Abstract

A method to determine the refractive index and thickness of silver halide emulsions used in holography is presented. The emulsions are in the form of a layer of film deposited on a thick glass plate. The experimental reflectances of p-polarized light are measured as a function of the incident angles, and the values of refractive index, thickness, and extinction coefficient of the emulsion are obtained by using the theoretical equation for reflectance. As examples, five commercial holographic silver halide emulsions are analyzed. The procedure to obtain the measurements and the numerical analysis of the experimental data are simple, and agreement of the calculated reflectances, by use of the thickness and refractive index obtained, with the measured reflectances is satisfactory.

© 2002 Optical Society of America

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References

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  1. H. I. Bjelkhagen, Silver Halide Recording Materials for Holography and Their Processing (Springer-Verlag, Berlin, 1993).
  2. C. Neipp, I. Pascual, A. Beléndez, “Recent advances in new holographic silver halide materials,” in Recent Research Developments in Optics, Vol. I (Research Signpost, Trivandrum, India, 2001), pp. 35–56.
  3. C. Neipp, I. Pascual, A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsion,” J. Opt. A. Pure Appl. Opt. 3, 504–513 (2001).
    [CrossRef]
  4. C. Neipp, I. Pascual, A. Beléndez, “Bleached silver halide volume holograms recorded on Slavich PFG-01 emulsion: The influence of the developer,” J. Mod. Opt. 48, 1479–1494 (2001).
    [CrossRef]
  5. S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).
  6. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 69–87.
  7. A. A. Dakhel, “Optical constants of evaporated gadolinium oxide,” Pure Appl. Opt. 3, 452–454 (2001).
  8. T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” Appl. Opt. 29, 5069–5073 (1989).
    [CrossRef]
  9. J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D.: Appl. Phys. 34, 2489–2496 (2001).
    [CrossRef]
  10. R. Z. Vitlina, G. I. Surdotovich, “A ‘blurred film’ model inpolarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
    [CrossRef]
  11. C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
    [CrossRef]
  12. J. Lekner, “Determination of complex refractive index and thickness of a homogeneous layer by combined reflection and transmission ellipsometry,” J. Opt. Soc. Am. A 11, 2156–2158 (1994).
    [CrossRef]
  13. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).
  14. R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. 8, 201–205 (1977).
    [CrossRef]
  15. Y. Cui, R. M. A. Azzam, “Determination of the refractive index and thickness of transparent pellicles by use of the polarization-independent absentee-layer condition,” Appl. Opt. 35, 5040–5043 (1996).
    [CrossRef] [PubMed]
  16. M-H. Chiu, J-Y. Lee, D-C Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999).
    [CrossRef]
  17. H. D. Thöll, M. Dömen, C. D. Stojanoff, “Determination of the mean refractive index and the thickness of dichromated gelatin holographic films using the thin film resonance method,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 76–87 (1997).
  18. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).
  19. A. Beléndez, C. Neipp, I. Pascual, “Analysis and elimination of boundary reflections in transmission holograms,” Opt. Laser Technol. 30, 555–556 (1999).
    [CrossRef]
  20. R. J. Martín-Palma, J. M. Martínez-Duart, A. Malats, “Determination of the optical constants of thin oxide and silver thick fims for their use in multilayer low-emissivity coatings,” Bol. R. Soc. Esp. Cerám. Vidrio 39, 472–475 (2000).

2001 (6)

C. Neipp, I. Pascual, A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsion,” J. Opt. A. Pure Appl. Opt. 3, 504–513 (2001).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Bleached silver halide volume holograms recorded on Slavich PFG-01 emulsion: The influence of the developer,” J. Mod. Opt. 48, 1479–1494 (2001).
[CrossRef]

A. A. Dakhel, “Optical constants of evaporated gadolinium oxide,” Pure Appl. Opt. 3, 452–454 (2001).

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D.: Appl. Phys. 34, 2489–2496 (2001).
[CrossRef]

R. Z. Vitlina, G. I. Surdotovich, “A ‘blurred film’ model inpolarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
[CrossRef]

2000 (1)

R. J. Martín-Palma, J. M. Martínez-Duart, A. Malats, “Determination of the optical constants of thin oxide and silver thick fims for their use in multilayer low-emissivity coatings,” Bol. R. Soc. Esp. Cerám. Vidrio 39, 472–475 (2000).

1999 (2)

A. Beléndez, C. Neipp, I. Pascual, “Analysis and elimination of boundary reflections in transmission holograms,” Opt. Laser Technol. 30, 555–556 (1999).
[CrossRef]

M-H. Chiu, J-Y. Lee, D-C Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999).
[CrossRef]

1996 (1)

1994 (1)

1989 (1)

1977 (1)

R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. 8, 201–205 (1977).
[CrossRef]

Azzam, R. M. A.

Y. Cui, R. M. A. Azzam, “Determination of the refractive index and thickness of transparent pellicles by use of the polarization-independent absentee-layer condition,” Appl. Opt. 35, 5040–5043 (1996).
[CrossRef] [PubMed]

R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. 8, 201–205 (1977).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).

Beléndez, A.

C. Neipp, I. Pascual, A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsion,” J. Opt. A. Pure Appl. Opt. 3, 504–513 (2001).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Bleached silver halide volume holograms recorded on Slavich PFG-01 emulsion: The influence of the developer,” J. Mod. Opt. 48, 1479–1494 (2001).
[CrossRef]

A. Beléndez, C. Neipp, I. Pascual, “Analysis and elimination of boundary reflections in transmission holograms,” Opt. Laser Technol. 30, 555–556 (1999).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Recent advances in new holographic silver halide materials,” in Recent Research Developments in Optics, Vol. I (Research Signpost, Trivandrum, India, 2001), pp. 35–56.

Bissoli, F.

C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
[CrossRef]

Bjelkhagen, H. I.

H. I. Bjelkhagen, Silver Halide Recording Materials for Holography and Their Processing (Springer-Verlag, Berlin, 1993).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).

Chiu, M-H.

Cui, Y.

Dakhel, A. A.

A. A. Dakhel, “Optical constants of evaporated gadolinium oxide,” Pure Appl. Opt. 3, 452–454 (2001).

Dömen, M.

H. D. Thöll, M. Dömen, C. D. Stojanoff, “Determination of the mean refractive index and the thickness of dichromated gelatin holographic films using the thin film resonance method,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 76–87 (1997).

González-Leal, J. M.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D.: Appl. Phys. 34, 2489–2496 (2001).
[CrossRef]

Kihara, T.

Kumonko, P. I.

S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).

Lee, J-Y.

Lekner, J.

Malats, A.

R. J. Martín-Palma, J. M. Martínez-Duart, A. Malats, “Determination of the optical constants of thin oxide and silver thick fims for their use in multilayer low-emissivity coatings,” Bol. R. Soc. Esp. Cerám. Vidrio 39, 472–475 (2000).

Márquez, E.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D.: Appl. Phys. 34, 2489–2496 (2001).
[CrossRef]

Martínez-Duart, J. M.

R. J. Martín-Palma, J. M. Martínez-Duart, A. Malats, “Determination of the optical constants of thin oxide and silver thick fims for their use in multilayer low-emissivity coatings,” Bol. R. Soc. Esp. Cerám. Vidrio 39, 472–475 (2000).

Martín-Palma, R. J.

R. J. Martín-Palma, J. M. Martínez-Duart, A. Malats, “Determination of the optical constants of thin oxide and silver thick fims for their use in multilayer low-emissivity coatings,” Bol. R. Soc. Esp. Cerám. Vidrio 39, 472–475 (2000).

Minkov, D. A.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D.: Appl. Phys. 34, 2489–2496 (2001).
[CrossRef]

Neipp, C.

C. Neipp, I. Pascual, A. Beléndez, “Bleached silver halide volume holograms recorded on Slavich PFG-01 emulsion: The influence of the developer,” J. Mod. Opt. 48, 1479–1494 (2001).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsion,” J. Opt. A. Pure Appl. Opt. 3, 504–513 (2001).
[CrossRef]

A. Beléndez, C. Neipp, I. Pascual, “Analysis and elimination of boundary reflections in transmission holograms,” Opt. Laser Technol. 30, 555–556 (1999).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Recent advances in new holographic silver halide materials,” in Recent Research Developments in Optics, Vol. I (Research Signpost, Trivandrum, India, 2001), pp. 35–56.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 69–87.

Pascual, I.

C. Neipp, I. Pascual, A. Beléndez, “Bleached silver halide volume holograms recorded on Slavich PFG-01 emulsion: The influence of the developer,” J. Mod. Opt. 48, 1479–1494 (2001).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsion,” J. Opt. A. Pure Appl. Opt. 3, 504–513 (2001).
[CrossRef]

A. Beléndez, C. Neipp, I. Pascual, “Analysis and elimination of boundary reflections in transmission holograms,” Opt. Laser Technol. 30, 555–556 (1999).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Recent advances in new holographic silver halide materials,” in Recent Research Developments in Optics, Vol. I (Research Signpost, Trivandrum, India, 2001), pp. 35–56.

Ratcliffe, D. B.

S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).

Razzetti, C.

C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
[CrossRef]

Romani, S.

C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
[CrossRef]

Ruíz-Pérez, J. J.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D.: Appl. Phys. 34, 2489–2496 (2001).
[CrossRef]

Sazonov, Y. A.

S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).

Skokov, G. R.

S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).

Stojanoff, C. D.

H. D. Thöll, M. Dömen, C. D. Stojanoff, “Determination of the mean refractive index and the thickness of dichromated gelatin holographic films using the thin film resonance method,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 76–87 (1997).

Su, D-C

Surdotovich, G. I.

R. Z. Vitlina, G. I. Surdotovich, “A ‘blurred film’ model inpolarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

Thöll, H. D.

H. D. Thöll, M. Dömen, C. D. Stojanoff, “Determination of the mean refractive index and the thickness of dichromated gelatin holographic films using the thin film resonance method,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 76–87 (1997).

Vitlina, R. Z.

R. Z. Vitlina, G. I. Surdotovich, “A ‘blurred film’ model inpolarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

Vorobyov, S. P.

S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).

Yokomori, K.

Zacharovas, S. J.

S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).

Zanotti, L.

C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
[CrossRef]

Zha, M.

C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
[CrossRef]

Appl. Opt. (3)

Bol. R. Soc. Esp. Cerám. Vidrio (1)

R. J. Martín-Palma, J. M. Martínez-Duart, A. Malats, “Determination of the optical constants of thin oxide and silver thick fims for their use in multilayer low-emissivity coatings,” Bol. R. Soc. Esp. Cerám. Vidrio 39, 472–475 (2000).

J. Mod. Opt. (1)

C. Neipp, I. Pascual, A. Beléndez, “Bleached silver halide volume holograms recorded on Slavich PFG-01 emulsion: The influence of the developer,” J. Mod. Opt. 48, 1479–1494 (2001).
[CrossRef]

J. Opt. (1)

R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. 8, 201–205 (1977).
[CrossRef]

J. Opt. A. Pure Appl. Opt. (2)

C. Razzetti, S. Romani, F. Bissoli, M. Zha, L. Zanotti, “Determination of the refractive indices by variable azimuth reflectometry from a single sample face,” J. Opt. A. Pure Appl. Opt. 3, 108–113 (2001).
[CrossRef]

C. Neipp, I. Pascual, A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsion,” J. Opt. A. Pure Appl. Opt. 3, 504–513 (2001).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. D. Appl. Phys. (1)

R. Z. Vitlina, G. I. Surdotovich, “A ‘blurred film’ model inpolarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

J. Phys. D.: Appl. Phys. (1)

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D.: Appl. Phys. 34, 2489–2496 (2001).
[CrossRef]

Opt. Laser Technol. (1)

A. Beléndez, C. Neipp, I. Pascual, “Analysis and elimination of boundary reflections in transmission holograms,” Opt. Laser Technol. 30, 555–556 (1999).
[CrossRef]

Pure Appl. Opt. (1)

A. A. Dakhel, “Optical constants of evaporated gadolinium oxide,” Pure Appl. Opt. 3, 452–454 (2001).

Other (7)

S. J. Zacharovas, D. B. Ratcliffe, G. R. Skokov, S. P. Vorobyov, P. I. Kumonko, Y. A. Sazonov, “Recent advances in holographic materials from Slavich,” in Holography 2000, T. H. Jeong, W. K. Sobotka, Proc. SPIE4149, 73–80 (2000).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 69–87.

H. I. Bjelkhagen, Silver Halide Recording Materials for Holography and Their Processing (Springer-Verlag, Berlin, 1993).

C. Neipp, I. Pascual, A. Beléndez, “Recent advances in new holographic silver halide materials,” in Recent Research Developments in Optics, Vol. I (Research Signpost, Trivandrum, India, 2001), pp. 35–56.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1989).

H. D. Thöll, M. Dömen, C. D. Stojanoff, “Determination of the mean refractive index and the thickness of dichromated gelatin holographic films using the thin film resonance method,” in Holographic Materials, T. J. Trout, ed., Proc. SPIE2405, 76–87 (1997).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).

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Figures (11)

Fig. 1
Fig. 1

Reflections from a single layer of absorbing material on a transparent substrate.

Fig. 2
Fig. 2

Calculated reflectance curves R and R 12 as a function of the angle of incidence for n 1 = 1, n 2 = 1.63, k 2 = 0.0035, n 3 = 1.52, d = 6 µm, and λ = 633 nm.

Fig. 3
Fig. 3

Difference between R and R 12 as a function of the angle of incidence for the numerical example considered in Fig. 2.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup.

Fig. 5
Fig. 5

Experimental procedure used to eliminate the back-reflected light produced at the glass–air interface at the rear side of the holographic plates.

Fig. 6
Fig. 6

Experimental procedure to eliminate the reflection produced at the glass–air interface of the parallel glass window.

Fig. 7
Fig. 7

Measured (open circles) and calculated (continuous wave) reflectances for PFG-01 emulsion while varying the angle of incidence from 25° to 55°. Light polarized parallel to the plane of incidence.

Fig. 8
Fig. 8

Measured (open circles) and calculated (continuous wave) reflectances for PFG-03M emulsion while varying the angle of incidence from 25° to 55°. Light polarized parallel to the plane of incidence.

Fig. 9
Fig. 9

Measured (open circles) and calculated (continuous wave) reflectances for BB-640 emulsion while varying the angle of incidence from 25° to 55°. Light polarized parallel to the plane of incidence.

Fig. 10
Fig. 10

Measured (open circles) and calculated (continuous wave) reflectances for BB-520 emulsion while varying the angle of incidence from 25° to 55°. Light polarized parallel to the plane of incidence.

Fig. 11
Fig. 11

Measured (open circles) and calculated (continuous wave) reflectances for Agfa 8E75 HD emulsion while varying the angle of incidence from 25° to 55°. Light polarized parallel to the plane of incidence.

Tables (1)

Tables Icon

Table 1 Best Fitting Parameters for the Optical Constants and the Thickness

Equations (20)

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

r=r12+r23 exp-2iβ1+r12r23 exp-2iβ,
β=4πλd2n2 cos θ2.
r12=n2 cos θ1-n1 cosθ2n2 cos θ1+n1 cosθ2,
r23=n3 cos θ2-n2 cosθ3n3 cos θ2+n2 cosθ3,
n2 cos θ2=u2-iv2,
n2 sin θ2=n1 sin θ1=n3 sinθ3.
r12=n2-ik22 cos θ1-n1u2+iv2n2-ik22 cos θ1+n1u2+iv2,
r23=n32u2+iv2-n2-ik22n32-n12 sin2 θ11/2n32u2+iv2+n2-ik22n32-n12 sin2 θ11/2,
β=2πλd2u2+iv2,
u22=12n22-k22-n12 sin2 θ1+n22-k22-n12 sin2 θ12+4n22k221/2,
v22=12-n22-k22-n12 sin2 θ1+n22-k22-n12 sin2 θ12+4n22k221/2.
R=|r|2,
R=fn1, n2, n3, k2, d2, θ1, λ.
χ2=1J2j=1JRn2, k2, d2, θ1j-Rexpθ1j2.
R12n2 cosθ1-n22-n12 sin2 θ11/2n2 cosθ1+n22-n12 sin2 θ11/22.
RBK7=rag2,
RBK7θ1=Irθ1Iiθ1.
fθ1=RBK7θ1RBK7θ1
Rexpθ1=fθ1Rθ1.
χ2=1J2j=1JRj-Rexp,j2,

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