Abstract

Conoscopic interferometry is applied for determining the crystal orientation of lithium niobate and other commonly employed substrate wafers for integrated-optic and surface-acoustic-wave devices. The method is particularly applicable for detecting the orientation of the optic axes of the strongly birefringent niobate but is less sensitive for lithium tantalate or quartz. Conoscopic interference is a low-cost and easy-to-use method that is especially suitable for laboratory usage.

© 1999 Optical Society of America

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    [CrossRef]
  40. X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
    [CrossRef]

1999

X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
[CrossRef]

1997

L. Zheng, O. A. Konoplev, D. D. Meyerhofer, “Determination of the optical-axis orientation of a uniaxial crystal by frequency-domain interferometry,” Opt. Lett. 22, 931–933 (1997).
[CrossRef] [PubMed]

M. Mansuripur, “Internal conical refraction,” Opt. Photon. News. 8(6), 43–45 (1997); “External conical refraction,” Opt. Photon. News. 8(8), 50–52 (1997).

L. Normie, “Conoscopy measures with high resolution,” Photon. Spectra 31, 31–32 (1997).

M. J. Guardalben, “Conoscopic alignment methods for birefringent optical elements in fusion lasers,” Opt. Photon. News. 8(8) , 37–39 (1997).

P. Äyräs, A. T. Friberg, M. Kaivola, M. M. Salomaa, “Conoscopic interferometry of wafers for surface-acoustic wave devices,” J. Appl. Phys. 82, 4039–4042 (1997).
[CrossRef]

E. Cojocaru, “Direction cosines and vectorial relations for extraordinary-wave propagation in uniaxial media,” Appl. Opt. 36, 302–306 (1997).
[CrossRef] [PubMed]

1996

X. Zhou, X. Xu, “A simple and convenient system for an optical method for crystal orientation,” Cryst. Res. Technol. 31, K9–K10 (1996).
[CrossRef]

1995

A. M. Yurek, P. G. Suchoski, S. W. Merritt, F. J. Leonberger, “Commercial LiNbO3 integrated optic devices,” Opt. Photon. News 6(6) , 26–30 (1995).
[CrossRef]

L. M. Mugnier, “Conoscopic holography: toward three-dimensional reconstructions of opaque objects,” Appl. Opt. 34, 1363–1371 (1995).
[CrossRef] [PubMed]

1994

J. Hatano, Y. Hanakai, H. Furue, H. Uehara, S. Saito, K. Murashiro, “Phase sequence in smectic liquid crystals having fluorophenyl group in the core,” Jpn. J. Appl. Phys. 33, 5498–5502 (1994).
[CrossRef]

S. T. Yang, R. C. Eckardt, R. L. Byer, “1.9-W cw ring-cavity KTP singly resonant optical parametric oscillator,” Opt. Lett. 19, 475–477 (1994).
[CrossRef] [PubMed]

1993

B. S. Perkalskis, “Demonstration of conoscopic pictures,” Am. J. Phys. 61, 1152 (1993).
[CrossRef]

Z. S. Hegedus, Z. Zelenka, G. Gardner, “Interference patterns generated by a plane-parallel plate,” Appl. Opt. 32, 2285–2288 (1993).
[CrossRef] [PubMed]

A. González-Cano, E. Bernabéu, “Automatic interference method for measuring transparent film thickness,” Appl. Opt. 32, 2292–2294 (1993).
[CrossRef] [PubMed]

J. Shao, J. A. Dobrowolski, “Multilayer interference filters for the far-infrared and submillimeter regions,” Appl. Opt. 32, 2361–2370 (1993).
[CrossRef] [PubMed]

S.-C. A. Lien, “Application of computer simulation to improve the optical performance of liquid crystal displays,” Opt. Eng. 32, 1762–1768 (1993).
[CrossRef]

T. Fujikawa, K. Hiraoka, T. Isozaki, K. Kajikawa, H. Takezoe, A. Fukuda, “Construction of dynamic conoscope observation system using CCD camera and image processor,” Jpn. J. Appl. Phys. 32, 985–988 (1993).
[CrossRef]

I. Mus̆evic̆, B. Z̆eks̆, R. Blinc, Th. Rasing, “Magnetic-field-induced biaxiality in an antiferroelectric liquid crystal,” Phys. Rev. E 47, 1094–1100 (1993).
[CrossRef]

L. M. Mugnier, G. Y. Sirat, D. Charlot, “Conoscopic holography: two-dimensional numerical reconstructions,” Opt. Lett. 18, 66–68 (1993).
[CrossRef] [PubMed]

1992

1990

Q.-T. Liang, “Simple ray tracing formulas for uniaxial optical crystals,” Appl. Opt. 29, 1008–1010 (1990).
[CrossRef] [PubMed]

A. R. MacGregor, “Method for computing homogeneous liquid-crystal conoscopic figures,” J. Opt. Soc. Am. A 7, 337–347 (1990).
[CrossRef]

E. Gorecka, A. D. Chandani, Y. Ouchi, H. Takezoe, A. Fukuda, “Molecular orientational structures in ferroelectric, ferrielectric and antiferroelectric smectic liquid crystal phases as studied by conoscope observation,” Jpn. J. Appl. Phys. 29, 131–137 (1990).
[CrossRef]

1985

1984

K. Ohtsuka, H. Ara, T. Ogawa, “A new, simple arrangement for conoscopic figures,” Jpn. J. Appl. Phys. 23, 1541–1542 (1984).
[CrossRef]

1979

Akir, C.

X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
[CrossRef]

Ara, H.

K. Ohtsuka, H. Ara, T. Ogawa, “A new, simple arrangement for conoscopic figures,” Jpn. J. Appl. Phys. 23, 1541–1542 (1984).
[CrossRef]

Äyräs, P.

P. Äyräs, A. T. Friberg, M. Kaivola, M. M. Salomaa, “Conoscopic interferometry of wafers for surface-acoustic wave devices,” J. Appl. Phys. 82, 4039–4042 (1997).
[CrossRef]

Bajor, A. L.

A. L. Bajor, “Application of imaging conoscope for optical inhomogeneity testing in LiNbO3 crystals and components,” in Laser Interferometry VIII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2860, 350–359 (1996).
[CrossRef]

Ballantine, D. S.

D. S. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Acoustic Wave Sensors. Theory, Design, and Physico-Chemical Applications (Academic, San Diego, Calif., 1997).

Bernabéu, E.

Blinc, R.

I. Mus̆evic̆, B. Z̆eks̆, R. Blinc, Th. Rasing, “Magnetic-field-induced biaxiality in an antiferroelectric liquid crystal,” Phys. Rev. E 47, 1094–1100 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Byer, R. L.

Calemczuk, R.

X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
[CrossRef]

Chandani, A. D.

E. Gorecka, A. D. Chandani, Y. Ouchi, H. Takezoe, A. Fukuda, “Molecular orientational structures in ferroelectric, ferrielectric and antiferroelectric smectic liquid crystal phases as studied by conoscope observation,” Jpn. J. Appl. Phys. 29, 131–137 (1990).
[CrossRef]

Charlot, D.

Chen, X.

X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
[CrossRef]

Cojocaru, E.

Dobrowolski, J. A.

Eckardt, R. C.

Feldman, M.

M. Feldman, J. Hénaff, Surface Acoustic Waves for Signal Processing (Artech, Boston, Mass., 1989).

Friberg, A. T.

P. Äyräs, A. T. Friberg, M. Kaivola, M. M. Salomaa, “Conoscopic interferometry of wafers for surface-acoustic wave devices,” J. Appl. Phys. 82, 4039–4042 (1997).
[CrossRef]

Frye, G. C.

D. S. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Acoustic Wave Sensors. Theory, Design, and Physico-Chemical Applications (Academic, San Diego, Calif., 1997).

Fujikawa, T.

T. Fujikawa, K. Hiraoka, T. Isozaki, K. Kajikawa, H. Takezoe, A. Fukuda, “Construction of dynamic conoscope observation system using CCD camera and image processor,” Jpn. J. Appl. Phys. 32, 985–988 (1993).
[CrossRef]

Fukuda, A.

T. Fujikawa, K. Hiraoka, T. Isozaki, K. Kajikawa, H. Takezoe, A. Fukuda, “Construction of dynamic conoscope observation system using CCD camera and image processor,” Jpn. J. Appl. Phys. 32, 985–988 (1993).
[CrossRef]

E. Gorecka, A. D. Chandani, Y. Ouchi, H. Takezoe, A. Fukuda, “Molecular orientational structures in ferroelectric, ferrielectric and antiferroelectric smectic liquid crystal phases as studied by conoscope observation,” Jpn. J. Appl. Phys. 29, 131–137 (1990).
[CrossRef]

Furue, H.

J. Hatano, Y. Hanakai, H. Furue, H. Uehara, S. Saito, K. Murashiro, “Phase sequence in smectic liquid crystals having fluorophenyl group in the core,” Jpn. J. Appl. Phys. 33, 5498–5502 (1994).
[CrossRef]

Gardner, G.

Gava, D.

D. Gava, F. Prêteux, “3D conoscopic vision,” in Statistical and Stochastic Methods in Image Processing II, F. Prêteux, J. L. Davidson, E. R. Dougherty, eds., Proc. SPIE3167, 196–209 (1997“Conoscopic vision: Principle and applications to quality control,” in Proceedings of the Second International Conference on Quality Control in Artificial Vision (QCAV’97), Le Creusot, France, May 1997, pp. 86–91 (1997).
[CrossRef]

Gibb, M. R. P.

M. R. P. Gibb, Optical Methods of Chemical Analysis (McGraw-Hill, New York, 1942).

González-Cano, A.

Gorecka, E.

E. Gorecka, A. D. Chandani, Y. Ouchi, H. Takezoe, A. Fukuda, “Molecular orientational structures in ferroelectric, ferrielectric and antiferroelectric smectic liquid crystal phases as studied by conoscope observation,” Jpn. J. Appl. Phys. 29, 131–137 (1990).
[CrossRef]

Guardalben, M. J.

M. J. Guardalben, “Conoscopic alignment methods for birefringent optical elements in fusion lasers,” Opt. Photon. News. 8(8) , 37–39 (1997).

Hanakai, Y.

J. Hatano, Y. Hanakai, H. Furue, H. Uehara, S. Saito, K. Murashiro, “Phase sequence in smectic liquid crystals having fluorophenyl group in the core,” Jpn. J. Appl. Phys. 33, 5498–5502 (1994).
[CrossRef]

Hartmann, C. S.

S. Jen, C. S. Hartmann, “Conoscope: an apparatus for determining the crystal orientation of SAW wafers,” in 1994 IEEE Ultrasonics Symposium, M. Levy, S. C. Schneider, B. R. McAvoy, eds. (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 397–401.

Hatano, J.

J. Hatano, Y. Hanakai, H. Furue, H. Uehara, S. Saito, K. Murashiro, “Phase sequence in smectic liquid crystals having fluorophenyl group in the core,” Jpn. J. Appl. Phys. 33, 5498–5502 (1994).
[CrossRef]

Hegedus, Z. S.

Hénaff, J.

M. Feldman, J. Hénaff, Surface Acoustic Waves for Signal Processing (Artech, Boston, Mass., 1989).

Hiraoka, K.

T. Fujikawa, K. Hiraoka, T. Isozaki, K. Kajikawa, H. Takezoe, A. Fukuda, “Construction of dynamic conoscope observation system using CCD camera and image processor,” Jpn. J. Appl. Phys. 32, 985–988 (1993).
[CrossRef]

Isozaki, T.

T. Fujikawa, K. Hiraoka, T. Isozaki, K. Kajikawa, H. Takezoe, A. Fukuda, “Construction of dynamic conoscope observation system using CCD camera and image processor,” Jpn. J. Appl. Phys. 32, 985–988 (1993).
[CrossRef]

Jen, S.

S. Jen, C. S. Hartmann, “Conoscope: an apparatus for determining the crystal orientation of SAW wafers,” in 1994 IEEE Ultrasonics Symposium, M. Levy, S. C. Schneider, B. R. McAvoy, eds. (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 397–401.

Kaivola, M.

P. Äyräs, A. T. Friberg, M. Kaivola, M. M. Salomaa, “Conoscopic interferometry of wafers for surface-acoustic wave devices,” J. Appl. Phys. 82, 4039–4042 (1997).
[CrossRef]

Kajikawa, K.

T. Fujikawa, K. Hiraoka, T. Isozaki, K. Kajikawa, H. Takezoe, A. Fukuda, “Construction of dynamic conoscope observation system using CCD camera and image processor,” Jpn. J. Appl. Phys. 32, 985–988 (1993).
[CrossRef]

Konoplev, O. A.

Lavorel, B.

X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
[CrossRef]

Leonberger, F. J.

A. M. Yurek, P. G. Suchoski, S. W. Merritt, F. J. Leonberger, “Commercial LiNbO3 integrated optic devices,” Opt. Photon. News 6(6) , 26–30 (1995).
[CrossRef]

Liang, Q.-T.

Lien, S.-C. A.

S.-C. A. Lien, “Application of computer simulation to improve the optical performance of liquid crystal displays,” Opt. Eng. 32, 1762–1768 (1993).
[CrossRef]

MacGregor, A. R.

Mansuripur, M.

M. Mansuripur, “Internal conical refraction,” Opt. Photon. News. 8(6), 43–45 (1997); “External conical refraction,” Opt. Photon. News. 8(8), 50–52 (1997).

Martin, S. J.

D. S. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Acoustic Wave Sensors. Theory, Design, and Physico-Chemical Applications (Academic, San Diego, Calif., 1997).

Mavrudis, T.

Mentel, J.

Merritt, S. W.

A. M. Yurek, P. G. Suchoski, S. W. Merritt, F. J. Leonberger, “Commercial LiNbO3 integrated optic devices,” Opt. Photon. News 6(6) , 26–30 (1995).
[CrossRef]

Meyerhofer, D. D.

Morgan, D. P.

D. P. Morgan, Surface-Wave Devices for Signal Processing (Elsevier, Amsterdam, The Netherlands, 1991).

Mugnier, L. M.

Murashiro, K.

J. Hatano, Y. Hanakai, H. Furue, H. Uehara, S. Saito, K. Murashiro, “Phase sequence in smectic liquid crystals having fluorophenyl group in the core,” Jpn. J. Appl. Phys. 33, 5498–5502 (1994).
[CrossRef]

Mus?evic?, I.

I. Mus̆evic̆, B. Z̆eks̆, R. Blinc, Th. Rasing, “Magnetic-field-induced biaxiality in an antiferroelectric liquid crystal,” Phys. Rev. E 47, 1094–1100 (1993).
[CrossRef]

Normie, L.

L. Normie, “Conoscopy measures with high resolution,” Photon. Spectra 31, 31–32 (1997).

Ogawa, T.

K. Ohtsuka, H. Ara, T. Ogawa, “A new, simple arrangement for conoscopic figures,” Jpn. J. Appl. Phys. 23, 1541–1542 (1984).
[CrossRef]

Ohtsuka, K.

K. Ohtsuka, H. Ara, T. Ogawa, “A new, simple arrangement for conoscopic figures,” Jpn. J. Appl. Phys. 23, 1541–1542 (1984).
[CrossRef]

Ouchi, Y.

E. Gorecka, A. D. Chandani, Y. Ouchi, H. Takezoe, A. Fukuda, “Molecular orientational structures in ferroelectric, ferrielectric and antiferroelectric smectic liquid crystal phases as studied by conoscope observation,” Jpn. J. Appl. Phys. 29, 131–137 (1990).
[CrossRef]

Perkalskis, B. S.

B. S. Perkalskis, “Demonstration of conoscopic pictures,” Am. J. Phys. 61, 1152 (1993).
[CrossRef]

Prêteux, F.

D. Gava, F. Prêteux, “3D conoscopic vision,” in Statistical and Stochastic Methods in Image Processing II, F. Prêteux, J. L. Davidson, E. R. Dougherty, eds., Proc. SPIE3167, 196–209 (1997“Conoscopic vision: Principle and applications to quality control,” in Proceedings of the Second International Conference on Quality Control in Artificial Vision (QCAV’97), Le Creusot, France, May 1997, pp. 86–91 (1997).
[CrossRef]

Psaltis, D.

Rajaonah, L.

X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
[CrossRef]

Rasing, Th.

I. Mus̆evic̆, B. Z̆eks̆, R. Blinc, Th. Rasing, “Magnetic-field-induced biaxiality in an antiferroelectric liquid crystal,” Phys. Rev. E 47, 1094–1100 (1993).
[CrossRef]

Ricco, A. J.

D. S. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Acoustic Wave Sensors. Theory, Design, and Physico-Chemical Applications (Academic, San Diego, Calif., 1997).

Saito, S.

J. Hatano, Y. Hanakai, H. Furue, H. Uehara, S. Saito, K. Murashiro, “Phase sequence in smectic liquid crystals having fluorophenyl group in the core,” Jpn. J. Appl. Phys. 33, 5498–5502 (1994).
[CrossRef]

Salce, B.

X. Chen, R. Calemczuk, B. Salce, B. Lavorel, C. Akir, L. Rajaonah, “Long-transient conoscopic pattern technique,” Solid State Commun. 110, 431–434 (1999).
[CrossRef]

Salomaa, M. M.

P. Äyräs, A. T. Friberg, M. Kaivola, M. M. Salomaa, “Conoscopic interferometry of wafers for surface-acoustic wave devices,” J. Appl. Phys. 82, 4039–4042 (1997).
[CrossRef]

Schmidt, E.

Shao, J.

Sirat, G.

Sirat, G. Y.

Skomorovsky, V. I.

V. I. Skomorovsky, “Advance of the design and technology of birefringent filters,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 413–421 (1994).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, Optics: Lectures on Theoretical Physics (Academic, New York, 1953), Vol. 4.

Suchoski, P. G.

A. M. Yurek, P. G. Suchoski, S. W. Merritt, F. J. Leonberger, “Commercial LiNbO3 integrated optic devices,” Opt. Photon. News 6(6) , 26–30 (1995).
[CrossRef]

Takezoe, H.

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Figures (12)

Fig. 1
Fig. 1

Notation used for biaxial crystals: The optical axes lie in the xz plane symmetrically with respect to the z axis. The vector ŝ denotes an arbitrary ray-propagation direction.

Fig. 2
Fig. 2

Definitions of the angles of refraction θ′ and θ″ for a birefringent crystal with parallel-plate geometry. The angle θ is the average: θ = (θ′ + θ″)/2.

Fig. 3
Fig. 3

Structure of a conoscope: The polarizer and the analyzer usually are placed perpendicular to each other. The screen may be replaced with a photographic plate or a CCD camera. The shape and the density of the interference fringes on the screen depend on the direction of the optical axes and the optical properties of the sample.

Fig. 4
Fig. 4

Measured interferogram for a Z-cut LiNbO3 wafer with the calculated circular cross sections of the Bertin surfaces (isochromates) for destructive interference superimposed. The dark brushes (or isogyres) are due to the crossed polarizers.

Fig. 5
Fig. 5

Measured interferogram for a Y-cut LiNbO3 wafer together with the calculated cross sections of the Bertin surfaces. These curves form hyperbolae. The optical axis is oriented from bottom to top in the figure.

Fig. 6
Fig. 6

Interference fringes from a 64°-rotated Y-cut LiNbO3 wafer together with the calculated destructive-interference lines.

Fig. 7
Fig. 7

(a) Measured (interference maxima) and (b) calculated minima (destructive interference) of a conoscopic interferogram for a 128°-rotated Y-cut LiNbO3 wafer.

Fig. 8
Fig. 8

Measured conoscopic interferograms together with the calculated interferograms for different SiO2 wafers. The cut angles are (a) 33°, (b) 35°, (c) 38°, (d) 42.75°.

Fig. 9
Fig. 9

Calculated interferograms for a 33°-cut (solid curves) and a 35°-cut (dashed–dotted curves) SiO2 wafer.

Fig. 10
Fig. 10

Measured interferogram for a 36°-cut LiTaO3 wafer superimposed on the calculated fringes for destructive interference.

Fig. 11
Fig. 11

Bertin surfaces of constant phase difference between the ordinary and the extraordinary waves for an optically biaxial crystal that forms a quartic surface.

Fig. 12
Fig. 12

Calculated interferogram (cross sections of the Bertin surfaces such as are shown in Fig. 11) for an optically biaxial KTP crystal. The thickness of the wafer is taken to be 0.5 mm, and the values used for the refractive indices are n x = 1.7636, n y = 1.7733, and n z = 1.8634. For our choice of the coordinate axes the optical axis is in the xz plane. The angle between the optical axis and the crystal axis depends on the values of the refractive indices. The crystal is cut in the xy plane, perpendicular to the z axis.

Tables (1)

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Table 1 Refractive Indices Used in Conoscopic Interference-Fringe Modeling

Equations (8)

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sx21vr2-1vx2-1+sy21vr2-1vy2-1+sz21vr2-1vz2-1=0
vr2=vo2,
vr-2=vo-2 cos2 ψ+ve-2 sin2 ψ,
1vr2=121vx2+1vz2+1vx2-1vz2cosψ1±ψ2,
tan β=±vzvxvx2-vy2vy2-vz21/2,
δ=2πhλn cos θ-n cos θ,
sin θ0=n sin θ=n sin θ,
I=I0 sin2δ2,

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