SIMULATION OF POLARIMETRIC OBSERVING FROM AMOS1

Mark Pesses1

John Tan1

Robert Swartz1, 2

Ryan Hash1, 3

David Downer1

SAIC, 4001 Fairfax Dr., Suite 450, Arlington, VA 222032Currently at University of Virginia, Charlottesville, VA3Currently at University of Maryland, College Park, MD

ABSTRACTWhile hyperspectral imaging provides a tool for detecting and identifying targets it does not utilize the information contained in the look-angle dependence of the Stokes polarization vector. This information can be exploited to discriminate between objects based on their angularity, electrical conductivity and surface roughness, as well as, their hyperspectraland temperature signatures. SAIC’s 3-D, LWIR spectropolarimetric signature model, Polar Heat, is used to simulate LWIR polarimetric observing from AMOS. Both imaging and non-imaging simulated observations are presented for spinningand tumbling satellites, as well as, RVs and decoys. Polar Heat is a1st principle model that extends microfacet based scattering models from intensity (scalar) to polarimetric (4-vector) using a computational approach that seamlessly integrates reflected and self-emitted radiation. Thermal self-emission is transmitted internal blackbody radiation that is modified by passing through the change in the index of refraction that occurs at the surface-space interface. Polar Heat includes coherent Fresnel and “BRDF” interactions, incoherent scattering, shadowing, obscuration, terrestrial and space emissions and CAD target objects. Multi-bounce and atmospheric transport effects are neglected in the results presented. Initial simulation runs suggest that polarimetric observations from AMOS could provide a more sensitive way to detect and identify space objects.

1. INTRODUCTIONWhile hyperspectral imaging provides a tool for detecting and identifying targets it does not utilize the information contained in the look-angle dependence of the Stokes polarization vector. This information can be exploited to discriminate between objects based on their angularity, electrical conductivity and surface roughness, as well as, their hyperspectraland temperature The earliest know study of LWIR spectropolarimetry was in 1824, when Arago [1] reported that the glow emitted by hot incandescent metalsis polarized. Seventy years later, Millikan [2] published papers on his research into the polarization of light emitted by incandescent solid and

1 This work has been support under contracts from AFOSR, DARPA/TTO, DARPA/IXO and subcontract from Raytheon and Teledyne Solutions.

liquid surfaces.The study of optical polarization applied to remote sensing has it roots with Lyot [3] who built a non-imaging polarimeter with remarkable sensitivity. In the early 1960s the initial IR spectropolarimetry measurements were first madeof astronomical objects [4], modeled in LWIR [5], and applied to natural targets [6]

The first microfacet spectropolarimetric signature model was developed by AFRL/VSS-Kirtland [7]. The Kirtland model predicts the long wave Infrared (LWIR) and visible (VIS) spectropolarimetric BRDF signatures for smooth and semi-rough 2-D slabs. Science Applications International Corporation (SAIC), under sponsorship of AFOSR, DARPA, Raytheon and USASMDC has also developed a model for predicting the spectropolarimetric BRDF signatures. SAIC’s Polar Heat is a 1st principle, 3-D, LWIR spectropolarimetric BRDF signature model.

Polar Heat extends microfacet based scattering models from intensity (scalar) to polarimetric (4-vector) using a computational approach that seamlessly integrates reflected and self-emitted radiation. Thermal self-emission is transmitted internal blackbody radiation that is modified by passing through the change in the index of refraction that occurs at the surface-space interface. Polar Heat includes coherent Fresnel and “BRDF” interactions, incoherent scattering, shadowing, obscuration, terrestrial and space emissionsand CAD target objects. Multi-bounce effects are currently being neglected inthe results presented. Microfacet pixel models are based on the assumption that the radiation emanating from each microfacet in the pixel can be combinedincoherently at the detector. In order for this assumption to be true, the pixel surface roughness correlation length must be much, much larger than the coherence length of the reflected and emitted radiation. When this condition is met, intensities for different ray paths can be added as their mutual coherence term is zero, and there is negligible diffraction of light off microfacet edges.Under these conditions, each microfacet can be approximated by a smooth flat surface and the radiation emanating from each microfacet can be modeled using the Fresnel equations.

2. POLARIMETRY NOMENCLATURE AND COORDINATE SYSTEMS

Natural sources of light consist of a linear superposition of individual lightwaves. The resultant wave is given by (1) where E is the electric intensity vector, t is time, z is distance, is wavelength, is angular frequency,

is phase angle, while ε̂a and ε̂b are orthogonal unit normal vector

E (λ,z,t )=[Ea (λ )eiδa (λ) ε̂a+Eb (λ )eiδb(λ )^εb]ei z - iω t

(1)

Ep = Es x k Ep = Es x k

nn

Es = k x nEs = k x nkk

Fresnel coordinate systemFresnel coordinate systemEp = Es x k Ep = Es x k

nn

Es = k x nEs = k x nkk

Fresnel coordinate systemFresnel coordinate system

Figure 1. The coordinate system used in this paper is the one inwhich Fresnel equations are valid.

Figure 1 shows the coordinate system in which ε̂a and ε̂b are defined. This is the coordinate system in which Fresnel’s equations for reflection and transmission are valid. It is also the coordinate system that the boundary conditions for Maxwell’s equations are evaluated and in. It is important to note that Fresnel coordinate system is not globally defined, but locally defined by two unit vectors n and k, where n is the surface normal of the reflecting and transmitting boundary, and k is the propagation direction the electromagnetic wave. In the Fresnel coordinate system, one component of E isperpendicular to both n and k and given by Es = k x n, and the other componentof E is perpendicular to both Es and k and given by Ep = Es x k.

The observational definitions of the components of the Stokes vector are

S0 = I(0∘,0)+I(90∘,0)

S1 = I(90∘,0)−I(0∘,0)

S2 = I(45∘,0)−I(135∘,0)

S3 = I(45∘,π /2)−I(135∘,π /2) (2)

Here, the observed intensity I at the sensor as a function of the linear polarization filter angle (the left-hand value inside parentheses) and the ¼ wave plate phase retardance (the right-hand value). To fully determine the value of the first three Stokes parameters require a set of four measurements with linear polarizers. To fully determine the value of the fourth the Stokesparameter requires two additional sets of measurements with quarter wave plates. The wave’s linear polarization anisotropy (LPA) is S1/ S0 and the

degree of linear polarization (DOLP) |S12+S2

2 /S0 .

In 1959 Born and Wolf [8] developed a statistical description of both natural and man-made light that is easily related to the Stokes polarization vector.

The four components of the Born and Wolf coherence matrix J in the Fresnel coordinate system are defined in (3),

Jαβ (λ,z )=1T∫0T E (λ,z )⋅ε̂αE

¿ (λ,z)⋅ε̂βdt (3)

Here the superscript “*” denotes complex conjugant and the integration time T >> 2. Substituting (1) into (3) and evaluating the results in the Fresnel coordinate system gives,

Jαβ (λ )=1T∫0

T Eα (λ,t)Eβ (λ,t )ei (δα ( λ, t )−δβ (λ,t))dt

(4)with, JPP=EP

2

JSS=ES2

JPS=i ⟨δp -δs ⟩EPESJPS= i ⟨δs -δp ⟩ESEP (5)

The relationships between the Stokes parameters the Born Wolf parameters is given in (6-8),

S0 = JPP+ JSSS1 = JPP− JSSS2 = JPS+ JSP

S3 = i(JPS− JSP ) (6)

JPP=(S0+S1)/2JSS=(S0−S1) /2JSP=(S2+iS3 )/2JPS=(S2−iS3)/2 (7)

JSS = I(0∘,0)

JPP = I(90∘,0)

JSP= 12 [I(45∘,0)−I(135∘,0)]+1

2 i [I(45∘,π /2)−I(135∘,π /2)]JPS=

12 [I(45∘,0)−I(135∘,0)]−1

2 i [I(45∘,π /2)−I(135∘,π /2)] (8)

Comparing (2) to (8) shows that all the Stokes parameters are real, while two of the four Born Wolf parameters can be complex.

2. POLAR HEAT MODEL

The Polar Heat model coordinate system is shown in Fig. 2. Here, k is the Poynting vector of the radiation observed at the sensor and n is the microfacet surface normal vector direction.

Figure 2. The Polar Heat local coordinate system. It is important to note that the coordinate system shown in Fig. 2 is a locally defined system and that the directions of Ep and Es vary with sensor location. On the other hand, the location of each scene object, each sensor, the center of each scene pixel, and the center of each sky patch are defined in a global coordinate system. The direction of the mean surface normal vector m of each pixel is also defined in a global coordinate system, while the direction of n is defined locally relative to m and also defined globally.The angle between n and the sensor position and n and external sources of

y

n

z || k

n

Es

x||=0

Ep

reflected

emitted = refraction angle = reflection angle = polarizer angle

illumination are carried out in the global coordinate system. Figure 2 also defines the reflection and transmission angles and , as well as the angle between the Es component of E and the linear polarization filter angle 0 setting. Surface roughness is modeled by assuming a Gaussian distribution for the angle between n and m for each facet in a pixel. The rougher the surface, the large the value of the standard deviationof .

The evaluation of the Fresnel reflection coefficients requires knowledge of value of the Snell reflection angle refraction angle If the index or refraction is real this is not a problem, but if n is complex the value of isalso complex. In this situation we used the Born and Wolf derived effective value for that has the property of conservation of energy in the transmission processes.

3.1 Intensity EquationsPolar Heat assumes that distance between a pixel and a sensor, is much, much greater than the size of a pixel. Therefore, no accuracy is lost by assuming that all microfacets are located at the center of a pixel. If both the temperature and index of refraction are constant and uniform over a microfacetsurface (but not necessarily thesame from one microfacet to the next), the observed intensity emanating from amicrofacet as a function of viewing geometry and polarizer filter settings is given by (9) where the Born Wolf parameters are for sake of computational easepresented as a 4-vector J⃗ .

(9)where, IS is the intensity observed at the sensor with filter settings and wave length and sensor-target microfacet angels S and S. The subscriptsand superscripts “T” and “R” referrer to the coherence vector of the internal transmitted and external reflected radiation sources.

J⃗T=(JSST

JPPT

JSPT

JPST ) {J⃗

R

=(JSSR

JPPR

JSPR

JPSR )¿

(10)

FT=[FSTFS

T* 0 0 00 FP

TFPT* 0 0

0 0 FSTFP

T* 00 0 0 FP

TFST* ]Coe

(11)

FR=[FSRFS

R* 0 0 00 FP

RFPR* 0 0

0 0 FSRFP

R* 00 0 0 FP

RFSR* ]

(12)

Here Fs and Fp are the Fresnel coefficients for the s and p components of E and the superscripts “T” and “R” referrer the Fresnel coefficients for transmission and reflection. The superscript “*” means complex conjugant. Coeis the conservation of energy term for transmitted light, where na and ns are the index of refraction of the air and surface respectively.

Coe =nacos (φ)

nscos (ψ )

(13)

and

(14)

Also,

M=[C2 S2 CS CS

S2 C2 -CS -CS-CS CS C2 -S2

-CS CS -S2 C2 ] C=Cos (Θ ) S=Sin (Θ ) (15)

(16)

And again, is the linear polarization filter angle and is the quarter-waveplate retardance angel.

4. RESULTS

4.1 Observations of Spatially Resolved ObjectsThe first space object to be modeled with Polar Heat is a Global Position System (GPS) spacecraft. A computer aided design (CAD) model of a GPS spacecraft with over 10,000 facets was used. Figure 3 shows a GPS spacecraft in 10 m light where it is “illuminated” by Earth glow and space glow. The false color image gives the combined intensity (S0) from reflection and thermal-self emission. In the results present here the surface of GPS’s solarcells are quartz-glass, the surface of the spacecraft bus is Aluminum and the surface of the antennas are silver. The spacecraft surface temperature is assumed to be uniform.

Figure 3. A GPS spacecraft in 10 m light.

Figure 4 shows false color images of a GPS spacecraft in 10m light. Three different views are shown in the left column for “S0” light. Three different views are shown in the middle column for “DOLP” light. The right column showsthree different views in. “S0/S1” light. In Fig 3, the DOLP parameter provides more false color variations as the GPS spins then either the SO and S0/S1 parameters. The bottom image in the middle column is an example of false coloring rainbowing, in which an object exhibits a full range of a polarization parameters values. Similar results occur are observed for other spacecraft.

4.2 Unresolved GPS ObservationsThere are two important classes of space objects that can not yet be resoled by the AMOS telescope. They are objects in geosynchronous Earth orbit (GEO) and small object in low Earth orbit. To simulate the observation of these objects the values of S0, S1, and S2 from each of its contributing facets are algebraically added together each rotation time period. The GPS integrated (sum of every visible facet) value of S0, S1, and S2 are plotted in Fig. 5 for1.05 periods of rotation. The GPS integrated value of the relative rate of change of S0, S1, and S2 are plotted in Fig .6 for 1.05 periods of rotation. The definition of relative rate of change (RROC) is given in (17). Figure 7 plots the GPS integrated value of S0/S0max, S1/S0 and the DOLP Vs time.

RROC (tn)=[S (tn+1 )−S (tn)]/[S (tn+1)+S (tn)] (17)

Figure 4. The left column shows three different false color views of a GPS in10m “S0” light. The middle column shows three different views of a GPS in 10m “DOLP” light. The right column shows three different views of a GPS in 10m “S0/S1” light.

Carbon

Aluminum

DOLP

8%

0% = 9 microns

Figure 5 (top) plots the GPS integrated value of S0, S1, and S2 Vs time. Figure 6 (bottom) plots the GPS integrated value of the relative rateof change of S0, S1, and S2 Vs time.

For the case of the GPS spacecraft modeled above, the RROC of the value of DOLP appears to “stick out” more than any of the other parameters shown. It is anticipated that for space object identification, polarimetric rotation signatures will be more effective than the currently used hyperspectral rotational signatures.

Figure 7 (top) plots the GPS integrated value of S0/S0max, S1/S0 and the DOLP Vs time. Figure 8 (bottom) compares modeled DOLP values for 2 Carbon coated reentry vehicles (RVs) and 2 Aluminum coated balloon decoys.

Relative Rate of Change of S0 S1 S2

-6

-4

-2

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Tim e

Rate

of C

hang

e

S0S1S2

S(t2)-S(t1)S(t2) +S(t1)

Unresolved GPS Spacecraft @ 10m

S0/S0m ax S1/S0 DOLP

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37Tim e

NS0LPADOLP

Unresolved GPS Spacecraft @ 10m m

SO S1 S2 Vs Tim e

-2000

-1000

0

1000

2000

3000

4000

5000

6000

7000

1 4 7 10 13 16 19 22 25 28 31 34 37Tim e

Intens

ity

S0S1S2

Unresolved G PS Spacecraft @ 10m

= 9 microns

4.3 RV – Decoy DiscriminationOne of the technical challenges to fielding a successful ballistic missile defense (BMD) system is the development of an effective method to discriminatereentry vehicles (RVs) from look-a-like balloon decoys. While RV decoys may be the same size and shape of real RVs, and even have the same surface temperature, the chemical composition and degree of roughness of their surfaceis significantly different. A comparison of modeled DOLP for Carbon coated RVs and Aluminum coated balloon decoys is presented in Figure 8. The RVs exhibit two to four times the amount of polarization at 9m than do the balloon decoys. A detailed study of the effectiveness of polarimetric techniques to locate RVs inside of chaff clouds is currently under way using the Army’s Space and Missiles Defense Command (USASMDC) Optical Signature Code.

5. REFERENCES

1. Arago, D. F., Extrait des Seances de l'Academie Rayale des Sciences, Ann. Chem. Phys. Ser., 89, 1824.

2. Millikan, R. A., A Study of the Polarization of the Light Emitted by Incandescent Solid and Liquid Surfaces, Physics Review, 177, 1895.

3. Lyot, B., Research on the Polarization of Light from Planets and from SomeTerrestrial Substances, Annals de L'Observatoire de Paris, VIII, 1929.

4. Heiles, C. E., and Drake, F. S., The Polarization and Intensity of ThermalRadiation from a Planetary Surface, Icarus, 2, 281-292, 1963.

5. Feofilov, P. P., The Physical Basis of Polarized Emission, Consultants Bureau, New York, 1961.

6. Hall Jr., F.F., The Polarized Emissivity of Water in the Infrared, Applied Optics, 3(6), 1964.

7. Wellems, D., Serna, M., Sposato, S. H., Fetrow, M. P., Bishop, K. P., Arko, S. A., and Caudill, R. R., Spectric Polarimetric BRDF Model and Comparison to Measurements from Isotropic Roughened Glass, AFRL-TR, 2000. 8. Born, M. and Wolf, E. Principles of Optics, Cambridge University Press, New York, NY, 1980.