Abstract

We describe an instrument for measuring the magnitude of birefringence of tomographic images and the principal directions of axes that uses thermal-light polarization-sensitive optical coherence tomography. The instrument permits full-field measurements with an axial resolution of 1.5 μm and a transverse resolution limited by diffraction. We obtained a sensitivity of 84 dB, limited by shot noise, when we integrated the signal for 1 s. We verified the validity of the measurement by measuring the birefringence of a variable phase shifter. We present typical results obtained with optical samples.

© 2003 Optical Society of America

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    [CrossRef]
  15. J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
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2003

2002

2001

2000

1999

1998

1997

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]

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

1995

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Beaurepaire, E.

Blanchot, L.

Boccara, A. C.

Boccara, A.-C.

Bondu, F.

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

Braccini, S.

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

Brisson, V.

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

Chen, Z.

Colston, B. W.

Da Silva, L. B.

de Boer, J. F.

de Groot, P.

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Deck, L.

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Dognin, L.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Dubois, A.

Everett, M. J.

Fercher, A. F.

Ferrante, I.

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

Ganau, P.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Götzinger, E.

Hitzenberger, C. K.

Izatt, J. A.

Kozak, J. A.

Lagrange, B.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Lebec, M.

Loriette, V.

Mackowski, J. M.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Maitland, D. J.

Malekafzali, A.

Michel, C.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Milner, T. E.

Milnerand, T. E.

Moreau, J.

Morgue, M.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

Nelson, J. S.

Park, B. H.

Pinard, L.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

Pircher, M.

Rollins, A. M.

Roth, J. E.

Saint-Jalmes, H.

Saxer, C. E.

Schoenenberger, K.

Srinivas, S. M.

Sticker, M.

Tournié, E.

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

Vabre, L.

van Gemert, M. J. C.

Vinet, J.-Y.

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

Wang, L. V.

Yao, G.

Yazdanfar, S.

Zhao, Y.

Appl. Opt.

Appl. Surf. Sci.

J. M. Mackowski, L. Pinard, L. Dognin, P. Ganau, B. Lagrange, C. Michel, M. Morgue, “Different approaches to improve the wavefront of low-loss mirrors used in the VIRGO gravitational wave antenna,” Appl. Surf. Sci. 151, 86–90 (1999).
[CrossRef]

J. Mod. Opt.

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Rev. D

J.-Y. Vinet, V. Brisson, S. Braccini, I. Ferrante, L. Pinard, F. Bondu, E. Tournié, “Scattered light noise in gravitational wave interferometric detectors: a statistical approach,” Phys. Rev. D 56, 6085–6095 (1997).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Schematic of the instrument described in this paper: NPBS, nonpolarizing beam-splitter cube; AQWPs, achromatic quarter-wave plates; PZT, piezoactuated translation stage.

Fig. 2
Fig. 2

Procedure used to fix the value of δ0: interferograms with (a) δ0 = 0.85 × δ0opt, (b) δ0 = δ0opt, and (c) δ0 = 1.15 × δ0opt.

Fig. 3
Fig. 3

Relation of estimated to true retardation of a Babinet compensator: squares, uncorrected data; crosses, data corrected for quarter-wave plate error following to Eq. (15).

Fig. 4
Fig. 4

Schematic of the multilayer optical coating mirror used as a sample.

Fig. 5
Fig. 5

Classic OCT tomography cut of the multilayer. Six interfaces can be distinguished.

Fig. 6
Fig. 6

En face birefringence image of the multilayer second interface on which a defect is visible: XY cut, 0.7 μm × 0.7 μm resolution. The noise in this image is estimated to be 2.9 × 10-4 rad.

Fig. 7
Fig. 7

Direction of the birefringence axes in the region about the defect on the multilayer second interface; XY cut. The contour lines indicate the locations of the birefringent structures.

Fig. 8
Fig. 8

High-resolution (0.7 μm × 1.5 μm, lateral × axial) birefringence image of the multilayer; XZ cut; same noise level as in Fig. 6. Dashed lines, positions of the six interfaces.

Fig. 9
Fig. 9

YZ cut.

Fig. 10
Fig. 10

Measured axial response of the system and best Gaussian envelope. The FWHM is 1.5 μm.

Fig. 11
Fig. 11

Spectrum of the light source used in the experiment as a function of wavelength.

Fig. 12
Fig. 12

Image SNR as a function of the number of images averaged. Circles, measurements; solid line, shot-noise limit; dashed curve, estimate of the SNR if an f -1 noise source is present; horizontal dashed-dotted line, SNR limit imposed by the f -1 noise.

Fig. 13
Fig. 13

Value of g as a function of birefringence magnitude φ and orientation of the quarter-wave in reference arm θ.

Fig. 14
Fig. 14

Value of g as a function of birefringence magnitude for θ = 11.26°.

Equations (15)

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ΣBS=-S1S+S2S+S3S-S4S,
ΣAS=-S1S+S2S-S3S+S4S,
ΣBP=-S1P+S2P+S3P-S4P,
ΣAP=-S1P+S2P-S3P+S4P;
tan2π δBλ0=tan-22θΘBΣAP2+ΘAΣBP2ΘBΣAS2+ΘAΣBS2,
tan2π δzλ0=ΘBΣASΘAΣBS
tan2β=ΘAΘBΣASΣBP-ΣAPΣBSΘA2ΣBSΣBP+ΘB2ΣASΣAP,
maxφ=2π Δzλ0.
SNRφ=SNRS×gφ, θ,
MQ=expiπ4+δQ00exp-iπ4+δQ.
tan2φapp2=sin2φ/2+hφ, β, δQcos2φ/2-hφ, β, δQ,
hφ, β, δQ=cos2φ/2-sin22βsin2φ/2sin22δQ-sinφsin2βcos4δQ.
tan2φapp2=sin22δQ1-sin22δQ4δQ21-4δQ2.
signsinφsin2β=signΣAPΣBS-ΣASΣBP,0θπ/4.
tan2φ2cos2φapp/2-hφapp, βapp, δQsin2φapp/2+hφapp, βapp, δQ.

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