Phase measurement using an optical vortex lattice produced with a three-beam interferometer

doi:10.1364/OE.20.013947

Phase measurement using an optical vortex lattice produced with a three-beam interferometer

Samuel A. Eastwood, Alexis I. Bishop, Timothy C. Petersen, David M. Paganin, and Michael J. Morgan »View Author Affiliations

Optics Express, Vol. 20, Issue 13, pp. 13947-13957 (2012)
http://dx.doi.org/10.1364/OE.20.013947

View Full Text Article

Enhanced HTML Acrobat PDF (2239 KB)

Journal Search
Article Lookup

Article Tools

Citations

Alert me when this article is cited
Export Citation/Save

Abstract
Article Info
References (25)
Cited By
Figures (5)
Metrics
Related Content

Abstract

A new phase-measurement technique is proposed, which utilizes a three-beam interferometer. Three-wave interference in the interferometer generates a uniform lattice of optical vortices, which is distorted by the presence of an object inserted in one arm of the interferometer. The transverse displacement of the vortices is proportional to the phase shift in the object wave. Tracking the vortices permits the phase of the object to be reconstructed. We demonstrate the method experimentally using a simple lens and a more complex object, namely the wing of a common house fly. Since the technique is implemented in real space, it is capable of reconstructing the phase locally.

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(050.4865) Diffraction and gratings : Optical vortices
(100.5088) Image processing : Phase unwrapping
(260.6042) Physical optics : Singular optics

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: March 29, 2012
Revised Manuscript: April 27, 2012
Manuscript Accepted: April 30, 2012
Published: June 8, 2012

Citation
Samuel A. Eastwood, Alexis I. Bishop, Timothy C. Petersen, David M. Paganin, and Michael J. Morgan, "Phase measurement using an optical vortex lattice produced with a three-beam interferometer," Opt. Express 20, 13947-13957 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-13947

Sort: Author | Year | Journal | Reset

References

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys.37(2), 642–649 (1966). [CrossRef]
M. Zhan, K. Li, P. Wang, L. Kong, X. Wang, R. Li, X. Tu, L. He, J. Wang, and B. Lu, “Cold atom interferometry,” J. Phys.: Conf. Ser. 80, 012047 (2007).
A. Tonomura, T. Matsuda, J. Endo, T. Arii, and K. Mihama, “Holographic interference electron microscopy for determining specimen magnetic structure and thickness distribution,” Phys. Rev. B Condens. Matter34(5), 3397–3402 (1986). [CrossRef] [PubMed]
U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965). [CrossRef]
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(1), 156–160 (1982). [CrossRef]
P. Senthilkumaran, J. Masajada, and S. Sato, “Interferometry with vortices,” Int. J. Opt.2012, 517591 (2012). [CrossRef]
A. Popiołek-Masajada, M. Borwinska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng.46(7), 073604 (2007). [CrossRef]
J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun.239(4-6), 373–381 (2004). [CrossRef]
M. Borwińska, A. Popiołek-Masajada, and P. Kurzynowski, “Measurements of birefringent media properties using optical vortex birefringence compensator,” Appl. Opt.46(25), 6419–6426 (2007). [CrossRef] [PubMed]
W. A. Woźniak and M. Banach, “Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator,” J. Opt. A, Pure Appl. Opt.11(9), 094024 (2009). [CrossRef]
W. Fraczek and J. Mroczka, “Optical vortices as phase markers to wave-front deformation measurement,” Metrol. Meas. Syst.15, 433–440 (2008).
D. M. Paganin, Coherent X-Ray Optics (Clarendon Press, 2006).
K. W. Nicholls and J. F. Nye, “Three-beam model for studying dislocations in wave pulses,” J. Phys. Math. Gen.20(14), 4673–4696 (1987). [CrossRef]
J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun.198(1-3), 21–27 (2001). [CrossRef]
K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express14(7), 3039–3044 (2006). [CrossRef] [PubMed]
G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75(6), 066613 (2007). [CrossRef] [PubMed]
S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt.46(15), 2893–2898 (2007). [CrossRef] [PubMed]
J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336(1605), 165–190 (1974). [CrossRef]
M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112(5-6), 321–327 (1994). [CrossRef]
J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature467(7313), 301–304 (2010). [CrossRef] [PubMed]
A. Popiołek-Masajada and W. Frączek, “Evaluation of a phase shifting method for vortex localization in optical vortex interferometery,” Opt. Laser Technol.43(7), 1219–1224 (2011). [CrossRef]
E. Frączek, W. Fraczek, and J. Mroczka, “Experimental method for topological charge determination of optical vortices in a regular net,” Opt. Eng.44(2), 025601 (2005). [CrossRef]
V. V. Volkov and Y. Zhu, “Deterministic phase unwrapping in the presence of noise,” Opt. Lett.28(22), 2156–2158 (2003). [CrossRef] [PubMed]
L. J. Allen, H. M. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E63(3), 037602 (2001). [CrossRef] [PubMed]
I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A50(6), 5164–5172 (1994). [CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965). [CrossRef]

Int. J. Opt.

P. Senthilkumaran, J. Masajada, and S. Sato, “Interferometry with vortices,” Int. J. Opt.2012, 517591 (2012). [CrossRef]

J. Appl. Phys.

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys.37(2), 642–649 (1966). [CrossRef]

J. Opt. A, Pure Appl. Opt.

W. A. Woźniak and M. Banach, “Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator,” J. Opt. A, Pure Appl. Opt.11(9), 094024 (2009). [CrossRef]

J. Opt. Soc. Am.

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(1), 156–160 (1982). [CrossRef]

J. Phys. Math. Gen.

K. W. Nicholls and J. F. Nye, “Three-beam model for studying dislocations in wave pulses,” J. Phys. Math. Gen.20(14), 4673–4696 (1987). [CrossRef]

Metrol. Meas. Syst.

W. Fraczek and J. Mroczka, “Optical vortices as phase markers to wave-front deformation measurement,” Metrol. Meas. Syst.15, 433–440 (2008).

Nature

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature467(7313), 301–304 (2010). [CrossRef] [PubMed]

Opt. Commun.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112(5-6), 321–327 (1994). [CrossRef]
J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun.198(1-3), 21–27 (2001). [CrossRef]
J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun.239(4-6), 373–381 (2004). [CrossRef]

Opt. Eng.

A. Popiołek-Masajada, M. Borwinska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng.46(7), 073604 (2007). [CrossRef]
E. Frączek, W. Fraczek, and J. Mroczka, “Experimental method for topological charge determination of optical vortices in a regular net,” Opt. Eng.44(2), 025601 (2005). [CrossRef]

Opt. Express

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express14(7), 3039–3044 (2006). [CrossRef] [PubMed]

Opt. Laser Technol.

A. Popiołek-Masajada and W. Frączek, “Evaluation of a phase shifting method for vortex localization in optical vortex interferometery,” Opt. Laser Technol.43(7), 1219–1224 (2011). [CrossRef]

Opt. Lett.

V. V. Volkov and Y. Zhu, “Deterministic phase unwrapping in the presence of noise,” Opt. Lett.28(22), 2156–2158 (2003). [CrossRef] [PubMed]

Phys. Rev. A

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A50(6), 5164–5172 (1994). [CrossRef] [PubMed]

Phys. Rev. B Condens. Matter

A. Tonomura, T. Matsuda, J. Endo, T. Arii, and K. Mihama, “Holographic interference electron microscopy for determining specimen magnetic structure and thickness distribution,” Phys. Rev. B Condens. Matter34(5), 3397–3402 (1986). [CrossRef] [PubMed]

Phys. Rev. E

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75(6), 066613 (2007). [CrossRef] [PubMed]

Phys. Rev. E

L. J. Allen, H. M. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E63(3), 037602 (2001). [CrossRef] [PubMed]

Proc. R. Soc. Lond. A

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336(1605), 165–190 (1974). [CrossRef]

Other

D. M. Paganin, Coherent X-Ray Optics (Clarendon Press, 2006).
M. Zhan, K. Li, P. Wang, L. Kong, X. Wang, R. Li, X. Tu, L. He, J. Wang, and B. Lu, “Cold atom interferometry,” J. Phys.: Conf. Ser. 80, 012047 (2007).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Click here to see a list of articles that cite this paper

Figures


Fig. 1	Fig. 2	Fig. 3


Fig. 4	Fig. 5

« Previous Article | Next Article »

OSA is a member of CrossRef.

[1] L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys.37(2), 642–649 (1966). [CrossRef]

[2] M. Zhan, K. Li, P. Wang, L. Kong, X. Wang, R. Li, X. Tu, L. He, J. Wang, and B. Lu, “Cold atom interferometry,” J. Phys.: Conf. Ser. 80, 012047 (2007).

[3] A. Tonomura, T. Matsuda, J. Endo, T. Arii, and K. Mihama, “Holographic interference electron microscopy for determining specimen magnetic structure and thickness distribution,” Phys. Rev. B Condens. Matter34(5), 3397–3402 (1986). [CrossRef] [PubMed]

[4] U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965). [CrossRef]

[5] 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(1), 156–160 (1982). [CrossRef]

[6] P. Senthilkumaran, J. Masajada, and S. Sato, “Interferometry with vortices,” Int. J. Opt.2012, 517591 (2012). [CrossRef]

[7] A. Popiołek-Masajada, M. Borwinska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng.46(7), 073604 (2007). [CrossRef]

[8] J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun.239(4-6), 373–381 (2004). [CrossRef]

[9] M. Borwińska, A. Popiołek-Masajada, and P. Kurzynowski, “Measurements of birefringent media properties using optical vortex birefringence compensator,” Appl. Opt.46(25), 6419–6426 (2007). [CrossRef] [PubMed]

[10] W. A. Woźniak and M. Banach, “Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator,” J. Opt. A, Pure Appl. Opt.11(9), 094024 (2009). [CrossRef]

[11] W. Fraczek and J. Mroczka, “Optical vortices as phase markers to wave-front deformation measurement,” Metrol. Meas. Syst.15, 433–440 (2008).

[12] D. M. Paganin, Coherent X-Ray Optics (Clarendon Press, 2006).

[13] K. W. Nicholls and J. F. Nye, “Three-beam model for studying dislocations in wave pulses,” J. Phys. Math. Gen.20(14), 4673–4696 (1987). [CrossRef]

[14] J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun.198(1-3), 21–27 (2001). [CrossRef]

[15] K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express14(7), 3039–3044 (2006). [CrossRef] [PubMed]

[16] G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75(6), 066613 (2007). [CrossRef] [PubMed]

[17] S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt.46(15), 2893–2898 (2007). [CrossRef] [PubMed]

[18] J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336(1605), 165–190 (1974). [CrossRef]

[19] M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun.112(5-6), 321–327 (1994). [CrossRef]

[20] J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature467(7313), 301–304 (2010). [CrossRef] [PubMed]

[21] A. Popiołek-Masajada and W. Frączek, “Evaluation of a phase shifting method for vortex localization in optical vortex interferometery,” Opt. Laser Technol.43(7), 1219–1224 (2011). [CrossRef]

[22] E. Frączek, W. Fraczek, and J. Mroczka, “Experimental method for topological charge determination of optical vortices in a regular net,” Opt. Eng.44(2), 025601 (2005). [CrossRef]

[23] V. V. Volkov and Y. Zhu, “Deterministic phase unwrapping in the presence of noise,” Opt. Lett.28(22), 2156–2158 (2003). [CrossRef] [PubMed]

[24] L. J. Allen, H. M. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E63(3), 037602 (2001). [CrossRef] [PubMed]

[25] I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A50(6), 5164–5172 (1994). [CrossRef] [PubMed]

Select a Conference
Session or Paper #
Year

OpticsInfoBase

Optics Express

Phase measurement using an optical vortex lattice produced with a three-beam interferometer

Article Tools

Abstract

References

Appl. Opt.

Appl. Phys. Lett.

Int. J. Opt.

J. Appl. Phys.

J. Opt. A, Pure Appl. Opt.

J. Opt. Soc. Am.

J. Phys. Math. Gen.

Metrol. Meas. Syst.

Nature

Opt. Commun.

Opt. Eng.

Opt. Express

Opt. Laser Technol.

Opt. Lett.

Phys. Rev. A

Phys. Rev. B Condens. Matter

Phys. Rev. E

Phys. Rev. E

Proc. R. Soc. Lond. A

Other

Cited By

Figures

Related Journal Articles

Related Conference Papers