Abstract

We present what we believe to be a new digital holographic imaging method that is able to determine simultaneously the distributions of intensity, phase, and polarization state at the surface of a specimen on the basis of a single image acquisition. Two reference waves with orthogonal polarization states interfere with the object wave to create a hologram that is recorded on a CCD camera. Two wave fronts, one for each perpendicular polarization state, are numerically reconstructed in intensity and phase. Combining the intensity and the phase distributions of these two wave fronts permits the determination of all the components of the Jones vector of the object-wave front. We show that this method can be used to image and measure the distribution of the polarization state at the surface of a specimen, and the obtained results indicate that precise quantitative measurements of the polarization state can be achieved. An application of the method to image the birefringence of a stressed polymethyl methacrylate sample is presented.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. de Boer, T. E. Milner, M. J. C. van Gemert, J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
    [CrossRef] [PubMed]
  2. M. J. Everett, K. Schoenenberger, B. W. Colston, L. B. Da Silva, “Birefringence characterization of biological tissue by use of optical coherence tomography,” Opt. Lett. 23, 228–230 (1998).
    [CrossRef]
  3. Q. Kemao, M. Hong, W. Xiaoping, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
    [CrossRef]
  4. N. Umeda, H. Iijima, M. Ishikawa, A. Takayanagi, “Birefringence imaging with illumination mode near field scanning optical microscope,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 13–17 (1998).
    [CrossRef]
  5. R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. (Oxford) 180, 140–147 (1995).
    [CrossRef]
  6. D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, 1990), Chap. 5.
  7. E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
    [CrossRef]
  8. D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
    [CrossRef]
  9. A. W. Lohmann, “Reconstruction of vectorial wavefronts,” Appl. Opt. 4, 1667–1668 (1965).
    [CrossRef]
  10. E. Cuche, P. Marquet, C. Depeursinge, “Spatial filtering for zero order and virtual image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
    [CrossRef]
  11. E. Cuche, P. Marquet, C. Depeursinge, “Aperture apodization using cubic spline interpolation: Application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
    [CrossRef]
  12. K. Ramesh, D. K. Tamrakar, “Improved determination of retardation in digital photoelasticity by load stepping,” Opt. Lasers Eng. 33, 387–400 (2000).
    [CrossRef]

2000 (3)

E. Cuche, P. Marquet, C. Depeursinge, “Aperture apodization using cubic spline interpolation: Application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

K. Ramesh, D. K. Tamrakar, “Improved determination of retardation in digital photoelasticity by load stepping,” Opt. Lasers Eng. 33, 387–400 (2000).
[CrossRef]

E. Cuche, P. Marquet, C. Depeursinge, “Spatial filtering for zero order and virtual image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

1999 (3)

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

Q. Kemao, M. Hong, W. Xiaoping, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. (Oxford) 180, 140–147 (1995).
[CrossRef]

1965 (1)

Beghuin, D.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

Colston, B. W.

Cuche, E.

E. Cuche, P. Marquet, C. Depeursinge, “Aperture apodization using cubic spline interpolation: Application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

E. Cuche, P. Marquet, C. Depeursinge, “Spatial filtering for zero order and virtual image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

Da Silva, L. B.

Dahlgren, P.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

de Boer, J. F.

Delacretaz, G.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

Depeursinge, C.

E. Cuche, P. Marquet, C. Depeursinge, “Aperture apodization using cubic spline interpolation: Application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

E. Cuche, P. Marquet, C. Depeursinge, “Spatial filtering for zero order and virtual image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

Everett, M. J.

Hong, M.

Q. Kemao, M. Hong, W. Xiaoping, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

Iijima, H.

N. Umeda, H. Iijima, M. Ishikawa, A. Takayanagi, “Birefringence imaging with illumination mode near field scanning optical microscope,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 13–17 (1998).
[CrossRef]

Ishikawa, M.

N. Umeda, H. Iijima, M. Ishikawa, A. Takayanagi, “Birefringence imaging with illumination mode near field scanning optical microscope,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 13–17 (1998).
[CrossRef]

Kemao, Q.

Q. Kemao, M. Hong, W. Xiaoping, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, 1990), Chap. 5.

Lewis, J. W.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, 1990), Chap. 5.

Lohmann, A. W.

Marquet, P.

Mei, G.

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. (Oxford) 180, 140–147 (1995).
[CrossRef]

Milner, T. E.

Nelson, J. S.

Oldenbourg, R.

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. (Oxford) 180, 140–147 (1995).
[CrossRef]

Ramesh, K.

K. Ramesh, D. K. Tamrakar, “Improved determination of retardation in digital photoelasticity by load stepping,” Opt. Lasers Eng. 33, 387–400 (2000).
[CrossRef]

Randall, C. E.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, 1990), Chap. 5.

Salathé, R. P.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

Schoenenberger, K.

Takayanagi, A.

N. Umeda, H. Iijima, M. Ishikawa, A. Takayanagi, “Birefringence imaging with illumination mode near field scanning optical microscope,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 13–17 (1998).
[CrossRef]

Tamrakar, D. K.

K. Ramesh, D. K. Tamrakar, “Improved determination of retardation in digital photoelasticity by load stepping,” Opt. Lasers Eng. 33, 387–400 (2000).
[CrossRef]

Umeda, N.

N. Umeda, H. Iijima, M. Ishikawa, A. Takayanagi, “Birefringence imaging with illumination mode near field scanning optical microscope,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 13–17 (1998).
[CrossRef]

van Gemert, M. J. C.

Xiaoping, W.

Q. Kemao, M. Hong, W. Xiaoping, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (1)

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, R. P. Salathé, “Single acquisition polarization imaging with digital holography,” Electron. Lett. 35, 2053–2055 (1999).
[CrossRef]

J. Microsc. (Oxford) (1)

R. Oldenbourg, G. Mei, “New polarized light microscope with precision universal compensator,” J. Microsc. (Oxford) 180, 140–147 (1995).
[CrossRef]

Opt. Commun. (1)

E. Cuche, P. Marquet, C. Depeursinge, “Aperture apodization using cubic spline interpolation: Application in digital holographic microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

Opt. Lasers Eng. (2)

K. Ramesh, D. K. Tamrakar, “Improved determination of retardation in digital photoelasticity by load stepping,” Opt. Lasers Eng. 33, 387–400 (2000).
[CrossRef]

Q. Kemao, M. Hong, W. Xiaoping, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

Opt. Lett. (2)

Other (2)

N. Umeda, H. Iijima, M. Ishikawa, A. Takayanagi, “Birefringence imaging with illumination mode near field scanning optical microscope,” in Far- and Near-Field Optics: Physics and Information Processing, S. Jutamulia, T. Asakura, eds., Proc. SPIE3467, 13–17 (1998).
[CrossRef]

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, 1990), Chap. 5.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

(a) Experimental setup: O, object wave; R1 and R2, polarized reference waves; Pol. δ°, polarizer oriented at δ°; λ/2, half-wave plate; λ/4, quarter-wave plate; M, mirror; BS, beam splitter. (b) Detail showing the off-axis geometry at the incidence on the CCD. The 0xy plane is parallel to the CCD camera.

Fig. 2
Fig. 2

Hologram of a resolution test target. Two fringe patterns can be observed, one for each reference wave. Their orientation is determined by the off-axis geometry given in Fig. 1(b).

Fig. 3
Fig. 3

(a) Amplitude-contrast image obtained by numerical reconstruction of the hologram shown in Fig. 2. Z is the zero order of diffraction: R1O* and R2O* are two real images corresponding to the horizontal and the vertical polarization states, respectively; and R1*O and R2*O are two virtual images corresponding to the horizontal and the vertical polarization states, respectively. The locations of these five different terms are fixed by the off-axis geometry given in Fig. 1(b). (b) Amplitude-contrast image obtained after zero-order and real images elimination by spatial filtering in the Fourier plane of the hologram and after numerical apodization. τ is the translation vector between the location of two reconstructed wave fronts Ψ(ξ, η) and Ψ(ξ, η).

Fig. 4
Fig. 4

Phase-contrast images obtained by numerical reconstruction of the hologram shown in Fig. 2. The parameters of the digital reference wave are adjusted (a) for the horizontally polarized reference wave (R D = R 1, parallel component) and (b) for the vertically polarized reference wave (R D = R 2, perpendicular component).

Fig. 5
Fig. 5

Fig. 5. Polarization ellipse. The ellipticity is defined by the ratio of the length of the semiminor axis to the length of the semimajor axis, b/ a = tan(ω). The ellipse is further characterized by its azimuth α, measured counterclockwise from the x′ axis. O and O are the maximum amplitudes of the x′ and the y′ components, respectively, of the electric vector, and tan(β) is defined by their ratio [see Eqs. (17)].

Fig. 6
Fig. 6

(a) Setup in the object arm for the results presented in Figs. 7 and 8. P1 is a linear polarizer with a variable orientation δ, P2 is a linear polarizer oriented at -45°, and λ/4 is a quarter-wave retarder oriented at 45°. In part B of the beam, which crosses P2 (oriented at 45°), similar intensities are expected for both components of the polarization state for any P1 orientation.

Fig. 7
Fig. 7

Reconstructed virtual images corresponding to (a), (c), (e) the horizontal polarization component; (b), (d), (f) the vertical polarization component. Three orientations δ of P1 are shown: (a), (b) δ = 0°; (c), (d) δ = 45°; (e), (f) δ = 90°.

Fig. 8
Fig. 8

Theoretical (solid curve) and experimental (circles) values for O and O as functions of the orientation δ of polarizer P1.

Fig. 9
Fig. 9

Setup in the object arm for the results presented in Figs. 10 and 11. λ/4 is a quarter-wave plate oriented at an angle δ; P1 and P2 are polarizers oriented at 45°. Part B, which crosses P2, serves as reference area for measuring the phase difference between the two reference waves.

Fig. 10
Fig. 10

Image of phase difference induced by a quarter-wave plate. A is an area in the object surface (quarter-wave plate), and B is an area in the reference part used to estimate Δφ R . We calculate the effective value of Δφ o by subtracting Δφ R from the phase difference measured in A.

Fig. 11
Fig. 11

Theoretical (solid curve) and experimental (triangles) values of the phase difference between the perpendicular and the parallel components of the polarization state induced by a quarter-wave plate oriented at an angle δ and illuminated by a linearly polarized wave at 45°.

Fig. 12
Fig. 12

Compressed PMMA sample. The circle is the illuminated area. Part A is the illuminated area of the plastic sheet, and part B serves as reference area.

Fig. 13
Fig. 13

Images obtained for a strained PMMA sample: (a) amplitude contrast RO , (b) amplitude contrast RO , (c) amplitude parameter β, (d) phase contrast for the horizontal polarization, (e) phase contrast for the vertical polarization, (f) phase difference Δφ o . The arrows indicate the compression points; the white lines delimit the PMMA samples (rectangles).

Equations (20)

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

IHx, y=|R1|2+|R2|2+|O|2+R1O*+R2O*+R1*O+R2*O.
O=Ox, yexpiφx, yOx, yexpiφx, yexpiϕ0x, y.
R1=Rexpiφ10expik1·r,R2=0Rexpiφ2expik2·r,
R1*O=ROx, yexpiφx, y-φ1×expiϕ0x, y-k1·r
R2*O=ROx, yexpiφx, y-φ2×expiϕ0x, y-k2·r
IHk, l=IHk, lrectxL, yL×k=-N/2N/2l=-N/2N/2 δx-kΔx, y-Δy,
Ψm, n=A expiπλdm2Δξ2+n2Δη2×FFTRDk, lIHk, l×expiπλdk2Δx2+l2Δy2m,n,
Δξ=Δη=λdNΔx=λdL.
RDk, l=exp2iπλkxkΔx+kylΔy,
RD1=expik1·r=R1, RD2=expik2·r=R2.
Ψ=RD1R1*O=ROx, yexpiφx, y-φ1expiϕ0x, y
Ψ=RD2R2*O=ROx, yexpiφx, y-φ2expiϕ0x, y
|ψξ, η|=ROξ, η, |ψξ, η|=ROξ, η,
argψξ, η=φξ, η-φ1+ϕ0ξ, η, argψξ, η=φξ, η-φ2+ϕ0ξ, η.
argψξ-τξ, η-τη-argψξ, η=φξ-τξ, η-τη-φξ, η-φ2-φ1=Δφoξ, η-ΔφR,
|ψξ-τξ, η-τη|/|ψξ, η|=Oξ, η/Oξ, η.
α=2-1arctan2 OO cosΔφo/O2-O2,β=arctanO/O,ω=2-1arcsinsin2βsinΔφo,
O=12cos2 δsin δ cos δsin δ cos δsin2 δ1i=12cos δsin δexpiδ.
O=12|cos δ||sin δ|expiγexpiδ=12OO expiγexpiδ,
O=12expiπ/4cos2 δ+exp-iπ/4sin2 δ2i sin δ cos δ2i sin δ cos δexp-iπ/4cos2 δ+expiπ/4sin2 δ11.

Metrics