Abstract

Ellipsometer measurements of the effective complex refractive index at a wavelength of 10.6 μm are made on a series of glass and aluminum surfaces of increasing surface roughness. The measured values are then used to calculate the degree of emission polarization and are shown to be in agreement with the experimentally determined values when depolarization is small. Comparisons are also made with calculations based on the Kirchhoff scattering theory. Both the theory and the experimental results indicate that it is the local surface slope and not the roughness magnitude that is the prime factor in determining the degree of emission polarization from the samples studied.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Arago, Ann. Chim. Phys. 27, 89–90 (1824).
  2. C. Acquista, “Polarization properties of natural background materials in the IR,” in Multispectral Image Processing and Enhancement, M. R. Weathersby, ed., Proc. SPIE933, 155–158 (1988).
  3. R. D. Tooley, “Man-made target detection using infrared polarization,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 52–58 (1989).
  4. T. J. Rogne, F. G. Smith, J. E. Rice, “Passive target detection using polarized components of infrared signatures,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. SPIE1317, 242–251 (1990).
    [CrossRef]
  5. D. L. Jordan, G. Lewis, “Measurements of the effect of surface roughness on the polarization state of thermally emitted radiation,” Opt. Lett. 19, 692–694 (1994).
    [CrossRef] [PubMed]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 622.
  7. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3, pp. 25–33.
  8. A. A. Maradudin, R. E. Luna, E. R. Mendez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
    [CrossRef]
  9. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1970), Chap. 11, pp. 55–59.
  10. F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,”Appl. Opt. 4, 767–773 (1965).
    [CrossRef]
  11. F. E. Nicodemus, “Reflectance nomenclature and directional reflectance and emissivity,” Appl. Opt. 9, 1474–1475 (1970).
    [CrossRef] [PubMed]
  12. S. F. Nee, “Ellipsometric analysis for surface roughness and texture,” Appl. Opt. 27, 2819–2831 (1988).
    [CrossRef] [PubMed]
  13. R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
    [CrossRef]
  14. D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
    [CrossRef]
  15. V. I. Sayapina, D. Ya. Svet, D. R. Popova, “Influence of surface roughness on the emissivity of metals,” Teplofizika Vys. Temp. 10, 528–535 (1972).
  16. D. V. Mikhailova, I. M. Fuks, Emissivity of a statistically rough surface including multiple reflections,” J. Commun. Tech. Electron. 38, 128–136 (1993).
  17. R. M. A. Azzam, “Ellipsometric configurations and techniques,” in Optical Characterization Techniques for Semiconductor Technology, D. E. Aspnes, S. So, R. F. Potter, eds., Proc. SPIE276, 180–187 (1981).
  18. J. R. Blanco, P. J. McMarr, “Roughness measurement of Si and Al by variable angle spectroscopic ellipsometry,” Appl. Opt. 30, 3210–3220 (1991).
    [CrossRef] [PubMed]
  19. J. R. Beattie, “Optical constants of metals in the infrared-experimental methods,” Philos. Mag. 46, 235–245 (1955).
  20. R. Anderson, “Polarized properties of the directional-hemispherical reflectance and emissivity of an opaque surface,” in Polarization and Remote Sensing, W. G. Egan, ed., Proc. SPIE1747, 49–59 (1992).
    [CrossRef]

1994

1993

A. A. Maradudin, R. E. Luna, E. R. Mendez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

D. V. Mikhailova, I. M. Fuks, Emissivity of a statistically rough surface including multiple reflections,” J. Commun. Tech. Electron. 38, 128–136 (1993).

1991

1988

1982

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

1972

V. I. Sayapina, D. Ya. Svet, D. R. Popova, “Influence of surface roughness on the emissivity of metals,” Teplofizika Vys. Temp. 10, 528–535 (1972).

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

1970

1965

1955

J. R. Beattie, “Optical constants of metals in the infrared-experimental methods,” Philos. Mag. 46, 235–245 (1955).

1824

F. Arago, Ann. Chim. Phys. 27, 89–90 (1824).

Acquista, C.

C. Acquista, “Polarization properties of natural background materials in the IR,” in Multispectral Image Processing and Enhancement, M. R. Weathersby, ed., Proc. SPIE933, 155–158 (1988).

Anderson, R.

R. Anderson, “Polarized properties of the directional-hemispherical reflectance and emissivity of an opaque surface,” in Polarization and Remote Sensing, W. G. Egan, ed., Proc. SPIE1747, 49–59 (1992).
[CrossRef]

Arago, F.

F. Arago, Ann. Chim. Phys. 27, 89–90 (1824).

Aspnes, D. E.

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

Azzam, R. M.

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1970), Chap. 11, pp. 55–59.

R. M. A. Azzam, “Ellipsometric configurations and techniques,” in Optical Characterization Techniques for Semiconductor Technology, D. E. Aspnes, S. So, R. F. Potter, eds., Proc. SPIE276, 180–187 (1981).

Bashara, N. M.

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1970), Chap. 11, pp. 55–59.

Beattie, J. R.

J. R. Beattie, “Optical constants of metals in the infrared-experimental methods,” Philos. Mag. 46, 235–245 (1955).

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3, pp. 25–33.

Blanco, J. R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 622.

Fuks, I. M.

D. V. Mikhailova, I. M. Fuks, Emissivity of a statistically rough surface including multiple reflections,” J. Commun. Tech. Electron. 38, 128–136 (1993).

Jordan, D. L.

Lewis, G.

Luna, R. E.

A. A. Maradudin, R. E. Luna, E. R. Mendez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, R. E. Luna, E. R. Mendez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

McMarr, P. J.

Mendez, E. R.

A. A. Maradudin, R. E. Luna, E. R. Mendez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

Mikhailova, D. V.

D. V. Mikhailova, I. M. Fuks, Emissivity of a statistically rough surface including multiple reflections,” J. Commun. Tech. Electron. 38, 128–136 (1993).

Nee, S. F.

Nicodemus, F. E.

Popova, D. R.

V. I. Sayapina, D. Ya. Svet, D. R. Popova, “Influence of surface roughness on the emissivity of metals,” Teplofizika Vys. Temp. 10, 528–535 (1972).

Rice, J. E.

T. J. Rogne, F. G. Smith, J. E. Rice, “Passive target detection using polarized components of infrared signatures,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. SPIE1317, 242–251 (1990).
[CrossRef]

Rogne, T. J.

T. J. Rogne, F. G. Smith, J. E. Rice, “Passive target detection using polarized components of infrared signatures,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. SPIE1317, 242–251 (1990).
[CrossRef]

Sayapina, V. I.

V. I. Sayapina, D. Ya. Svet, D. R. Popova, “Influence of surface roughness on the emissivity of metals,” Teplofizika Vys. Temp. 10, 528–535 (1972).

Smith, F. G.

T. J. Rogne, F. G. Smith, J. E. Rice, “Passive target detection using polarized components of infrared signatures,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. SPIE1317, 242–251 (1990).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3, pp. 25–33.

Svet, D. Ya.

V. I. Sayapina, D. Ya. Svet, D. R. Popova, “Influence of surface roughness on the emissivity of metals,” Teplofizika Vys. Temp. 10, 528–535 (1972).

Tooley, R. D.

R. D. Tooley, “Man-made target detection using infrared polarization,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 52–58 (1989).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 622.

Ann. Chim. Phys.

F. Arago, Ann. Chim. Phys. 27, 89–90 (1824).

Appl. Opt.

J. Commun. Tech. Electron.

D. V. Mikhailova, I. M. Fuks, Emissivity of a statistically rough surface including multiple reflections,” J. Commun. Tech. Electron. 38, 128–136 (1993).

Opt. Lett.

Philos. Mag.

J. R. Beattie, “Optical constants of metals in the infrared-experimental methods,” Philos. Mag. 46, 235–245 (1955).

Phys. Rev. B

R. M. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Teplofizika Vys. Temp.

V. I. Sayapina, D. Ya. Svet, D. R. Popova, “Influence of surface roughness on the emissivity of metals,” Teplofizika Vys. Temp. 10, 528–535 (1972).

Thin Solid Films

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

Waves Random Media

A. A. Maradudin, R. E. Luna, E. R. Mendez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

Other

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1970), Chap. 11, pp. 55–59.

C. Acquista, “Polarization properties of natural background materials in the IR,” in Multispectral Image Processing and Enhancement, M. R. Weathersby, ed., Proc. SPIE933, 155–158 (1988).

R. D. Tooley, “Man-made target detection using infrared polarization,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 52–58 (1989).

T. J. Rogne, F. G. Smith, J. E. Rice, “Passive target detection using polarized components of infrared signatures,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. SPIE1317, 242–251 (1990).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 622.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963), Chap. 3, pp. 25–33.

R. Anderson, “Polarized properties of the directional-hemispherical reflectance and emissivity of an opaque surface,” in Polarization and Remote Sensing, W. G. Egan, ed., Proc. SPIE1747, 49–59 (1992).
[CrossRef]

R. M. A. Azzam, “Ellipsometric configurations and techniques,” in Optical Characterization Techniques for Semiconductor Technology, D. E. Aspnes, S. So, R. F. Potter, eds., Proc. SPIE276, 180–187 (1981).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Coordinate system.

Fig. 2
Fig. 2

Normalized slope distribution for glass sample d. The points are measured values and the curves correspond to Gaussian and Cauchy distributions.

Fig. 3
Fig. 3

Experimental arrangement. CMT, HgCdTe.

Fig. 4
Fig. 4

Measured (symbols) and calculated (curves) values of the degree of emission polarization as a function of target angle for (a) glass surfaces and (b) aluminum surfaces.

Fig. 5
Fig. 5

Measured degree of emission polarization as a function of rms surface roughness for (a) glass surfaces and (b) aluminum surfaces.

Fig. 6
Fig. 6

Measured degree of emission polarization as a function of rms surface slope for (a) glass surfaces and (b) aluminum surfaces.

Fig. 7
Fig. 7

Ratio of measured degree of emission polarization from a rough surface to that from a smooth one versus rms surface slope: +, glass, θ = 40°; Δ, glass, θ = 60°; x, aluminum, θ = 40°; ●, aluminum, θ = 60°. Solid curves are theoretical ones for Gaussian and Cauchy slope distributions.

Tables (2)

Tables Icon

Table 1 Surface Parameters

Tables Icon

Table 2 Measured Depolarization

Equations (26)

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

tan 2 α = S 2 / S 1 .
sin 2 β = S 3 / ( S 1 2 + S 2 2 + S 3 2 ) 1 / 2 .
P = ( S 1 2 + S 2 2 + S 3 2 ) 1 / 2 / S 0 .
P = ( I max I min ) / ( I max + I min ) ,
e ( θ ) = 1 | R ( θ ) | 2 ,
e p ( θ ) = 1 | R p ( θ ) | 2 ,
e s ( θ ) = 1 | R s ( θ ) | 2 .
sin ψ = cos ϕ sin ξ / sin η ,
cos η = cos θ cos ξ + sin θ sin ϕ sin ξ .
E s = E s cos ψ + E p sin ψ ,
E p = E s sin ψ E p cos ψ .
I p I s = ( | R s ( η ) | 2 | R p ( η ) | 2 ) cos 2 ψ ,
I p + I s = 2 ( | R s ( η ) | 2 + | R p ( η ) | 2 ) .
P = I p I s I p + I s .
I p I s = 4 | 1 | 2 Re ( sin 2 η ) ( sin 2 η cos η 2 cos 2 ϕ sin 2 ξ cos η ) | ( cos η + sin 2 η ) ( cos η + sin 2 η ) | 2 ,
I p + I s = 4 cos η [ Re sin 2 η | cos η + sin 2 η | 2 + Re ( * sin 2 η ) | cos η + sin 2 η | 2 ] ,
P ( rough ) P ( smooth ) = cos ξ ( 1 5 2 sin 2 ξ ) .
P ( m ) d m = 2 m 0 2 exp ( m 2 m 0 2 ) m d m ( Gaussian ) ,
P ( m ) d m = m 0 m d m ( m 0 2 + m 2 ) 3 / 2 ( Cauchy ) ,
P ( rough ) P ( smooth ) = 5 m 0 2 ( 5 m 0 2 + 3 2 ) π m 0 exp ( 1 m 0 2 ) × erfc ( 1 m 0 ) ( Gaussian ) ,
P ( rough ) P ( smooth ) = 2 3 m 0 2 ( 1 + m 0 ) 2 ( Cauchy , | m 0 | < 1 ) .
P ( rough , ) = sec η ( sin 2 η 2 cos 2 ϕ sin 2 ξ ) sec η + cos η ,
P ( rough , ) = sin 2 θ 1 + cos 2 θ
n 2 k 2 = sin 2 θ p ( 1 + tan 2 θ p cos 4 β p ) ,
2 n k = sin 2 θ p tan 2 θ p sin 4 β p ) .
P ( θ ) = e p ( θ ) e s ( θ ) e p ( θ ) + e s ( θ ) .

Metrics