Abstract

Computation of Mueller matrix elements by infrared scattering from randomly rough two-dimensional surfaces and results of a method for graphic display of the data are presented. A full wave electromagnetic scattering model first generates raw data elements of the 4 × 4 Mueller matrix F(θ,nλ,kλ,σS2,h2) in beam backscattering angle (θ) ranging from normal to oblique incidence, in refractive index of the beam scatterer (nλikλ) spanning the 9 ≤ λ ≤ 12.5 μm midinfrared band, and in mean-squared slope (σS2) and mean-squared height (〈h2〉) of the scattering surface. These data are next compressed into a graphics format file occupying considerably less computer storage space and mapped into color images of the Mueller elements as viewed on a high-resolution graphics terminal. The diagonal and two off-diagonal elements are animated in the λ–θ plane according to variations in σS2 and 〈h2〉. Predicted elements for polarized IR beam energies on vibrational resonance of the surface molecules, and particularly the off-diagonal elements, show subtle properties of the scatterer as viewed in the animation sequences.

© 1993 Optical Society of America

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  1. A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).
  2. S. M. Haugland, E. Z. Bahar, A. H. Carrieri, “Identification of contaminant coatings over rough surfaces using polarized IR scattering,” Appl. Opt. 31, 3847–3852 (1992).
    [Crossref] [PubMed]
  3. E. Bahar, “Review of the full wave solutions for rough surface scattering and depolarization: comparisons with geometric and physical optics, perturbation, and two-scale hybrid solutions,” J. Geophys. Res. 92, 5209–5224 (1987).
    [Crossref]
  4. E. Bahar, “Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. AP-29, 443–454 (1981).
    [Crossref]
  5. E. Bahar, “Scattering and depolarization of electromagnetic waves—full wave solutions,” Internal Report RADC-TR-83-118 (Rome Air Development Center, Air Force Systems Command, Griffiss Air Force Base, N.Y., 1983).
  6. E. Bahar, M. A. Fitzwater, “Scattering cross sections for composite rough surfaces using the unified full wave approach,” IEEE Trans. Antennas Propag. AP-32, 730–734 (1984).
    [Crossref]
  7. E. Bahar, M. A. Fitzwater, “Copolarized and cross-polarized incoherent specific intensities for waves at oblique incidence upon a layer of finitely conducting particles with rough surfaces,” J. Opt. Soc. Am. A 4, 41–56 (1987).
    [Crossref]
  8. M. R. Querry, “Optical constants of minerals and other materials from the millimeter to the ultraviolet,” Internal Report CRDEC-CR-88009 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1987); M. R. Querry, Department of Physics, University of Missouri–Kansas City, Kansas City, Mo., and M. E. Milham, U. S. Army Edgewood Research, Development, and Engineering Center, Aberdeen Proving Ground, Md. (personal communication, 1986).
  9. R. Piffath, U.S. Army Edgewood Research, Development, and Engineering Center, Aberdeen Proving Ground, Md. (personal communication, 1988).
  10. H. F. Hameka, A. H. Carrieri, J. O. Jensen, “Calculations of the structure and the vibrational infrared frequencies of some methylphosphonates,” Phosph. Sulfur Silicon Related Elem. 66, 1–11 (1992).
    [Crossref]

1992 (2)

S. M. Haugland, E. Z. Bahar, A. H. Carrieri, “Identification of contaminant coatings over rough surfaces using polarized IR scattering,” Appl. Opt. 31, 3847–3852 (1992).
[Crossref] [PubMed]

H. F. Hameka, A. H. Carrieri, J. O. Jensen, “Calculations of the structure and the vibrational infrared frequencies of some methylphosphonates,” Phosph. Sulfur Silicon Related Elem. 66, 1–11 (1992).
[Crossref]

1987 (2)

E. Bahar, “Review of the full wave solutions for rough surface scattering and depolarization: comparisons with geometric and physical optics, perturbation, and two-scale hybrid solutions,” J. Geophys. Res. 92, 5209–5224 (1987).
[Crossref]

E. Bahar, M. A. Fitzwater, “Copolarized and cross-polarized incoherent specific intensities for waves at oblique incidence upon a layer of finitely conducting particles with rough surfaces,” J. Opt. Soc. Am. A 4, 41–56 (1987).
[Crossref]

1984 (1)

E. Bahar, M. A. Fitzwater, “Scattering cross sections for composite rough surfaces using the unified full wave approach,” IEEE Trans. Antennas Propag. AP-32, 730–734 (1984).
[Crossref]

1981 (1)

E. Bahar, “Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. AP-29, 443–454 (1981).
[Crossref]

Bahar, E.

E. Bahar, “Review of the full wave solutions for rough surface scattering and depolarization: comparisons with geometric and physical optics, perturbation, and two-scale hybrid solutions,” J. Geophys. Res. 92, 5209–5224 (1987).
[Crossref]

E. Bahar, M. A. Fitzwater, “Copolarized and cross-polarized incoherent specific intensities for waves at oblique incidence upon a layer of finitely conducting particles with rough surfaces,” J. Opt. Soc. Am. A 4, 41–56 (1987).
[Crossref]

E. Bahar, M. A. Fitzwater, “Scattering cross sections for composite rough surfaces using the unified full wave approach,” IEEE Trans. Antennas Propag. AP-32, 730–734 (1984).
[Crossref]

E. Bahar, “Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. AP-29, 443–454 (1981).
[Crossref]

E. Bahar, “Scattering and depolarization of electromagnetic waves—full wave solutions,” Internal Report RADC-TR-83-118 (Rome Air Development Center, Air Force Systems Command, Griffiss Air Force Base, N.Y., 1983).

Bahar, E. Z.

Bottiger, J. R.

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Carrieri, A. H.

H. F. Hameka, A. H. Carrieri, J. O. Jensen, “Calculations of the structure and the vibrational infrared frequencies of some methylphosphonates,” Phosph. Sulfur Silicon Related Elem. 66, 1–11 (1992).
[Crossref]

S. M. Haugland, E. Z. Bahar, A. H. Carrieri, “Identification of contaminant coatings over rough surfaces using polarized IR scattering,” Appl. Opt. 31, 3847–3852 (1992).
[Crossref] [PubMed]

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Fitzwater, M. A.

E. Bahar, M. A. Fitzwater, “Copolarized and cross-polarized incoherent specific intensities for waves at oblique incidence upon a layer of finitely conducting particles with rough surfaces,” J. Opt. Soc. Am. A 4, 41–56 (1987).
[Crossref]

E. Bahar, M. A. Fitzwater, “Scattering cross sections for composite rough surfaces using the unified full wave approach,” IEEE Trans. Antennas Propag. AP-32, 730–734 (1984).
[Crossref]

Hameka, H. F.

H. F. Hameka, A. H. Carrieri, J. O. Jensen, “Calculations of the structure and the vibrational infrared frequencies of some methylphosphonates,” Phosph. Sulfur Silicon Related Elem. 66, 1–11 (1992).
[Crossref]

Haugland, S. M.

S. M. Haugland, E. Z. Bahar, A. H. Carrieri, “Identification of contaminant coatings over rough surfaces using polarized IR scattering,” Appl. Opt. 31, 3847–3852 (1992).
[Crossref] [PubMed]

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Henry, C. E.

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Herzinger, C. M.

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Jensen, J. L.

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Jensen, J. O.

H. F. Hameka, A. H. Carrieri, J. O. Jensen, “Calculations of the structure and the vibrational infrared frequencies of some methylphosphonates,” Phosph. Sulfur Silicon Related Elem. 66, 1–11 (1992).
[Crossref]

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Owens, D. J.

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Piffath, R.

R. Piffath, U.S. Army Edgewood Research, Development, and Engineering Center, Aberdeen Proving Ground, Md. (personal communication, 1988).

Querry, M. R.

M. R. Querry, “Optical constants of minerals and other materials from the millimeter to the ultraviolet,” Internal Report CRDEC-CR-88009 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1987); M. R. Querry, Department of Physics, University of Missouri–Kansas City, Kansas City, Mo., and M. E. Milham, U. S. Army Edgewood Research, Development, and Engineering Center, Aberdeen Proving Ground, Md. (personal communication, 1986).

Schmidt, K. E.

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (2)

E. Bahar, “Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope,” IEEE Trans. Antennas Propag. AP-29, 443–454 (1981).
[Crossref]

E. Bahar, M. A. Fitzwater, “Scattering cross sections for composite rough surfaces using the unified full wave approach,” IEEE Trans. Antennas Propag. AP-32, 730–734 (1984).
[Crossref]

J. Geophys. Res. (1)

E. Bahar, “Review of the full wave solutions for rough surface scattering and depolarization: comparisons with geometric and physical optics, perturbation, and two-scale hybrid solutions,” J. Geophys. Res. 92, 5209–5224 (1987).
[Crossref]

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

Phosph. Sulfur Silicon Related Elem. (1)

H. F. Hameka, A. H. Carrieri, J. O. Jensen, “Calculations of the structure and the vibrational infrared frequencies of some methylphosphonates,” Phosph. Sulfur Silicon Related Elem. 66, 1–11 (1992).
[Crossref]

Other (4)

A. H. Carrieri, J. R. Bottiger, D. J. Owens, C. E. Henry, C. M. Herzinger, S. M. Haugland, J. O. Jensen, K. E. Schmidt, J. L. Jensen, “Mid infrared polarized light scattering: applications for the remote detection of chemical and biological contaminations,” Internal Report CRDEC-TR-318 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1992).

M. R. Querry, “Optical constants of minerals and other materials from the millimeter to the ultraviolet,” Internal Report CRDEC-CR-88009 (U.S. Army Chemical Research, Development, and Engineering Center, Aberdeen Proving Ground, Md., 1987); M. R. Querry, Department of Physics, University of Missouri–Kansas City, Kansas City, Mo., and M. E. Milham, U. S. Army Edgewood Research, Development, and Engineering Center, Aberdeen Proving Ground, Md. (personal communication, 1986).

R. Piffath, U.S. Army Edgewood Research, Development, and Engineering Center, Aberdeen Proving Ground, Md. (personal communication, 1988).

E. Bahar, “Scattering and depolarization of electromagnetic waves—full wave solutions,” Internal Report RADC-TR-83-118 (Rome Air Development Center, Air Force Systems Command, Griffiss Air Force Base, N.Y., 1983).

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Figures (2)

Fig. 1
Fig. 1

Backscattering (horizontal axis in degrees) infrared (vertical axis in micrometers) predictions by full theory of diagonal and two off-diagonal Mueller matrix elements of an absorbing DMMP liquid layer on a randomly rough soil substrate. The coating is optically thick with 10-μm2 mean-squared height and 0.20 mean-squared slope in the top row of elements, 10 μm2 and 0.70 in the bottom row. We computed these data by using the Gaussian autocorrelation function of Eq. (4). (Using N = 6 or N = 8 statistics does not affect the results in any appreciable way.) Molecular absorption in DMMP maximizes at wavelengths listed in Table 1 and is shown in k(λ) of Fig. 2.

Fig. 2
Fig. 2

Infrared refractive-index measurements N(λ) = n(K) − ik(λ) of liquid analyte DMMP. The real and imaginary parts are shown as the top and bottom curves, respectively, and molecular vibrational modes are identifed in Table 1. These data are reproduced with the permission of M. Querry.

Tables (1)

Tables Icon

Table 1 Infrared Wavelengths of Relative Intense Absorption and Their Vibrational Mode Assignments for the Chemical Analyte DMMP

Equations (9)

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I M ( S 0 S 1 s 3 s 4 ) , I S ( s 0 s 1 s 2 s 3 ) = ( S 0 + S 1 S 0 S 1 s 2 s 3 ) ,
F = A F B ,
A = ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 ) , B = ( 1 2 1 2 0 0 1 2 1 2 0 0 0 0 0 0 0 0 0 1 ) ,
F = ( Σ υ υ υ υ Σ υ h υ h 0 0 Σ h υ h υ Σ h h h h 0 0 0 0 Re { Σ υ υ h h + Σ υ h h υ } Im { Σ υ υ h h } 0 0 Im { Σ υ υ h h } Re { Σ υ υ h h Σ υ h h υ } ) ,
i j k l Q D i j D k l * ( n · a y ) 2 P 2 p S d h x d h z ,
Q = 1 2 k 0 2 0 { exp [ υ y 2 h 2 ( 1 r h h ) ] exp ( υ y h 2 ) } × J 0 ( υ x z r d ) r d d r d .
r h h ( r d ) = exp ( r d 2 l c 2 ) .
r h h ( r d ) = [ 1 3 ζ 2 8 + ζ 4 32 + ζ 6 3072 ] ζ K 1 ( ζ ) + [ 1 2 ζ 2 4 ζ 4 96 ] ζ 2 K 0 ( ζ ) , ζ r d κ 8 , κ 8 2 0 . 4 σ S 2 h 2 .
r h h ( r d ) = [ 1 3 ζ 2 4 ζ 4 96 ] ζ K 1 ( ζ ) + [ 1 2 + 3 ζ 2 16 ] ζ 2 K 0 ( ζ ) , ζ r d κ 6 , κ 6 2 σ S 2 h 2 .

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