Measured Degree of Infrared Polarization 

for a Variety of Thermal Emitting Surfaces 

by Kristan P. Gurton, Rachid Dahmani, and Gordon Videen 

ARL-TR-3240 June 2004 

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Army Research Laboratory 

Adelphi, MD 20783-1197 

ARL-TR-3240 June 2004 

Measured Degree of Infrared Polarization 

for a Variety of Thermal Emitting Surfaces 

Kristan P. Gurton, Rachid Dahmani, and Gordon Videen 

Computational and Information Sciences Directorate, ARL 

Approved for public release; distribution unlimited. 
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Measured Degree of Infrared Polarization for a Variety of Thermal Emitting 

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Kristan P. Gurton, Rachid Dahmani, and Gordon Videen 

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14. ABSTRACT 

We report on a series of parametric measurements designed to measure the attenuative effects that surface roughness and 

aerosol contamination play in reducing polarized thermal surface emission. In particular, we measure the spectrally resolved 

linear degree of polarization (LDOP) for a series of roughened borosilicate (Pyrex1

) glass substrates as a function of roughness 

parameter, Ra, root mean square slope, m, and the angle of observation, θ. Spectrally resolved LDOP is measured over the 

waveband region 4 to13 μm by a modified Fourier transform IR spectrometer in which a wire-grid polarizer and an 

achromatic quarter-wave plate are used in conjunction to measure all four Stokes parameters. 

A second set of measurements is conducted on similar smooth glass substrates that are subjected to varying degrees of dew 

formation and aerosol contamination. Test substrates are oriented at a high grazing angle of 80 degrees and placed in a closed

chamber. Dew or attenuative particulates, i.e., carbon black, potassium bromide, or pollen particles, are allowed to 

condense/settle on the thermal emitting surface while a band-averaged LDOP is recorded with a long-wave polarimetric IR 

imaging system. Measured results are then compared with predictive calculations based on a weighted Fresnel relation. 

1

Pyrex® is a registered trademark of Corning. 

15. SUBJECT TERMS

Polarization, infrared, dew, surface contamination 

16. SECURITY CLASSIFICATION OF:

19a. NAME OF RESPONSIBLE PERSON

Kristan Gurton 

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Prescribed by ANSI Std. Z39.18 
iii 

Contents 

List of Figures iv

Acknowledgments vi

1. Introduction 1

2. Experiment: Surface Roughness 4

3. Results: Surface Roughness 7

4. Experiment: Dew Formation and Aerosol Contamination 11

5. Results: Dew Formation and Aerosol Contamination 17

6. Discussion 19

7. References 23

Distribution List 25
iv 

List of Figures 

Figure 1. Complex indices of refraction used for the borosilicate (Pyrex) glass plates (14)..........4 

Figure 2. Measured rms slope distribution for the three roughened borosilicate (Pyrex) glass 

substrates. (Here we have assumed a Gaussian distribution.) ..................................................5 

Figure 3. Simple schematic showing the experimental setup used during the surface 

roughness spectro-polarimetric measurement............................................................................5 

Figure 4. Measured LDOP as a function of wavelength and angle of incidence for a smooth

borosilicate glass substrate heated to 65 oC. (Also shown [triangular data points] is the 

corresponding calculated LDOP for an emission wavelength of 9.28 μm based on the 

Fresnel relations of equations 4 through 6.)...............................................................................8 

Figure 5. Measured LDOP for a lightly roughened borosilicate plate with Ra=3.98μm and 

rms slope=9.67 degrees, as a function of wavelength and angle of incidence. (Plate 

temperature was held at 65 oC.) .................................................................................................8 

Figure 6. Measured LDOP for a moderately roughened borosilicate plate with Ra=4.80μm 

and rms slope=8.60 degrees, as a function of wavelength and angle of incidence. (Plate 

temperature was held at 65 oC.) .................................................................................................9 

Figure 7. Measured LDOP for a very rough borosilicate plate with Ra=6.68μm and rms 

slope=11.90 degrees, as a function of wavelength and angle of incidence. (Plate 

temperature was held at 65 oC.) .................................................................................................9 

Figure 8. Measured LDOP as a function of wavelength and angle of incidence for a smooth 

borosilicate plate coated with a thin layer of black Krylon paint. (Plate temperature was 

held at 65 oC.) ..........................................................................................................................10 

Figure 9. Measured LDOP as a function of wavelength and angle of incidence for a smooth 

borosilicate plate coated with a thin layer of a green CARC paint. (Plate temperature was 

held at 65 oC.) ..........................................................................................................................11 

Figure 10. Diagram showing the experimental setup used for the dew/aerosol contamination 

study. (The test plate is oriented at a fixed angle of 80 degrees and held at room 

temperature.) ............................................................................................................................12 

Figure 11. Video image series showing the dew condensation process. (Shown in each 

image is the corresponding coverage ratio, [i.e., surface area covered divided by the total 

area], and the corresponding measured LDOP for θ=80°.) .....................................................14 

Figure 12. Sample calibrated LWIR polarimetric image used to determine the LDOP for a 

smooth glass substrate contaminated by a modest amount of carbon black particles. 

(LDOP is determined from the gray scale values for the pixels that represent the heated 

glass surface.)...........................................................................................................................15 

Figure 13. Sample visible images showing various forms of aerosols contamination 

considered, i.e., orchard pollen (top left), carbon black (top right), and KBr particles 

(bottom)....................................................................................................................................16 
v 

Figure 14. Measured LDOP for varying degrees of dew (water) coverage on the surface of a 

smooth borosilicate glass substrate at 22 oC, θ=80°. (Also shown is the calculated LDOP 

by the geometric approach of Videen (12).) ............................................................................18 

Figure 15. Measured LDOP for a smooth borosilicate glass plate held at 22 oC, contaminated 

with varying degrees of carbon black, KBr particles, or pollen, that were evenly dispersed 

on the surface. (Substrates mounted at θ=80° [the dashed line shown represents the 

corresponding curve fit]. Also shown is the calculated LDOP based on the geometric 

approach put forth by Videen.) ................................................................................................18 

Figure 16. Comparison of measured LDOP (taken at 9.90 μm) as a function substrate 

orientation for various roughened glass plates. (Also shown are the measured and 

Fresnel-based calculations for smooth glass substrates [top dashed line] and results from 

Jordan and Lewis [bottom dashed line] (7).) ..........................................................................20 
vi 

Acknowledgments 

We would like thank Dr. Huey Anderson of the U.S. Army Aviation and Missile Command for 

his continued support and assistance in conducting this research. Also we would like to thank 

Dr. David Chenault, Mr. Graig Farlow, and Mr. Michael Gulley of SY Technologies, Inc., for 

their insight and development of the LWIR polarimetric camera system used in research. 
1 

1. Introduction 

It is generally accepted that smooth surfaces emit thermal radiation that is partially polarized, 

depending on the angle of observation (1,2). This induced polarized emission originates from 

differences in orthogonal components of the directional spectral emissivity, ε (λ,T,θ ,φ) (3). 

Because many man-made objects tend to possess surface structures that are more uniform when 

compared to common, naturally occurring background materials (e.g., soil, vegetation, trees, 

etc.), it has been suggested that by examining the polarization state of the IR image forming 

radiation, one can significantly improve the ability to see objects that are obscured by 

background clutter (4,5,6). 

In order to understand the conditions necessary for polarized thermal emission to occur, we start 

by considering an object with a planar surface bound by air with directional spectral emissivity, 

ε (λ,T,θ ,φ). By considering the steady state form of Kirchhoff’s law, we can express 

directional spectral emissivity in terms of the directional spectral absorptivity, ) α(λ,T,θ ,φ , and 

reflectivity, ) r(λ,T,θ ,φ , i.e., 

ε (λ,T,θ,φ) = α(λ,T,θ ,φ) = 1− r(λ,T,θ,φ) . (1) 

The angles φ and θ represent the surface azimuth and the angle between the surface normal, nˆ , 

and the detector’s line of sight (LOS), respectively. 

If we now express the total emissivity in terms of two orthogonal components, ⊥ ε and // ε , we 

have 

ε(λ,T,θ,φ) =

2

( , , , ) ( , , , ) ε ⊥ λ T θ φ + ε // λ T θ φ (2) 

in which the symbols ⊥ and // designate the directions perpendicular and parallel to the plane 

of emission, i.e., the plane defined by the surface normal and the LOS. Similarly, by expressing 

the absorptivity and reflectivity in terms of their orthogonal components, we find that ⊥ ε and // ε

can be expressed as 

ε (λ,T,θ ,φ) α (λ,T,θ.φ) 1 r (λ,T,θ,φ) ⊥ = ⊥ = − ⊥ (3a) 

( , , , ) ( , , , ) 1 ( , , , ) ε // λ T θ φ = α // λ T θ φ = − r// λ T θ φ . (3b) 

Let us now define a linear degree of emission polarization, ) LDOP(λ,θ , as the difference 

between the two orthogonal emissivities divided by the total emittance. We find 

( , ) ( ( , ) ( , )) ( ( , ) ( , )) LDOP λ θ = ε ⊥ λ θ − ε // λ θ ε ⊥ λ θ + ε // λ θ , (4) 
2 

in which we have temporarily omitted the temperature dependences for brevity. By representing 

the reflectivity in terms of Fresnel coefficients, we find two representations for the orthogonal 

components of the emissivity, depending on whether the emitting surface is a dielectric or a 

metal (3). 

For a moderately absorbing dielectric surface, we find 

2

2 2 1/ 2

2 2 1/ 2

(( ( ) ( )) sin ) cos

(( ( ) ( )) sin ) cos ( , ) 1













− − +

− − − ⊥ = − λ λ θ θ

λ λ θ θ

ε λ θ

n ik

n ik

 (5a) 

2

2 2 2 1/ 2

2 2 2 1/ 2

// ( ( ) ( )) cos (( ( ) ( )) sin )

( ( ) ( )) cos (( ( ) ( )) sin ) ( , ) 1













− − + − −

− − − − − = − λ λ θ λ λ θ

λ λ θ λ λ θ

ε λ θ

n ik n ik

n ik n ik

 (5b) 

and for a pure metallic surface, 

cos 2 ( ) cos ( ) ( )

4 ( ) cos ( , ) 2 2 2 θ λ θ λ λ

λ θ

ε λ θ

n n k

n

+ + + ⊥ = (6a) 

( ( ) ( )) cos 2 ( ) cos 1

4 ( ) cos ( , ) // 2 2 2 + + + = λ λ θ λ θ

λ θ

ε λ θ

n k n

n

 (6b) 

in which air is assumed to be surrounding the surface with the index of refraction taken to be 1, 

and the complex refractive index for the surface is defined as ) m(λ) = n(λ) − ik(λ . 

Equations 4 through 6 are valid only for smooth, homogenous surfaces that are contamination 

free. As a result, the predicted linear degree of polarization (LDOP) expressed by equation 4 

should be considered an ideal case. Minor surface anomalies can result in great differences 

between measured and calculated LDOP. 

Various models have been proposed to calculate the attenuation seen in the polarized emission 

when the surface in question is either roughened or contaminated by small particles. Jordan and 

Lewis first reported both measured and calculated attenuated thermal emission over the 

waveband 10 to 11 μm for a series of roughened glass and aluminum substrates as a function of 

surface orientation and a measured slope distribution (7,8). In their report, they present a 

modified Fresnel model that effectively weights the predicted emissivity by the normalized slope 

distribution. They report good agreement between measured and calculated LDOP for light to 

moderately roughened surfaces, but agreement was less certain as the roughened facets became 

larger. 
3 

 Separately, both Shaw and Chang expand on the slope-weighted Fresnel approach by taking into 

account facet shadowing and multiple scattering (9,10,11). Similar to the Jordan approach, they 

treat the roughened surface as a series of infinitesimally small planar facets and integrate over all 

possible orientations described by the normalized slope distribution. 

Recently, Videen has proposed a geometric model that describes the attenuation of polarized 

emittance for smooth surfaces that become contaminated by a varying density of small spherical 

particles (12). 

Regardless of the type of surface anomaly, most models attribute the attenuation of polarized 

emission to a reduction of the effective emitting area; i.e., surfaces that are rough or partially 

covered by contaminating particles reduce the effective area that contributes to the polarized 

emission. 

In order to understand how polarized thermal emission is affected by various surface conditions, 

a series of spectral IR polarimetric measurements is conducted on a variety of modified 

substrates. 

In particular, the LDOP is measured at various angles of observation for a variety of wellcharacterized glass substrates that were either a) roughened to varying degrees by sand blasting 

of the plates, or b) exposed to varying degrees of aerosol or dew formation. 

For studies concerning substrates that are roughened, the LDOP is measured over the entire 

wavelength region of 4 to 13 μm. A polarimetrically modified Fourier transform IR 

interferometer (FTIR) is used to measure the spectrally resolved Stokes parameters, S0, S1, S2, 

S3, and thus, the resultant LDOP, for different surface orientations angles and measured 

roughness slope distributions (13). 

For surfaces contaminated by aerosol/dew formation, a prototype long wavelength infrared 

(LWIR) imaging polarimeter was used to measure the LDOP. The polarimetric imaging system 

effectively measures the band-averaged LDOP over the wavelength region, 8.5 to 10.5 μm. The 

LWIR polarimetric camera is developed by SY Technologies, Inc., Huntsville, AL, and uses a 

proprietary optic design in which a spinning wave-plate retarder is placed at the focal plane of 

the focal plane array (FPA). As a result, SY Technologies, Inc., reports pixel mis-registration of 

less than 1/10 of a pixel. The imaging system is designed to produce well-calibrated real-time 

polarimetric and/or stokes video imagery. 

Three types of particulates are considered for the aerosol contamination portion of the study. 

Contamination by absorbing, transparent, and semi-transparent aerosol particles is examined, i.e., 

carbon black, potassium bromide (KBr) particles, and orchard grass pollen, respectively. 

Finally, all measured LDOP values are compared with a predicted LDOP value based on a 

simple geometric model that uses an effective “coverage ratio” as a primary input, i.e., we define 

the coverage ratio as the area covered by the contaminant divided by the total area, when viewed 

along the surface normal. 
4 

2. Experiment: Surface Roughness 

Borosilicate glass (Pyrex1) plates are chosen as the sample substrate because of their initial 

smoothness, readily available indices of refraction, and a high emissivity value of 0.94. Figure 1 

shows the complex indices of refraction used in our Fresnel calculations for the plates (14). 

Three-inch square glass plates are sand blasted with various types of abrasives and pressures. 

Surface roughness (Ra) and the root mean square (rms) slope, m0, are measured for each plate at 

a number of different locations with a Teliform surface profilometer via American National 

Standards Institute standards. Because of the crystalline structure of the glass, a large variance in 

Ra values between samples was difficult to achieve. As a result, only four glass plates were 

considered, one smooth and three roughened. Values for the surface roughness Ra, were found 

to be 0.007 μm (smooth), 3.98 μm, 4.80 μm, and 6.68 μm (very rough), with the corresponding 

measured rms slope for the three roughened samples found to be 9.76, 8.60, and 11.90 degrees, 

respectively. Figure 2 shows the respective rms slope distributions where we have assumed a 

Gaussian form. 

0

0.5

1

1.5

2

2.5

3

5 6 7 8 9 10 11 12 13 14

Wavelength (um)

Index

of 

refraction

real index n

complex index k

Figure 1. Complex indices of refraction used for the borosilicate (Pyrex) glass plates (14). 

 1

Pyrex® is a registered trademark of Corning. 
5 

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

-50 -40 -30 -20 -10 0 10 20 30 40 50

Roughness Slope (degrees) 

AU

Ra = 3.98um

RMS slope = 9.76

Ra = 4.80um

RMS slope = 8.60

Ra = 6.68 um

RMS slope = 11.90 

Figure 2. Measured rms slope distribution for the three roughened borosilicate 

(Pyrex) glass substrates. (Here we have assumed a Gaussian distribution.) 

Borosilicate glass substrates are mounted to a brass heating element that is designed with a 

rotation 0° ≤ θ ≤ 90°, in which θ is the angle between the surface normal and the LOS. Thermal 

continuity between the substrate and the brass heating element is maintained by application of a 

thin layer of a heat-sink compound. 

As mentioned earlier, the spectro-polarimetric measurements for roughened substrates are 

measured with a modified FTIR spectrometer. A simple diagram showing the various 

components of the experiment is seen in figure 3. An approximate 1-cm2 region of the heated 

substrate is subtended by a f#10, barium fluoride (BaF2) lens shown in the figure. The resultant 

collimated radiation is polarimetrically filtered with a IR wire-grid polarizer (extinction ratio of 

Figure 3. Simple schematic showing the experimental setup used during the surface roughness spectro-polarimetric 

measurement. 

Cold-plates 

θ

nˆ

BaF2 lens 

FTIR 

spectrometer 

Achromatic 

quarter-wave 

retarder Wire-grid IR 

polarizer 

Roughened 

glass sample 
6 

approximately 170) in conjunction with an achromatic zinc selenide (ZnSe) Fresnel rhomb 

quarter-wave plate. Filtered radiation is coupled to a Bomem FTIR spectrometer via a f#7 BaF2 

lens which effectively matched the entrance pupil of the spectrometer. This polarimetric 

configuration allows for analysis of select linear and circular polarized components necessary to 

calculate all four Stokes vectors, as well as the LDOP. 

We keep polarization anomalies induced by the optics/instrumentation to a minimum by ensuring 

that all angles between the refracted rays and a particular optical element are kept to less than 20 

degrees. This condition is easily achieved for polarimetric sampling optics but was less certain 

for the internal beam path of the FTIR. Crandall and Chipman analyzed the cross-beam 

configuration found in most conventional FTIRs and concluded that the aberrations induced by 

one arm of the interferometer/beam splitter perfectly cancel when combined with the second arm 

(15). Nevertheless, we did encounter a slight asymmetry in polarimetric response of the FTIR 

when randomly polarized thermal radiance is sampled. We attribute this relatively small 

polarimetric aberration to the dispersion inherent in the BaF2 wire-grid polarizer. As a result, a 

minor correction is applied to all spectro-polarimetric data measured in order to compensate for 

the wavelength dependence of the polarizer. 

Great effort is made to shield the measurement from ambient thermal radiation inherent to the 

laboratory. We achieved this by placing numerous “cold shields” at various locations around the 

experiment (see figure 3). 

Target plates are heated to approximately 65 °C and are monitored with an embedded 

thermocouple. This temperature is sufficient to produce a good signal-to-noise (S/N) ratio when 

compared to the ambient levels generated within the laboratory. Each sample plate is oriented at 

a particular angle within the 0° ≤ θ ≤ 80° range, at 10o increments, in which 0o orientation 

represents the condition when the surface normal is parallel to the LOS. A roughened sample 

plate is set at a given angle while the Fresnel rhomb and wire-grid polarizer are oriented in such 

a way to only pass linear states at 0o, 90o, ±45o, as well as the right- and left-handed circular 

states. Once a set of polarimetric data is measured, the angle of sample orientation is changed 

and the measurement is repeated. 

Because no fine structure is expected in the polarimetric spectra, the FTIR was operated at a 

relatively modest resolution of 8 cm-1, while a Bartlett apodization function is applied to each 

interferogram. The resultant interferogram is converted to an emission spectrum by the 

application of a Fourier transform. 

The Stokes vectors that totally describe the polarization state of the thermal emission are 

calculated via the following relationships: 

2 2 2 1/ 2 S0 = (S1 + S2 + S3 ) (7) 

in which S1, S2, and S3 are defined as 
7 

 ) S1 = I(0) − I(90 (8) 

S2 = I(+45) − I(−45) (9) 

 ) S3 = I(R) − I(L (10) 

and I(0), I(90), I(±45) represent the recorded emission spectra for polarization states at 0, 90, ±45 

degrees, respectively, and I(R) or I(L) are measured spectra when only right- or left-handed 

radiation is sampled. 

Additionally, we calculate the LDOP and circular degree of polarization (CDOP) using the 

following: 

 LDOP = 

0

1 2 2 2

S

S + S (11) 

and 

 CDOP=S3/S0. (12) 

Finally, we should note that for all samples measured, S2, S3, and subsequently CDOP, were 

found to be within the noise of the experiment and were taken to be zero. 

3. Results: Surface Roughness 

To establish a baseline set of measurements, we considered a smooth substrate first. Figure 4 

shows the spectral LDOP as a function of angle of incidence for the smooth glass sample held at 

a temperature of 65 oC. Also shown in the figure is a series of Fresnel calculations conducted for 

an arbitrary wavelength of 9.28 μm, where the complex indices n and k of figure 1 were used 

(see triangular data points). As one can see in figure 4, agreement between the measured LDOP 

and the Fresnel-calculated LDOP is quite good. Other Fresnel calculations conducted at other 

wavelengths showed similarly good agreement. 
8 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Wavelength (um)

LDOP

80 degrees

70 degrees

60 degrees

50 degrees 

40 degrees

20 degrees

Figure 4. Measured LDOP as a function of wavelength and angle of incidence for a 

smooth borosilicate glass substrate heated to 65 oC. (Also shown [triangular data 

points] is the corresponding calculated LDOP for an emission wavelength of 

9.28 μm based on the Fresnel relations of equations 4 through 6.) 

Figures 5 through 7 show a similar series of measurements for the three roughened plates. As 

one can see in these figures, a noticeable reduction in the measured LDOP occurs as the glass 

substrates become progressively rougher. 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Wavelength (um)

LDOP 

80 degrees 

70 degrees 

60 degrees 

50 degrees 

20 degrees 40 degrees 

Figure 5. Measured LDOP for a lightly roughened borosilicate plate with Ra=3.98μm 

and rms slope=9.67 degrees, as a function of wavelength and angle of incidence. 

(Plate temperature was held at 65 oC.) 
9 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Wavelength (um)

LDOP 

80 degrees 

70 degrees 

60 degrees 

50 degrees 

40 degrees 

20 degrees 

Figure 6. Measured LDOP for a moderately roughened borosilicate plate with Ra=4.80μm and 

rms slope=8.60 degrees, as a function of wavelength and angle of incidence. (Plate 

temperature was held at 65 oC.) 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Wavelength (um)

LDOP

80 degrees 

70 degrees 

60 degrees 

50 degrees 

40 degrees 

20 degrees 

Figure 7. Measured LDOP for a very rough borosilicate plate with Ra=6.68μm and rms 

slope=11.90 degrees, as a function of wavelength and angle of incidence. (Plate 

temperature was held at 65 oC.) 
10 

We contrast the strong spectral dependence of the LDOP shown in figures 4 through 7 by 

examining what happens to the same substrate when a thin dielectric layer is applied, i.e., a 

painted substrate. We considered two types of coatings of particular interest, 1) a common 

commercially available “Krylon1” black spray paint and 2) a chemical agent-resistant coating 

(CARC) paint which is a multi-component epoxy resin often used on military vehicles. 

Figures 8 and 9 show the measured LDOP for the two smooth painted surfaces. In applying the 

paints, we intentionally coated the surfaces with relatively thick layers in order to reproduce 

conditions most often seen in real-life applications. As a result, the spectral characteristics of the 

paint/substrate combination seen in figures 8 and 9 are primarily a function of the pigment only. 

As seen in both figures, the strong spectral characteristics seen for the plain glass plate are 

completely suppressed by somewhat featureless spectral emissivity for the two paints considered. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Wavelength (um)

LDOP

80 degrees 

70 degrees 

40 degrees 

60 degrees 

50 degrees 

20 degrees 

Figure 8. Measured LDOP as a function of wavelength and angle of incidence for a smooth 

borosilicate plate coated with a thin layer of black Krylon paint. (Plate temperature 

was held at 65 oC.) 

 1

Krylon® is a registered trademark of the Sherwin-Williams Company. 
11 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Wavelength (um)

LDOP

80 degrees

20 degrees

40 degrees

50 degrees

60 degrees

70 degrees

Figure 9. Measured LDOP as a function of wavelength and angle of incidence for a smooth 

borosilicate plate coated with a thin layer of a green CARC paint. (Plate 

temperature was held at 65 oC.) 

4. Experiment: Dew Formation and Aerosol Contamination 

The second portion of our study involved measuring the attenuation of polarized surface 

emission attributable to either dew formation or aerosol contamination. Again, smooth 

borosilicate glass substrates are mounted to a rotation plate that allows for continuous orientation 

of the surface normal from 0 to 90 degrees. In order to induce an initially strong LDOP, the test 

plates are positioned at a near horizontal angle of 80 degrees (see figure 10). 
12 

Figure 10. Diagram showing the experimental setup used for the dew/aerosol contamination study. (The test plate 

is oriented at a fixed angle of 80 degrees and held at room temperature.) 

For this particular study, substrates are maintained at or near room temperature in order to 

facilitate dew formation. Samples for both the dew and particulate contamination study are 

placed in a large 2.0-m3

 chamber that allows for controlled dissemination of either water vapor 

(dew) or one of the three aerosol particulates (i.e., carbon black, KBr powder, and orchard grass 

pollen). 

When one is conducting IR measurements on objects at or below room temperature, great care 

must be taken to reduce or eliminate all ambient thermal radiation inherent to the laboratory. We 

eliminated much of the ambient laboratory-induced thermal radiation by placing a series of cold 

shields at various locations about the sample. Cold plates are held at a temperature of –10 oC by 

the circulation of a chilled ethylene glycol and water mixture through copper lines embedded in 

the cold plates. 

To detect the room temperature emittance generated by the contaminated substrates, a new/novel 

polarimetric LWIR thermal imager is used. The imaging system consists of two primary 

components: a polarimetric module that houses a spinning achromatic cadmium selenide (CdSe) 

wave plate mounted in series with a fixed wire-grid polarizer, and a camera module that consists 

of a liquid nitrogen-cooled, 240x360 pixel, mercury cadmium telluride (HgCdTe) focal plane 

array (16). The spectral response for the FPA is limited to the waveband region 8.5 to 10.5 μm. 

Before each run, the camera gain and offset are adjusted to take advantage of the FPA/frame 

grabbers’ full dynamic range. Sequential LWIR polarimetric images of the test plates are 

recorded digitally at a rate as fast as 240 images/second and synchronized to the rotation of the 

spinning CdSe wave plate. The spinning wave plate and fixed wire-grid polarizer combination 

effectively acts like a variable polarimetric filter. As a result, each digital image recorded is 

Contaminated 

glass sample 

Cold-plates 

LWIR

polarimetric 

imager 

D

θ = 80

nˆ
13 

generated by polarized emittance of a particular state. Although the maximum acquisition rate is 

240 frames/second, the present data were acquired at 128 frames/second. With the speed of the 

spinning wave plate set at 8 revolutions/second, 16 frames were measured every 125 ms and 

averaged over many revolutions. The averaged frames were then used in conjunction with the 

calibration files to determine all four Stokes parameters. 

The obvious limitation of a “sequential frame” approach used here is that the test object must be 

stationary for an exposure period of at least 125-msec. Because our particular test objects were 

stationary, we could, if needed, operate at the full 240-Hz frame rate and average over many 

Stokes images to produce a better S/N ratio. 

We calibrate the LWIR polarimetric imager by recording the radiometric response when we 

observe known linear and circular polarization states. We generate known states by polarizing 

the radiance from a high precision, 14- by 14-inch extended area blackbody. Radiance is linearly 

and circularly polarized by the identical wire-grid/quarter wave rhomb combination described in 

the spectro-polarimetric measurement. This allowed for exposure of the camera system to 

known linear and circular polarization states that are as close to ideal as possible (i.e., to provide 

uniform coverage over the entire Poincare sphere). A set of calibration frames is generated at the 

beginning and ending of each day. Each image frame represents one of the six necessary states 

needed to calculate the four Stokes vectors seen in equations 7 through 10, i.e., I(0°), I(90°), 

I(±45°), I(R), and I(L). These calibration files are used to calculate the system’s modulation 

transfer function (MTF), which is used later to correct for any aberrations observed during the 

measurement and to calculate the Stokes parameters. 

When one is considering contamination attributable to dew formation, warm humid air is 

generated by the evaporation of distilled water via a commercially available humidifier and is 

directed into the test chamber via a 4-inch-diameter vent. The water vapor quickly begins 

condensing on the cooler glass surface, and small micron-size dew particles begin to form (see 

figure 11). 
14 

Figure 11. Video image series showing the dew condensation process. (Shown in 

each image is the corresponding coverage ratio, [i.e., surface area covered 

divided by the total area], and the corresponding measured LDOP for θ=80°.) 

1.60 mm 
15 

Polarimetric data are recorded continuously as the dew-forming process continues. Data are 

recorded until either the dew droplets grow to form a continuous layer or the LDOP is no longer 

measurable. A sample thermal polarimetric image used to determine the emitted LDOP is seen 

in figure 12. The chamber is evacuated, the target plate cleaned, and the polarimetric 

measurement is repeated. 

Figure 12. Sample calibrated LWIR polarimetric 

image used to determine the LDOP for 

a smooth glass substrate contaminated 

by a modest amount of carbon black 

particles. (LDOP is determined from 

the gray scale values for the pixels that 

represent the heated glass surface.) 

Three types of aerosols are considered for the contamination portion of the study. Each 

particulate chosen was based on the degree of optical absorption that each material possessed, 

i.e., finely milled KBr particles (weak absorber), orchard grass pollen particles (moderate 

absorber), and carbon black (strong absorber). 

To generate varying degrees of particulate contamination, the test substrate is placed in a 2.0-m3

chamber. In order to aerosolize the particulates efficiently, a specially designed pneumatic 

nozzle was constructed. Dry pressurized air is used to inject the particulates through a 

cylindrical nozzle that contains a spiraling array of fine stainless steel wires. A vortex created 

within the nozzle effectively separates and disperses the particles with minimal agglomeration. 

A small quantity of the particulate (typically less than 0.20 gram) is placed in the dispersing 

nozzle and is injected into the sealed chamber. A small fan in a corner of the chamber is used to 

stir the aerosol to ensure that a uniform distribution is achieved. The fan is turned off and the 

aerosol is allowed to settle onto the target plate. 
16 

A real-time video log of the contaminating process is recorded periodically during the 

polarimetric measurement. We accomplished this by swinging a high-power video microscope 

into a fixed position slightly above the test surface. Once a series of images is recorded, the 

video microscope is removed and the recording of the LWIR polarimetric data continues. Later, 

analysis of the digital images is used to determine particle size, shape, and concentration; for 

example, see figures 11 and 13. Although not easily seen from the images of figure 13, 

qualitative, analysis conducted on the samples yielded an approximate nominal diameter range of 

0.20 to 0.35 μm for carbon black, 0.5 to 0.8 μm for KBr, and 30 to 40 μm for the orchard pollen 

(17). 

The polarimetric measurement is conducted on each plate with the same procedure described in 

the dew portion. Once a set of measurements is completed, the plate is removed, subjected to 

further contamination, and remeasured. 

Figure 13. Sample visible images showing various forms of aerosols contamination considered, i.e., 

orchard pollen (top left), carbon black (top right), and KBr particles (bottom). 

1.60 mm 

pollen 

1.60 mm 

Carbon 

1.60 mm 

KBr 
17 

5. Results: Dew Formation and Aerosol Contamination 

Figure 14 shows the measured and calculated LDOP for varying degrees of dew coverage. Each 

data point shown represents a single polarimetric measurement in which we calculated the 

coverage ratio (i.e., covered surface area divided by the total surface area) by analyzing a series 

of photographs similar to those seen in figures 11 and 13. Also shown in figure 14 is the 

corresponding geometric-based calculation in which the complex index for water and the glass 

substrate is taken to be 1.193+0.05i and 2.4+0.5i, respectively, for the waveband region 8.5 to 

10.5 μm (12,18,19). Figure 15 shows a similar set of measurements except now the 

contaminating medium consists of a variety aerosol particulates, i.e., carbon black, KBr powder, 

and pollen. 

Finally, because each data point seen in figures 14 and 15 represents a single measurement, 

rather than a statistical average of values, uncertainties inherent to the measurement are best 

represented by examination of the magnitude of scatter within the data. Since we determine the 

coverage ratios by applying a machine vision algorithm to a series of photographs, the error 

associated with these values is primarily related to the number of sample images used. We found 

little variation in coverage ratio after analysis of approximately 10 to 12 images. For most data 

seen in figures 14 and 15, the number of images used in the analysis often exceeded 20 frames. 

As a result, we believe the uncertainty associated with determining the coverage ratio to be less 

than 5 to 7%. Analysis of the polarimetric calibration yield uncertainties on the order of 10 to 

18% primarily because of limitations of the wire-grid polarizer, i.e., the extinction ratio for the 

wire grid was found to be approximately 170 over the wavelength range of 8.5 to 10.5 μm. 
18 

0

2

4

6

8

10

12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Coverage Ratio 

LDOP (%)

Calculated (Videen)

Measured

Figure 14. Measured LDOP for varying degrees of dew (water) coverage on the surface 

of a smooth borosilicate glass substrate at 22 oC, θ=80°. (Also shown is the 

calculated LDOP by the geometric approach of Videen (12).) 

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Coverage Ratio

LDOP (%)

KBr powder (scattering particle)

Carbon black (absorbing particle)

Pollen Orchard grass (moderate 

absorber) 

Carbon black (calculated)

KBr (calculated) 

Figure 15. Measured LDOP for a smooth borosilicate glass plate held at 22 oC, contaminated 

with varying degrees of carbon black, KBr particles, or pollen, that were evenly 

dispersed on the surface. (Substrates mounted at θ=80° [the dashed line shown 

represents the corresponding curve fit]. Also shown is the calculated LDOP based 

on the geometric approach put forth by Videen.) 
19 

6. Discussion 

When we entered into the surface roughness study, we had hoped to create a sample set of 

roughened surfaces that spanned as large a range as possible. Inspection shortly after bead 

blasting of the glass surfaces suggested that a broad range of roughness values had been 

achieved. It was only much later during the formal surface characterization process that we 

realized the limited range values for either Ra or the localized rms slope, i.e., our values ranged 

from Ra= 3.98 to 6.68 μm and rms slope 8.60 to 11.90 degrees. We attribute our inability to 

generate a more diverse set of test surfaces to the crystalline structure of the borosilicate glass 

plates. Jordan and Lewis experienced similar limitations in creating test surfaces of either glass 

or aluminum. Initially, we had hoped to create a surface so diffuse that the measured emittance 

showed no preferential polarization. Neither we nor Jordan were able to produce such 

conditions. For angles of orientation in excess of 40o, we report a measurable LDOP for all 

roughened samples considered. 

Although the rms slope distribution is thought by many theorists to be the most important 

parameter influencing the attenuation of polarized emission attributable to surface roughness, in 

practice, accurate determination of this parameter is quite problematic. Bennett et al. reports that 

even during the best of conditions, measurement of the rms slope can vary by as much as a factor 

of 50 from one practitioner to another, depending on the instrumentation used, cutoff length, 

profilometer stylus geometry, scan rate, etc. (20). Much of the emphasis placed on the use of the 

rms slope is based on the premise that roughened surface facets may be treated as series of 

infinitesimally small planar surfaces oriented at various angles described by the rms slope 

distribution. Even if good reproducible rms slope values exist, researchers must then “assume” a 

type of distribution to apply the rms measurement to that distribution. For example, Jordan and 

Lewis report significant variance in the calculated LDOP for a series of roughened surfaces, 

depending on whether a Gaussian or Cauchy distribution is applied (7). Regardless of the 

difficulty inherent to measuring an accurate surface profile, it is not entirely clear that a simple 

geometric approach is truly valid when the dimensions of the facets are comparable or smaller 

than the emission wavelength, as is the case here. 

Finally, figure 16 shows a comparison of measured LDOP values taken at the emission 

wavelength 9.90 μm as a function of surface roughness and orientation. Also shown are the 

LDOP results of Jordan and Lewis for their roughened glass substrate, Ra = 9.89 μm and rms 

slope = 24.5 degrees (7). One startling feature seen in figure 16 is that with the exception of a 

few data points for the Ra = 3.98 μm sample, the measured functional dependence appears to be 

the same for all roughened samples considered (including those of Jordan and Lewis), regardless 

of surface roughness parameter or rms slope. One would hope to see different polarimetric 

responses as the substrates transition from a specular to a diffuse surface as the roughened facets 
20 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

10 20 30 40 50 60 70 80 90

Angle between surface normal and LOS (degrees) 

LDOP 

smooth

Ra= 3.98 um, RMS slope 9.76 degrees 

Ra= 4.80 um, RMS slope 8.60 degrees

Ra= 6.68 um, RMS slope 11.90 degrees

Fresnel calculation (smooth)

measured (Jordan&Lewis) Ra= 9.89 um, RMS slope 24.5

degrees 

Figure 16. Comparison of measured LDOP (taken at 9.90 μm) as a function substrate orientation for 

various roughened glass plates. (Also shown are the measured and Fresnel-based 

calculations for smooth glass substrates [top dashed line] and results from Jordan and 

Lewis [bottom dashed line] (7).) 

become larger. We speculate that this apparent insensitivity to changes in various surface 

features is attributable to an insufficient range of Ra values considered. We believe the transition 

from specular to diffuse surfaces in the measured LDOP would be evident if more moderately 

roughened samples were examined, e.g., Ra values between 0.5 and 2.0 μm. An informal survey 

of measured Ra values (measured with a hand-held profilometer) taken from numerous civilian 

and military type vehicles shows a fairly narrow range of Ra values, i.e., 0.02 to 3.65 μm, where 

the higher values could be loosely described as quite abrasive. 

The spectrally resolved LDOP shown in figures 4 through 7 highlights the strong wavelength 

dependence that polarized thermal emission exhibits for certain types of materials. As a result, 

care must be taken to ensure that all spectral dependences for the surface being considered (as 

well as the polarimetric optics used for the measurement) are well defined. For example, 

consider figure 4. It is apparent that one would get quite different values for the measured LDOP 

if the responsivity of the instrument is limited (either by optical components or the detector) to a 

narrow band about 9.4 μm or is allowed to integrate over a wider wavelength region, say 8.0 to 

9.5 μm. 
21 

We had hoped to highlight this point further by applying various coatings to the surface (i.e., 

black Krylon and CARC paint), but unfortunately, the pigments chosen did not exhibit the 

complex emission spectra we had originally hoped for. Rather, one can see from figures 8 and 9 

that the paints chosen exhibited emission spectra that are fairly featureless, compared to figure 4, 

and suppressed the underlying emission from the heated borosilicate glass substrate. 

Now let us consider the dew/aerosol contamination portion of the study. As mentioned earlier, 

the LDOP is a measure of asymmetry exhibited by a sample. An asymmetric system/particle 

tends to emit a preferred polarization signal, whereas, a symmetric system/particle has no 

preferred polarization emission and its radiometric contribution results in unpolarized noise. In 

our samples, the smooth plane substrate provides a polarized signal, whereas, the randomly 

oriented particulates provide the noise. These particles not only reduce the polarization by 

contributing an unpolarized component to the total signal, but also shadow the substrate, 

preventing the polarized signal from reaching the detector. As one can see from figures 14 and 

15, the total attenuation of the LDOP occurs for all contaminants considered as the coverage 

ratio approaches 0.5 to 0.6 (note that coverage ratios are determined for observation along the 

surface normal). Since all dew/aerosol contaminant measurements are conducted while the 

plates are orientated at a high grazing angle of 80o degrees, the projected shadows cast by the 

particles on the plane surface at this angle are nearly 6 times their size at normal incidence. The 

particles cast their shadows not only on the substrate but also on other particles. The shadowing 

of particles by other particles is not random and tends to cover the bottom portion of the 

particles, disrupting their symmetry. As a result, this asymmetric shadowing may be considered 

another source of the polarization signal (12). With no particle-on-particle shadowing, the 

LDOP response shows a linear decrease proportional to the coverage ratio. Partial shadowing of 

particles introduces a new nonlinear term. For relatively small coverage ratios, we expect partial 

shadowing to be negligible and the LDOP to show a linear decrease. This linear term 

approaches zero for spherical contaminants when the coverage ratio equals the cosine of the 

detection angle. If the particles are oriented with 100% efficiency so that they cast their shadows 

only on the plane surface and not on other particles, the LDOP would equal zero at coverage 

ratios of approximately 17%. As the coverage ratio increases, we expect to see a nonlinear term 

to be introduced that gives rise to a tail in the LDOP signals shown in figures 14 and 15. 

It is significant that figure 14 shows a nearly linear response of the LDOP to coverage ratio. We 

attribute the divergence between measured and calculated LDOP at intermediate values of the 

coverage ratio to the fact that the calculations assume a monodispersed drop size for dew. The 

nonlinear response seen in the model calculations results from shadowing of dew particles by 

other dew. In this case, the bottom portions of the dew are shadowed and a nonlinear term is 

introduced into the total LDOP signal. However, the dew shown in figure 11 is far from 

monodispersed. The dew consists of some large particles and many smaller particles. As a 

result, the shadowing is non-uniform. Either a small portion of the bottom of the large particles 

is shadowed by smaller particles, or entire small particles are shadowed by large particles. 
22 

Partial shadowing plays a minor role. As a result, the nonlinear term in the LDOP is suppressed, 

and the resulting measured response is nearly linear, as is seen in figure 14. 

Figure 15 shows the LDOP response measured from three other atmospheric aerosol particles: 

pollen, carbon black, and KBr particles. When one is comparing figures 11 and 13, it is apparent 

that these particles have a narrower size distribution than the dew particles. The percentage of 

large or agglomerated particles is much lower than that for the dew sample, so there is a 

significant amount of partial shadowing of other particles, rather than complete shadowing, as 

seen in the dew sample. As a result, the LDOP for these particles shows a much stronger 

nonlinear term than that of the dew particles, demonstrating that partial shadowing plays a 

significant role in determining the LDOP for these systems. 

We note that the LDOP for the highly absorbing carbon black is nearly identical to the 

transparent KBr particles. This should not be cause for concern. The particles composing the 

samples are non-spherical, and the LDOP is the average signal over this shape polydispersity. 

Just as two completely different scattering systems may have similar scattering coefficients, they 

also may have similar LDOPs. However, the carbon and KBr particle systems have a common 

feature that may also explain this similarity: they are both agglomerates of Rayleigh-size 

particles. The nominal sizes of the individual components comprising these particle systems are 

submicron. Like polarized Rayleigh scattering, polarized emission from particles small 

compared to the wavelength does not depend on particle emissivity. This appears to be reflected 

in the properties of the agglomerated particle systems shown in figure 15. It is interesting to note 

that as the surface density of these agglomerated particles increases, the LDOP response is very 

similar to the theoretical response shown in figure 14. Although the theoretical description of 

Videen is wholly inadequate to describe this system, it appears from the nonlinear shape of these 

curves that partial shadowing is a primary physical mechanism. 

Figure 15 also shows the LDOP of the orchard pollen particles. These particles are not Rayleigh, 

being 30 to 40 μm in size; however, their shape is irregular and composition is heterogeneous. It 

is apparent in this case that the nonlinear shadowing term is a significant component for this 

system. The LDOP response of the orchard pollen is reduced significantly from that of the two 

Rayleigh agglomerates. 

Finally, we should note that because the carbon and KBr particles are sub-micron, we were 

unable to resolve visible images until the particulates agglomerated into larger sizes, say 1.0 μm, 

and that is the reason there are no coverage values below 0.10. 
23 

7. References 

1. Sandus, O. A review of emission polarization. Appl. Opt. 1965, 4 (12), 1634–1642. 

2. Bertilone, D. C. Stokes parameters and partial polarization of far-field radiation emitted by 

hot bodies. J. Opt. Soc. Am. A 1994, 11 (8), 2298–2304. 

3. For an excellent treatment of the directional properties associated with thermal radiation see; 

Siegel, Robert; Howell, J. R. Thermal Radiation Heat Transfer; McGraw-Hill Co.: New 

York, 1981. 

4. Tooley, R. Man-made target detection using Infrared polarization. SPIE Conf. Polarization 

Considerations for Optical Systems II 1989, 1166, 52–58. 

5. Cooper, A.; Lentz, J. Infrared polarization ship images and contrast in the MAPTIP 

Experiment. SPIE 1996, 2828, 85–96. 

6. Rogne, T.; Smith, F. Passive target detection using polarized components of infrared 

signatures. SPIE Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray 1990, 1317, 

242–251. 

7. Jordan, D. L.; Lewis, G. D. Emission polarization of roughened glass and aluminum 

surfaces. Appl. Opt., 35 (19), 3583–3590. 

8. Jordan, D. L.; Lewis, G. Measurement of the effect of surface roughness on the polarization 

state of thermally emitted radiation. Opt. Letters 1994, 19 (10), 692–694. 

9. Shaw, J. A. Degree of linear polarization in spectral radiances from water-viewing infrared 

radiometers. Appl. Opt. 1999, 38 (15), 3157–3165. 

10. Shaw, J. A.; Marston, C. Polarized infrared emissivity for a rough water surface. Optics 

Express 2000, 7 (11), 375–380. 

11. Chang, P. C.; Flitton, J. C. Importance of shadowing and multiple reflections in emission 

polarization. Waves in Random Media 2002, 12 (1), 1–19. 

12. Videen, G. Polarized Infrared Emissivity from Dew Droplets on a Surface. Appl. Opt. LP

2003, 42 (27), 5557–5560. 

13. Chenault, D.; Chipman, R. Infrared spectropolarimetry. SPIE Symposium on Polarization 

Considerations for Optical Systems II 1989, 1166, 254–266. 

14. Lane, D. W. The optical properties and laser irradiation of some common glasses. J. Phys. 

D: Appl. Phys. 1990, 23, 1727–1734. 
24 

15. Crandall, D. G.; Chipman, R. A. Polarization aberration of crossed folding mirrors. Novel 

Optical Systems Design and Optimization, Proc. SPIE 1995 2537, 83–93. 

16. Chenualt, D.; Chipman, R. Infrared birefringence spectra for cadmium sulfide and cadmium 

selenide. Appl. Opt. 1993 32 (22), 4223–4227. 

17. Putscher, R.; McCrone, W. C. Characterization of air particles giving false responses with 

biological detectors; Tech. # ED-CR-75025, Edgewood Arsenal Technical Report: National 

Technical Information Service, July 1975. 

18. Segelstein, D. J. Complex refractive index of water. MS Thesis, University of Missouri, 

Kansas City, MI, 1981. 

19. Lane, D. W. The optical properties and laser irradiation of some common glasses. J. Phys. 

D: Appl. Phys. 1990, 23, 1727–1734. 

20. Bennet, J. M.; Mattson, L. Introduction to Surface Roughness and Scattering; Optical 

Society of America Press: Washington D.C. (1989). 
25 

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