Imaging sensor constellation for tomographic chemical cloud mapping

Imaging sensor constellation for tomographicchemical cloud mapping

Bogdan R. Cosofret,1,* Daisei Konno,1 Aram Faghfouri,1 Harry S. Kindle,1

Christopher M. Gittins,1 Michael L. Finson,1 Tracy E. Janov,1

Mark J. Levreault,2 Rex K. Miyashiro,3

and William J. Marinelli1

1Physical Sciences Inc., 20 New England Business Center, Andover, Massachusetts 01810-1077, USA2Vtech Engineering Corporation, 20 New England Business Center, Andover, Massachusetts 01810-1077, USA

3Research Support Instruments, 4325B Forbes Boulevard, Lanham, Maryland 20706, USA

*Corresponding author: [email protected]

Received 18 August 2008; revised 30 January 2009; accepted 25 February 2009;posted 2 March 2009 (Doc. ID 100165); published 24 March 2009

A sensor constellation capable of determining the location and detailed concentration distribution of che-mical warfare agent simulant clouds has been developed and demonstrated on government test ranges.The constellation is based on the use of standoff passive multispectral infrared imaging sensors to makecolumn density measurements through the chemical cloud from two or more locations around its pe-riphery. A computed tomography inversion method is employed to produce a 3D concentration profileof the cloud from the 2D line density measurements. We discuss the theoretical basis of the approachand present results of recent field experiments where controlled releases of chemical warfare agentsimulants were simultaneously viewed by three chemical imaging sensors. Systematic investigationsof the algorithm using synthetic data indicate that for complex functions, 3D reconstruction errorsare less than 20% even in the case of a limited three-sensor measurement network. Field data resultsdemonstrate the capability of the constellation to determine 3D concentration profiles that account for∼h86%i of the total known mass of material released. © 2009 Optical Society of America

OCIS codes: 280.0280, 280.4991.

1. Introduction

The improvement of ground test validation capabilityin the form of rapid and accurate evaluation of sensortechnologies has recently been targeted by the JointProgramExecutiveOffice forChemical andBiologicalDefense (JPEO-CBD) as an important technical ob-jective [1]. The goal of the effort reported in this paperis to develop a system that is capable of providing ac-curate 3D concentration distributions of chemicalwarfare agent simulant clouds released on testranges. Sucha systemenhances the ability to validatenew chemical and biological sensing technology, as

well as provides a better understanding of the fateand transport of chemical releases through chemicalreaction models. Currently employed technology ser-ving this purpose makes use of single-pixel passiveFourier transform infrared spectrometers that scana viewing area every 15 s [2]. Information on the col-umn density of the chemical cloud obtained from theFourier transform infrared units is coupled to dataprovided by point sensors located across the test area.Themajority of this information isnot currently avail-able for near-real-time processing and is collectedmanually after a test is completed. One goal of thiseffort is the development of the capability to providethe concentration profiles in real time as well as spe-cific data presentation approaches to enable rapidevaluation of the performance of systems under test.

0003-6935/09/101837-16$15.00/0© 2009 Optical Society of America

1 April 2009 / Vol. 48, No. 10 / APPLIED OPTICS 1837

The method of computed tomography (CT) allowsthe 3D reconstruction of a chemical cloud density dis-tribution from a series of 2D measurements of theline-of-sight column density through the cloud at dif-ferent viewing angles. The use of CT with multispec-tral passive infrared measurements of individualcomponents in a chemical cloud parallels the ap-proach used in x-ray-based medical imaging andcan be an important tool in understanding chemicalcloud dynamics.In this paper, we describe the development and

application of an imaging sensor constellation for to-mographic chemical cloud mapping that providesnear-real-time detection, tracking, and full 3D con-centration information on chemical clouds, both intest situations as well as potentially during emer-gency events. We utilize the results of chemical ima-ging experiments conducted during the summer of2006 by employing three long-wavelength infraredimaging Fabry–Perot spectrometers developed byPhysical Sciences Inc. (PSI) to evaluate the perfor-mance of the system. The instrument is known asan adaptive infrared imaging spectroradiometer,trade name AIRIS [3]. The experiments involvedimaging a series of controlled chemical vapor re-leases at Dugway Proving Ground (DPG). An illus-tration of the system configuration is shown inFig. 1. The field study was focused on the dissemina-tion of several chemical warfare agent simulantsviewed from three fixed locations approximately2:8km away from the release point.Passive sensing of chemical vapor clouds relies on

both the spectral signatures of the target species aswell as the radiance contrast between the vapor andthe background scene. The AIRIS sensor units arecomposed of a long-wavelength infrared focal planearray-based camera that views the far field througha low-order, tunable Fabry–Perot etalon [4,5]. Thetunable etalon provides the spectral resolution ne-cessary to resolve structured absorption and emis-sion from molecular vapors. The focal plane array(FPA) permits radiance measurements of sufficientsensitivity that the species-specific column densitiesof chemical clouds may be determined with only acouple of degrees effective temperature difference be-tween the vapor and the background. We present asynopsis of the development of the PSI tomographicsystem by first describing results obtained by usingsynthetic data. This exercise has allowed us to better

understand the absolute capability of the algorithmin the case of limited measurement network (onlythree sensors). Finally, we present the results ob-tained from the tomographic analysis of the infraredimagery from the DPG disseminations.

2. Experimental Configuration and Theoretical Basisof the Approach

A. AIRIS Sensor Technology

The AIRIS–wide-area-detector (WAD) instrumenthas been described in detail elsewhere [6,7]. The ba-sic AIRIS optical configuration is shown in Fig. 2.The concept is based on the insertion of a tunableFabry–Perot interferometer (etalon) into the fieldof view (FOV) of an infrared FPA. The infraredFPA views the far field through the piezoelectric-actuated etalon placed in an afocal region of theoptical train. The tunable etalon is operated in loworder (mirror spacing comparable with the wave-length of the light transmitted) and functions asan interference filter that selects the wavelengthviewed by the FPA. The optical configuration de-picted in Fig. 2 affords a wide FOV, high opticalthroughput, and broad wavelength coverage at highspectral resolution. The interferometer tuning timeis ∼2ms between transmission wavelengths. Fore-optics and integrated blackbody calibration sources,not depicted in Fig. 2, enable control of the sensor’sfield of regard and absolute radiometric calibrationof the data. The AIRIS units operated in the studyprovided 256pixel × 256pixel imagery at 2:2 ×2:2mrad instantaneous field-of-view (IFOV) per pix-el. This configuration resulted in a 32° × 32° field ofregard.

The three AIRIS units were configured to acquireimagery between 7.9 and 11:2 μm at ∼0:08 μm(8 cm−1) spectral resolution. The AIRIS FPA acquiresframes at 200Hz, and typically eight frames wereaveraged at each observation wavelength. The etalontuning time to observation wavelengths is much lessthan the FPA framing period, and the typicaldata-cube acquisition time was ∼0:8 s. Data cubeswere acquired once every ∼1:7 s. The noise-equivalent spectral radiance of the data was

Fig. 1. Imaging sensor constellation for tomographic chemicalcloud mapping.

Fig. 2. Technical concept for Fabry–Perot imaging spectrometer.The interferometer is located in an afocal region of the opticaltrain.

1838 APPLIED OPTICS / Vol. 48, No. 10 / 1 April 2009

∼1:5 μWcm−2 sr−1 μm−1 (μFlicks) over the entire oper-ating range and is equivalent to a noise-equivalenttemperature difference ∼0:1K. Radiometric calibra-tion of the data was accomplished by using atwo-point gain and offset correction with internalblackbody calibration sources set for two tempera-tures: Tcold ∼ 288K and Thot ∼ 308K. A calibrationof the system was executed once every 30min for ac-curate radiometric measurements. The spectral radi-ance of ambient temperature objects was typically∼800 μWcm−2 sr−1 μm−1 over the typical field tem-perature range, and the change in radiance withtemperature is ∼15 μWcm−2 sr−1 μm−1 K−1. Each256pixel × 256pixel × 20wavelength AIRIS datacube is used to create a 256pixel × 256pixel arrayof chemical vapor column density values by usingthe approach described below.

B. Radiative Transfer and Sensor Signal Model

The detection approach is based on the change inpassive infrared radiation received by the spectrallyresolving sensor due to the presence of a chemicalcloud. The basic process can be described by athree-layer model, as shown by Flanigan [8], andis illustrated in Fig. 3. The total infrared radianceincident on the sensor at a given wavelength isthe sum of the contributions from each layer andis given by

NsensorðλÞ ¼ tAtCNBðλ;T1ÞεBðλÞ þ tA½1 − tC�NCðλ;T2Þþ ½1 − tA�NAðλ;T3Þ; ð1Þ

where NBεB is the Planck radiance of the back-ground, NC is the Planck function radiance at thethermodynamic temperature of the chemical cloud,and NA is the Planck function radiance at the ther-modynamic temperature of the atmosphere. Thequantities tC and tA are the spectral transmissionof the cloud and the atmosphere between the cloudand the sensor, respectively. The first term inEq. (1) describes the radiance from the backgroundas attenuated by the chemical cloud and interveningatmosphere. The second term describes the radianceof the chemical species in the cloud as attenuated by

the atmosphere between the cloud and the sensor. Fi-nally, the third term in Eq. (1) describes the radianceof the atmosphere between the cloud and the sensor.The transmission of the cloud, layer 2, is computedfrom the spectral properties of the chemical speciescontained therein:

tCðλÞ ¼ exp�−X

σiðλÞρi�; ρi ¼ Ciℓ; ð2Þ

whereCi is the average concentration of the chemicalcompound over the line of sight through the cloud, ℓ(ρi is the chemical column density), and σiðλÞ is thewavelength-dependent absorption coefficient. Thesum over index i in Eq. (2) is over all spectrallyrelevant chemical species.

The differential radiance observed by the sensor asa result of the presence of the chemical cloud can beapproximated as

ΔNðλÞ ¼ ½tAtCNBðλ;T1ÞεBðλÞ þ tA½1 − tC�NCðλ;T2Þþ ½1 − tA�NAðλ;T3Þ� − N̂ðλÞ; ð3Þ

where N̂ðλÞ is the radiance measured at the sensor inthe absence of the chemical cloud (tC → 1) and isdefined as

N̂ðλÞ ¼ tANBðλ;T1ÞεBðλÞ þ ½1 − tA�NAðλ;T3Þ: ð4Þ

To determine the chemical simulant spectral trans-mission, tC, from measured sensor radiometricsand therefore obtain its column density, we use a fun-damental assumption: we assume that the chemicalcloud attains atmospheric temperature because ofrapid mixing with the surrounding air. This assump-tion allows the approximation that NC ≈NA, and NAcan be determined from a measurement of the localair temperature. Furthermore, to first order, this as-sumption also relaxes the need to have implicitknowledge of the atmospheric attenuation, tA, be-tween the cloud and the sensor. This approachhas been used in previous work [9]. We note that at-mospheric temperature generally decreases withincreasing height above ground level and that forclouds that rise high (several hundred meters) abovethe ground, it is necessary to address the decrease inair temperature with altitude, as the cloud mass willbe underestimated if the cloud temperature is pre-sumed to be equal to the ground-level atmospherictemperature. The majority of the concentration pro-files estimated in this work are calculated for eleva-tions within tens of meters of the ground, however, sowe do not address variation of air temperature withaltitude here.

With the assumption that the cloud temperature isequal to the ambient air temperature, the cloudtransmission can be determined from Eqs. (1) and(4) as follows:

Fig. 3. Schematic diagram of three-layer radiative transfermodel.


tCðλÞ ¼NsensorðλÞ −NAðλÞ

N̂ðλÞ −NAðλÞ; ð5Þ

where Nsensor is the sensor measurement and NA isthe Planck radiance for a blackbody at ambient airtemperature, which can be measured locally. Thetemperature values are typically obtained from aweather station that is positioned in proximity tothe chemical release.The most complex problem left to be addressed in

order to solve Eq. (5) is the determination of N̂ðλÞ, thescene radiance in the absence of the chemical cloud.As a result of the fact that we do not have a prioriknowledge of the background characteristics (spec-tral features and temperature, T1), and as a resultof the constant change of the background tempera-ture with time, we utilize statistical methods forthe determination of N̂ðλÞ. This approach allowsthe identification of detector pixels containing thechemical simulant, as well as the calculation of theradiance in the absence of the chemical cloud evenwhen the simulant cloud is present in the FOV.The mathematical underpinnings of this analysismethod are described below.The adaptive cosine estimator (ACE)-based ap-

proach to target detection is described in more detailelsewhere [10]. ACE follows from an unstructured-background model. The unstructured-backgroundmodel assumes that, while one can determine anaverage spectrum for a background type, there is in-herent spectral variability within the material typeand that, with the exception of lucky coincidences,one cannot accurately represent a measured spec-trum by a linear combination of the average spectraof each material type (as is commonly used in thesubspace-generalized likelihood ratio test approach[10]). For the field data that we have investigatedto date, the unstructured-background model appearsto provide a better estimate of the observed back-grounds than subspace-generalized likelihood ratiotest approaches. Within this model, the spectra ofbackground pixels are described as random vectorswhose likelihood of occurrence is described by aprobability distribution function. The unstructured-background model can be described by the followingexpression:

x ¼ μþ Sαþ ν ð6Þ

where μ is the mean spectrum of the spectral or spa-tial data cube, S is a reference spectrum (absorptioncoefficients) for the chemical vapor of interest, and νis a random vector that is characterized by a prob-ability distribution function. The parameter Sα, asdefined in Eq. (6), is the differential radiance spec-trum due to the presence of the chemical cloud as ex-pressed in Eq. (3). In the event that ν is normallydistributed or elliptically distributed, Eq. (6) canbe expressed in terms of a noise-whitened variable:

z ¼ Γ̳ −1=2ðx − μÞ ¼ Γ̳ −1=2Sαþ n; ð7Þ

where Γ̳ is the covariance matrix of the non-target-containing pixels and n is a random vector whoseelements, when averaged over the entire data cube,have zero mean and unit standard deviation. Byworking in a noise-whitened space, bands with lowsignal-to-noise ratios are deweighted in the analysis,and bands with high signal-to-noise ratios receiveproportionally higher weights.

Following Eq. (7), the ACE detection metric is

DACEðzÞ ¼zTðΓ̳ −1=2SÞðSTΓ̳ −1SÞ−1ðΓ̳ −1=2SÞTz

zT z: ð8Þ

Values of DACE range from zero to unity, where unityindicates perfect correlation between the test spec-trum and the target spectrum and zero indicatesno correlation. “Target present” is declared whenDACE exceeds a user-specified threshold. One of thepractical challenges in applying ACE is determiningwhich pixels in the scene to use to calculate μ and Γ̳ .Equation (7) may be inverted to calculate target spec-trum amplitudes. Pixels exhibiting anomalouslylarge values of Mahalanobis distance, typicallyvalues greater than that which would lead to inclu-sion of 99% of data from a multivariate normaldistribution, are identified and the mean and covar-iance are recalculated with those points excluded. Inpractice, when the cloud occupies a small fraction ofthe scene, nominally several percent of the pixels orless, this method of estimating the background meanand covariance has the effect of excluding most of thetarget-signature-containing pixels.

The least-squares-optimum estimate of targetsignature amplitude is

α̂ ¼ ðSTΓ̳ −1SÞ−1ðSÞTΓ̳ −1ðx − μÞ: ð9Þ

Based on Eq. (9), the differential radiance spec-trum resulting from the presence of the chemicalin the FOV of the sensor (ΔN ¼ Sα̂) is determinedfor each data-cube acquisition and for each pixelsatisfying the DACE user-specified threshold. Conse-quently, the radiance at the sensor in the absence ofthe chemical cloud is calculated as follows:

N̂ðλÞ ≈ NsensorðλÞ − Sα̂; ð10Þ

where NsensorðλÞ is the measured radiance spectrumand S α̂ is the best fit to the model as defined above.Equation (10) can be used directly in conjunctionwith Eq. (5) to calculate the cloud transmission foreach pixel identified as containing the chemical si-mulant. Finally, following Eq. (2), the chemical simu-lant column density (ρi) of chemical species i iscalculated as

ρ̂i ¼ α̂ih∂L=∂Ti

hNA − ðNsensor − Sα̂Þi ; ð11Þ


where h∂L=∂Ti is the derivative Planck function withrespect to temperature averaged over the wave-lengths in the data cube and hNA − ðNsensor − Sα̂Þiis the average differential radiance between a black-body at the air temperature and the estimatedbackground spectrum.The capability of the detection approach to accu-

rately measure the chemical column density was in-itially validated under controlled conditions in thelaboratory. The laboratory testing involved observingvarying concentrations of a chemical in an absorp-tion cell of known length viewed against a blackbodyof known temperature. The cell was filled with agiven mixture ratio of 1,1,1,2-tetrafluoroethane(R134a) and nitrogen, such that column densitiesof 100–500mg=m2 were achieved. Directly behindthe absorption cell, a large-surface-area blackbodywas heated to achieve a temperature differential of∼3°C with respect to the ambient temperature. Datawas acquired for several R134a column densities,and the imagery was processed according to the prin-ciples described above. Figure 4 illustrates R134aidentification for all pixels inside the absorption cell.Figure 5 shows the comparison between the knowncolumn density and the calculated chemical columndensity based on the application of Eq. (11). Resultsindicate that errors associated with ACE-based col-umn density estimation are less than 10% whenthe uncertainty in the ambient temperature mea-surement is ∼� 0:3°C.The primary error contributions to the chemical

cloud density measurement are defined through asimple error propagation analysis of Eq. (11). The un-certainty in the column density value is evaluated asfollows:

σρ2 ¼�∂ρ∂α

�2σα2 þ

�∂ρ

∂Nsensor

�2σNsensor

2

þ�

∂ρ∂NA

�2�∂NA

∂TA

�2σTA

2; ð12Þ

where σα is the uncertainty in the ACE-based statis-tical estimate of the target spectrum amplitude,σNsensor

is the error associated with the sensor radio-metric measurement (results from the uncertainty

associated with the radiometric calibration of thesensor as well as the sensor noise-equivalent spectralradiance), and σTA

is the uncertainty in the ambienttemperature measurement. Figure 6 illustrates theoverall error contributions from each of these ele-ments under typical measurement conditions. In afield deployment situation, where a single weatherstation can be positioned some distance away fromthe actual chemical cloud, the uncertainty in the am-bient temperature measurement can easily approach�1:0°C. Consequently, it can be observed from Fig. 6that the uncertainty associated with the tempera-ture measurement introduces the largest error(∼17 μFlicks) to the overall sensor radiometricmeasurements.

3. Computed Tomography Algorithm for Use withPassive Standoff Detection of Chemical Clouds

Combinations of an integrating measurement tech-nique and CT have been used in many different fieldsfor the study of diverse phenomena [11]. Severalexamples include measurement of soot volume frac-tions in a flame based on integrated light absorptionmeasurements [12], measurement of plasma emis-sion intensity distributions by use of integratedemission measurements [13], and measurement ofdensity distributions in fluid flows by use of inter-ferometry via integration of the refractive index [14].

Fig. 4. Chemical simulant identification in laboratory absorptioncell.

Fig. 5. ACE-estimated column density versus mass-flow-derivedcolumn density.

Fig. 6. Error contribution to the sensor radiometric measure-ment; 1 μFlux=μFlick ¼ 1 μW=ðcm2 sr μmÞ.


The most difficult problem for optical tomographyas applied to chemical cloud concentration mappingis the lack of sufficient projection data for reconstruc-tion; it is not feasible (it is cost prohibitive) to acquirecolumn density from the cloud by using very manysensors. The ability to provide a good tomographicreconstruction of a chemical cloud is dependent onthe number of sensors used as well as the geometricpositioning of the sensors. The quality of the recon-struction as a function of these parameters was a pri-mary focus in determining the tomographic methodused for the system.We are given a number of optical density projec-

tions ψpðx; zÞ≡ ρðψpðx; zÞÞ, where ψp is the columndensity measurement at each pixel identified ascontaining the simulant in the 2D plane orthogonalto the sensor line of sight, and from which the che-mical cloud concentration function Cðx; y; zÞ is to bereconstructed:

ψpðx; zÞ≡ZL

0

Cðx; y; zÞdy; ð13Þ

where the integration is along the line of sight y.Therefore, given ψp for p ¼ 1;…;P, one needs to findan estimate of Cðx; y; zÞ. The full 3D Cðx; y; zÞ is gen-erated by stacking each of the reconstructed 2D con-centration distributions, Cðx; yÞ. Many algorithmshave been developed for the reconstruction process,and the choice of use is governed by factors suchas computational power and speed, as well as thespacing and projection data available. The choiceof CT algorithm for our application was based onthe need to generate the highest-fidelity reconstruc-tions with limited projection data and without any apriori knowledge of the chemical cloud concentrationdistribution. There are generally two types of CTalgorithm that have been extensively used in thephysical sciences: transform based and series-expansion based.The transform algorithms are based on the Fourier

and Radon transforms. The Fourier algorithms makeuse of the projection (or central-section) theorem[15], which relates the 1D Fourier transform of a pro-jection of an object to the 2D transform of the objectitself. In a limited projection data case, however,there are gaps in the transform information thatmust be filled before the inverse transformationcan provide a reasonable reconstruction of the origi-nal object [11]. The Radon-transform-based recon-struction algorithms are iterative methods similarto the Fourier approaches but with the iteration car-ried out between the object domain and the Radon(projection) domain. Support and range constraintsare applied on the object in the spatial domain,and the measured projections are injected at eachiteration into the projection space [11]. The transfor-mations are carried out by projection and filteredbackprojection. The fundamental problem withtransform-based algorithms is that they implicitlyassume that the number of projections is very large.

Feng [16] proposed an optimization approach to tryto do a reconstruction from only three separate pro-jection views. This approach, however, works only forcontinuous and smooth object density functions.Furthermore, the algorithms require the line inte-grals to be taken along uniformly spaced and parallelprojections. Even though transform-based algo-rithms are computationally very fast, their limita-tions in dealing with reduced projection data fieldsdo not make them good candidates for use in theapplication proposed in this paper.

A better solution to the reconstruction of chemicalclouds interrogated by only a few sensors is accom-plished via the use of expansion-based algorithms.In the series-expansion formalism, Cðx; y; zÞ is mod-eled as a linear combination of object coefficients,each of which corresponds to the value of the chemi-cal cloud concentration at a point on a rectangulargrid. Expansion algorithms are iterative methodsthat divide the volume of interest into voxels, andone tries to assign a concentration value to each voxelin such a way that the inferred path integrals matchthe observed integrals. The mathematical definitionof the algorithm is as follows [11]:

ψp ¼XMNQ

j

Oj

Zsbpðx − xj; y − yj; z − zjÞds; ð14Þ

where Oj is the jth object concentration value corre-sponding to position ðxj; yj; zjÞ in the reconstructionspace and b is a basis function that weights the con-tribution of each voxel. The ðxj; yj; zjÞ positions form arectangular space with M (x direction), N (y direc-tion), and Q (z direction) sides. The ðx; zÞ plane isthe plane of the column density image, and the inte-gral is along y. Equation (14) can be written in simplematrix form, ψ ¼ WO, where ψ is the measurementvector,W is the projection matrix, and O is the objectvector:

�ψp

�¼

�Wij

��Oj

�: ð15Þ

Here Oj is the local value of the object field Cðx; y; zÞat the jth voxel, and Wij is the weighting factor thatrelates the proportion of the jth voxel being interro-gated by the finite width. The projection matrix is de-termined by the number of sensors and the sensorpositioning geometry used in the measurement.The column density inferred from a single sensormeasurement along a viewing projection is thus de-fined as a summation of the concentration values forall voxels that are intersected by that projectionweighted by the fraction of each voxel intersectedby an individual sensor pixel IFOV. While the sen-sors provide fan beam projections through the vo-lume of interest, because the cloud is in the farfield and we are interested in estimating the concen-tration field only over a narrow range of elevationangles near the horizontal, we approximate the 3D


distribution as a stack of noninteracting 2D horizon-tal layers, and the CTalgorithm is applied separatelyto each layer to simplify the calculation. Within each2D horizontal layer, however, each viewing projectionincorporates a fan beam approach. This procedure isillustrated in Fig. 7.In the formalism defined by Eq. (15), one would

like to solve the set of P linear algebraic equations(one equation for each measured line integral) inMNQ unknowns. Equation (15) may suggest thatin order to determine concentration values (Oj) onewould only need to do a straightforward matrix in-version. However, one needs to consider some impor-tant factors: (1) the number of projections must bethe same as the number of cells; (2) for cases wherethere are more unknowns than equations, conven-tional matrix inversion is no longer possible; and(3) if the data suffer from the usual random fluctua-tions and noise, an exact solution will not be possible.Clearly, in the case of limited measurement network(limited number of sensors), the system defined byEq. (15) is severely underdefined. There are severalmethods that can be applied to provide the best solu-tion to such a system.In the algebraic reconstruction technique (ART),

the solution to the matrix equation is establishedthrough an iterative process in which an initial esti-mate of Cðx; yÞ for each cell in a single plane is given,followed by a calculation of the column density, ψp,which is compared with the measured value forthe projection. A correction to the initial value ofCðx; yÞ is then performed, and the process is repeateduntil a given convergence criteria is achieved. TheART technique is a widely used reconstruction meth-od and is generally simple and flexible. Verhoeven[11] presented a study on the effectiveness of thisalgorithm and looked at its reconstruction abilityby investigating the reconstruction of three simu-lated objects from three different geometries. Hisconclusion was that the best reconstruction is pro-duced in the geometry including fewer views, butwhich are spread over a larger angle.There are several other expansion-based algo-

rithms that attempt to solve the matrix equation. Ac-cording to work by Todd and Bhattacharyya [17],reconstructions performed by the maximum likeli-hood expectation maximization (MLEM) technique

are found to be statistically better than ART. MLEMis a simultaneous method. At each iteration, all vox-els are corrected simultaneously after an entire set ofbeam projection data is read. The tomography recon-struction algorithm that we implemented for usewith infrared passive standoff detection of chemicalclouds is a combination of the ART and MLEMtechniques. The formalism follows Eq. (15), andthe correction (update) to Cðx; yÞ in each iterationis determined by maximizing the log-likelihood func-tion of observing a given line integral through thecloud. The mathematical underpinnings of theapproach are described below.

Let us define Cðxj; yj; zjÞ ¼ Oj as the object con-centration value at the jth voxel, as suggested pre-viously. In this case, for each voxel, there is a Poissondistributed random variable Oj, with mean �Oj thatcan be generated independently. (While the pre-sumption that projection measurements follow Pois-son statistics is not rigorously correct for the columndensities estimated here, in practice it appears to bea reasonable assumption, and it has the benefit ofconstraining estimated concentration values to begreater than zero.)

PðOjÞ ¼ e− �Oj

�OjOj

Oj!: ð17Þ

The jth voxel produces a line integral at ψp, whichis an independent Poisson variable with an expecta-tion value defined as (the projection of the estimatedoptical density vector)

~ψp¼

XMNQ

j

wpjOj: ð18Þ

wpj is the probability (projection) matrix identical tothe transfer matrix from voxel j to the set of parallelprojections p [defined in Eq. (15)]. Since Oj are inde-pendent variables, a linear combination of these twovariables follows Poisson statistics. Therefore, thelikelihood of the observed data is

PðψpÞ ¼YPp¼1

e−~ψ

p

~ψp

ψp

ψp!: ð19Þ

In other words, this is the probability under thePoisson model that the given line integrals ψp are ob-served if the true optical density is Oj.

The log-likelihood function under MLEM formal-ism is then defined asFig. 7. Graphical representation of the reconstruction technique.


lnðPðψpÞÞ ¼ −XPp¼1

ð~ψpÞ þ

XPp¼1

ln�~ψ

p

ψp

ψp!

�

¼ −XPp¼1

ð~ψpÞ þ

XPp¼1

ψp lnð~ψpÞ −

XPp¼1

lnðψpÞ

¼ −XPp¼1

XMNQ

j

wpjOj þXPp¼1

ψp lnðXMNQ

j

wpjOjÞ

−XPp¼1

lnðψpÞ: ð20Þ

MLEM tries to maximize the function in Eq. (20). Todo this maximization, one looks at the first derivativeof the function with respect toOj and solves the equa-tion when the derivative is zero. Thus

∂

∂Oj½lnðPðψpÞ� ¼ −

XPp¼1

XMNQ

j¼1

wpj þXPp¼1

ψpPMNQj¼1 Oj

¼ 0:

ð21Þ

Dividing all sides by −P

Pp¼1

PMNQj¼1 wpj, then multi-

plying by Oj and combining with Eq. (18), one gets

Onþ1j ¼

XPp¼1

ψpOjwpjPMNQj¼1 wpjOj

¼ Onj

XPp¼1

ψpwpjPMNQj¼1 wpjOj

¼ Onj

PPp¼1 wpj

�ψp=~ψp

�Pjwpj

: ð22Þ

Equation (22) defines the basis for the tomographicreconstruction. ~ψp is the projection of the estimatedconcentration vector O at a given iteration n. Let

Tn ¼P

Pp¼1 wpj

�ψp=~ψp

�Pjwpj

;

then Onþ1j ¼ On

j Tnj , where T is the multiplicative

coefficient that updates the value of the jth voxelat the nþ 1 iteration. The iterations are stoppedwhen the following convergence criteria is satisfied:jVnþ1 − Vnj ≤ Vn=100, where Vn is the object varianceat the nth iteration. At each iteration, all estimatedconcentrations are updated simultaneously. We initi-alize the concentration values by assuming that theyare the same at each voxel. We have also tried usingdifferent initial guesses with similar convergence re-sults. The algorithm typically converges in 10–20iterations.To better understand the capabilities of the tomo-

graphy algorithm in reconstructing chemical cloudconcentration distributions utilizing a limited num-ber of views, we considered sample objects of increas-

ing spatial complexity as viewed by an increasingnumber of sensors and compared the reconstructedfunctions with the original analytical objects. We de-fine the metric for the goodness of reconstruction asthe nearness [17] (the lower the nearness values, thebetter the reconstruction):

0 < nearness ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPxy

j ðO�j �OjÞ2Pxy

j ðO�j �O�

avgÞ2

vuut ≤ 1; ð23Þ

withO�j the jth voxel value of the original function,Oj

the jth voxel value of the reconstructed function, andO�

avg the original function’s average value.The original analytical functions to be recon-

structed are shown in Fig. 8. The first, function A,is a simple 2D cosine function (Fig. 8A). FunctionsB (Fig. 8B) and C (Fig. 8C) have the 2D cosine func-tion as their basis but offer increased complexitywith the addition of multiple peaks. Function D(Fig. 8D) is a combination of multiple 2D Gaussians,where the symmetry axis is not normal to either ofthe primary axes of the grid.

We first evaluated the algorithm for two orthogo-nal sensor views (0° and 90°) with 128 projections perview for a total of 256 projections through the object.Reconstruction of function A yields a nearness valueof 0.08. The overall shape and maximum values arewell reproduced with errors less than 5%, even in thelimited case of two sensor views. The reconstructionresult is shown in Fig. 9A along with the reconstruc-tion error distribution. Function B is reconstructedwith a nearness value of 0.17 and is shown in Fig. 9B.The overall shape and maximum values are still wellreproduced. There is, however, a clear decrease infidelity at higher spatial frequencies, resulting inreconstruction errors as large as ∼10%.

The reconstruction of function C is shown inFig. 9C. As a result of the increased spatial complex-ity of function C, two sensor views cannot providesufficient projection data to permit accurate estima-tion of the third strongest peak of the function. It isapparent that some of the intensity is distributedalong the entire estimation grid. The estimated dis-tribution has a nearness value of 0.38, and estimatedconcentrations are in error by as much as 40%. Theneed for additional projection data becomes evenmore evident when the CT algorithm is used to esti-mate function D. In the case of only two sensors,when cloud’s axis of symmetry is not parallel toone of the viewing axes, nonzero column density mea-surements can be interpreted only as increaseddispersion. This effect can be observed in the recon-struction of function D, as shown in Fig. 9D; theestimated distribution is characterized by an in-creased width along one of the axes. The nearnessvalue is 0.70 and is indicative of a low-fidelity estima-tion; estimation errors are as high as 50%. These er-rors point out the need for an additional instrumentto reduce the ambiguity in the two-sensor data set.


For comparison with the two-sensor simulation weadded a third sensor whose line of sight was orientedat 45° with respect to the first two sensors and usedthe CT algorithm to estimate function D again. Theestimated function is illustrated in Fig. 10. The ad-dition of the third sensor decreases (improves) thenearness value from 0.70 to 0.27. The errors asso-ciated with the reconstruction were reduced from

∼50% to <20%, and the directionality of functionD with respect to the two orthogonal primary gridaxes is now accurately estimated. As might be ex-pected, the addition of a fourth sensor (at 135°) re-duces estimation errors to <10% and improves thenearness value to 0.10. The reconstruction of func-tion D with four sensors is shown in Fig. 11.

In summary, our simulations lead us to concludethat the tomography algorithm cannot accurately re-produce spatially complex clouds when only twoorthogonal views are used for the cloud reconstruc-tion. However, for clouds approximately describedby smooth varying functions with propagation alongone of the viewing center lines, estimated syntheticcloud concentrations were accurate to within 10% orless, even when only two projection views are used.The addition of a third view significantly increasesthe fidelity of the reconstruction for spatially com-plex clouds with changing direction of propagation,resulting in errors of less than 20%. From the per-spective of a perfect synthetic projection data field,simulations indicate that four sensors may be suffi-cient to provide full 3D reconstructions of chemicalcloud concentrations that are accurate to within10%, even for very complex distributions. It is impor-tant to note, however, that in real field deploymentscenarios the ability of the sensors to achieve ahighly accurate determination of the cloud columndensity is dependent on the level of air temperatureto background thermal contrast encountered by thesensors from each viewing location. As a result, it isvery likely that some sensors may not provide en-ough column density (projection) data needed to gen-erate accurate 3D concentration distributions.

A four-sensor constellation may be degraded to athree- or even a two-sensor constellation dependingon the quality of the column density measurementassociated with each sensor. As a consequence, froma real world application perspective, it is importantto provide a sufficient number of sensors to obtainquality column density data from at least 3–4 view-ing projection angles that are needed for accuratereconstructions.

4. Dugway Proving Ground Field Data andTomographic Results

The data acquired by the sensor constellation duringthe field trials at DPG in 2006 were based on obser-ving explosive disseminations of glacial acetic acid(AA), triethyl phosphate (TEP), and R134a. All threechemicals display unique spectral signatures in the8–11 μm spectral region and are amenable to stand-off detection by passive infrared sensors such asAIRIS. The majority of the releases involved dissemi-nation of between 15 and 120kg of material; how-ever, three disseminations exceeded 220kg. Wepresent analysis of seven dissemination experimentshere.

Three sensors were available for field measure-ments, and they were deployed in the 0°, 45°, 90° con-figuration described in the previous section. While in

Fig. 8. Test Functions for validating the reconstruction algo-rithm. A, 2D cosine function. B, 2D cosine function as basis withone additional peak. C, 2D cosine function as basis with two addi-tional peaks. D, combination of multiple 2D Gaussians with ran-dom spatial distribution providing a propagation axis that is notnormal to either of the primary axes of the grid.


Fig. 9. Reconstruction results using 2 views (0°, 90°) and 128 projections per view: A, function A; B, function B; C, function C;D, function D.


principle deployment at 0°, 60°, and 120° could per-mit more accurate estimation of the chemical concen-tration distribution, the 0°, 45°, 90° configurationhad the logistical advantage that if one of the sensorsfailed then two sensors could be immediately de-ployed at the 0° and 90° degree locations withouthaving to resurvey the deployment area, as wouldbe necessary if moving a sensor from the 60° or120° to 90° deployment position. The sensor constel-lation was arranged such that the FOVof each sensorwas centered in azimuth on the location of the explo-sive releases. Each AIRIS-WAD sensor unit waslocated 2:8km from the grid center, and the geometrydefined a 0°, 45°, 90° configuration as developed andvalidated by using the simulation study described inthe previous section. Each pixel in the image mappedto a plane∼6:0m× 6:0m at grid center. The absoluteposition of each sensor was established to centi-meter-level accuracy by using differential GPS mea-surements. Extreme care was also taken to aligneach sensor’s FOV with fiduciary markers on the testrange to ensure that the sensor views were coplanarand that the projections through the reconstructionvolume were known to high accuracy. Projection an-gles and coplanarity are believed to be accurate to

better than 1mrad, i.e., significantly less than thesingle-pixel IFOV, 2:2mrad.

Figure 12 shows an example of data products gen-erated by using data acquired simultaneously by thethree sensors. The cloud detected in Fig. 12 (top) ori-ginated from a 120kg burst release of AA, and theimagery was acquired∼1 min after the burst. AA de-tections correspond to the white pixels near the cen-ter of each image. The detection in Fig. 12 (bottom)corresponds to a 90kg TEP dissemination. The ACE,as described in Section 2, identifies and flags pixelsthat meet a given correlation criteria between thedifferential radiance spectrum and the referencespectrum of the species in the cloud. The horizontallines in Fig. 12 determine the vertical overlap bound-aries within which the tomography algorithm can beapplied to generate the concentration distribution foreach altitude bin (row of pixels) within the detectiongrid. The detection grid is defined as a ∼1:2km ×1:2km truth box in which all three sensors have over-lapping FOVs. The full 3D cloud reconstructions areobtained by stacking the concentration distributionsfrom each altitude bin. Figure 13 illustrates thenumber of detected pixels from each sensor as a func-tion of time after the initial release for both the AAand TEP disseminations shown in Fig. 12. The data

Fig. 10. Reconstruction of function D with three sensor views (0°, 45°, 90°).

Fig. 11. Reconstruction of function D with four sensor views (0°, 45°, 90°, 135°).


shows that the sensor constellation detected thechemical simulants within ∼30 s of the release. Inthe case of the AA release, the cloud moved out ofthe sensors’ fields-of-view∼2:5 min after the dissem-ination and reentered the FOV of the sensor at theNE position ∼80 s later. Typical sensor constellationdetection times were approximately 5–6 min before

the clouds cleared the detection grid. However, lowwind conditions allowed some chemical releases,such as the TEP case in Fig. 12 (bottom) to be de-tected for as long as 14 min. In Fig. 12, the AA cloudwas observed as high as 100m above the ground, butthe TEP cloud climbed as high as ∼300m. [As notedin Section 2, concentration values estimated at eleva-tions hundreds of meters above ground level arelikely underestimated. Calculations suggest thatΔTeff (effective thermal contrast) may be overesti-mated by as much as 10%–20% at the highest cloudelevations in Fig. 12 (bottom) if one assumes that thecloud temperature is equal to the air temperature atground level; estimated concentrations would be un-derestimated by a corresponding amount.] Most ofthe detected releases stayed relatively low to theground because of the formation of low atmosphericinversion layers that are prevalent at DPG duringthe night. The background scenes observed by thesensors during the DPG releases typically providedair temperature to background radiance thermalcontrast that was >2K. Even in cases when1K < ΔT < 2K, the sensors demonstrated the cap-ability to detect the chemical simulant clouds.

Based on detection maps obtained from each of thesensors, the chemical cloud column densities werecalculated for each pixel detected by using the meth-odology previously described. The column densitieswere reported in units of milligrams per square me-ter. Column density data was then used as input forthe tomography algorithm to generate concentrationvalues in units of milligrams per cubic meter asso-ciated with each voxel in the 3D grid. Furthermore,

Fig. 12. Simultaneous detection of (top) AA and (bottom) TEP from all three AIRIS-WAD sensors.

Fig. 13. Number of detected pixels for each of the sensors as afunction of time after initial burst: top, 120kgAA release;bottom, 90kg TEP release.


the uncertainties associated with each columndensity measurement were also determined andpropagated through the tomography algorithm togenerate the magnitude of the concentration error.As a consequence of the fact that the tomography al-gorithm is iterative and computationally intensive,and since the analysis described in this paper wasperformed on a slow IDL platform, we binned thesensor imagery from 256 × 256 down to 128 × 128to reduce the computation time. As a result, all ofthe chemical cloud 3D reconstruction had a nominalvoxel volume spatial resolution of 12m × 12m×12m. Given the truth box resolution, and taking ad-vantage of observed low wind speeds (<2m=s) andslow moving clouds, we coaveraged data cubes overa transit time of ∼20 s prior to calculation of columndensity maps. This approach improved overall detec-tion statistics and increased sensor tomography over-lap. We have recently implemented the tomographyalgorithm on a Math Kernel Library C-based plat-form utilizing a sparse matrix format, which is cur-rently capable of processing a single 256 × 256 slicein ∼0:3 s, which represents ∼103 times improvementin computational speed. This recent accomplishmentallows the generation of tomographic results in near-real time. More recent deployment of the real-timesystem has demonstrated the ability to temporallymatch data cubes within a 5 s window and generate3D concentration distributions at a rate of 0:1Hz.The processing period includes time for all three sen-sors to acquire data cubes, reduction of data cubes toα̂ values, calculation of ρ̂ estimates at each sensor,wireless transmission of ρ̂ values to a central proces-sing computer, and the CT calculation at the centralprocessing computer.For demonstration purposes, we focus only on the

AA release shown in Fig. 12 (top) and then provide asummary of the complete analysis. An example of theAA concentration distribution within the first 12mabove the ground level is shown in Fig. 14. Figure 14is a 5km × 4km representation of the area indicatingthe position of each of the sensors along with the1:2km square detection grid in which all three

sensors have overlapping FOVs. The calculated AAconcentration distribution is overlaid on top of thegrid display. The maximum concentration detectedis ∼175mg=m3. Figure 15 shows the concentrationdistribution within the next 12m layer abovethe ground. The maximum concentration is∼90mg=m3, indicating that, in the case of the AA re-lease, most of the chemical cloud stayed relativelylow to the ground. Figure 16 shows a magnified viewof the AA concentration distributions at the two ele-vation levels above the ground.

To validate the results associated with the chemi-cal cloud concentration distributions, we conducted amass conservation analysis for each individual re-lease. The only known piece of information regardingthe dissemination of the simulants is the amount ofmaterial released. Unfortunately, the amount ofmaterial present in the gas phase was not knownprecisely. While R134a is a gas at ambient tempera-ture and 1 atm pressure, both AA and TEP haverelatively low vapor pressures at ambient tempera-ture, ∼16Torr and ∼70mTorr, respectively, and itwas not possible to measure the partitioning of ma-terial between the gas and the liquid phases follow-ing dissemination. The amount of liquid used in thedissemination is an upper bound on the amount ofmaterial that could be present in the gas phase.The tomographic analysis of chemical releases pro-duces concentration values (milligram per cubic me-ter) for each voxel in the 3D detection grid. Based onthe spatial resolution of the sensor (dictated by the32° × 32° FOV and the 2:8km standoff distance),the volume of each voxel was calculated. Informationon the voxel concentration in conjunction with the as-sociated volume provides knowledge of the mass ofthe simulant detected in each voxel. The total massin the 3D volume was then obtained by summingover all voxels detected as containing the simulant.This measurement was then compared with theknown release mass. Figure 17 illustrates the totalmass measured based on the tomographic analysisof the release shown in Figure 14 (left) as a functionof time after the burst. No data is shown after

Fig. 14. AA concentration distribution at 0–12m elevation above ground: contour map (left) and surface plot (right).


18:02:30 because the cloud left the volume sampledby all three sensors. The errors associated with eachmass measurement were calculated by propagatingthe column density errors through the tomographyalgorithm and are also indicated in Fig. 17. The max-imum amount of AA detected is ∼107� 30kg. Whencompared with the actual amount disseminated dur-ing this release (120kg), this value suggests that thesensor constellation in conjunction with the tomo-graphic methodology is capable of accounting for∼90%� 25% of the total mass released on the testgrid. The lower mass estimates at early times afterthe burst are the result of the inability to accuratelymeasure the full column density as a result of the op-tical thickness of the clouds. The simulant columndensities in these clouds cannot be determined byusing our established radiative transfer model. Withtime, the chemical cloud disperses and reachesthe optically thin limit. Under these conditions, an

accurate determination of the chemical column den-sity is possible. Eventually, the cloud disperses to thepoint where column densities drop below the detec-tion limit corresponding to the detection approachdescribed in Section 2.

Similar analyses were conducted for several of theother releases observed during the 2006 DPG trials.A summary of the mass estimates (as percentage ofthe total known mass released) based on the tomo-graphic reconstruction of the chemical clouds foreach of the runs is shown in Fig. 18. It can be ob-served that for cases in which the amount of chemicalsimulant released was ≤120kg, the tomographic con-stellation is capable, on average, of accounting for∼86% of the total mass disseminated. There werethree runs that were characterized by releases great-er than 240kg of material, which resulted in averagemass estimates only of the order of ∼20%. Furtherexamination of these releases indicate the formation

Fig. 15. AA concentration distribution at 12–24m elevation above ground: contour map (left) and surface plot (right).

Fig. 16. AA concentration distributions at 0–12m (left) and 12–24m (right) above ground.


of optically thick clouds for a significant fraction ofthe time in which the chemical clouds are withinthe detection truth box. Preliminary reanalysis ofthe data indicates that correcting for optical thick-ness effects increases the estimated mass by a factorof 2–3. Analysis conducted so far suggests that theaverage measurement error corresponding to themass estimate calculations is of the order of 30%or less.The 2006 DPG results demonstrate the ability of

the system to account for a large fraction of the che-mical simulant mass released on test ranges throughCT reconstruction of cloud concentration distribu-tions. More recently, however (Summer 2008), thereal-time tomographic sensor constellation has beendeployed in conjunction with 25 ion-mobility-basedpoint sensors. We are in the process of validatingthe concentration results obtained from the tomo-graphic reconstruction of standoff passive AIRISdata against the raw concentration measurementscollected with the point sensors. This approach willprovide a better understanding for the ability of theproposed CTmethod to accurately retrieve cloud con-centrations observed from true standoff ranges.

5. Conclusions

We have defined the methodology and demonstratedthe ability to use passive infrared multispectral ima-ging to track and quantify chemical clouds via com-puted tomography (CT). The CT algorithm has beendemonstrated to be capable of 3D reconstruction ofchemical clouds using 2D column density data withas few as three sensors. Errors associated with thereconstruction methods are less than 20% even forcomplex chemical cloud concentration distributions.The statistical method for the calculation of chemicalcloud column densities from sensor radiometric datahas been experimentally demonstrated to producechemical cloud column density values that are accu-rate to within ∼10% or less. The primary source oferror in the field measurements was in the determi-nation of the local air temperature. The total mea-surement error for field data is estimated to be∼30%. Unfortunately, lack of ground truth data pre-cludes assessment of the absolute accuracy of concen-tration distributions estimated from field testmeasurements; however, the mass closure calcula-tions indicate that the amount of material estimatedusing the CTalgorithm is in good agreement with theknown amount of material released. The release oflarge amounts of simulant into small volumes duringconditions of low inversion layers produced opticallythick clouds. The simulant column densities in theseclouds could not be determined by using our estab-lished radiative transfer model. This effect led toan underestimation of the mass detected by thesystem.

This work was supported by the U.S. Army Edge-wood Chemical Biological Center under contractW911SR-06-C-0022. The authors acknowledgeJames Jensen, Waleed Maswadeh, and Pete Snyderof the U.S. Army Edgewood Chemical Biological Cen-ter, Shing Chang, Dave Rossi, and Teoman Ustun ofPhysical Sciences Inc., as well as Scott Rhodes ofVtech Engineering Corporation for their efforts indeveloping and operating the AIRIS-WAD units usedin this work.

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Imaging sensor constellation for tomographic chemical cloud mapping