Abstract

Centripetal forces modify the optical properties of a rotating glass disk, thus creating a circularly symmetric distortion in the refractive index. This centripetal birefringence has a strong radial dependency and increases with the square of the spin speed. The effect on a polarized beam transmitted through the glass may be reduced mathematically to that of an effective wave plate whose retardance and orientation may be calculated from knowledge of the stress distribution in the disk. Alternatively, one can directly measure the Jones-matrix elements that correspond to the effective wave plate by use of polarization phase measurements at two or more locations on the disk. This direct measurement compensates the centripetal birefringence in the instrumentation employed by the data-storage industry to measure the flying height of read–write heads.

© 1998 Optical Society of America

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References

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  1. C. Lin, “Techniques for the measurement of air-bearing separation—a review,” IEEE Trans. Magn. MAG-9, 673–677 (1973).
  2. J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
    [CrossRef]
  3. T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. Am. Soc. Mech. Eng., 110, 148–155 (1988).
  4. C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” in Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, San Jose, Calif., 1992), pp. 27–42.
  5. G. Sommargren, “Flying height and topography measuring interferometer,” U.S. patent5,218,424 (June8, 1993).
  6. P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
    [CrossRef] [PubMed]
  7. C. Lacey, C. Duran, IDEMA Insight, 9(6), 1 (1996).
  8. P. de Groot, “Optical gap measuring apparatus and method” U.S. patent5,557,399 (September17, 1996).
  9. P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecky, ed., Proc. SPIE2782, 47–57 (1996).
    [CrossRef]
  10. P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.
  11. W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
    [CrossRef]
  12. W. A. Challener, T. A. Rinehart, “Jones matrix analysis of magnetooptical media and read-back systems,” Appl. Opt. 26, 3974–3980 (1987).
    [CrossRef] [PubMed]
  13. A. Takahashi, M. Mieda, Y. Murakami, K. Ohta, H. Yamaoka, “Influence of birefringence on the signal quality of magnetooptic disks using polycarbonate substrates,” Appl. Opt. 27, 2863–2866 (1988).
    [CrossRef] [PubMed]
  14. M. Horie, “Simple birefringence measurement method for coated optical disks with a fixed incident angle ellipsometer,” Appl. Opt. 34, 5715–5719 (1995).
    [CrossRef] [PubMed]
  15. H. Fu, S. Sugaya, J. K. Erwin, M. Mansuripur, “Measurement of birefringence for optical recording of disk substrates,” Appl. Opt. 33, 1938–1949 (1994).
    [CrossRef] [PubMed]
  16. W. C. Young, Roark’s Formulas for Stress and Strain, 6th ed. (McGraw-Hill, New York, 1989), p. 704.
  17. For an analysis based on the index ellipsoid, see, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 674.
  18. The matrix v is the differential portion of the electric impermeability tensor in the principal axis frame. Because the index changes are small (<10-4), this differential form is a sufficient description of the optical anisotropy of the glass.
  19. A formal justification of the neglect of the u terms in the transformed index matrix v′ follows from Eqs. (6.3–6.13) of B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), p. 217.
  20. The symmetry argument that allows us to equate waveplates B1 and B2 in Fig. 3 requires that we neglect the slight difference in position within the glass of the incident and the reflected beams. This approximation simplifies the model but introduces an error that may be significant at small radii.
  21. G. Fowles, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1975), pp. 33–36.
  22. Estimates of the accuracy of approximations in this paper all assume the disk geometry defined in Section 2, i.e., inner radius qins=3.18 mm, outer radius qout=53 mm, disk thickness T=7 mm.
  23. As an alternative to linear input polarization, Lacey, Womack have proposed using circular polarization [U.S. patent5,638,178, “Imaging polarimeter detector for measurement of small spacings” (June10, 1997)]. However, a linear input polarization substantially reduces the effect of polarization mixing attributable to disk birefringence.
  24. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 62 and 40.
  25. H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, Boston, 1993), p. 17.
  26. Centripetal birefringence measurement and compensation are covered by U.S. patent5,644,562 to P. de Groot entitled “Method and apparatus for measuring and compensating birefringence in rotating disks” (July1, 1997).
  27. T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

1996 (2)

1995 (1)

1994 (1)

1990 (1)

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

1988 (2)

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. Am. Soc. Mech. Eng., 110, 148–155 (1988).

A. Takahashi, M. Mieda, Y. Murakami, K. Ohta, H. Yamaoka, “Influence of birefringence on the signal quality of magnetooptic disks using polycarbonate substrates,” Appl. Opt. 27, 2863–2866 (1988).
[CrossRef] [PubMed]

1987 (1)

1974 (1)

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

1973 (1)

C. Lin, “Techniques for the measurement of air-bearing separation—a review,” IEEE Trans. Magn. MAG-9, 673–677 (1973).

Adams, J. A.

C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” in Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, San Jose, Calif., 1992), pp. 27–42.

Anders, S.

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

Biegen, J.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecky, ed., Proc. SPIE2782, 47–57 (1996).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 62 and 40.

For an analysis based on the index ellipsoid, see, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 674.

Challener, W. A.

Cormier, A.

C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” in Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, San Jose, Calif., 1992), pp. 27–42.

de Groot, P.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, “Optical gap measuring apparatus and method” U.S. patent5,557,399 (September17, 1996).

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

Centripetal birefringence measurement and compensation are covered by U.S. patent5,644,562 to P. de Groot entitled “Method and apparatus for measuring and compensating birefringence in rotating disks” (July1, 1997).

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecky, ed., Proc. SPIE2782, 47–57 (1996).
[CrossRef]

Deck, L.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecky, ed., Proc. SPIE2782, 47–57 (1996).
[CrossRef]

Dergevorkian, A.

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

Duran, C.

C. Lacey, C. Duran, IDEMA Insight, 9(6), 1 (1996).

Erickson, T.

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

Erwin, J. K.

Fleischer, J. M.

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

Fowles, G.

G. Fowles, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1975), pp. 33–36.

Fu, H.

Fukuzawa, T.

T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

Grigg, U.

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

Hisano, T.

T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

Horie, M.

Ikarugi, K.

T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

Kishegami, J.

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. Am. Soc. Mech. Eng., 110, 148–155 (1988).

Lacey,

As an alternative to linear input polarization, Lacey, Womack have proposed using circular polarization [U.S. patent5,638,178, “Imaging polarimeter detector for measurement of small spacings” (June10, 1997)]. However, a linear input polarization substantially reduces the effect of polarization mixing attributable to disk birefringence.

Lacey, C.

C. Lacey, C. Duran, IDEMA Insight, 9(6), 1 (1996).

C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” in Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, San Jose, Calif., 1992), pp. 27–42.

Lin, C.

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

C. Lin, “Techniques for the measurement of air-bearing separation—a review,” IEEE Trans. Magn. MAG-9, 673–677 (1973).

Löwer, H.

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

Mansuripur, M.

Mieda, M.

Morace, J.

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

Murakami, Y.

Noda, K.

T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

Ohkubo, T.

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. Am. Soc. Mech. Eng., 110, 148–155 (1988).

Ohta, K.

Ozawa, Y.

T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

Pavlat, R.

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

Rateike, F. M.

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

Rinehart, T. A.

Ross, E. W.

C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” in Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, San Jose, Calif., 1992), pp. 27–42.

Saleh, B. E. A.

A formal justification of the neglect of the u terms in the transformed index matrix v′ follows from Eqs. (6.3–6.13) of B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), p. 217.

Schmid, H.

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

Siebourg, W.

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

Sommargren, G.

G. Sommargren, “Flying height and topography measuring interferometer,” U.S. patent5,218,424 (June8, 1993).

Soobitsky, J.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecky, ed., Proc. SPIE2782, 47–57 (1996).
[CrossRef]

Sugaya, S.

Takahashi, A.

Teich, M. C.

A formal justification of the neglect of the u terms in the transformed index matrix v′ follows from Eqs. (6.3–6.13) of B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), p. 217.

Tompkins, H. G.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, Boston, 1993), p. 17.

Watabe, H.

T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

Wolf, E.

For an analysis based on the index ellipsoid, see, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 674.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 62 and 40.

Womack,

As an alternative to linear input polarization, Lacey, Womack have proposed using circular polarization [U.S. patent5,638,178, “Imaging polarimeter detector for measurement of small spacings” (June10, 1997)]. However, a linear input polarization substantially reduces the effect of polarization mixing attributable to disk birefringence.

Yamaoka, H.

Young, W. C.

W. C. Young, Roark’s Formulas for Stress and Strain, 6th ed. (McGraw-Hill, New York, 1989), p. 704.

Appl. Opt. (4)

IBM J. Res. Develop. (1)

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

IDEMA Insight (1)

C. Lacey, C. Duran, IDEMA Insight, 9(6), 1 (1996).

IEEE Trans. Magn. (1)

C. Lin, “Techniques for the measurement of air-bearing separation—a review,” IEEE Trans. Magn. MAG-9, 673–677 (1973).

Opt. Lett. (1)

Polym. Eng. Sci. (1)

W. Siebourg, H. Schmid, F. M. Rateike, S. Anders, U. Grigg, H. Löwer, “Birefringence—an important property of plastic substrates for magneto-optical storage disks,” Polym. Eng. Sci. 30, 1133–1139 (1990).
[CrossRef]

Trans. Am. Soc. Mech. Eng. (1)

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. Am. Soc. Mech. Eng., 110, 148–155 (1988).

Other (17)

C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” in Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, San Jose, Calif., 1992), pp. 27–42.

G. Sommargren, “Flying height and topography measuring interferometer,” U.S. patent5,218,424 (June8, 1993).

P. de Groot, “Optical gap measuring apparatus and method” U.S. patent5,557,399 (September17, 1996).

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecky, ed., Proc. SPIE2782, 47–57 (1996).
[CrossRef]

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials AssociationSan Diego, Calif., 1997), pp. 89–94.

W. C. Young, Roark’s Formulas for Stress and Strain, 6th ed. (McGraw-Hill, New York, 1989), p. 704.

For an analysis based on the index ellipsoid, see, for example, M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 674.

The matrix v is the differential portion of the electric impermeability tensor in the principal axis frame. Because the index changes are small (<10-4), this differential form is a sufficient description of the optical anisotropy of the glass.

A formal justification of the neglect of the u terms in the transformed index matrix v′ follows from Eqs. (6.3–6.13) of B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), p. 217.

The symmetry argument that allows us to equate waveplates B1 and B2 in Fig. 3 requires that we neglect the slight difference in position within the glass of the incident and the reflected beams. This approximation simplifies the model but introduces an error that may be significant at small radii.

G. Fowles, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1975), pp. 33–36.

Estimates of the accuracy of approximations in this paper all assume the disk geometry defined in Section 2, i.e., inner radius qins=3.18 mm, outer radius qout=53 mm, disk thickness T=7 mm.

As an alternative to linear input polarization, Lacey, Womack have proposed using circular polarization [U.S. patent5,638,178, “Imaging polarimeter detector for measurement of small spacings” (June10, 1997)]. However, a linear input polarization substantially reduces the effect of polarization mixing attributable to disk birefringence.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 62 and 40.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, Boston, 1993), p. 17.

Centripetal birefringence measurement and compensation are covered by U.S. patent5,644,562 to P. de Groot entitled “Method and apparatus for measuring and compensating birefringence in rotating disks” (July1, 1997).

T. Fukuzawa, T. Hisano, K. Ikarugi, Y. Ozawa, H. Watabe, K. Noda, “Two-dimensional flying-height measurement for new-generation heads,” in Digest of the IEEE International Magnetics Conference (Institute of Electronical and Electronics Engineers, Piscataway, N.J., 1995), HC-01.

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Figures (12)

Fig. 1
Fig. 1

Polarization interferometer for flying-height testing of magnetic read–write sliders. A rotating glass substrate takes the place of the magnetic disk to facilitate optical inspection of the gap. The receiver measures the polarization-dependent complex reflectivity of the slider–glass interface.

Fig. 2
Fig. 2

Theoretical refractive-index distortions as a function of measurement radius in a glass disk for a spin speed of 9 krpm. The in-plane distortion (Δn in the text) is equal to half the difference in the radial and tangential refractive-index changes. The perpendicular distortion (Δn in the text) is equal to the z-axis index change minus the average of the radial and tangential refractive-index changes.

Fig. 3
Fig. 3

Simplified model of the optical system shown in Fig. 1 in which disk birefringence has been reduced to two effective waveplates B1 and B2. These elements modify the polarization state before and after the slider–glass reflection.

Fig. 4
Fig. 4

Coordinate transform for centripetal birefringence initially oriented with one principal axis parallel to the disk axis. There are two coordinate rotations, involving first a skew angle ζ and then the oblique transmission angle ϕ. The beam propagates along the u axis, p is in the plane of incidence, and s is in the plane of the disk.

Fig. 5
Fig. 5

Effective wave-plate retardance δ and orientation angle γ as a function of measurement radius. These data are calculated from the stress analysis of Sections 2–4 for a spin speed ω of 9 krpm and a skew angle ζ of 20°. The results for B1 and B2 shown in Fig. 3 are identical, apart from a sign change on the orientation angle.

Fig. 6
Fig. 6

Measured variation in the sp phase as a function of radius for spin speeds ω of 9 krpm at a skew angle ζ=±10° (upper graph) and ω=12 krpm at ζ=±20° (lower graph). The solid curves were generated according to the theory developed in Sections 2–4.

Fig. 7
Fig. 7

Measured variation in the sp phase as a function of skew angle ζ for a spin speeds ω of 10 krpm at a radius q of 30 mm. The small differences observed at -200° and -30° are attributable to the thin-disk approximation, which neglects beam displacement through the glass.

Fig. 8
Fig. 8

Variation in the sp phase as a function of spin speed. The solid curve is a least-squares second-order fit, illustrating the quadratic speed dependence predicted by the theory.

Fig. 9
Fig. 9

Relaxation phenomenon for centripetal birefringence. The disk is spinning at 12 krpm and is abruptly stopped at time = 0 s. This effect makes it difficult to predict birefringence from the stress equations without taking into account rapid changes in spin speed.

Fig. 10
Fig. 10

Theoretical sp phase as a function of flying height for a slider index n of 2.2+0.4 i, with the optical system of Fig. 1. The two curves are for two different spin speeds. Centripetal birefringence is negligible at 1 krpm but has a significant effect at 12 krpm.

Fig. 11
Fig. 11

Theoretical ellipsometric s/p intensity ratio and total s+p intensity curves as a function of flying height, with the same parameters as for Fig. 10. The variation of the s/p ratio is dominated by birefringence. The total intensity, however, is nearly independent of the birefringence phenomena.

Fig. 12
Fig. 12

Midpoint height of a read–write slider as a function of spin speed, measured with polarization interferometry. With use of the direct detection algorithm for birefringence compensation, the observed linearity is ±0.9 nm. If the effects of centri- petal birefringence are neglected, the processed data show an unlikely nonlinear behavior above 6 krpm.

Equations (69)

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σx=-ρω23+μ8qout2+qins2-qout2qins2q2-q2
σy=-ρω23+μ8qout2+qins2+qout2qins2q2-1+3µ3+μq2,
σz=0
ΔnxΔnyΔnz=κ1κ2κ2κ2κ1κ2κ2κ2κ1σxσyσz.
ΔnxΔn
Δny-Δn
ΔnzΔn,
2Δn=Δnx-Δny
2Δn=2Δnz-(Δnx+Δny).
v=Δnx000Δny000Δnz.
sin(ϕG)=nG-1 sin(ϕ).
v=RvRT,
R=1000cos(ϕG)sin(ϕG)0-sin(ϕG)cos(ϕG)cos(ζ)sin(ζ)0-sin(ζ)cos(ζ)0001.
v=ΔnsΔnspΔnsuΔnspΔnpΔnpuΔnsuΔnpuΔnu.
v=ΔnsΔnspΔnspΔnp.
Δns=Δn cos(2ζ)
Δnp=Δn sin(ϕG)2-Δn cos(2ζ)cos(ϕG)2.
Δnsp=Δn sin(2ζ)cos(ϕG)
vD=ND
D=DsDp,
ΔN=(Δns-Δnp)2+4Δnsp2.
δ=kLΔN,
tan(γ)=Dp+/Ds+.
tan(γ)=ΔN+(Δns-Δnp)2Δnsp.
E=B1E,
E=EsEp.
B1(δ, γ)=R(γ)B(δ)R(-γ),
B(δ)=exp(-iδ/2)00exp(+iδ/2),
R(γ)=cos(γ)sin(γ)-sin(γ)cos(γ).
B1=biaiab*,
B2=b-ia-iab*,
a=sin(2γ)sin(δ/2),
b=cos(δ/2)+i cos(2γ)sin(δ/2).
G=rs00rp,
EG=(B2GB1)E.
αδ sin(2ζ)cos(ϕG),
bexp(iΦ/4),
Φ=2δ sin(ϕG)2-2δ[1+cos(ϕG)2]cos(2ζ),
δ=kLn,
δ=kLn.
E=11.
EG=b-ia-iab*rs00rpb+iab*+ia.
argb+iab*+ia(1+a)Φ/2.
|b+ia|21+aΦ/2,
|b*+ia|21-aΦ/2.
EGrsb2-iarpb*rpb*2-iarsb.
θG-argrprsb*2b21-iab3rs/rp1-iab*3rp/rs,
θG-π+Φ-arg1-ia rs2b3-rp2b*3rprs.
rsb3+rpb*3rprsrs2-rp2rprs+rs2+rp2rprs 3Φ4.
θG-π+Φ-aU,
U=rs2-rp2rsrp,
IsGrs2,
IpGrp2.
a12[θ(-)-θ(+)]/U,
Φ12[θ(-)+θ(+)]+π.
S=zs00zp,
zp(β)=rp+rp exp(iβ)1+rprp exp(iβ),
zs(β)=rs+rs exp(iβ)1+rsrs exp(iβ),
β=2kh cos(ϕ).
ES=(B2SB1)E.
θ=arg(zs/zp)
Isp=|zsp|2.
θbθ+Δθ,
IsbIs-ΔI,
IpbIp+ΔI,
Δθ=Φ+a Is-IpIsIpcos(θ),
ΔI=2aIsIp sin(θ),
I=Is+Ip
χ2(β)=[Iexp-I]2+[θexp-θb]2,

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