Abstract

We propose and demonstrate a new interferometric approach in which a uniform phase difference between the arms of the interferometer manifests itself as spatially varying intensity distribution. The approach is based on interfering two orthogonal spatially varying vector fields, the radially and azimuthally polarized beams, and measuring the projection of the obtained field on an analyzer. This method provides additional spatial information that can be used to improve the smallest detectable phase change as compared with a conventional Michelson interferometer.

© 2009 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. Y. S. Changm P. Y. Chien andM. W. Chang, “Distance and velocity measurements by the use of an orthogonal Michelson Interferometer,” Appl. Opt. 36, 258–264 (2008).
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2009

2008

2007

J. A. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing,” Phys. Rev. A 76(5), 053815 (2007).
[CrossRef]

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[CrossRef]

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Opt. Express 15(6), 3550–3556 (2007).
[CrossRef] [PubMed]

2006

2005

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

2004

2003

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

2002

Q. Zhan and J. R. Leger, “Interferometric measurement of the geometric phase in space-variant polarization manipulations,“ Opt. Commun. 213, (Iss. 4-6), 241–245 (2002).

2000

Bokor, N.

Brown, T. G.

Chang, M. W.

Davidson, N.

Dennis, M. R.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Dultz, W.

J. A. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing,” Phys. Rev. A 76(5), 053815 (2007).
[CrossRef]

Fainman, Y.

Ferrari, J. A.

J. L. Flores, J. A. Ferrari, and C. D. Perciante, “Faraday current sensor using space-variant analyzers,” Opt. Eng. 47(12), 123603 (2008).
[CrossRef]

J. A. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing,” Phys. Rev. A 76(5), 053815 (2007).
[CrossRef]

Flores, J. L.

J. L. Flores, J. A. Ferrari, and C. D. Perciante, “Faraday current sensor using space-variant analyzers,” Opt. Eng. 47(12), 123603 (2008).
[CrossRef]

Flossmann, F.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

Frins, E.

J. A. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing,” Phys. Rev. A 76(5), 053815 (2007).
[CrossRef]

Hao, B.

Kozawa, Y.

Leger, J.

Leger, J. R.

Q. Zhan and J. R. Leger, “Interferometric measurement of the geometric phase in space-variant polarization manipulations,“ Opt. Commun. 213, (Iss. 4-6), 241–245 (2002).

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Levy, U.

Maier, M.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

Nishiyama, I.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[CrossRef]

Otani, Y.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[CrossRef]

Pang, L.

Perciante, C. D.

J. L. Flores, J. A. Ferrari, and C. D. Perciante, “Faraday current sensor using space-variant analyzers,” Opt. Eng. 47(12), 123603 (2008).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Sato, S.

Schmitzer, H.

J. A. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing,” Phys. Rev. A 76(5), 053815 (2007).
[CrossRef]

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

Tsai, C. H.

Umeda, N.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[CrossRef]

Yoshida, N.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[CrossRef]

Youngworth, K. S.

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009).
[CrossRef]

Q. Zhan and J. R. Leger, “Interferometric measurement of the geometric phase in space-variant polarization manipulations,“ Opt. Commun. 213, (Iss. 4-6), 241–245 (2002).

Adv. Opt. Photon.

Appl. Opt.

Issues

Q. Zhan and J. R. Leger, “Interferometric measurement of the geometric phase in space-variant polarization manipulations,“ Opt. Commun. 213, (Iss. 4-6), 241–245 (2002).

Meas. Sci. Technol.

I. Nishiyama, N. Yoshida, Y. Otani, and N. Umeda, “Single-shot birefringence measurement using radial polarizer fabricated by direct atomic force microscope stroking method,” Meas. Sci. Technol. 18(6), 1673–1677 (2007).
[CrossRef]

Opt. Eng.

J. L. Flores, J. A. Ferrari, and C. D. Perciante, “Faraday current sensor using space-variant analyzers,” Opt. Eng. 47(12), 123603 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

J. A. Ferrari, W. Dultz, H. Schmitzer, and E. Frins, “Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing,” Phys. Rev. A 76(5), 053815 (2007).
[CrossRef]

Phys. Rev. Lett.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95(25), 253901 (2005).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Schematic representation of the RPI.

Fig. 2
Fig. 2

Schematic representation of the polarization fields before the analyzer for a few values of ϕ. The vector sum (green arrows) of the radial (blue arrow) and azimuthal (red arrows) is shown for each case. the rotation direction is shown as well (purple arrows) when the field has a circular polarization. Simulated intensity distribution after the analyzer is shown for each case. White color represents high intensity.

Fig. 3
Fig. 3

Representative intensity distribution after passing through the analyzer: (a, b) separate intensity distribution as obtained from arms 1 and 2 respectively. (c, d) interference pattern of the two arms with 0 and π phase difference between them, respectively.

Fig. 4
Fig. 4

Intensity as a function of the azimuthal angle and the phase difference between the interferometer’s arms. The experimental results (upper panel) were calculated from each interferogram by integration along the radial coordinate. The theoretical intensity distribution is shown as well for comparison (lower panel). The accumulated phase is measured relative to an arbitrary reference point.

Fig. 5
Fig. 5

Contrast of interferograms as a function of the accumulated phase difference.

Fig. 6
Fig. 6

Intensity as a function of the azimuthal angle and the illumination wavelength.

Fig. 7
Fig. 7

Contrast of the interferograms as a function of the illumination wavelength. The contrast has a period of π where each maximum in the contrast plot has an intensity distribution that is 90° rotated with respect to the adjacent maxima.

Fig. 8
Fig. 8

Phase difference (relative to a reference value) as a function of the angular frequency of all the maximum points shown in Fig. 7. a linear fit is shown as well.

Fig. 9
Fig. 9

Ratio of the minimal detectable phase change in a CMI and the RPI as a function of the phase difference between the interferometer’s arms.

Fig. 10
Fig. 10

phase change reading of the two interferometers as a function of the phase difference between the interferometer’s arms. (a) Noise amplitudes of 1 LSB. (b) Noise amplitudes of 0.1 LSB. The accurate phase change value is shown as well for reference (green).

Fig. 11
Fig. 11

Interferograms generated by the CMI (left) and the RPI (right) when a lens with a circular symmetric quadratic phase profile is inserted into one of the interferometer’s arms.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I 1 ( ϕ ) = 1 2 ( 1 + cos ϕ )
I 2 ( ϕ , θ , ϕ p ) | T p ( V r e i ϕ + V a ) | 2
I 2 ( ϕ , θ , ϕ p ) = 1 2 ( 1 + sin ( 2 ( ϕ p θ ) ) cos ϕ )
I 2 ( ϕ , θ ) = 1 2 ( 1 + cos 2 θ cos ϕ )

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