Long-wave infrared (LWIR) polarimetric signatures provide the potential for day-night detection and identification of objects in remotely sensed imagery. The source of optical energy in the LWIR is usually due to thermal emission from the object in question, which makes the signature dependent primarily on the target and not on the external environment. In this paper we explore the impact of thermal equilibrium and the temperature of (unseen) background objects on LWIR polarimetric signatures. We demonstrate that an object can completely lose its polarization signature when it is in thermal equilibrium with its optical background, even if it has thermal contrast with the objects that appear behind it in the image.
©2007 Optical Society of America
Imaging polarimetry has emerged as a powerful tool to aid in the detection and identification of objects in remotely sensed imagery in all regions of the optical spectrum . Polarimetric imagers are usually designed to sense the polarization properties of the reflected polarization signatures, though it is well known that emitted radiation can also be partially polarized . In order to have enough emitted radiation to reliably detect the polarization signatures, it has been necessary to either work with very hot targets or sense in the long-wave infrared (LWIR, 8–12 μm). There has been interest in LWIR imaging polarimetry dating back more than 20 years , with many imaging and non-imaging devices built and tested in the intervening years . The purported advantages of polarimetric sensing in the LWIR include independence from any external source of radiation and invariance of signatures with respect to time-of-day. These advantages are assumed to come from the fact that the source of radiation is thermal emission from objects in the scene.
Emission polarimetry has been thoroughly studied by many authors. Early experiments were done by Millikan [4, 5], and a thorough review is provided by Sandus . The experimental evidence has demonstrated that conservation of energy must be satisfied for the two polarization states independently:
where ε is the emissivity and r is the power reflectivity in the s- and p- polarization states and θ is the direction of observation as indicated in fig. 1. Eqn. (1) assumes that the object is isotropic, opaque, that all energy is either reflected or absorbed, and that the absorptivity is equal to the emissivity in each polarization state. Any feature of the object that allows mixing of s- and p-polarization states such as chirality, anisotropy, or severe multiple scattering will force the use of a more exact model. Eqn. (1) further neglects bidirectional reflection, but is approximately accurate for highly emissive targets . The s- and p- reflectivity are calculated using the standard Fresnel reflection coefficients  with appropriate complex index of refraction ñ = n + ik that can effectively take surface roughness into account [2, 6]. If an object is significantly warmer than its background, then the polarization signature is dominated by emission from the object. When this is the case the polarization signature is independent of time of day, specific object temperature, etc.
Consider the geometry shown in fig. 1. Given (1), and assuming an unpolarized background with emissivity equal to unity and temperature Tb, we have the total s-polarized spectral radiance leaving the object at temperature To in direction θ(in [W/cm2/sr/μm])
where P(T) is the Planck blackbody radiance curve at temperature T. A similar equation holds for the p-polarized radiance. In (3) we assume that the emissivity and reflectivity are spectrally flat over the wavelength range of interest, which is a reasonable assumption when working in the LWIR. It is important to note that Tb in (3) refers to the optical background, i.e. the object that is in the specular direction with respect to the observer as depicted in fig. 1. The background does not refer to the scene background. Strictly speaking, (3) should be replaced by the complete radiative transfer equation , but the expression as written is accurate enough for reasonably smooth objects in air.
Using (1) in (3) gives us for s- and p-polarization
There are three different regimes that exist for exploiting polarimetric signatures as summarized by Rogne . The first is the reflective regime where Tb >> To. In this case the measured polarization signature is primarily due to reflections from the surface of the object. This is the operating regime for most terrestrial imaging applications in the spectral range 0.4 – 2.5 μm.
The second regime occurs when the object is significantly warmer than the background (To >> Tb). In this case the surface transmission of thermally emitted radiation is the dominant polarization mechanism. For most outdoor terrestrial imaging applications this condition is met in the LWIR, especially when the cold sky is the optical background . Most LWIR polarimetric sensors are designed to exploit data in this operating regime.
When the object is close in temperature with its optical background, both the reflection and emission contribute significantly to the total radiance leaving the object in the direction of the observer. In such a case it is possible to completely eliminate the polarization signature even when there is thermal contrast within the image. It is generally known that an object in thermal equilibrium with its optical background cannot have a polarization signature. However,the role of the optical background and scene background as defined in fig. 1 are not widely known. It is clear from (4) and (5) that when To = Tb, the s and p radiances coming from the object are identical, and there is hence no polarization signature. This condition is usually satisfied in the mid-wave infrared (3–5μm) , and might be true whether or not there is thermal contrast between the object and the scene background.
2. Sensor description and data processing
The sensor used to gather the data presented in this paper is a LWIR microgrid polarimeter. The polarimeter contains a 640 × 480 HgCdTe array bonded to an array of wire grid micropolarizers manufactured by DRS Sensors & Tracking Systems. The camera is sensitive to radiation from 8 – 10 μm. The details of the polarimeter and its calibration are described in more detail elsewhere [10, 11].
The simplest scheme for estimating the Stokes vector at each point in the FPA uses the expressions
where L 0, L 45, L 90, and L 135 are the calibrated radiances measured at the neighboring pixels with linear polarizers at the indicated angles. Eqn. (6) ignores the fact that the four pixels have different instantaneous fields of view (IFOV). This IFOV error will result in polarimetric errors in regions of the image where the underlying image is spatially varying. This is an important effect, but is not treated in detail here. Various calibration and compensation strategies have been discussed elsewhere [12, 13].
The camera was radiometrically calibrated using a 2-point calibration with an unpolarized blackbody source at 15 C and 50 C. The data reduction matrices (DRMs) that allow reconstruction of the reduced Stokes vector from a set of intensity measurements [14, 11] for the individual super pixels were computed as well. The DRM was determined by experimentally measuring the extinction ratio and orientation angle of the wire grid polarizers on a pixel-by-pixel basis . Dead pixels in the FPA were not replaced.
3. Polarimetric imagery
The test target used for this study is an emissive gray body sphere shown in a visible photograph in fig. 2. The sphere is a 45-cm hollow brass shell painted with Krylon flat black paint. Experimental measurements indicate that the effective index of refraction in the LWIR is ñ = 1.6 + i0.1. The sphere was heated by placing an incandescent light bulb inside the hollow region and covering the opening with aluminum foil to reduce convective cooling.
For this data collection, the sphere was placed outside our laboratory on a sunny but cool spring day in Albuquerque, NM. The ambient air temperature fluctuated, but was approximately 15 C. The top half of the sphere has the cold sky as a background, with apparent temperature much lower than 0 C . The bottom half of the sphere had the ground as its background. The temperature of the ground was measured to be 28 C using the same thermocouple used to measure the sphere temperature. The sphere was heated to approximately 50 C, and was then allowed to cool until the measured temperature was approximately equal to the ground temperature. Thermocouple measurements indicated that the lower portion of the sphere ranged in temperature from 27 C – 30 C.
We expect the polarization signature of the target to be as follows [2, 16]. For regions of the sphere that have the sky as their optical background, the object is primarily emissive, and we expect the polarization to be partially p-polarized. The degree of polarization should be largest near the rim of the sphere where the observation angle is near grazing, and should reduce to zero at the center of the sphere where the observation angle is near normal. The angle of polarization should vary from 0° (with respect to vertical) at the top and bottom of the of the sphere to ±90° on the sides.
Fig. 3 shows the reconstructed s 0 and s 1 image of the gray body sphere. We see from fig. 3 that the polarization signature of the object is strongly dependent on the nature of the background. The entire sphere appears to be approximately thermally flat in the s 0 image, but the top half of the sphere, which has Tb << To in (4), has a strong polarization signature. The bottom half of the sphere, which has Tb ≈ To has virtually no polarization signature.
To strengthen this effect, fig. 4a shows the s 0 image of same object imaged under slightly different circumstances. In this case, a human hand with T ≈ 36 C was placed above the sphere so that the reflected radiation from the hand would reach the imager after reflection from the surface of the sphere. The s 0 image shows that there is a slight increase in apparent temperature due to the reflected radiation from the human hand (as well as the body, which is somewhat less apparent). The reflected radiation from the human hand has little effect on the s 0 image because the object is estimated to have an unpolarized emissivity at normal of 95%.
where H, S, and V are the color parameters hue, saturation, and value, ψ is the angle of polarization, and DoLP is the degree of linear polarization. For the imagery in fig. 4 the DoLP is normalized to the maximum measured value of 10% to enhance the saturation of the colors.
4. Discussion and conclusions
LWIR thermal imagery has the significant advantage that thermal contrast is not dependent on the existence of an external source. Any object that is warmer or cooler than the rest of the scene (in terms of apparent temperature, at least) will have thermal contrast. The polarization properties of emissive objects are more complicated. They depend not only on the object temperature and the temperature of the surrounding objects, but also depend on the temperatures of the optical background objects that might not even be in the image. We see from fig. 4b that the presence of the human hand virtually eliminates the polarization signature. Even through the object has low reflectivity (< 5%), the presence of the warm object in the background causes T o = T b, rendering the DoLP as approximately zero. It is intuitive that objects outside the image would be important for both polarized and unpolarized imaging of reflective targets, but the imagery in fig. 3 and fig. 4 shows that the background is just as important for polarized imaging of emissive objects. Even in this case, where the emissivity of the object is close to 1 and almost all of the light reaching the sensor is emitted radiation, the temperature of the background that is seen by the object strongly affects the measured polarization signature.
These results are similar to those presented for spectropolarimetric sensing of the air-water interface. Shaw  demonstrated that radiation coming from water in the visible, near IR, and short-wave IR is primarily reflective, while in the LWIR it is primarily emissive. The crossover between these two regimes usually occurs in the mid-wave IR (3–5 μm), and the polarization signature is often quite low there for remote sensing of water.
The authors are grateful to David Wellems and Rakesh Kumar for discussions during preparation of this manuscript. Mike Ratliff at Ratliff Metal Spinning Company in Dayton, OH, provided the spherical test target. This work was funded in part by the Air Force Office of Scientific Research, award #FA9550-05-1-0090 and the National Science Foundation under award # 0238309.
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