Abstract

A laser marking process is described which is based upon a unique phenomenon of photothermally transforming oriented microcrystallites of a vapor-deposited dichroic dye. It is shown that writing with linearly polarized laser light on an oriented film improves contrast and sensitivity over the unoriented film. The improvement stems from the increased optical sensitivity when an oriented film of one polymorphic form of the dye is photothermally transformed by irradiation with suitably oriented linearly polarized laser light. It is shown that the laser marking process proceeds via three stages. At low power the laser pulse causes a crystal-crystal transformation within microcrystallites of an oriented film of the dichroic dye. At medium power the dye also migrates and coalesces around nucleating sites in the written spot during the crystal transformation process. At the highest powers the unovercoated film ablates. A simple polishing process is described for producing large areas of oriented thin vapor-deposited films.

© 1984 Optical Society of America

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References

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  1. R. A. Bartolini, H. A. Weakliem, B. F. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99 (1976).
    [Crossref]
  2. A. E. Bell, “The Design and Optimization of the Optical Data Disk,” Proc. Soc. Inf. Disp. 24, 17 (1983).
  3. T. H. DiStefano, “Optical Data Storage,” Laser Focus 18(1), 92–95 (Jan.1982).
  4. P. Kivits, R. deBont, J. van der Veen, “Vanadyl Phthalocyanine: An Organic Material for Optical Data Recording,” Appl. Phys. A 26, 101 (1981); U.S. Patent4,298,975 (1981).
    [Crossref]
  5. K. Y. Law, G. E. Johnson, “Ablative Optical Recording using Organic Dye-in-Polymer Thin Films: Some Mechanistic Aspects,” J. Appl. Phys. 54, 4799 (1983) and references therein.
    [Crossref]
  6. V. B. Jipson, C. R. Jones, “Infrared Dyes for Optical Storage,” J. Vac. Sci. Technol. 18, 105 (1981).
    [Crossref]
  7. D. J. Gravesteijn, C. Steenbergen, J. Van der Veen, “Single Wavelength Optical Recording in Pure, Solvent Coated Infrared Dye Layers,” in SPIE Proceedings on Optical Storage Media, Arlington, Va. (June 1983).
  8. N. F. Borelli, P. L. Young, “Read-Write Eraseable Thin Film Optical Recording Medium,” in Laser Scanning and Recording for Advanced Image and Data Handling, Proc. Soc. Photo-Opt. Instrum. Eng. 222, 48 (1980).
    [Crossref]
  9. C-K. Wu, “Photodichroic Silicate Glass Surface,” Opt. Eng. 19, 769 (1980).
    [Crossref]
  10. L. A. Ageev, V. K. Miloslavskii, “Nature of Weigert Effect in Thin AgI-Ag Films,” Opt. Spectrosc. USSR 48, 442 (1980).
  11. L. A. Ageev, V. K. Milislavskii, “Photoinduced Dichroism in Thin Ag-CuCl Films,” Opt. Spectrosc. USSR 50, 507 (1981).
  12. V. G. Zdanov et al., “Photoinduced Dichroism in As2S3,” Opt. Commun. 30, 329 (1979).
    [Crossref]
  13. E. D. Krasnikov, V. M. Kozenkov, “Photodichroism of Photochromic Spiropyrans,” Proc. Acad. Sci. USSR, Phys. Chem. 245, 314 (1979).
  14. V. Y. Merritt, “Organic Photovoltaic Materials: Squarylium and Cyanine-TCNQ Dyes,” IBM J. Res. Dev. 22, 353 (1978).
    [Crossref]
  15. C. J. Eckhardt et al., “Strong Coupling in the Polymorphs of a Squarylium Dye,” Chem. Phys. Lett. 98, 57 (1983).
    [Crossref]
  16. J. Cognard, “Alignment of Nematic Liquid Crystals and their Mixtures,” Mol. Cryst. Liq. Cryst. Suppl. Ser. 1, 1 (1982).
  17. L. A. Goodman et al., “Topography of Obliquely Evaporated Silicon Oxide Films and its Effect on Liquid Crystal Orientation Devices,” ED-24, 795 (1977) and references therein.
  18. M. W. Geiss, D. C. Flanders, H. I. Smith, “Crystallographic Orientation of Silicon on an Amorphous Substrate using an Artificial Surface Relief Grating and Laser Crystallization,” Appl. Phys. Lett. 35, 71 (1979).
    [Crossref]
  19. P. P. Luff, M. White, “The Structure and Properties of Evaporated Polyethylene Thin Films,” Thin Solid Films 6, 175 (1970).
    [Crossref]
  20. A. Peterlin, “Structure and Properties of Oriented Polymers,” I. M. Ward, Ed. (Wiley, New York, 1975), Chap. 2.
  21. M. Chen, V. Marrello, U. G. Gerber, “Ablative Hole Formation Process in Thin Tellurium-Alloy Films,” Appl. Phys. Lett. 41, 894 (1982).
    [Crossref]
  22. V. Marrello, M. Chen, R. Weiss, W. Martin, U. Gerber, “Mapping of Defects on Optical Recording Disks,” in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1982), paper WH4.

1983 (3)

K. Y. Law, G. E. Johnson, “Ablative Optical Recording using Organic Dye-in-Polymer Thin Films: Some Mechanistic Aspects,” J. Appl. Phys. 54, 4799 (1983) and references therein.
[Crossref]

A. E. Bell, “The Design and Optimization of the Optical Data Disk,” Proc. Soc. Inf. Disp. 24, 17 (1983).

C. J. Eckhardt et al., “Strong Coupling in the Polymorphs of a Squarylium Dye,” Chem. Phys. Lett. 98, 57 (1983).
[Crossref]

1982 (3)

J. Cognard, “Alignment of Nematic Liquid Crystals and their Mixtures,” Mol. Cryst. Liq. Cryst. Suppl. Ser. 1, 1 (1982).

T. H. DiStefano, “Optical Data Storage,” Laser Focus 18(1), 92–95 (Jan.1982).

M. Chen, V. Marrello, U. G. Gerber, “Ablative Hole Formation Process in Thin Tellurium-Alloy Films,” Appl. Phys. Lett. 41, 894 (1982).
[Crossref]

1981 (3)

P. Kivits, R. deBont, J. van der Veen, “Vanadyl Phthalocyanine: An Organic Material for Optical Data Recording,” Appl. Phys. A 26, 101 (1981); U.S. Patent4,298,975 (1981).
[Crossref]

V. B. Jipson, C. R. Jones, “Infrared Dyes for Optical Storage,” J. Vac. Sci. Technol. 18, 105 (1981).
[Crossref]

L. A. Ageev, V. K. Milislavskii, “Photoinduced Dichroism in Thin Ag-CuCl Films,” Opt. Spectrosc. USSR 50, 507 (1981).

1980 (3)

N. F. Borelli, P. L. Young, “Read-Write Eraseable Thin Film Optical Recording Medium,” in Laser Scanning and Recording for Advanced Image and Data Handling, Proc. Soc. Photo-Opt. Instrum. Eng. 222, 48 (1980).
[Crossref]

C-K. Wu, “Photodichroic Silicate Glass Surface,” Opt. Eng. 19, 769 (1980).
[Crossref]

L. A. Ageev, V. K. Miloslavskii, “Nature of Weigert Effect in Thin AgI-Ag Films,” Opt. Spectrosc. USSR 48, 442 (1980).

1979 (3)

V. G. Zdanov et al., “Photoinduced Dichroism in As2S3,” Opt. Commun. 30, 329 (1979).
[Crossref]

E. D. Krasnikov, V. M. Kozenkov, “Photodichroism of Photochromic Spiropyrans,” Proc. Acad. Sci. USSR, Phys. Chem. 245, 314 (1979).

M. W. Geiss, D. C. Flanders, H. I. Smith, “Crystallographic Orientation of Silicon on an Amorphous Substrate using an Artificial Surface Relief Grating and Laser Crystallization,” Appl. Phys. Lett. 35, 71 (1979).
[Crossref]

1978 (1)

V. Y. Merritt, “Organic Photovoltaic Materials: Squarylium and Cyanine-TCNQ Dyes,” IBM J. Res. Dev. 22, 353 (1978).
[Crossref]

1977 (1)

L. A. Goodman et al., “Topography of Obliquely Evaporated Silicon Oxide Films and its Effect on Liquid Crystal Orientation Devices,” ED-24, 795 (1977) and references therein.

1976 (1)

R. A. Bartolini, H. A. Weakliem, B. F. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99 (1976).
[Crossref]

1970 (1)

P. P. Luff, M. White, “The Structure and Properties of Evaporated Polyethylene Thin Films,” Thin Solid Films 6, 175 (1970).
[Crossref]

Ageev, L. A.

L. A. Ageev, V. K. Milislavskii, “Photoinduced Dichroism in Thin Ag-CuCl Films,” Opt. Spectrosc. USSR 50, 507 (1981).

L. A. Ageev, V. K. Miloslavskii, “Nature of Weigert Effect in Thin AgI-Ag Films,” Opt. Spectrosc. USSR 48, 442 (1980).

Bartolini, R. A.

R. A. Bartolini, H. A. Weakliem, B. F. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99 (1976).
[Crossref]

Bell, A. E.

A. E. Bell, “The Design and Optimization of the Optical Data Disk,” Proc. Soc. Inf. Disp. 24, 17 (1983).

Borelli, N. F.

N. F. Borelli, P. L. Young, “Read-Write Eraseable Thin Film Optical Recording Medium,” in Laser Scanning and Recording for Advanced Image and Data Handling, Proc. Soc. Photo-Opt. Instrum. Eng. 222, 48 (1980).
[Crossref]

Chen, M.

M. Chen, V. Marrello, U. G. Gerber, “Ablative Hole Formation Process in Thin Tellurium-Alloy Films,” Appl. Phys. Lett. 41, 894 (1982).
[Crossref]

V. Marrello, M. Chen, R. Weiss, W. Martin, U. Gerber, “Mapping of Defects on Optical Recording Disks,” in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1982), paper WH4.

Cognard, J.

J. Cognard, “Alignment of Nematic Liquid Crystals and their Mixtures,” Mol. Cryst. Liq. Cryst. Suppl. Ser. 1, 1 (1982).

deBont, R.

P. Kivits, R. deBont, J. van der Veen, “Vanadyl Phthalocyanine: An Organic Material for Optical Data Recording,” Appl. Phys. A 26, 101 (1981); U.S. Patent4,298,975 (1981).
[Crossref]

DiStefano, T. H.

T. H. DiStefano, “Optical Data Storage,” Laser Focus 18(1), 92–95 (Jan.1982).

Eckhardt, C. J.

C. J. Eckhardt et al., “Strong Coupling in the Polymorphs of a Squarylium Dye,” Chem. Phys. Lett. 98, 57 (1983).
[Crossref]

Flanders, D. C.

M. W. Geiss, D. C. Flanders, H. I. Smith, “Crystallographic Orientation of Silicon on an Amorphous Substrate using an Artificial Surface Relief Grating and Laser Crystallization,” Appl. Phys. Lett. 35, 71 (1979).
[Crossref]

Geiss, M. W.

M. W. Geiss, D. C. Flanders, H. I. Smith, “Crystallographic Orientation of Silicon on an Amorphous Substrate using an Artificial Surface Relief Grating and Laser Crystallization,” Appl. Phys. Lett. 35, 71 (1979).
[Crossref]

Gerber, U.

V. Marrello, M. Chen, R. Weiss, W. Martin, U. Gerber, “Mapping of Defects on Optical Recording Disks,” in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1982), paper WH4.

Gerber, U. G.

M. Chen, V. Marrello, U. G. Gerber, “Ablative Hole Formation Process in Thin Tellurium-Alloy Films,” Appl. Phys. Lett. 41, 894 (1982).
[Crossref]

Goodman, L. A.

L. A. Goodman et al., “Topography of Obliquely Evaporated Silicon Oxide Films and its Effect on Liquid Crystal Orientation Devices,” ED-24, 795 (1977) and references therein.

Gravesteijn, D. J.

D. J. Gravesteijn, C. Steenbergen, J. Van der Veen, “Single Wavelength Optical Recording in Pure, Solvent Coated Infrared Dye Layers,” in SPIE Proceedings on Optical Storage Media, Arlington, Va. (June 1983).

Jipson, V. B.

V. B. Jipson, C. R. Jones, “Infrared Dyes for Optical Storage,” J. Vac. Sci. Technol. 18, 105 (1981).
[Crossref]

Johnson, G. E.

K. Y. Law, G. E. Johnson, “Ablative Optical Recording using Organic Dye-in-Polymer Thin Films: Some Mechanistic Aspects,” J. Appl. Phys. 54, 4799 (1983) and references therein.
[Crossref]

Jones, C. R.

V. B. Jipson, C. R. Jones, “Infrared Dyes for Optical Storage,” J. Vac. Sci. Technol. 18, 105 (1981).
[Crossref]

Kivits, P.

P. Kivits, R. deBont, J. van der Veen, “Vanadyl Phthalocyanine: An Organic Material for Optical Data Recording,” Appl. Phys. A 26, 101 (1981); U.S. Patent4,298,975 (1981).
[Crossref]

Kozenkov, V. M.

E. D. Krasnikov, V. M. Kozenkov, “Photodichroism of Photochromic Spiropyrans,” Proc. Acad. Sci. USSR, Phys. Chem. 245, 314 (1979).

Krasnikov, E. D.

E. D. Krasnikov, V. M. Kozenkov, “Photodichroism of Photochromic Spiropyrans,” Proc. Acad. Sci. USSR, Phys. Chem. 245, 314 (1979).

Law, K. Y.

K. Y. Law, G. E. Johnson, “Ablative Optical Recording using Organic Dye-in-Polymer Thin Films: Some Mechanistic Aspects,” J. Appl. Phys. 54, 4799 (1983) and references therein.
[Crossref]

Luff, P. P.

P. P. Luff, M. White, “The Structure and Properties of Evaporated Polyethylene Thin Films,” Thin Solid Films 6, 175 (1970).
[Crossref]

Marrello, V.

M. Chen, V. Marrello, U. G. Gerber, “Ablative Hole Formation Process in Thin Tellurium-Alloy Films,” Appl. Phys. Lett. 41, 894 (1982).
[Crossref]

V. Marrello, M. Chen, R. Weiss, W. Martin, U. Gerber, “Mapping of Defects on Optical Recording Disks,” in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1982), paper WH4.

Martin, W.

V. Marrello, M. Chen, R. Weiss, W. Martin, U. Gerber, “Mapping of Defects on Optical Recording Disks,” in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1982), paper WH4.

Merritt, V. Y.

V. Y. Merritt, “Organic Photovoltaic Materials: Squarylium and Cyanine-TCNQ Dyes,” IBM J. Res. Dev. 22, 353 (1978).
[Crossref]

Milislavskii, V. K.

L. A. Ageev, V. K. Milislavskii, “Photoinduced Dichroism in Thin Ag-CuCl Films,” Opt. Spectrosc. USSR 50, 507 (1981).

Miloslavskii, V. K.

L. A. Ageev, V. K. Miloslavskii, “Nature of Weigert Effect in Thin AgI-Ag Films,” Opt. Spectrosc. USSR 48, 442 (1980).

Peterlin, A.

A. Peterlin, “Structure and Properties of Oriented Polymers,” I. M. Ward, Ed. (Wiley, New York, 1975), Chap. 2.

Smith, H. I.

M. W. Geiss, D. C. Flanders, H. I. Smith, “Crystallographic Orientation of Silicon on an Amorphous Substrate using an Artificial Surface Relief Grating and Laser Crystallization,” Appl. Phys. Lett. 35, 71 (1979).
[Crossref]

Steenbergen, C.

D. J. Gravesteijn, C. Steenbergen, J. Van der Veen, “Single Wavelength Optical Recording in Pure, Solvent Coated Infrared Dye Layers,” in SPIE Proceedings on Optical Storage Media, Arlington, Va. (June 1983).

van der Veen, J.

P. Kivits, R. deBont, J. van der Veen, “Vanadyl Phthalocyanine: An Organic Material for Optical Data Recording,” Appl. Phys. A 26, 101 (1981); U.S. Patent4,298,975 (1981).
[Crossref]

D. J. Gravesteijn, C. Steenbergen, J. Van der Veen, “Single Wavelength Optical Recording in Pure, Solvent Coated Infrared Dye Layers,” in SPIE Proceedings on Optical Storage Media, Arlington, Va. (June 1983).

Weakliem, H. A.

R. A. Bartolini, H. A. Weakliem, B. F. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99 (1976).
[Crossref]

Weiss, R.

V. Marrello, M. Chen, R. Weiss, W. Martin, U. Gerber, “Mapping of Defects on Optical Recording Disks,” in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1982), paper WH4.

White, M.

P. P. Luff, M. White, “The Structure and Properties of Evaporated Polyethylene Thin Films,” Thin Solid Films 6, 175 (1970).
[Crossref]

Williams, B. F.

R. A. Bartolini, H. A. Weakliem, B. F. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99 (1976).
[Crossref]

Wu, C-K.

C-K. Wu, “Photodichroic Silicate Glass Surface,” Opt. Eng. 19, 769 (1980).
[Crossref]

Young, P. L.

N. F. Borelli, P. L. Young, “Read-Write Eraseable Thin Film Optical Recording Medium,” in Laser Scanning and Recording for Advanced Image and Data Handling, Proc. Soc. Photo-Opt. Instrum. Eng. 222, 48 (1980).
[Crossref]

Zdanov, V. G.

V. G. Zdanov et al., “Photoinduced Dichroism in As2S3,” Opt. Commun. 30, 329 (1979).
[Crossref]

Appl. Phys. A (1)

P. Kivits, R. deBont, J. van der Veen, “Vanadyl Phthalocyanine: An Organic Material for Optical Data Recording,” Appl. Phys. A 26, 101 (1981); U.S. Patent4,298,975 (1981).
[Crossref]

Appl. Phys. Lett. (2)

M. W. Geiss, D. C. Flanders, H. I. Smith, “Crystallographic Orientation of Silicon on an Amorphous Substrate using an Artificial Surface Relief Grating and Laser Crystallization,” Appl. Phys. Lett. 35, 71 (1979).
[Crossref]

M. Chen, V. Marrello, U. G. Gerber, “Ablative Hole Formation Process in Thin Tellurium-Alloy Films,” Appl. Phys. Lett. 41, 894 (1982).
[Crossref]

Chem. Phys. Lett. (1)

C. J. Eckhardt et al., “Strong Coupling in the Polymorphs of a Squarylium Dye,” Chem. Phys. Lett. 98, 57 (1983).
[Crossref]

IBM J. Res. Dev. (1)

V. Y. Merritt, “Organic Photovoltaic Materials: Squarylium and Cyanine-TCNQ Dyes,” IBM J. Res. Dev. 22, 353 (1978).
[Crossref]

J. Appl. Phys. (1)

K. Y. Law, G. E. Johnson, “Ablative Optical Recording using Organic Dye-in-Polymer Thin Films: Some Mechanistic Aspects,” J. Appl. Phys. 54, 4799 (1983) and references therein.
[Crossref]

J. Vac. Sci. Technol. (1)

V. B. Jipson, C. R. Jones, “Infrared Dyes for Optical Storage,” J. Vac. Sci. Technol. 18, 105 (1981).
[Crossref]

Laser Focus (1)

T. H. DiStefano, “Optical Data Storage,” Laser Focus 18(1), 92–95 (Jan.1982).

Laser Scanning and Recording for Advanced Image and Data Handling (1)

N. F. Borelli, P. L. Young, “Read-Write Eraseable Thin Film Optical Recording Medium,” in Laser Scanning and Recording for Advanced Image and Data Handling, Proc. Soc. Photo-Opt. Instrum. Eng. 222, 48 (1980).
[Crossref]

Mol. Cryst. Liq. Cryst. Suppl. Ser. (1)

J. Cognard, “Alignment of Nematic Liquid Crystals and their Mixtures,” Mol. Cryst. Liq. Cryst. Suppl. Ser. 1, 1 (1982).

Opt. Commun. (1)

V. G. Zdanov et al., “Photoinduced Dichroism in As2S3,” Opt. Commun. 30, 329 (1979).
[Crossref]

Opt. Eng. (2)

R. A. Bartolini, H. A. Weakliem, B. F. Williams, “Review and Analysis of Optical Recording Media,” Opt. Eng. 15, 99 (1976).
[Crossref]

C-K. Wu, “Photodichroic Silicate Glass Surface,” Opt. Eng. 19, 769 (1980).
[Crossref]

Opt. Spectrosc. USSR (2)

L. A. Ageev, V. K. Miloslavskii, “Nature of Weigert Effect in Thin AgI-Ag Films,” Opt. Spectrosc. USSR 48, 442 (1980).

L. A. Ageev, V. K. Milislavskii, “Photoinduced Dichroism in Thin Ag-CuCl Films,” Opt. Spectrosc. USSR 50, 507 (1981).

Proc. Acad. Sci. USSR (1)

E. D. Krasnikov, V. M. Kozenkov, “Photodichroism of Photochromic Spiropyrans,” Proc. Acad. Sci. USSR, Phys. Chem. 245, 314 (1979).

Proc. Soc. Inf. Disp. (1)

A. E. Bell, “The Design and Optimization of the Optical Data Disk,” Proc. Soc. Inf. Disp. 24, 17 (1983).

Thin Solid Films (1)

P. P. Luff, M. White, “The Structure and Properties of Evaporated Polyethylene Thin Films,” Thin Solid Films 6, 175 (1970).
[Crossref]

Topography of Obliquely Evaporated Silicon Oxide Films and its Effect on Liquid Crystal Orientation Devices (1)

L. A. Goodman et al., “Topography of Obliquely Evaporated Silicon Oxide Films and its Effect on Liquid Crystal Orientation Devices,” ED-24, 795 (1977) and references therein.

Other (3)

D. J. Gravesteijn, C. Steenbergen, J. Van der Veen, “Single Wavelength Optical Recording in Pure, Solvent Coated Infrared Dye Layers,” in SPIE Proceedings on Optical Storage Media, Arlington, Va. (June 1983).

A. Peterlin, “Structure and Properties of Oriented Polymers,” I. M. Ward, Ed. (Wiley, New York, 1975), Chap. 2.

V. Marrello, M. Chen, R. Weiss, W. Martin, U. Gerber, “Mapping of Defects on Optical Recording Disks,” in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1982), paper WH4.

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Figures (6)

Fig. 1
Fig. 1

Structure of squarylium.

Fig. 2
Fig. 2

Spectrum of OHSQ/polished PE.

Fig. 3
Fig. 3

Contrast vs writing energy (static): unpolarized reflection.

Fig. 4
Fig. 4

Contrast vs writing energy (static): polarized transmission (min.)

Fig. 5
Fig. 5

Contrast vs writing energy (static): polarized transmission (max.)

Fig. 6
Fig. 6

SNR vs writing energy (dynamic).

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

R = I T / I 0 I T / I 0 .
I A + I T + I R = I 0 , I T I T = I R I R .
I 0 = I 0 or P 0 = P 0 , I 0 = I 0 + I 0 = 2 × I 0 ,
I 0 = 0.5 I 0 and P 0 = 0.5 P 0 .
I R I 0 = I R + I R I 0 = I R I 0 ( 1 + R )
I R I 0 = I R I 0 ( 1 1 + R ) , I R I 0 = I R I 0 = I R 0.5 I 0 ( 1 1 + R ) = I R I 0 ( 2 1 + R ) .
P A = P 0 ( 1 - I T I 0 - I R I 0 ) , P A = P 0 ( 1 - I T I 0 ) + P 0 ( 1 - I T I 0 - I R I 0 ) .
P A = 0.5 P 0 [ 1 - I 0 I 0 - I R I 0 ( 2 1 + R ) ] , P A = 0.5 P 0 [ 2 - I T I 0 ( R + 1 R ) - 2 I R I 0 ] .
F = P A / P 0 P A / P 0 = 2 P A P A = 2 × [ 1 - I T I 0 - I R I 0 ( 2 1 + R ) ] [ 2 - I T I 0 ( 1 + R R ) - 2 I R I 0 ] .
D = 0.84 = - log ( I t / I 0 )
D = 0.11 = - log ( I T / I 0 )

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