).
[Crossref]

R. Aalipour, “Calculation of Fresnel diffraction from 1D phase step by discrete Fourier transform,” Opt. Commun. 382, 651–655 (2017).
[Crossref]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[Crossref]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
[Crossref]

Opt. Eng. (1)

A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (2)

M. G. Beygi, R. Karimzadeh, and M. Dashtdar, “Nonlinear refractive index measurement by Fresnel diffraction from phase object,” Opt. Laser Technol. 66, 151–155 (2015).
[Crossref]

A. Sabatyan and M. T. Tavassoly, “Determination of refractive indices of liquids by Fresnel diffraction,” Opt. Laser Technol. 41, 892–896 (2009).
[Crossref]

Opt. Lett. (4)

Opt. Photon. Soc. Iran (1)

Y. Ganjkhani, M. T. Tavassoly, S. R. Hosseini, M. Jafari Siavashani, and A. Koohian, “Thickness measurement using the extrema of the intensity profile in Fresnel diffraction from a phase step,” Opt. Photon. Soc. Iran 21, 777–780 (2015).

Proc. SPIE (3)

M. T. Tavassoly, H. Sahlol-bai, M. Salehi, and H. R. Khalesifard, “Fresnel diffraction from a step in reflection and transmission modes,” Proc. SPIE 3749, 560–561 (1999).
[Crossref]

M. T. Tavassoly, M. Dashtdar, and M. Amiri, “Spectral modification by diffraction and scattering,” Proc. SPIE 7388, 738806 (2009).
[Crossref]

M. T. Tavassoly, A. Darudi, H. R. Khalesifard, and M. R. Sadat Hossaini, “Applications of Fresnel diffraction from phase objects,” Proc. SPIE 4399, 98–106 (2001).
[Crossref]

Other (3)

M. Jafari Siavashani, M. T. Tavassoly, E. Ahadi Akhlaghi, and S. R. Hosseini, “Measuring refractive index and thickness of transparent thin films using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1473–1476.

A. Saber and M. T. Tavassoly, “Measuring of diffusion coefficient of liquids using Fresnel diffraction from phase step,” in Proceedings of 21st Conference on Optics and Photonics (Optics and Photonics Society of Iran, 2015), pp. 1053–1056.

S. R. Hosseini and M. T. Tavassoly, “Investigation of correlation properties of light fields by Fresnel diffraction from a step,” in 11th International Conference on Correlation Optics (International Society for Optics and Photonics, 2013), pp. 906607.

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Figures (6)

Fig. 1.
Fig. 1. Experimental diffraction patterns for different orientations of the step’s plates: (a) a step with parallel plates, (b) a step with plates making a wedge, (c) a step resembling the Fresnel’s double mirror, (d) a step with plates in arbitrary orientation.
Fig. 2.
Fig. 2. Geometry used to describe Fresnel diffraction from a step with arbitrary orientation of its plates, in reflection mode.
Fig. 3.
Fig. 3. Simulations of the diffraction patterns for a step with different orientations of its plates: (a) for a step with parallel plates, (b) for a wedge shape step, (c) for a step resembling Fresnel’s double mirror, and (d) for a step with arbitrary orientations of its plates. The plots (a′), (b′), (c′), (d′) and (a′′), (b′′), (c′′), (d′′) represent the normalized intensity profiles along directions normal and parallel to the step edge, the x and y directions, respectively.
Fig. 4.
Fig. 4. Schemes of the experimental setup (a) for zero angle of incidence, (b) for changeable angle of incidence.
Fig. 5.
Fig. 5. Experimental diffraction patterns for different orientations of the step plates: (a) a step with parallel plates, (b) a wedge shape step, (c) a step resembling the Fresnel’s double mirror, and (d) a step with arbitrary orientation of the plates. The corresponding experimental normalized intensity profiles, the dotted curves, in the directions perpendicular and parallel to the step edge, x and y directions, are plotted in (a′), (b′), (c′), (d′) and (a′′), (b′′), (c′′), (d′′), respectively. The solid lines are the fitted theoretical intensity functions.
Fig. 6.
Fig. 6. (a) Experimental diffraction pattern in which the zero intensity spots are specified, (b) the experimental normalized intensity profile, the dotted curve, in the direction perpendicular to the step edge fitted by the corresponding normalized intensity function, solid line. (c) Experimental normalized intensity profile, dotted curve, in the direction parallel to the step edge and the fitted corresponding normalized intensity function, solid line.

Equations (49)

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U ( P ) = K D [ r L 0 d x e i k ( r 1 + r 1 ) r 1 r 1 d y + r R 0 d x e i k ( r 2 + r 2 ) r 2 r 2 d y ] ,
U ( P ) = K D e i k ( R + R ) R R [ r L x 0 e i k γ X 1 2 d X 1 e i k γ Y 1 2 d Y 1 + r R e i φ x 0 X 0 e i k γ X 2 2 d X 2 e i k γ Y 2 2 d Y 2 ] ,
γ = 1 2 ( 1 R + 1 R ) , X 0 = tan β cos θ / γ , Y 0 = tan α cos θ / γ ,
{ X 1 = x 1 x 0 Y 1 = y 1 y 0 ,
{ X 2 = ( x 2 x 0 ) X 0 Y 2 = ( y 2 y 0 ) Y 0 ,
φ = k Δ = 2 k [ h 0 cos θ + ( tan β cos θ ) x 0 + ( tan α cos θ ) y 0 + ( tan β cos θ ) 2 / 2 γ + ( tan α cos θ ) 2 / 2 γ ] .
{ k γ X 1 2 = π v 1 2 2 k γ Y 1 2 = π u 1 2 2 ,
{ k γ X 2 2 = π v 2 2 2 k γ Y 2 2 = π u 2 2 2 ,
{ V = 2 k γ π x 0 V 0 = 2 k γ π X 0 = 2 k π γ tan β cos θ .
U ( P ) = K D e i k ( R + R ) R R [ r L π 2 k γ V e i π v 1 2 2 d v 1 e i π u 1 2 2 d u 1 + r R e i φ π 2 k γ V V 0 e i π v 2 2 2 d v 2 e i π u 2 2 2 d u 2 ]
U ( P ) = K D e i k ( R + R ) R R π k γ ( 1 + i ) 2 × [ r L V e i π v 1 2 2 d v 1 + r R e i φ V V 0 e i π v 2 2 2 d v 2 ] .
0 V e i π v 2 2 d v = C ( V ) + i S ( V ) ,
{ C ( ) = 1 2 C ( 0 ) = 0 C ( ) = 1 2 , { S ( ) = 1 2 S ( 0 ) = 0 S ( ) = 1 2 ,
U ( P ) = ( 1 + i 2 ) U 0 { A + i B } ,
U 0 = K D e i k ( R + R ) R R π k γ r L = K D λ e i k ( R + R ) R + R r L ,
{ A = [ 1 2 + C ( V ) ] + [ 1 2 C ( V V 0 ) ] cos φ + [ 1 2 S ( V V 0 ) ] sin φ B = [ 1 2 + S ( V ) ] + [ 1 2 S ( V V 0 ) ] cos φ [ 1 2 C ( V V 0 ) ] sin φ .
I ( P ) = 1 2 I 0 { A 2 + B 2 } ,
I 0 = U 0 U 0 * .
W = 2 k γ / π y 0 , W 0 = 2 k / π γ tan α cos θ ,
φ = ( 4 π / λ ) h 0 cos θ π ( V V 0 V 0 2 / 2 ) π ( W W 0 W 0 2 / 2 ) .
I n = I 1 + I 2 cos φ + I 3 sin φ ,
{ I 1 = 1 2 { [ 1 2 + C ( V ) ] 2 + [ 1 2 + S ( V ) ] 2 + [ 1 2 C ( V V 0 ) ] 2 + [ 1 2 S ( V V 0 ) ] 2 } I 2 = [ 1 2 + C ( V ) ] [ 1 2 C ( V V 0 ) ] + [ 1 2 + S ( V ) ] [ 1 2 S ( V V 0 ) ] I 3 = [ 1 2 + C ( V ) ] [ 1 2 S ( V V 0 ) ] [ 1 2 + S ( V ) ] [ 1 2 C ( V V 0 ) ] .
φ = ( 4 π / λ ) h 0 cos θ .
I n = cos 2 ( φ / 2 ) + 2 [ C 2 ( V ) + S 2 ( V ) ] sin 2 ( φ / 2 ) + [ C ( V ) S ( V ) ] sin φ ,
φ = ( 4 π / λ ) h 0 cos θ π ( W W 0 W 0 2 / 2 ) .
φ = ( 4 π / λ ) h 0 cos θ π ( V V 0 V 0 2 / 2 ) .
I n = I 1 ( 1 + cos φ ) ,
π W 0 2 k γ / π δ y 0 = 2 π ,
W 0 = 2 / ( 2 k γ / π δ y 0 ) .
tan α = λ / ( 2 δ y 0 cos θ ) .
{ r 1 = R + ( T 1 r 0 ) r 1 = R ( T 1 r 0 ) ,
{ r 2 = R + ( T 2 r 0 ) + h 0 = R + ( T 2 , x y r 0 ) + ( T 2 , z + h 0 ) r 2 = R ( T 2 r 0 ) h 0 = R + ( T 2 , x y r 0 ) + ( T 2 , z + h 0 ) ,
{ T 1 = x 1 x ^ + y 1 y ^    T 2 = x 2 x ^ + y 2 y ^ + z 2 z ^ r 0 = x 0 x ^ + y 0 y ^ .
r 1 + r 1 ( R + R ) + 1 2 ( x 1 x 0 ) 2 ( 1 R + 1 R ) + 1 2 ( y 1 y 0 ) 2 ( 1 R + 1 R ) .
r 1 + r 1 ( R + R ) + γ ( x 1 x 0 ) 2 + γ ( y 1 y 0 ) 2 .
r 2 + r 2 ( R + R ) + γ [ ( x 2 x 0 ) 2 + ( y 2 y 0 ) 2 ] 2 z 2 ( x 2 , y 2 ) cos θ 2 h 0 cos θ .
n ^ · T 2 = [ x ^ x + y ^ y + z ^ z ] · [ x ^ x 2 + y ^ y 2 + z ^ z 2 ] = 0 ,
n ^ = x ^ cos α sin β y ^ sin α + z ^ cos α cos β .
( cos α sin β ) x 2 + ( sin α ) y 2 + ( cos α cos β ) z 2 = 0 ,
z 2 = tan β x 2 + tan α cos β y 2 .
z 2 = tan β    x 2 + tan α    y 2 .
r 2 + r 2 = ( R + R ) + γ [ ( x 2 x 0 ) 2 + ( y 2 y 0 ) 2 ] 2 ( h 0 + tan β x 2 + tan α y 2 ) cos θ .
r 2 + r 2 = ( R + R ) + γ [ ( x 2 x 0 ) tan β cos θ / γ ] 2 + γ [ ( y 2 y 0 ) tan α cos θ / γ ] 2 2 [ h 0 cos θ + ( tan β cos θ ) x 0 + ( tan α cos θ ) y 0 + ( tan β cos θ ) 2 / 2 γ + ( tan α cos θ ) 2 / 2 γ ] .
Δ = 2 [ h 0 cos θ + ( tan β cos θ ) x 0 + ( tan α cos θ ) y 0 + ( tan β cos θ ) 2 / 2 γ + ( tan α cos θ ) 2 / 2 γ ] ,
{ X 2 = ( x 2 x 0 ) X 0 Y 2 = ( y 2 y 0 ) Y 0 ,
X 0 = tan β cos θ / γ , Y 0 = tan α cos θ / γ ,
{ X 1 = x 1 x 0 Y 1 = y 1 y 0 ,
{ r 1 + r 1 = ( R + R ) + γ X 1 2 + γ Y 1 2       r 2 + r 2 = ( R + R ) + γ X 2 2 + γ Y 2 2 Δ .
U ( P ) = K D e i k ( R + R ) R R [ r L x 0 e i k γ X 1 2 d X 1 e i k γ Y 1 2 d Y 1 + r R e i φ x 0 X 0 e i k γ X 2 2 d X 2 e i k γ Y 2 2 d Y 2 ] ,

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