Abstract

An optical system of off-axis digital holography for imaging the Jones vector of an object wave is improved, and a Faraday rotator for the reference wave is also newly constructed. To evaluate the accuracy of the polarization analysis, quarter- and half-wave plates are used as the object, and the distribution of the polarization state of the transmitted light is analyzed for various orientations of the wave plates. The polarization analysis is also simulated, and the effect of a finite value of the extinction ratio and the modulation error for the reference wave is investigated numerically.

© 2008 Optical Society of America

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References

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  1. J. Moreau, V. Loriette, and A.-C. Boccara, “Full-field birefringence imaging by thermal-light polarization-sensitive optical coherence tomography. 2. Instrument and results,” Appl. Opt. 42, 3811-3817 (2003).
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    [CrossRef]
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    [CrossRef]
  5. K. Oka and T. Kaneko, “Compact complete imaging polarimeter using birefringent wedge prisms,” Opt. Express 11, 1510-1519 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
    [CrossRef]
  9. T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481-483 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
    [CrossRef]
  12. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-180 (1994).
    [CrossRef] [PubMed]
  13. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef] [PubMed]

2007 (2)

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481-483 (2007).
[CrossRef] [PubMed]

2006 (1)

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13, 405-409 (2006).
[CrossRef]

2005 (1)

2004 (1)

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
[CrossRef]

2003 (2)

2002 (1)

2001 (2)

1997 (1)

1994 (1)

1993 (1)

K. Oka and Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44-48 (1993).
[CrossRef]

Asundi, A.

Beghuin, D.

Berezhna, S.

Berezhnyy, I.

Boay, C. G.

Boccara, A.-C.

Colomb, T.

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
[CrossRef]

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27-37 (2002).
[CrossRef] [PubMed]

Cuche, E.

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
[CrossRef]

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27-37 (2002).
[CrossRef] [PubMed]

Dahlgren, P.

Depeursinge, C.

Depeursinge, Ch.

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
[CrossRef]

Hawkes, N. C.

Javidi, B.

Jüptner, W.

Kaneko, T.

Kuldkepp, M.

Loriette, V.

Marquet, P.

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
[CrossRef]

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27-37 (2002).
[CrossRef] [PubMed]

Montfort, F.

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
[CrossRef]

Moreau, J.

Murata, S.

Nitanai, E.

Nomura, T.

Numata, T.

Ohtsuka, Y.

K. Oka and Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44-48 (1993).
[CrossRef]

Oka, K.

K. Oka and T. Kaneko, “Compact complete imaging polarimeter using birefringent wedge prisms,” Opt. Express 11, 1510-1519 (2003).
[CrossRef] [PubMed]

K. Oka and Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44-48 (1993).
[CrossRef]

Rachlew, E.

Schnars, U.

Schunke, B.

Takashi, M.

Terui, Y.

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13, 405-409 (2006).
[CrossRef]

Tong, L.

Voloshin, A.

Yamaguchi, I.

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13, 405-409 (2006).
[CrossRef]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
[CrossRef] [PubMed]

Yokota, M.

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13, 405-409 (2006).
[CrossRef]

Zhang, T.

Appl. Opt. (6)

Exp. Mech. (1)

K. Oka and Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44-48 (1993).
[CrossRef]

Opt. Commun. (1)

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and Ch. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. 231, 137-147(2004).
[CrossRef]

Opt. Eng. (1)

M. Yokota, Y. Terui, and I. Yamaguchi, “Polarization analysis with digital holography by use of polarization modulation for single reference beam,” Opt. Eng. 46, 055801 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Rev. (1)

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13, 405-409 (2006).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Experimental setup: LD, laser diode; OI, optical isolator; FFR, flint glass fiber Faraday rotator; M, mirror; HWP, half-wave plate; BS, beam splitter, L, lenses; Pol, polarizers; CCD, charge coupled device; PC, personal computer.

Fig. 2
Fig. 2

Configuration of the object arm between Pol2 and BS2 in Fig. 1. The object wave consists of two areas: area A is filled with a linear polarization state with an orientation of γ, and area B is used for analysis.

Fig. 3
Fig. 3

Phase variation of the interference fringe at a CCD in the old and new optical systems when a direct modulation current of 1.0 A is applied to the modulation coil of the FFR.

Fig. 4
Fig. 4

Transmission property of the aperture apodization obtained with cubic spline interpolation applied for the filled circles.

Fig. 5
Fig. 5

Reconstructed (a) amplitude and (b) phase of virtual image of the QWP with the orientation of θ = 0 ° for horizontal polarization (h). The area Ais for the reference (Pol3) and area B is for analysis (QWP).

Fig. 6
Fig. 6

Amplitude ratio angle and phase difference of object waves transmitted through the QWP accompanied by their theoretical and simulated values.

Fig. 7
Fig. 7

Amplitude ratio angle and phase difference of object waves transmitted through the HWP accompanied by their theoretical and simulated values.

Fig. 8
Fig. 8

Reconstructed (a) amplitude and (b) phase of simulated hologram of the QWP with the orientation of θ = 0 ° for horizontal polarization (h). The area in the dotted square is for analysis (QWP).

Fig. 9
Fig. 9

Dependence of error on the value of the extinction ratio for the reference wave: (a), (b) QWP; (c), (d) HWP.

Fig. 10
Fig. 10

Dependence of error on the value of modulation error for reference wave: ((a), (b) QWP; (c), (d) HWP.

Tables (3)

Tables Icon

Table 1 Standard Deviation ϵ of the Difference among Theoretical, Experimental, and Simulated values of α and Δ ϕ for a QWP and a HWP

Tables Icon

Table 2 Dependence of Averaged Error (deg)ϵ on Value of Extinction Ratio of Reference Wave

Tables Icon

Table 3 Dependence of Averaged Error (deg)ϵ on Modulation Error for Reference Wave

Equations (15)

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U R h ( x , y ) = [ A R h ( x , y ) exp [ i { ϕ R h ( x , y ) + k x sin θ R h } ] 0 ] ,
U ( x , y ) = [ U h ( x , y ) U v ( x , y ) ] = [ A h ( x , y ) exp { i ϕ h ( x , y ) } A v ( x , y ) exp { i ϕ v ( x , y ) } ] ,
I h ( x , y ) = | U R h | 2 + | U | 2 + U R h * U h + U R h U h * = A 1 ( x , y ) 2 + A h ( x , y ) exp { i ϕ h ( x , y ) } A R h exp { i ( ϕ R h + k x sin θ R h ) } + A h ( x , y ) exp { i ϕ h ( x , y ) } A R h exp { i ( ϕ R h + k x sin θ R h ) } ,
U R v ( x , y ) = [ 0 A R v ( x , y ) exp [ i { ϕ R v ( x , y ) + k x sin θ R h } ] ] ,
I v ( x , y ) = A 2 ( x , y ) 2 + A v ( x , y ) exp { i ϕ v ( x , y ) } A R v exp { i ( ϕ R v + k x sin θ R h ) } + A v ( x , y ) exp { i ϕ v ( x , y ) } A R v exp { i ( ϕ R v + k x sin θ R h ) } ,
U I h ( v ) ( X , Y , Z ) = A exp { i π λ Z ( X 2 + Y 2 ) } · T ( x , y ) · R D ( x , y ) · I h ( v ) ( x , y ) exp { i π λ Z ( x 2 + y 2 ) } exp { i 2 π λ Z ( x X + y Y ) } d x d y ,
U O h ( X , Y , z O ) = [ A R h ( X , Y ) A h ( X , Y ) exp [ i { ϕ h ( X , Y ) ϕ R h ( X , Y ) } ] 0 ] ,
U O v ( X , Y , z O ) = [ 0 A R v ( X , Y ) A v ( X , Y ) exp [ i { ϕ v ( X , Y ) ϕ R v ( X , Y ) } ] ] ,
tan α ( X , Y ) = A v ( X , Y ) A h ( X , Y ) = | U O v ( X , Y ) | | U O h ( X , Y ) |
Δ ϕ ( X , Y ) = ϕ v ( X , Y ) ϕ h ( X , Y ) Δ ϕ R ,
Δ ϕ C ( X , Y ) = Δ ϕ ( X , Y ) + Δ ϕ R = ϕ v ( X , Y ) ϕ h ( X , Y ) .
U T = ( U T h ( x , y ) U T v ( x , y ) ) = ( cos θ sin θ sin θ cos θ ) [ exp ( i Δ ) 0 0 exp ( i Δ ) ] ( cos θ sin θ sin θ cos θ ) ( 1 1 ) ,
U R h = [ U R h x ( x , y ) U R h y ( x , y ) ] = [ 1 i / η ] exp ( i k x sin θ R h ) .
U R v = M ( 90 + Δ θ m ) · U R h = [ U R v x ( x , y ) U R v y ( x , y ) ] = [ cos ( 90 + Δ θ m ) sin ( 90 + Δ θ m ) sin ( 90 + Δ θ m ) cos ( 90 + Δ θ m ) ] ( exp ( i k x sin θ R h ) i / η exp ( i k x sin θ R h ) ) .
I h ( x , y ) = | U R h x ( x , y ) | 2 + | U T h ( x , y ) | 2 + | U T v ( x , y ) | 2 + U R h x * ( x , y ) · U T h ( x , y ) + U R h x ( x , y ) · U T h * ( x , y ) + | U R h y ( x , y ) | 2 + U R h y * ( x , y ) · U T v ( x , y ) + U R h y ( x , y ) · U T v * ( x , y ) ̲

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