We report results of an ongoing study designed to assess the ability for enhanced detection of recently buried land-mines and/or improvised explosive devices (IED) devices using passive long-wave infrared (LWIR) polarimetric imaging. Polarimetric results are presented for a series of field tests conducted at various locations and soil types. Well-calibrated Stokes images, S0, S1, S2, and the degree-of-linear-polarization (DoLP) are recorded for different line-of-sight (LOS) slant paths at varying distances. Results span a three-year time period in which three different LWIR polarimetric camera systems are used. All three polarimetric imaging platforms used a spinning-achromatic-retarder (SAR) design capable of achieving high polarimetric frame rates and good radiometric throughput without the loss of spatial resolution inherent in other optical designs. Receiver-operating-characteristic (ROC) analysis and a standardized contrast parameter are used to compare detectability between conventional LWIR thermal and polarimetric imagery. Results suggest improved detectability, regardless of geographic location or soil type.
©2012 Optical Society of America
Both military and civilian personnel are facing an ever-evolving threat from buried/concealed landmines and improvised explosive devices (IEDs). There has been significant research dedicated to the detection of buried explosive devices [1–6]. One particular technology that has shown promise is forward-looking ground penetrating radar (FLGPR) [7–9]. However, recent studies have identified several inherent problems associated with FLGPR, e.g., buried explosives that are formed from dielectric- or polymer-based materials (plastics) are difficult to detect due to the small electromagnetic (EM) radar cross-sections for non-conducting materials [10,11]. In addition, FLGPR systems are plagued by unacceptable false-alarm rates due to the detection of commonly buried debris. A consensus has emerged that two or more complimentary technologies will most likely be required to improve detectability while reducing false-alarm rates. One such complimentary approach may involve a combination of a FLGPR system with an optically based imaging platform capable of detecting surface anomalies, i.e., disturbed earth (DE), that result when explosive devices are buried/concealed near the surface of a given terrain.
One suggested imaging technique for the remote detection of DE involves various forms of spectroscopic imaging in the thermal infrared (IR), sometimes termed multi- or hyper-spectral imaging [12–14]. These techniques attempt to exploit the so-called “reststrahlen” effect, in which the bulk emissivity for a particular soil changes within 8–10μm spectral range due to absorption at the reststrahlen frequencies, which are approximately equal to the natural frequencies of certain crystalline structure associated with small semi-transparent silica-based particles [15–17] Although well-documented, the reststrahlen effect has been shown to be quite variable depending on geographic location and soil composition. Most research shows a 3–5% variance in the IR emissivity associated to the reststrahlen phenomena under optimal conditions.
We consider a new imaging approach based on changes in polarization state associated with radiation that is emitted and/or reflected from a surface that has recently been altered [18–20]. The premise for considering polarimetric imaging is based on the fact that both manmade and naturally occurring terrain establishes an “average” polarization profile or pattern that results from vehicle traffic, weathering, or just the passage of time. Since the polarization state of the image forming radiation is extremely sensitive to subtle changes in the geometry of reflecting/emitting surface, resultant differences in polarization signatures arise for localized surface regions that have recently been disturbed.
For our application, we chose to use a Stokes parameter approach to describe the polarization state of the radiation that is emitted and/or reflected from a target area . We apply the Stokes methodology to an imaging application where we define the Stokes “images” S1, S2, and S0, by the usual convention shown in Eqs. (1)–(3),
For total linear polarization, the total radiance image, S0, is defined as,Eqs. (1)–(3), the S1 image represents a relative measure of the vertical compared to the horizontal component, the S2 image represents a relative measure of the difference between the two ± 45° diagonal states, and the S0 image is merely a conventional “intensity only” image.
This study represents a compilation of results spanning a three-year period. The three field-tests presented here were conducted in 2008, 2009, and 2011, to assess the viability for using passive LWIR (8-12µm) polarimetric imaging to identify regions of recently DE. The primary goal was threefold—1) objectively measure the ability to detect regions of disturbed soil associated with the placement of buried land-mines and/or IEDs; 2) assess how detectability is effected varying soil type and composition; and 3) determine how LWIR polarimetric DE signatures are effected by atmospheric conditions, e.g., clear sky, cloud cover, rain, wind, etc.
During the time period that this report encompasses, three different LWIR polarimetric imaging platforms were used, and all were produced by Polaris Sensor Technologies, Inc., located in Huntsville, AL. It should be noted that the use of three different LWIR polarimetric imagers was dictated not by choice, but rather by necessity. After an initial proof-of-concept study in 2008, a first-generation LWIR polarimetric imager experienced technical issues that delayed further study. Early in 2009, a LWIR microbolometer-based polarimetric sensor became available, which allowed for our work to continue. Finally, in 2010, a state-of-the-art LWIR polarimetric imager became available and was used in the final phase of the study.
Although there are a variety of optical configurations appropriate for polarimetric imaging, (e.g., division-of-amplitude (DoA), division-of-focal-plane (DoFP), and division-of-aperture (DoAP)), we chose a division-of-time (DoT) approach based on a spinning achromatic retarder (SAR) design for recording calibrated LWIR Stokes imagery [22–26]. Because the DoT method relies on the capture and differencing of sequentially recorded images, it is only appropriate for imaging objects that are slowly moving or static within the scene. Although somewhat limited by the sequential nature of the recorded imagery, it is by far the best choice for basic research applications due to maximum radiometric throughput, spatial resolution, and polarimetric sensitivity.
2. Spinning achromatic retarder (SAR) polarimetric sensors
A spinning achromatic retarder (SAR) imaging polarimeter operates by capturing a sequence of images in time. Each image in the sequence is recorded at a different orientation position of a spinning achromatic retarder. In its principle mode of operation, the system acquires a set of 16 images per rotation of the retarder—i.e., images are captured at 0, 22.5, 45… to 337.5°.
Figure 1 shows the basic design of a LWIR SAR-based imaging polarimeter in which either a room-temperature microbolometer, or a cryogenically cooled Mercury Cadmium Telluride (MCT) focal-plane-array (FPA) detector is positioned at the image-plane of the sensor. In general, we have found the cooled MCT-based FPAs to exhibit a noise-equivalent DoLP or NEDoLP (similar to NEΔT for conventional thermal) on the order of ± 0.1%, whereas the microbolometer-based systems typically exhibit NEDoLP values in the range of ± 0.3-0.5%.
For MCT-based systems, much of the optical train is held under vacuum within a Dewar and cooled to an approximate temperature of 88K. The achromatic retarder is mounted just outside the Dewar window and is mounted to a precision set of frictionless bearings. A series of relay optics are used to reduce any beam wander generated by the rotating optic, and by using this configuration pixel, registration error between sequential frames is typically less than 1/20th of a pixel. The retarder is rotated continuously by a stepper motor at variable rates, depending on the specified integration period and application. All three SAR-based systems used in this study are designed to record/display a user-specified set of Stokes and/or polarimetric image products at processing rates approaching real-time. An excellent review of current polarimetric imaging technologies can be found in Tyo, Goldstein, Chenault, and Shaw .
3. Detection analysis
Perhaps one of the more difficult tasks involved with image detection analysis is developing an objective evaluation metric that consistently and correctly identifies the “best” image type for maximum detectability. Much of the difficulty arises from the fact that optimum detectability is so heavily dependent on the type of end-user one considers, e.g., human or computer algorithm. To address this, we chose to use two established image evaluation metrics—i.e., detection calculations based on a receiver-operational-characteristic (ROC) curve approach, and the more intuitive, standardized contrast parameter method. Since both techniques have inherent strengths and weaknesses, we present to the reader actual LWIR thermal and polarimetric image sets for subjective, yet sometimes more informative, evaluation.
The receiver-operational-characteristic (ROC) analysis is often the tool of choice among researchers within the artificial intelligence (Ai) and automated-target-recognition (ATR) community. The ROC method was originally developed for signal detection analysis but is now widely applied in many different disciplines [28–30]. ROC curve analysis is used to compare target detectability between different image sets recorded or processed by different means. In order to do this, some a priori knowledge about the location of the actual target is necessary so that a “truth” image can be generated. Figure 2(a) shows an image histogram of an example truth image where the large Gaussian like curve on the left represents the pixel values associated with the background, and the smaller distribution on the right represents the pixel values associated with the target. The vertical line in the figure represents an arbitrary threshold point. Also shown are regions defined by the intersection of the two histograms, as well as regions to the right and left of the threshold line identified as true-negative (TN), true-positive (TP), false-positive (FP), and false-negative (FN) regions.
A ROC curve is generated by comparing the overlapping regions TN, TP, FP, and FN, as the threshold point is swept right to left across the histogram. Figure 2(b) shows a resultant ROC curve for the histograms shown in Fig. 2(a). The area under the ROC curve is defined as the normalized probability for detection of the target identified in the truth image.
One inherent weakness associated with the ROC curve approach stems from the fact that it is a purely statistical method and fails to take into account addition spatial information associated with localized target pixel location and/or clustering—an important aspect of visual cognitive detection. The human eye can often decipherer target regions within a scene based on very subtle variations among clusters of pixels that form a particular distinguishable shape. Nevertheless, the ROC method is a readily accepted metric among Ai/ATR community and does offer an objective measure of target detectability.
A second evaluation method for grading imagery for maximum detectability involves calculating a “standardized” contrast parameter . At the most fundamental level, the ability to detect a given object within an image is heavily dependent on the magnitude of the difference between pixel values associated with the object and its associated background, i.e., contrast. However, in order to compare pixel values that result from different image types—e.g., thermal, Stokes, DoLP, etc.—a standardization process must be applied to the entire image set. This is a common procedure used to normalize multivariate image sets before applying a particular evaluation metric. The standardization process effectively translates each image histogram (derived from different physical quantities) onto the same basis set of coordinate axes. The standardization procedure involves subtracting the mean pixel value derived by the entire image, and dividing the resultant histogram by the standard deviation. This multivariate normalization process by no means affects overall integrity and information content of the image. After image standardization, separate ROIs are defined for the target and background regions for a given image set, and the average pixel value for each region is computed. Finally, a standardized contrast parameter is calculated for each image and is defined as,
4. Experiment (test sites) and results
The first test was conducted on May 22, 2008, and was located at the U.S. Army Research Laboratory (ARL), Adelphi, MD, on a test surface best described as a well-traveled dirt road consisting of a gravel-clay-soil mixture that was well-compacted. The test was conducted over a 6-h period during mid-afternoon under clear skies, with relative humidity approximately 50% and temperatures varying from 77 to 81 °F. Holes were dug approximately 12 in into the hardened road surface and surrogate IED targets were buried at different locations, see Fig. 3 .
For this particular test, we used our lowest resolution 256 x 256 MCT FPA-based SAR polarimetric camera system. The polarimetric imager was mounted on a tripod and positioned 2.75 m above the ground and was focused on the DE region at an approximate distance of 10 m away as shown in Fig. 4 . A 50 mm LWIR objective lens was fitted to the polarimetric sensor, which produced an effective field-of-view (FOV) of 15°. The camera LOS was angled to the DE region, resulting in a range of grazing angles from 15 to 20° defined by the LOS and the road surface. It should be noted that for this first proof-of-concept test, great care was taken to camouflage the disturbed region as best as possible, i.e., not readily noticeable to a casual observer, see Fig. 3(b). After the disturbed regions reached thermal equilibrium after approximately 1 h, a series of four image sets were recorded at 15-min intervals.
Figure 5 shows the resultant imagery consisting of a conventional LWIR thermal image, S0, the two Stokes images, S1 and S2, and DoLP image, where a false color has been applied to all the original grey-scale images. Note that all Stokes image values presented here are normalized with respect S0, and range from –1 to 1. Table 1 shows the average absolute radiance and normalized Stokes values for ROIs that are defined as either the DE or background regions.
As one can see in Fig. 5(a), the ability to distinguish disturbed from undisturbed soil regions is quite poor for the conventional LWIR thermal image, S0, and reflected by the lowest calculated ROC curve value, 0.256 (Fig. 6 ), and the lowest contrast parameter value, 0.056, shown in Table 2 . The DE region becomes visible in the Stokes image S1 (Fig. 5b), where contrast arises from the fact that the DE region emits thermal radiation that is slightly less polarized, when compared to the surrounding undisturbed area (Table 1). Note that since all normalized S1 values are negative, the majority of the polarization lies in the horizontal plane, based on the definitions shown in Eqs. (1-2), which is associated with “emission” dominant polarization. Conversely, a positive S1 value implies that the vertical component is dominant, and the majority of the received radiance is due to “reflection” of the ambient optical background.
Similar evaluation of the S2 image shows further improvement in target detectability and is reflected by the highest calculated ROC curve and contrast parameter values of 0.958 and 1.745, respectively. Again, since the values for the normalized S2 image shown in Table 1 are negative, the dominant polarization state is oriented at –45°, with respect to the vertical. In a scene in which the LOS to the lay of the surface is perfectly symmetric, we would expect the values of the S2 image to be nearly zero—i.e., ground is surface flat and level, and the region of interest is centered. However, due to the slope of the ground surface and the fact that the camera mount was off-center with respect to the DE region, a larger than normal difference arose between the + 45° and –45° states. Figure 5(d) shows the DoLP image, which is merely the normalized superposition of the Stokes images S1 and S2. A lower contrast parameter value of 0.993 is not unexpected since the DoLP product contains noise components from S1, S2, and S0, which in this case, results in a slight reduction in the overall contrast for the DoLP product image.
A follow-on series of DE tests were conducted over a multi-day period from August 27– September 4, 2009. The location was again the Adelphi, MD, area, which included the original May 22, 2008, dirt road site, as well as two new locations in which the soil compositions for each location is characterized as red-clay-silt mixture, and a topsoil type material, rich in organic material and small stone. As previously mentioned, the original liquid nitrogen (LN2)-cooled 256 x 256 MCT FPA SAR polarimetric sensor was unavailable during this period and a new 324 x 256 FPA microbolometer-based SAR polarimetric imager was substituted in its place.
The first test was conducted on August 27, 2009, at a local baseball field in Adelphi, MD. The site was chosen due to its unique soil type similar to what is found in various regions of Southeast Asia, see Fig. 7(a) . Once again, holes were dug and surrogate objects were buried at various locations at depths < 1 m. Similar to the first test conducted in 2008, each hole was carefully raked and brushed over to camouflage the fact that digging had occurred, see Fig. 7(b). The microbolometer SAR polarimetric imager was set up in a similar manner as in prior tests, with the exception that the camera was mounted at a slightly lower to a height of 2 m above the ground. This resulted in a viewing angle (as defined by the LOS and the soil surface) that ranged from 10 to 16°, depending on the location of interest within the scene. Once the disturbed regions reached thermal equilibrium with the surrounding background, capture of polarimetric imagery began and was recorded every 15 min for approximately 4 h.
Figure 8 shows the resultant thermal and polarimetric image set recorded at the red-clay-silt site on August 27, 2009. Two large DE regions are visible only in the Stokes and DoLP images shown in Figs. 8(b)-8(d) and are identifiable as either light regions in image, 8(b), or dark regions in images 8(c) and 8(d). Average thermal and polarimetric values for the disturbed and background ROIs are shown in Table 3 .
Review of the values shown in Table 3 again shows negative values for the normalized S1 image, which implies that the polarization state results primarily from surface emission, rather than reflection of the ambient background radiation. Because the camera was well-centered with respect to the disturbed regions, greater symmetry was created within the scene, resulting in normalized S2 values that were effectively zero. As with the earlier test, the disturbed region was less polarized than the undisturbed background, resulting in DoLP values of 1.00% and 1.43%, respectively.
The results of the ROC curve and contrast parameter analysis are shown Table 4 and indicate that the DoLP image is ranked highest in detectability, followed closely by the S1 image. However, issues associated with the ROC curve approach become apparent when considering the S2 image, which registered the lowest probability of detection with a value of 0.312, although the DE regions are clearly visible in the S2 image, shown Fig. 8(c).
On September 3, 2009, we returned to the first test-site location of May 22, 2008, and repeated the measurement with the microbolometer-based SAR polarimetric sensor. This time, two surrogate targets were buried, and after thermal equilibrium between the DE and backgrounds surfaces was reached, polarimetric images sets were recorded, see Fig. 9 . Note that the bright spots seen in the S0 image, Fig. 9(a), was a result of localized heating due to direct sunlight that was filtered through a series of trees located on the right side of the test site.
On September 4, 2009, we chose a test location containing a topsoil mixture consisting of fine dirt and gravel that was “shadowed” from the afternoon sun by a large building, see Fig. 10(a) . This location was specifically chosen to assess how shadowing, as well as radiant loading resulting from the building, would affect the ability to polarimetrically resolve regions of DE. Only one surrogate target was buried for the test, and after a period of about 2 h (needed for thermal equilibrium to occur), recording of polarimetric imagery was started, see Fig. 10.
Until now, all of the studies have been short in duration—i.e., a single day—and the obvious question is, “How long and under what conditions will such disturbances continue to be detectable using a polarimetric imaging method?”
The resultant radiance and polarimetric values for the DE and background ROIs, as well as the corresponding detection metrics for the September 3–4, 2009, tests are shown in Tables 5 and 6 . Review of the contrast parameter and ROC curve results shows that the degree of detectability for the polarimetric derived imagery is consistently greater than the conventional thermal image, S0. However, there is disagreement on whether the S1 or DoLP image is actually superior, since the September 3 contrast parameter implies the DoLP image to be best, while the ROC curve results for both September 3 and 4 show the S1 to be the superior detection image. Again, the dilemma of what is the “best” image is left to the observer, and after comparing the image sets shown in Figs. 9 and 10, one could make a good argument for either the S1 or DoLP for being the superior detection image.
To address this issue partially, we conducted a multi-day field test that occurred over a five-day period spanning October 1–5, 2011. The term “partially” is used because even after a week in the field, in which we experienced a variety of weathering conditions including a series of modest rain events and monsoon type winds, many of the DE regions were still visible to the polarimetric sensor.
This final test was conducted in an arid southwest region of the United States located at the Energetic Materials Research and Testing Center (EMRTC) in Socorro, NM, where the soil type is characterized as loam—i.e., a soil composed of sand, silt, and clay at about 40-40-20% concentrations respectively. For this particular study, our most sensitive LWIR MCT-based polarimetric sensor became available. The 640 LWIR SAR Polarimetric imager, produced by Polaris Sensor Technologies, housed a Stirling-cooled 640x480 MCT FPA detector, which was provided by DRS Technologies, Inc. The system was designed for maximum radiometric throughput and sensitivity that results from efficient sensor design, and a usually wide spectral response of 7.5 to 11.1μm, for the FPA.
The final test was held in conjunction with another experiment in which a vehicle-mounted, forward-looking-ground-penetrating-radar (FLGPR) was being evaluated. In order to get quasi-registered LWIR polarimetric imagery with the FLGPR system, the polarimetric sensor was mounted on an elevated platform located above the FLGPR transmitter/receiver. This resulted in the sensor being 4.5 m above the ground, as shown in Fig. 11(a) . The polarimetric sensor-FLGPR platform was tilted downward at an angle of 24° with respect to the LOS and test surface. A variety of surrogate objects were buried and camouflaged by hand in one of three test lanes, see Figs. 11(b) and 11(c). A series of five DE regions were imaged every other day during the period of October 1–5, 2011, in which meteorological conditions varied greatly. Weather conditions for each of the three days were as follows: October 1—clear sky, low relative humidity with a temperatures range of 69-78 °F; October 3—overcast with, low relative humidity, temperatures slightly cooler in the range of 65-73°F; and October 5—ground surface damp as a result of a rain storm that occurred during the prior day and much cooler, with a temperature range of 50-60°F.
The effects of weathering are displayed in a series of images shown in Figs. 12(a) -12(c). Each column displays a visible image, a conventional LWIR thermal image, S0, the Stokes image, S1, and a DoLP image for the DE target 2 (TG 2). Tabulated radiant and polarimetric values for all DE targets (TG) 1-5, recorded from October 1–5, 2011, as well as their corresponding background (BG) regions, are shown in Table 7 . A similar list of tabulated ROC curve and contrast parameter values for the same period is shown in Table 8 .
The overall trend seen in the 2009 and 2010 studies continues, and is reflected in the values shown in Table 7. Specifically, 1) the polarization state for the S1 images continue to result from emission dominant radiance; 2) the DoLP for DE regions is always less than the undisturbed background surfaces; and 3) the highest ranked image type for detectability continued to be the S1 image, followed closely by the DoLP images. The values for the normalized S1 images record on October 3 (dense cloud cover) were, on average, slightly lower than S1values recorded on either October 1 or October 5.
However, based on our prior experience, we would have expected even lower S1 values for the October 3 test data, considering the overcast conditions, which is often associated with large ambient radiant loading. This is because the linear polarization that occurs when ambient radiance is reflected from a surface is always orthogonal to the linear polarization that results purely from emission, and the net effect results in an overall reduction in the total linear polarization exhibited by the surface. This effect is most often seen in MidIR polarimetry, where it is not uncommon to see the sign of various regions within an S1 image flip with quickly changing meteorological conditions .
Perhaps the most interesting aspect of the study resulted after the rain event that occurred on October 4. Although not readily apparent in the image set shown in 12c, the modest rainfall of October 4 appeared to actually improve the contrast between the DE and surrounding undisturbed areas. We have always expected that after a sufficient amount of weathering and/or traffic has occurred, the ability to polarimetrically detect regions of recently disturbed soil would not be possible. However, based on these preliminary results, modest weathering events like blowing wind and rain may actually serve to enhance the effect, at least initially. In this particular case, the rain events appear to produce a net “smoothing” of the undisturbed regions, while the DE regions were far less affected. This is also reflected by the relatively large DoLP values recorded on October 5 for both the target (TG) and background (BG) surfaces shown in Table 7.
We have shown that by using passive LWIR polarimetric imaging, one can improve the ability to remotely detect localized regions of recently DE that is often associated with the bearing of landmines and IEDs. The results stem from a series of tests conducted at a variety of different geographic locations with varying soil types in which three different LWIR polarimetric imaging platforms were used. In light of the multitude of changing parameters and sensors, the final results were surprisingly consistent.
First, based on objective detection metrics used in this study—i.e., ROC curve analysis and standardized contrast parameter calculations—the ability to detect localized regions of DE was greatest for the polarimetric images S1 and DoLP. We believe the DE contrast seen in the Stokes images S1 is a direct result of the symmetric slant-path imaging arrangement used in the study. We expect for an elevated nadir type detection arrangement that the DoLP image would be the image type of choice for detecting regions of DE.
Second, all measured S1 signatures were due to emission induced polarization—i.e., linearly polarized in the horizontal plane. As mentioned earlier, situations in which the ambient optical background is changing, as is the case when stratus or nimbostratus cloud-cover is present, the sign of specific regions in the Stokes images S1 or S2 are often observed changing, signifying that the mechanism for generating linear polarization has switched from being emission to reflection dominant, or vice versa. However, observations also show that even during these events, the polarimetric contrast between a given target and the corresponding background is preserved 
Finally, the polarimetric contrast necessary to distinguish DE regions from the undisturbed surrounding areas results from the fact that undisturbed surfaces tend to exhibit higher degrees of linear polarization compared to DE areas. Put more generally, polarimetric contrast between disturbed and undisturbed surface regions arises when symmetry of the surface is altered. Such symmetry may result from naturally occurring events, e.g., prolong wind and rain storms, or by a manmade process associated with vehicular and pedestrian travel. Once a soil surface is altered, very subtle, yet quite measurable, differences in the polarization state of the reflected or emitted radiation occurs at the boundary that defines disturbed from undisturbed surface areas.
We have shown for the cases considered here a net reduction in the linear polarization for the DE regions (relative to the surround undisturbed regions) on the order of 20-100% or more. Although all of the imagery recorded involved a slant-path LOS, the authors believe the ability to detect regions of DE using passive LWIR polarimetric imaging would greatly benefit if conducted from an aerial platform. This would allow for imaging of much larger surface areas in which a “change-detection” method could be applied. We are currently planning a series of such studies using a nadir LOS where DE regions are polarimetrically imaged in both the MidIR and LWIR to assess the benefit for using a dual-band approach.
References and links
2. C. Bohling, K. Hohmann, D. Scheel, D. Nodop, C. Bauer, J. Burgmeier, W. Schade, and G. Holl, “Real-time detection of mines and explosives by laser-induced breakdown spectroscopy,” in Conference on Lasers and Electro-Optics, 2006 and 2006 Quantum Electronics and Laser Science (CLEO/QELS. 2006).
4. J. A. Shaw, N. L. Seldomridge, D. L. Dunkle, P. W. Nugent, L. H. Spangler, J. J. Bromenshenk, C. B. Henderson, J. H. Churnside, and J. J. Wilson, “Polarization lidar measurements of honey bees in flight for locating land mines,” Opt. Express 13(15), 5853–5863 (2005). [CrossRef] [PubMed]
6. J. S. Tyo, B. M. Ratliff, J. K. Boger, W. T. Black, D. L. Bowers, and M. P. Fetrow, “The effects of thermal equilibrium and contrast in LWIR polarimetric images,” Opt. Express 15(23), 15161–15167 (2007). [CrossRef] [PubMed]
7. R. Harr and M. Polcha, “Preliminary investigation of the reststrahlen phenomenology at low-grazing angles,” Proc. SPIE 5794, 978–987 (2005). [CrossRef]
8. Y. Wang, L. Li, and Y. Sun, “Adaptive imaging for forward-looking ground penetrating radar,” IEEE Trans. Aerosp. Electron. Syst. 41(3), 922–936 (2005). [CrossRef]
9. J. Kositsky, R. Cosgrove, and C. Amazeen, “Results from a forward-looking GPR mine detection system,” Proc. SPIE 4742, 206–217 (2002). [CrossRef]
11. K. Stone, J. Keller, K. Ho, M. Busch, and P. D. Gader, “On the registration of FLGPR and IR data for a forward-looking landmine detection system and its use in eliminating FLGPR false alarms,” Proc. SPIE 6953, 695314, 695314-12 (2008). [CrossRef]
12. E. Winter, M. Miller, C. Simi, and A. Hill, “Mine detection experiments using hyper-spectral sensors,” Proc. SPIE 5415, 1035–1041 (2004). [CrossRef]
13. E. M. Winter and M. S. Silvious, “Spectral method to detect surface mines,” Proc. SPIE 6953, 69530R, 69530R-9 (2008). [CrossRef]
14. A. C. Goldberg, T. Fischer, and Z. Derzko, “Application of dual-band infrared focal plane arrays to tactical and strategic military problems,” Proc. SPIE 4820, 500–514 (2003). [CrossRef]
15. G. Koh, E. Winter, and M. Schatten, “Rainfall degradation of LWIR disturbed soil signature,” Proc. SPIE 6217, 62170G, 62170G-8 (2006). [CrossRef]
16. W. Wolfe and G. Zissis, The Infrared Handbook, Environmental Research Institute of Michigan, Office of Naval Research, Dept. of Navy, Washington, DC (1978).
17. G. Zissis, ed., The Infrared & Electro-Optical System Handbook, Sources of Radiation, (SPIE Optical Press, 1993), Vol. 1.
18. J. Sergio, Z. Wang, J. Tyo, and B. Hoover, “Target Detection with Partial Mueller Polarimeters,” in Frontiers in Optics(FIOS), OSA Technical Digest (Optical Society of America, 2008), paper FThO7.
19. J. S. Tyo, B. M. Ratliff, J. K. Boger, W. T. Black, D. L. Bowers, and M. P. Fetrow, “The effects of thermal equilibrium and contrast in LWIR polarimetric images,” Opt. Express 15(23), 15161–15167 (2007). [CrossRef] [PubMed]
21. E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979), Vol. 22, pp. 4223–4227.
22. M. Kudenov, L. Pezzaniti, and G. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009). [CrossRef]
23. C. S. L. Chun, D. L. Fleming, and E. J. Torok, “Polarization sensitive, thermal imaging,” in Automatic Object Recognition IV, F. A. Sadjadi, ed., Proc. SPIE 2234, 275–286 (1994).
24. J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V, 58880V-12 (2005). [CrossRef]
25. J. L. Pezzaniti and R. A. Chipman, “Imaging polarimeters for optical metrology,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman and J. W. Morris, eds., Proc. SPIE 1317, 280–294 (1990).
26. J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995). [CrossRef]
28. T. Fawcett, “An introduction to ROC analysis,” Pattern Recognit. Lett. 27(8), 861–874 (2006). [CrossRef]
29. A. P. Bradley, “The use of the area under the ROC curve in the evaluation of machine learning algorithms,” Pattern Recognit. 30(7), 1145–1159 (1997). [CrossRef]
31. W. Dillon and M. Goldstein, Multivariate Analysis Methods and Applications (John Wiley & Sons, 1984).
32. M. Felton, K. P. Gurton, J. L. Pezzaniti, D. B. Chenault, and L. E. Roth, “Measured comparison of the crossover periods for mid- and long-wave IR (MWIR and LWIR) polarimetric and conventional thermal imagery,” Opt. Express 18(15), 15704–15713 (2010). [CrossRef] [PubMed]