Abstract

A highly sensitive and automated technique has been developed for measuring the birefringence in transparent optical materials. The spatially scanning modulated transmission ellipsometer maps the birefringence of a transparent material by probing it with a polarization-modulated He–Ne laser beam. Computer-controlled voltage biasing of a Pockels cell permits self-calibration and background subtraction of the system retardance. The technique is capable of resolving differential retardances as small as 0.1 nm (λ/6328) through a range of ±λ/2, where λ = 632.8 nm. Samples typically range in size from 50 μm to 10 cm in diameter within the sample plane and as much as 400 mm along the optical axis.

© 1993 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1990 (4)

1989 (1)

J. Greener, R. Kesel, B. A. Contestable, “The birefringence problem in optical disk substrates: a modeling approach,” AIChE J. 35, 449–458 (1989).
[CrossRef]

1988 (4)

1986 (1)

R. S. Craxton, R. L. McCrory, J. M. Soures, “Progress in laser fusion.” Sci. Am. 255, 68–79 (1986).
[CrossRef]

1984 (1)

Y. Shindo, R. Takigaura, “An improved highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 25, 378–380 (1984).

1983 (1)

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

1973 (1)

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472 (1973).
[CrossRef]

1961 (1)

1948 (1)

Braunstein, M.

M. E. Pedinoff, M. Braunstein, O. M. Stafsudd, “Modulated light ellipsometry at 10.6 μm,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam, D. L. Coffeen, eds., Proc. Soc. Photo-Opt. Instrum. Eng.112, 74–81 (1977).

Bruhat, G.

G. Bruhat, Optique (Cours de Physique Générale), 5th ed., (Masson, Paris, 1959).

Cerqua, K. A.

K. A. Cerqua, J. E. Hayden, W. C. LaCourse, “Stress measurements in solgel films,” J. Non-Cryst. Solids 100, 471–478(1988).
[CrossRef]

Chang, K.

Chou, C.

Contestable, B. A.

J. Greener, R. Kesel, B. A. Contestable, “The birefringence problem in optical disk substrates: a modeling approach,” AIChE J. 35, 449–458 (1989).
[CrossRef]

Craxton, R. S.

R. S. Craxton, R. L. McCrory, J. M. Soures, “Progress in laser fusion.” Sci. Am. 255, 68–79 (1986).
[CrossRef]

Dill, F. H.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472 (1973).
[CrossRef]

Greener, J.

J. Greener, R. Kesel, B. A. Contestable, “The birefringence problem in optical disk substrates: a modeling approach,” AIChE J. 35, 449–458 (1989).
[CrossRef]

Hanabusa, H.

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

Harris, G. L.

K. H. Jackson, P. Z. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “Measurement of stress in semiconductor materials using the photoelastic effect,” in Conference on Lasers and Electro-Optics, Vol. 7 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 266.

K. H. Jackson, P. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “The measurement of stress in silicon carbide using the photoelastic effect,” in Proceedings of the First International Conference on Amorphous and Crystalline Silicon Carbide and Related Materials, G. L. Harris, C. Y.-W. Yang, eds. (Springer-Verlag, Berlin, 1989), Vol. 34, pp. 129–132.
[CrossRef]

Hauge, P. S.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472 (1973).
[CrossRef]

Hayden, J. E.

K. A. Cerqua, J. E. Hayden, W. C. LaCourse, “Stress measurements in solgel films,” J. Non-Cryst. Solids 100, 471–478(1988).
[CrossRef]

S. D. Jacobs, J. E. Hayden, A. L. Hrycin, “Practical measurements of adhesion and strain for improved optical coatings,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.678, 66–78 (1986).

Hrycin, A. L.

S. D. Jacobs, J. E. Hayden, A. L. Hrycin, “Practical measurements of adhesion and strain for improved optical coatings,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.678, 66–78 (1986).

Jackson, K. H.

K. H. Jackson, P. Z. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “Measurement of stress in semiconductor materials using the photoelastic effect,” in Conference on Lasers and Electro-Optics, Vol. 7 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 266.

K. H. Jackson, P. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “The measurement of stress in silicon carbide using the photoelastic effect,” in Proceedings of the First International Conference on Amorphous and Crystalline Silicon Carbide and Related Materials, G. L. Harris, C. Y.-W. Yang, eds. (Springer-Verlag, Berlin, 1989), Vol. 34, pp. 129–132.
[CrossRef]

Jacobs, S. D.

S. D. Jacobs, J. E. Hayden, A. L. Hrycin, “Practical measurements of adhesion and strain for improved optical coatings,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.678, 66–78 (1986).

Jellison, G. E.

Jerrard, H. G.

Jones, E.

K. H. Jackson, P. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “The measurement of stress in silicon carbide using the photoelastic effect,” in Proceedings of the First International Conference on Amorphous and Crystalline Silicon Carbide and Related Materials, G. L. Harris, C. Y.-W. Yang, eds. (Springer-Verlag, Berlin, 1989), Vol. 34, pp. 129–132.
[CrossRef]

K. H. Jackson, P. Z. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “Measurement of stress in semiconductor materials using the photoelastic effect,” in Conference on Lasers and Electro-Optics, Vol. 7 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 266.

Kesel, R.

J. Greener, R. Kesel, B. A. Contestable, “The birefringence problem in optical disk substrates: a modeling approach,” AIChE J. 35, 449–458 (1989).
[CrossRef]

LaCourse, W. C.

K. A. Cerqua, J. E. Hayden, W. C. LaCourse, “Stress measurements in solgel films,” J. Non-Cryst. Solids 100, 471–478(1988).
[CrossRef]

Lin, C.

Major, F. G.

McCrory, R. L.

R. S. Craxton, R. L. McCrory, J. M. Soures, “Progress in laser fusion.” Sci. Am. 255, 68–79 (1986).
[CrossRef]

Modine, F. A.

Nakadate, S.

Pedinoff, M. E.

M. E. Pedinoff, M. Braunstein, O. M. Stafsudd, “Modulated light ellipsometry at 10.6 μm,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam, D. L. Coffeen, eds., Proc. Soc. Photo-Opt. Instrum. Eng.112, 74–81 (1977).

Runwen, W.

Shindo, Y.

Y. Shindo, R. Takigaura, “An improved highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 25, 378–380 (1984).

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

Soures, J. M.

R. S. Craxton, R. L. McCrory, J. M. Soures, “Progress in laser fusion.” Sci. Am. 255, 68–79 (1986).
[CrossRef]

Spencer, M. G.

K. H. Jackson, P. Z. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “Measurement of stress in semiconductor materials using the photoelastic effect,” in Conference on Lasers and Electro-Optics, Vol. 7 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 266.

K. H. Jackson, P. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “The measurement of stress in silicon carbide using the photoelastic effect,” in Proceedings of the First International Conference on Amorphous and Crystalline Silicon Carbide and Related Materials, G. L. Harris, C. Y.-W. Yang, eds. (Springer-Verlag, Berlin, 1989), Vol. 34, pp. 129–132.
[CrossRef]

Stafsudd, O. M.

M. E. Pedinoff, M. Braunstein, O. M. Stafsudd, “Modulated light ellipsometry at 10.6 μm,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam, D. L. Coffeen, eds., Proc. Soc. Photo-Opt. Instrum. Eng.112, 74–81 (1977).

Takasaki, H.

Takigaura, R.

Y. Shindo, R. Takigaura, “An improved highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 25, 378–380 (1984).

Yao, L.

Zhiyao, Z.

Zhou, P.

K. H. Jackson, P. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “The measurement of stress in silicon carbide using the photoelastic effect,” in Proceedings of the First International Conference on Amorphous and Crystalline Silicon Carbide and Related Materials, G. L. Harris, C. Y.-W. Yang, eds. (Springer-Verlag, Berlin, 1989), Vol. 34, pp. 129–132.
[CrossRef]

Zhou, P. Z.

K. H. Jackson, P. Z. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “Measurement of stress in semiconductor materials using the photoelastic effect,” in Conference on Lasers and Electro-Optics, Vol. 7 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 266.

AIChE J. (1)

J. Greener, R. Kesel, B. A. Contestable, “The birefringence problem in optical disk substrates: a modeling approach,” AIChE J. 35, 449–458 (1989).
[CrossRef]

Appl. Opt. (4)

IBM J. Res. Dev. (1)

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472 (1973).
[CrossRef]

J. Non-Cryst. Solids (1)

K. A. Cerqua, J. E. Hayden, W. C. LaCourse, “Stress measurements in solgel films,” J. Non-Cryst. Solids 100, 471–478(1988).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Polym. Commun. (2)

Y. Shindo, H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240–244 (1983).

Y. Shindo, R. Takigaura, “An improved highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 25, 378–380 (1984).

Sci. Am. (1)

R. S. Craxton, R. L. McCrory, J. M. Soures, “Progress in laser fusion.” Sci. Am. 255, 68–79 (1986).
[CrossRef]

Other (5)

K. H. Jackson, P. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “The measurement of stress in silicon carbide using the photoelastic effect,” in Proceedings of the First International Conference on Amorphous and Crystalline Silicon Carbide and Related Materials, G. L. Harris, C. Y.-W. Yang, eds. (Springer-Verlag, Berlin, 1989), Vol. 34, pp. 129–132.
[CrossRef]

K. H. Jackson, P. Z. Zhou, E. Jones, G. L. Harris, M. G. Spencer, “Measurement of stress in semiconductor materials using the photoelastic effect,” in Conference on Lasers and Electro-Optics, Vol. 7 of OSA 1988 Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 266.

M. E. Pedinoff, M. Braunstein, O. M. Stafsudd, “Modulated light ellipsometry at 10.6 μm,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam, D. L. Coffeen, eds., Proc. Soc. Photo-Opt. Instrum. Eng.112, 74–81 (1977).

G. Bruhat, Optique (Cours de Physique Générale), 5th ed., (Masson, Paris, 1959).

S. D. Jacobs, J. E. Hayden, A. L. Hrycin, “Practical measurements of adhesion and strain for improved optical coatings,” in Optical Thin Films II: New Developments, R. I. Seddon, ed., Proc. Soc. Photo-Opt. Instrum. Eng.678, 66–78 (1986).

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Figures (10)

Fig. 1
Fig. 1

MTE optical configuration.

Fig. 2
Fig. 2

MTE signal processing and computer control.

Fig. 3
Fig. 3

Biased retardance modulation of the Pockels cell for a scan of five different beam positions used to cancel system retardance during a sample scan. The frequency shown is much lower than 5 kHz to emphasize technique.

Fig. 4
Fig. 4

Intensity at tho dotector through one cycle of the modulator for five different retardance biases.

Fig. 5
Fig. 5

Ratio of 1f and 2f lock-in amplifiers (LIA’s) and the arctangent of the ratio of the 1f LIA and 2f LIA outputs used for system calibration and the corresponding third-order polynomial fit.

Fig. 6
Fig. 6

Error from the third-order polynomial fit to the data as the Pockels cell is biased through ±λ/4.

Fig. 7
Fig. 7

MTE retardance image and retardance cross section of a 100-mm-diameter transparent compact disk.

Fig. 8
Fig. 8

(a) MTE retardance image and retardance cross section of an injection-molded diffractive lens, (b) MTE retardance image and retardance cross section of diamond-turned diffractive lenses.

Fig. 9
Fig. 9

Retardance lineouts of semitransparent copper thin-film versus current.

Fig. 10
Fig. 10

Three-dimensional MTE retardance profile of a 90-mm-diameter neodymium-doped laser rod.

Tables (1)

Tables Icon

Table 1 MTE Retardance Map Statistics

Equations (5)

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I ( x , y ω t ) = I 0 sin 2 { π λ [ Γ ( x , y , ω t ) MOD + Γ ( x , y ) SMP + Γ ( x , y ) MTE ] } .
Γ = δλ 2 π ,
Γ ( x , y , ω t ) mod = Γ ( ω t ) ac + Γ ( ω t ) dc ,
Γ ( ω t ) ac = λ 4 sin ( ω t ) ,
σ ( kgf cm 2 ) = c 0 ( kgf nm × cm ) × Γ ( nm ) t ( cm ) ,

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