Abstract

This paper describes a method to determine the phase retardation of birefringent optical components by combining spectral interferometry and the Fourier transform method. The retardation of each orthogonal polarization component was resolved by using two rotatable linear polarizers in the interferometer. The phase retardation measured by using suggested method was compared to that measured using the conventional polarimetric method. The results of independent methods were well matched, which confirms the validity of the proposed method.

© 2013 Optical Society of America

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References

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2013 (1)

P. Zhang, Y. Tan, W. Liu, and W. Chen, “Methods for optical phase retardation measurement: a review,” Sci. China Tech. Sci. 56, 1155–1163 (2013).
[CrossRef]

2012 (1)

2008 (1)

2004 (3)

2000 (1)

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

1999 (1)

1998 (2)

H. Delbarre, C. Przygodzki, and D. Boucher, “Determination of dispersion characteristics in anisotropic materials using ultrashort pulses,” Appl. Phys. B 66, 169–173 (1998).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “A temporal method for dispersion measurements with ultrashort pulses in the visible and near-infrared region,” Int. J. Infrared Milli. 19, 441 (1998).

1996 (1)

1995 (3)

1993 (2)

1990 (2)

Boucher, D.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “Determination of dispersion characteristics in anisotropic materials using ultrashort pulses,” Appl. Phys. B 66, 169–173 (1998).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “A temporal method for dispersion measurements with ultrashort pulses in the visible and near-infrared region,” Int. J. Infrared Milli. 19, 441 (1998).

Brabec, T.

Chen, W.

P. Zhang, Y. Tan, W. Liu, and W. Chen, “Methods for optical phase retardation measurement: a review,” Sci. China Tech. Sci. 56, 1155–1163 (2013).
[CrossRef]

Chériaux, G.

Curley, P. F.

Dantus, M.

DeFreitas, J. M.

J. M. DeFreitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt. 42, 1875–1899 (1995).
[CrossRef]

Delbarre, H.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “Determination of dispersion characteristics in anisotropic materials using ultrashort pulses,” Appl. Phys. B 66, 169–173 (1998).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “A temporal method for dispersion measurements with ultrashort pulses in the visible and near-infrared region,” Int. J. Infrared Milli. 19, 441 (1998).

Diddams, S.

Diels, J.-C.

Hammer, D. X.

Hong, K.-H.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, “Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry,” Rev. Sci. Instrum. 75, 2266–2270 (2004).
[CrossRef]

Hybl, O.

Imran, T.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, “Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry,” Rev. Sci. Instrum. 75, 2266–2270 (2004).
[CrossRef]

Joffre, M.

Khos-Ochir, T.

Kim, H. W.

Kim, J. S.

Krausz, F.

Lepetit, L.

Liu, W.

P. Zhang, Y. Tan, W. Liu, and W. Chen, “Methods for optical phase retardation measurement: a review,” Sci. China Tech. Sci. 56, 1155–1163 (2013).
[CrossRef]

Lozovoy, V. V.

Lu, K.

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Mogi, K.

Munkhbaatar, P.

Myung-Whun, K.

Naganuma, K.

Nam, C. H.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, “Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry,” Rev. Sci. Instrum. 75, 2266–2270 (2004).
[CrossRef]

Narayana Rao, D.

Nirmal Kumar, V.

Noojin, G. D.

Ohkubo, K.

K. Ohkubo and J. Ohtsubo, “Evaluation of LCTV as a spatial light modulator,” Opt. Commun. 102, 116–124 (1993).
[CrossRef]

Ohtsubo, J.

K. Ohkubo and J. Ohtsubo, “Evaluation of LCTV as a spatial light modulator,” Opt. Commun. 102, 116–124 (1993).
[CrossRef]

Pastirk, I.

Pavlícek, P.

Player, M. A.

J. M. DeFreitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt. 42, 1875–1899 (1995).
[CrossRef]

Przygodzki, C.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “Determination of dispersion characteristics in anisotropic materials using ultrashort pulses,” Appl. Phys. B 66, 169–173 (1998).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “A temporal method for dispersion measurements with ultrashort pulses in the visible and near-infrared region,” Int. J. Infrared Milli. 19, 441 (1998).

Rockwell, B. A.

Saleh, B. E. A.

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Schmidt, A. J.

Soubusta, J.

Spielmann, Ch.

Stolarski, D. J.

Tan, Y.

P. Zhang, Y. Tan, W. Liu, and W. Chen, “Methods for optical phase retardation measurement: a review,” Sci. China Tech. Sci. 56, 1155–1163 (2013).
[CrossRef]

Tassou, M.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Thomas, R. J.

Welch, A. J.

Wintner, E.

Yamada, H.

Yang, B. K.

Yu, T. J.

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, “Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry,” Rev. Sci. Instrum. 75, 2266–2270 (2004).
[CrossRef]

Zhang, P.

P. Zhang, Y. Tan, W. Liu, and W. Chen, “Methods for optical phase retardation measurement: a review,” Sci. China Tech. Sci. 56, 1155–1163 (2013).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (2)

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

H. Delbarre, C. Przygodzki, and D. Boucher, “Determination of dispersion characteristics in anisotropic materials using ultrashort pulses,” Appl. Phys. B 66, 169–173 (1998).
[CrossRef]

Int. J. Infrared Milli. (1)

H. Delbarre, C. Przygodzki, and D. Boucher, “A temporal method for dispersion measurements with ultrashort pulses in the visible and near-infrared region,” Int. J. Infrared Milli. 19, 441 (1998).

J. Mod. Opt. (1)

J. M. DeFreitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt. 42, 1875–1899 (1995).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

J. Opt. Soc. Korea (1)

Opt. Commun. (1)

K. Ohkubo and J. Ohtsubo, “Evaluation of LCTV as a spatial light modulator,” Opt. Commun. 102, 116–124 (1993).
[CrossRef]

Opt. Eng. (1)

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

T. Imran, K.-H. Hong, T. J. Yu, and C. H. Nam, “Measurement of the group-delay dispersion of femtosecond optics using white-light interferometry,” Rev. Sci. Instrum. 75, 2266–2270 (2004).
[CrossRef]

Sci. China Tech. Sci. (1)

P. Zhang, Y. Tan, W. Liu, and W. Chen, “Methods for optical phase retardation measurement: a review,” Sci. China Tech. Sci. 56, 1155–1163 (2013).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Experimental setup for polarimetry. (b) Experimental setup for spectral interferometry: HL, halogen lamp; C, multimode optical fiber cable; L, collimating lense; P, polarizer; QWP, quarter waveplate; A, analyzer; SM, spectrometer; BS, beam splitters; S, sample; M, mirror; MM, movable mirror.

Fig. 2.
Fig. 2.

Spectral interferogram of a BK7 glass plate (thin solid line) showed sharp interference. The spectral intensity of reference beam (thick solid line) and signal beam (dashed line) are presented.

Fig. 3.
Fig. 3.

(a) Solid circles are the interferometrically measured higher-order phase change due to a BK7 glass plate. The overlaid solid line is fitted by using Eq. (2). The solid squares and solid triangles are the higher-order phase change due to an achromatic QWP and TN-SLM, respectively. The solid line is the fitting function. (b) The difference between higher-order phase changes of two orthogonal polarizations for the QWP (solid circles) and the polynomial fitting curve (dashed line). The same data for a TN SLM (open circles) and the polynomial fitting curve (dotted–dashed line). The polarization directions were 45° and 45° against the horizontal direction (see text).

Fig. 4.
Fig. 4.

Phase retardation due to an achromatic QWP interferometrically measured while rotating the sample (dashed line) and rotating the analyzer (solid line). While rotating the analyzer, the transmission axis of the polarizer (P) was fixed at 0° and the fast axis of the QWP at 45° against the horizontal direction. The analyzer was aligned to 45° and 45° against the horizontal direction. The polarimetric data (dotted–dashed line) confirms the validity of the interferometric methods.

Fig. 5.
Fig. 5.

Phase retardation due to SLM for numerous gray levels measured by using the interferometric method when the analyzer was aligned to 45° and 45° against the horizontal direction. The inset shows the gray level dependence of the phase retardation at 800 nm marked by the vertical dotted line.

Fig. 6.
Fig. 6.

Phase retardation of an achromatic QWP interferometrically measured with various beam splitters while rotating the analyzer. The dotted–dashed line is polarimetric data for comparison. The solid circles, the solid squares, and the solid triangles represent the data measured with the pellicle, the cube, and the plate beam splitter, respectively.

Equations (13)

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Δφ(ω)=ω·d·[n(ω)1]c.
Δφ(ω)=Δφ0+Δφ1(ωω0)+12Δφ2(ωω0)2+
E(ω)=S(ω)·exp[iφ(ω)].
S(ω)=Re{2f(ω)exp(iωτ)},
F1S(ω)=f(tτ)+f(tτ).
Δϕ(ω)=Arg[E(ω)].
E⃗sig=eiφx(ExEyei(φxφy)).
E⃗ref=ELeiφL(11).
E⃗=JA(E⃗sig+E⃗ref)=(cos2(θ45°)sin(θ45°)cos(θ45°)sin(θ45°)cos(θ45°)sin2(θ45°))·(Exeiφx+ELeiφLEyeiφy+ELeiφL).
Sxtot=|Ex|2+|EL|2+2|Ex||EL|cos(φxφL),
Sytot=|Ey|2+|EL|2+2|Ey||EL|cos(φyφL),
Eout=JA·Jλ4·JP·Ein=(1000)·eiΔϕx·(cos2θ+ei(ΔϕxΔϕy)sin2θ(1ei(ΔϕxΔϕy))·cosθ·sinθ(1ei(ΔϕxΔϕy))·cosθ·sinθsin2θ+ei(ΔϕxΔϕy)cos2θ)·(1000)·Ein.
T(θ,λ)=|Eout|2|Ein|2=14{3+cos4θ+(1cos4θ)cos[Δϕ(λ)]}.

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