Terahertz imaging system performance model for concealed-weapon identification

Terahertz imaging system performance modelfor concealed-weapon identification

Steven R. Murrill,1,* Eddie L. Jacobs,2 Steven K. Moyer,3 Carl E. Halford,2

Steven T. Griffin,2 Frank C. De Lucia,4 Douglas T. Petkie,5

and Charmaine C. Franck6

1Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783, USA2Department of Electrical and Computer Engineering, University of Memphis,

206 Engineering Science Building, Memphis, Tennessee 38152, USA3U.S. Army Night Vision and Electronic Sensors Directorate, 10221 Burbeck Road, Fort Belvoir, Virginia 22060, USA

4Department of Physics, Ohio State University, 191 W. Woodruf Avenue, Columbus, Ohio 43210 USA5Department of Physics, Wright State University, 248 Fawcett Hall, Dayton, Ohio 45435, USA

6CACI Technologies Incorporated, 10221 Burbeck Road, Fort Belvoir, Virginia 22060, USA

*Corresponding author: [email protected]

Received 2 October 2007; accepted 20 November 2007;posted 1 February 2008 (Doc. ID 88100); published 18 March 2008

The U.S. Army Night Vision and Electronic Sensors Directorate (NVESD) and the U.S. Army ResearchLaboratory have developed a terahertz (THz) -band imaging system performance model for detection andidentification of concealed weaponry. The MATLAB-based model accounts for the effects of all criticalsensor and display components and for the effects of atmospheric attenuation, concealment material at-tenuation, and active illumination. The model is based on recent U.S. Army NVESD sensor performancemodeling technology that couples system design parameters to observer–sensor field performance byusing the acquire methodology for weapon identification performance predictions. This THz modelhas been developed in support of the Defense Advanced Research Project Agencies’ Terahertz ImagingFocal-Plane Technology (TIFT) program and is currently being used to guide the design and developmentof a 0:650THz active–passive imaging system. This paper will describe the THz model in detail, provideand discuss initial modeling results for a prototype THz imaging system, and outline plans to calibrateand validate the model through human perception testing. © 2008 Optical Society of America

OCIS codes: 110.6795, 220.4830, 110.4100, 110.3000.

1. Introduction

Events over the past decade or so, most notably themilitant attacks on civilians in London (July 2005),Madrid (March2004), andNewYorkandWashington,D.C. (September 2001), have led to the increasingneed formore effective personnel andaccessory secur-ity screening. Although techniques exist and are nowbeing utilized for the detection of a variety of threats

such as handheld weapons or concealed explosives,most rely on x-ray imaging–inspection, portal andhandheld metal detection technology, and manualsearch with random chemical-trace-detection sam-pling [1]. These techniques are currently deficientin two key respects: they provide essentially nostand-off detection capability, and the associatedtechnology is expensive and can typically be deployedonly in fixed, controlled environments. Other defi-ciencies include a limited ability to detect weaponsthat contain small amounts of metal, ceramic weap-ons, or explosivematerials, especiallywhen concealed

0003-6935/08/091286-12$15.00/0© 2008 Optical Society of America

1286 APPLIED OPTICS / Vol. 47, No. 9 / 20 March 2008

under a suspect’s clothing. While emerging technolo-gies such as backscatter x-ray and millimeter-waveimagingmayprovide additional capabilities, theywillstill have notable limitations. The backscatter x-raytechnology produces ionizing radiation which raiseshealth concerns for personnel use; the millimeter-wave technology, while potentially portable, has lim-ited spatial resolution and thus limited stand-offcapability.The potential of imaging systems designed to oper-

ate in the terahertz (THz) electromagnetic spectrum(typically defined as ranging from 0.3 to 10THz [2]) istwofold. The higher frequencies of THz radiation rela-tive to millimeter-wave radiation yield higher spatialresolutions and thus greater imaging stand-off poten-tial but are able to penetrate many nonconducting,nonpolar materials such as clothing, paper, card-board, and plastic packaging (between approximately0.3and1:0THz [3,4])withonlymoderateattenuation.Above approximately 1:0THz, the spectral signaturesof many explosive solid materials are available forcapture [5] by using, e.g., THz time-domain spectro-scopy (THz-TDS) for imaging [4]. Recent advancesin THz generation and detection technologies [6] en-able the design and development of more compactand potentially portable THz imaging systems. Sub-stantial stand-off threat detection–discriminationwill beacrucialaspect ofall futureTHz-basedsecurityimaging systems intended to effectively counter to-day’s asymmetric terrorist threats. Accurate model-ing of such systems will play a significant role inthe development of system technology, system archi-tectures, and security procedures.The objective of this research has been to develop

an imaging system performance model for the THzband applied to concealed-weapon identification(ID). The performance model has been designed toallow the calculation of observer–imager perfor-mance for conceptual designs using either active orpassive illumination, scanning or focal-plane-array(FPA) detector technologies, and arbitrary, but defin-able, display scenarios. The model will also allow forimager design and imager evaluation. The model hasbeen designed to incorporate the effects of target andbackground source phenomenology including atmo-spheric and concealment-material (e.g., clothing)radiation transmission.Sensor characterization is seen in threeways: theo-

reticalmodels, fieldperformance,and laboratorymea-surements (Fig. 1). Theoretical models are developedthat describe sensor sensitivity, resolution, and hu-man performance for the purpose of evaluating newconceptual sensors. Acquisition models, and othermodels, are developed to relate the theoreticalmodelsto field performance. This linkallows theoreticalmod-els to be converted to field performance quantities(e.g., probabilities of detection, recognition, and ID).Field performance is measured in the field so thatthetheoreticalmodelscanberefinedandbecomemoreaccurate with advanced sensor developments. Sincefieldperformanceactivitiesare so expensive,methods

for the directmeasurement of sensor performance aredeveloped for the laboratory. Field performance test-ing of every imaging sensor built, including buy-off,acceptance, and life-cycle testing is prohibitive. La-boratorymeasurements of sensorperformancearede-velopedsuchthat,giventhesemeasurements,thefieldperformance of a system can be predicted.

Every successful military sensor program has allthree of these sensor elements: a theoretical modelfor sensor performance, a conversion for field perfor-mance, and laboratory measurements. This researchprovides the sensor theoretical model. Conversionfor field performance and the link to laboratoryperformance measurements will be addressed asfuture work.

This paper will first provide an overview of the ar-chitecture used in the development of the THz perfor-mance model, followed by a detailed description of itscomponents. Preliminary modeling results for a pro-totype THz imaging system will be provided and dis-cussed. Finally, plans to calibrate and validate themodel through human perception testing will beoutlined.

2. THz Performance Model Architecture

The overall goal of this effort was to develop aMATLAB-based [7] imaging system performancemodel for the THz band applied to concealed-weaponID. Themodel has been designed to allow the calcula-tion of observer–imager performance using either ac-tive or passive target illumination or self-emission,scanning or FPA detector technologies, and arbitrary,but definable, display scenarios. The model has beendesigned to account for the effects of target and back-ground source phenomenology including atmosphericand concealment-material (e.g., clothing) radiationtransmission.

The overall approach was to adapt the latest U.S.ArmyNightVisionandElectronicSensorsDirectorate(NVESD) sensor modeling technology to the THz re-gime. The approach essentially requires coupling ofaTHzradiometrictransfermodelwiththelatestArmytask performance model for humans viewing dis-

Fig. 1. Imaging system relationships.

20 March 2008 / Vol. 47, No. 9 / APPLIED OPTICS 1287

played images, along with THz-specific detector tech-nology parameters. The THzmodel must then be cali-brated and verified through human perceptionexperiments on simulated and/or real THz imagery.While the U.S. Army NVESD currently releases

several different models for different sensors, at theircore, they are essentially all the same. Conceptually,the performance models accept inputs that describesensor characteristics, target–background phenom-enology, radiometric propagation properties, and de-tection, recognition, and/or ID task difficulty factor(s)along with display characteristics, to generate prob-ability of performance as a function of range curve(s)(see Fig. 2). Mathematically, the models consist ofthree primary equations: the system contrast thresh-old function (CTF), the target task performance me-tric, and the target transform probability function(TTPF). These equations follow from two fundamen-tal assumptions: that target acquisition performanceis related to the image quality through the sensor,and that image quality is related to threshold visionof the observer through the sensor.Threshold vision of the observer in the absence of a

sensor can be defined in terms of the CTF of the eye,which defines the response of an observer to a sinewave grating. In this model, we utilize an empiricalequation for CTF developed by Barten [8] that ac-counts for the variability associated with differentobservers, light levels, and display sizes. This equa-tion is a curve fit to an ensemble of CTF measure-

ments and is given by

CTFeyeðf Þ ¼�af e−bf

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ cebf

p �−1; ð1Þ

where f is the spatial frequency in cycles per degree,

a ¼540

�1þ 0:7

L

�−0:2

1þ 12

w

�1þf

3

�2

; ð2Þ

w is the size of the display in degrees, L is the displayluminance in candelas per square meter,

b ¼ 0:3

�1þ 100

L

�0:15

; ð3Þ

and c is 0.06.In an imaging system, the CTF of the eye is de-

graded by the blur and noise of the sensor. Vollmer-hausen [9] has shown that this degradation of theCTF is predicted by the following equation;

CTFsysðf Þ ¼CTFeyeðf ÞHsysðf Þ

�1þ α2 σ

2ðf ÞL2

�1=2

; ð4Þ

where CTFsys is the degraded CTF of the observerthrough the sensor system, Hsys is the modulation

Fig. 2. (Color online) Performance model architecture. Note that the task difficulty factor(s) are determined independently through hu-man perception testing.


transfer function (MTF) of the system, σ is the stan-dard deviation of the perceived noise on the display, Lis the average display luminance, and α is an empiri-cally determined calibration constant. The perceivednoise on the display is given by

σ2ðf Þ ¼Z

∞

−∞

SnðξÞjHPostðξÞHPerðξ; f Þj2dξ; ð5Þ

where Sn is the power spectral density of the noisesource, HPost is any filter in the sensor that occursafter the point where noise is generated, and HPeris a filter describing the perception process.HPost gen-erally includes the MTFs associated with the displayand the eye. General expressions for these filters canbe found in the NVESD NVTherm manual [10]. Theperceptual filter is a bandpass filter designed to mi-mic the spatial frequency channels of the human vi-sual system. In psychophysical tests, it has beenshown that it is only the noise within an octave ofthe center frequency that interferes with the percep-tion of a sine wave. In the model(s), an expressionintroduced by Barten [11]is used and is given by

HPerðξ; f Þ ¼ exp�−2:2 log2

�ξf

��; ð6Þ

where ξ is spatial frequency and f is the center fre-quency of the filter.Again, assuming that threshold vision is related to

image quality, performance should be related to somemetric applied to the system CTF. The standard ap-proach since 1958 has been to use limiting frequency(see Fig. 3) as a measure of image quality. This is thebasis of the Johnson criteria [12]. Recently, Vollmer-hausen [13] has introduced the target task perfor-mance (TTP) metric. This metric has significantlyimproved the accuracy of predictions especially withregard to effects present in modern sensors. The TTPmetric is defined by the root integral of excess con-trast weighted by the inverse of the CTF, or

TTP ¼Z

f limit

f lo

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCt

CTFsysðf Þ

sdf ; ð7Þ

where Ct is the target-to-background contrast ratioand the limits of integration are determined by

CTFsysðf Þjf lo;f limit¼ Ct ; f limit > f lo: ð8Þ

Note that if the CTF is taken as equal to the targetcontrast, then the TTP reduces to the Johnson limit-ing frequency (since f lo is approximately zero). In amanner analogous to the Johnson limiting frequencyapproach, range performance is dictated by theeffective number of cycles on the target, which iscalculated by

VðRÞ ¼ffiffiffiffiffiAt

pR

TTP; ð9Þ

where At is the area of the target and R is the rangeto the target.

The TTPF gives the probability of an observer per-forminga task (detection, recognition, or ID) as a func-tion of both the effective cycles on target and apredetermined set of criteria for that task. Sincethe effective number of cycles on the target inEq. (9) is a function of range, theTTPFgives the rangeperformance for a given task. The TTPF is given by

Ptask ¼

�VðRÞ

V50ðtaskÞ

�E

�1þ

�VðRÞ

V50ðtaskÞ

�E ; ð10Þ

where V50 is the number of effective cycles needed toperform a given task (with a 50% probability of suc-cess). E is an exponent determined by fittingEq. (10) to perception experiments. For our prelimin-arymodeling,weuseda value ofE thathadpreviouslybeen determined from perception experiments withinfrared imagery, namely,

E ¼ 1:51þ 0:24

�VðRÞV50

�: ð11Þ

Note that in the older literature onNVESDmodels,Nand N50 replace V and V50 in Eqs. (10) and (11). Theswitch to the V and V50 notation (value and value50)was done to prevent confusion with the older Johnsoncycle criteria.

The methodology described here, while developedfor thermal and electro-optical sensors, is applicableto any sensor that provides a display to an observer.The only things that change are the way target con-trast is mapped into display luminance (radiometry)and the task difficulty.

3. Terahertz Model Components

As previously stated, the NVESD imaging systemperformance models and the subject THz imagingsystem performance model consist mathematicallyof three primary equations: the system contrastthreshold function (CTFsys), the target task perfor-mance metric (TTP), and the target transform prob-ability function (TTPF). The following sections

Fig. 3. Relationship between systemCTF, limiting frequency, andexcess contrast.


provide detailed descriptions of all of the componentsthat make up the three primary model equations.

A. Image Blur

Image blur, described in Eq. (4) asHsysðf Þ, consists ofspatial blurring from the system optics, the detectorsize and shape, display system parameters such asthe pixel size and shape, the pixel pitch, viewing dis-tance, electronic zoom, average display luminance,and the human eye. Each of these spatial blurringelements are described in the spatial frequency do-main as MTFs and are multiplied together to gener-ate the system MTF, Hsysðf Þ.For thismodel, the opticsMTF is assumed to be the

diffraction-limited MTF generated from a circular fo-cusing element and is described (in one dimension) by

Hdiff ðξÞ ¼2π

�cos−1

� ξξcut

�−

� ξξcut

��1 −

� ξξcut

�2�1=2

; ×

ξ ≤ ξcut; ð12Þ

where

ξcut ¼ Dap=ðλ × 1000Þ: ð13Þ

Dap is the diameter of the circular focusing element(aperture) in meters, λ is the wavelength of the ima-ging radiation inmeters, and ξ is in units of cycles permilliradian [14].The detector MTF depends on the detector size and

shape. For a square detector, the MTF is described(again, in one dimension) by

HdetspðξÞ ¼ sincðDASxξÞ; ð14Þ

where

sincðπxÞ ¼ sinðπxÞ=πx ; ð15Þ

and DASx is the detector angular subtense in milli-radians [15].For a circular detector, the MTF is described by

HdetspðρÞ ¼2J1ð2πρrÞ

2πρr ; ð16Þ

where J1 is a Bessel function of the first kind (order1) and r is the detector radial angular subtense inmilliradians [16].For single-detector, scanned imaging systems, an

antenna horn will typically be used to couple theTHz radiation into the detector element. For thiscase, the effective aperture size of either a squareor circular antenna horn is approximated by

Aeff ¼ Gmaxλ24π ; ð17Þ

where Gmax is the gain of the antenna [17]. Aeff is

used as the detector size in computing the detec-tor MTF.

The display MTF depends on the pixel size andshape. For a square pixel in a flat-panel display,the MTF is described (in one dimension) by

HdispðξÞ ¼ sincðXangleξÞ; ð18Þ

where Xangle is the pixel size dimension converted toan equivalent angular space in the sensor’s field ofview [15].

For a pixel in a CRT display, a Gaussian intensitydistribution is assumed; the MTF is described by

HdispðξÞ ¼ GausðσangleξÞ; ð19Þ

where σangle is the pixel spot size dimension con-verted to an equivalent angular space in the sensor’sfield-of-view [15].

Electronic zoom is accomplished by using bilinearinterpolation which, adds an interpolation MTF com-ponent. The model can simulate 2×, 4×, or 8× zoom,which is often used to increase system magnificationand to reduce any out-of-band spurious response ef-fects from aliased, undersampled configurations [15].

The human eye MTF used in the subject model isdescribed in [15], and is dependent on the averagedisplay luminance and the system magnification.

B. Image Noise

In the calculation of the perceived noise on the dis-play [Eq. (5)], the term for the power-spectral-densityof the noise source, Sn, is a spatiotemporal quantitywith nominal units of fL2 smrad. For this model, Snis the power spectral density of the detector noiseand is given by

Sn ¼ ðNEPdetÞ2Pspbw

; ð20Þ

where NEPdet is the noise equivalent power (NEP)of the detector in W=Hz1=2, and Pspbw is the one-dimensional pixel spatial bandwidth in cycles/mrad.Sn now has units of W2 smrad. To properly map de-tector noise to display noise, the average displayluminance (L) in Eq. (4) must be equated to the in-cident average THz-band power received by the de-tector and is given by

L ¼ PdetIFOVηant; ð21Þ

where PdetIFOV is the average power received by thedetector instantaneous field of view (IFOV), and ηantis the coupling efficiency of the antenna structure.For this model, Hpost in Eq. (5) comprises the displayMTF, the human eye MTF, and the interpola-tion MTF.

The calibration factor, α2, in Eq. (4) subsumes atemporal eye integration component that is assumedto be essentially constant over a broad range of eyeillumination levels. If detector noise is temporally


varying at a fairly rapid rate through the sequentialdisplay of changing image frames, then the eye–brain system temporally filters detector noise inthe same way as eye noise. If, however, a snapshot(single frame image) is captured and then displayedrepeatedly at a fairly rapid rate, eye integration is nolonger as effective in reducing noise, and the noiseterm in Eq. (4) must be scaled by a factor given by

tscale ¼teyetact

; ð22Þ

where teye is the integration time of the eye and tact isthe actual detector frame integration time [18].The dependence of the eye on display luminance

can be approximated by

teye ¼ 0:0192þ 0:0633ðLÞ−0:17 ð23Þ

where L is the display luminance in foot-Lambertsand teye is the eye integration time in seconds [18].

C. Radiometry

The radiometric transfer process developed for thisTHz imaging system performance model is designedto accurately compute radiant power from the sceneinto the system detector(s) from either active illumi-nation or passive emission while accounting for thepropagation effects of atmosphere and any target con-cealment material located between the target andsensor. The model includes a capability to definesource beam propagation characteristics for the ac-tive-illumination case and to define both target andbackground reflectivity properties through a parame-terized specular–Lambertian reflection model.Development of the radiometric transfer process

beganwith the construction of a formalmathematicalprocedure to trackpower exiting thehornantennaof asource to the target and back to another horn antenna

receiver–detector via a focusing mirror. This proce-dure treats the target reflectance as a weightedsum of a Lambertian surface and aGaussian functiontomodel the specular component. Figure 4 illustratesthis process. Note that, because the mathematicalforms of the illuminating beam and the target reflec-tance do not always allow correlation (convolution) tobe done in closed form, numerical correlationwas per-formed. This formal, numerical procedurewasused tocalculate power onto the detector for several active-illumination configurations and several passive-emission cases at a fixed sensor-to-target distanceof 10m. These data are given in Section 4.

For ease of implementation and flexibility of use, asecond, less-rigorous radiometric transfer processwas developed for active illumination. This processis based on a radar radiometric transfer approach[19], and is the one currently used in the MATLAB-based imaging system performance model. Referringto Fig. 5, the radiation transfer process begins with adescription of the THz source beam propagation char-acteristics. The source beam is characterized by an in-itial spot size andadivergenceangle representative ofa beam exiting either a horn antenna or a horn anten-na with collimating optics. The beam is then propa-gated through the atmosphere and through anytarget concealment–obscurant material to the targetplane a distance R away, and the target–backgroundirradiance is calculated. The target–background irra-diance at range R is calculated from

Etgtplane ¼Psourceτatmτobsc

Ai; ð24Þ

where Etgtplane is the target–background irradiance inwatts per square meter, Psource is the source power inwatts, τatm is the atmospheric transmission throughrange R, τobsc is the concealment–obscurant materialtransmission, andAi is the target–background illumi-

Fig. 4. (Color online) Illustration of the formal, horn-antenna radiation transfer process: illustration of (a) the numerical correlation(outer curve) of the source beam (middle curve) with the target reflectance (inner curve), and (b) the return irradiance across a 12 in:focusing mirror (upper curve) and the weighting of that irradiance by the pattern of a 22dB gain receiver–detector horn antenna (lowercurve). The power received by the detector is the integration of the product of the two functions.


nation area in square meters given by

AiðRÞ ¼ π�α2× Rþ Bd

2

�2; ð25Þ

where α is the source divergence full angle in radians,Bd is the initial beam spot diameter in meters, and Ris the range in meters.Next, the power reflected from the target plane

into the detector’s IFOV is calculated from

Prefl ¼ EtgtplaneAdoðRÞRnormal; ð26Þ

where Rnormal is the reflectivity of the target or back-ground at normal incident angle and AdoðRÞ is thedetector area in object space given by

AdoðRÞ ¼ π�IFOV

2R

�2; ð27Þ

and where IFOV is the detector’s IFOV.The reflected power, Prefl, is then propagated back

through any target concealment–obscurant materialand through the atmosphere to the receiver aperturelocated a distance R away, and the receiver apertureirradiance is calculated. The irradiance at the recei-ver aperture is given by

Eaperture ¼Prefl × τatm × τobsc

4πR2 × Gain ; ð28Þ

where Gain is the reflective gain from the target orbackground surface given by

Gain ¼ 4πΩrefl

ð29Þ

and Ωrefl is the solid angle of the reflected beam

(reradiated power) in steradians. For specular reflec-tions, Ωrefl is taken to be twice the full width at half-maximum (FWHM) planar angle of the surfacereflectivity measured in radians; for Lambertianreflections, Ωrefl is π steradians, yielding Gain ¼ 4.

Finally, the power incident on the detector is cal-culated to be

PdetIFOV¼ Eaperture × Aaperture × τaperture; ð30Þ

where Aaperture is the area of the aperture in squaremeters and τaperture is the transmission of theaperture.

Power incident on the detector from a source reflec-tion in a target region comprises power from the tar-get’s specular reflection component and power fromthe target’s Lambertian reflection component. Therelative amounts of power reflected as specularand Lambertian are user definable.

Power incident on the detector from a source reflec-tion in a background region comprises power from thebackground’s specular reflection component andpower from the background’s Lambertian reflectioncomponent. Again, the relative amounts of power re-flectedasspecularandLambertianareuserdefinable.

D. Image Contrast

Given the radiometric transfer process describedabove, image contrast in the MATLAB-based ima-ging system performance model is defined as

Contrastimage

¼ jPdetIFOVðTargetÞ � PdetIFOV

ðBackgroundÞjPdetIFOV

ðTargetÞ þ PdetIFOVðBackgroundÞ :

ð31Þ

It should be noted that the underlying assumption inthe above definition of image contrast is that the at-mosphere causes little to no scattering of THz-band

Fig. 5. (Color online) Illustration of the present radiometric model for active target–background illumination. Note that the input aper-ture is that of either a lens or a mirror focusing element.


radiation, and thus causes no reduction in image con-trast. This assumption arises from the facts thatthere is strong molecular absorption of THz-band ra-diation from atmospheric water vapor and that thewavelengths of THz-band radiation are too long rela-tive to the sizes of most atmospheric particulates (in-cluding fog and mist particles) for any significantscattering to occur.

4. Preliminary Modeling Results and Discussion

Modeling results for both passively emitting and foractively illuminated targets and backgrounds are gi-ven in the following sections. In order to compare thebenefits of active illumination over only passivelyemitting targets and backgrounds, the formal radio-metric transfer process described in Subsection 3.Cwas used to compute power at the input aperturefor several actively illuminated cases and power intothe receiving detector for several passive-emissioncases. Performance modeling results for several ac-tively illuminated scenarios were computed usingthe subject MATLAB-based imaging system perfor-mance model. All active-illumination calculationswere based on a 650GHz, commercially availablesource generating 0:5mW of output power.

A. Radiometric Results

The results of the radiometric calculations describedabove are given in Tables 1 and 2. All calculations arebased on a sensor-to-target distance of 10m (refer toFig. 5). For the active-illumination cases, the targetis assumed to be a metal surface with a normal re-flectivity of 0.95; the reflected radiation is assumedto have the angular properties given in Fig. 4(a). Forthe passive-emission cases, the target–source emis-sion is assumed to be a 300 °K blackbody Lambertiansurface with emissivity ðεÞ ¼0:7. The broadband ra-diant exitance EðW=m2Þ was calculated by using aspectral band from 0.5 to 1:0THz; for the narrow-band case, the radiant exitance was calculated byusing a spectral band from 0.645 to 0:655THz. Ex-cept where indicated, attenuation due to the atmo-sphere was included in all calculations.Because of the weighting of the irradiation pattern

across the 12 in: focusing mirror by the acceptancepattern of the receiver–detector horn antenna [seeFig. 4(b)], power onto the detector for the active illu-mination cases is only approximately 20% of thepower at the input aperture. Even so, approximately2 orders of magnitude more power can be delivered tothe receiver detector by using a noncollimated, activeillumination source than detecting only broadband

passive radiation. Comparing the focused, Gaussian-spot, active-illumination case to the passive, narrow-band case yields an approximately 6 order of magni-tude increase in power onto the detector for theactive-illumination case.

B. Active-Illumination Performance Prediction Results

Performance modeling of concealed-weapon identifi-cation (ID) was performed for a prototype, active-illumination system using relevant system parameters and the subject MATLAB-based imaging systemperformance model. The prototype system is basedon a Virginia Diodes [20] heterodyne 650GHzsource–receiver subsystem using an optical config-uration consistent with the radiometric model shownin Fig. 5.

Parameters that remained fixed (except wherenoted) for all simulations are as follows: basic sys-tem parameters, focal length 1:0m; display para-meters, type CRT, pixel pitch 0:24mm, detectorpixels displayed 160 × 120, interpolation factor 2(4× zoom), viewing distance 45:72 cm, display lumi-nance 30:0 cd=m2; illumination parameters, XMTRpower 0:5mW; atmospheric parameters, attenu-taion 30:0dB=km; detector/noise parameters, anten-na coupling efficiency 0.50; obscurant parameters,transmission of obscurant 0.7; target parameters,critical dimension 7:62 cm, ID task difficulty criteria20.8 cycles. Only the Lambertian components of thetarget and background reflective properties wereutilized in these simulations; the specular compo-nents will be included in future simulations as suffi-cient phenomenological data become available.Spatial sampling was adequate to avoid aliasingfor all simulations.

Figure 6 illustrates one of the main graphicaloutputs from the MATLAB-based imaging systemperformancemodel and contains performance predic-tions for a best-case,maximum-performance scenariowhere several system parameters have been chosento yield maximum results. Optimized parametersare as follows: basic system parameters, main aper-ture diameter 1:0m (f -number 1.0), detector size0:5mm (minimal impact from the detectorMTF); tar-get parameters, target reflectivity 0.9, background re-flectivity 0.0 (contrast ratio 1.0). From the chart in thebottom-right quadrant of Fig. 6, the maximum rangethat an object with a critical dimension of 7:62 cm (ap-proximately 3 in:) can be identified is predicted to beapproximately 55m (with a 50% probability of suc-cess), for the case where there is no system noise,no atmospheric attenuation, andno target-concealing

Table 1. Summary of Active-Illumination Radiometric Results

ConditionPeak Irradiation atTarget (μW=m2)

Peak Irradiation at InputAperture (μW=m2)

Power at InputAperture (μW)

Beam Radius atTarget (cm)

Beam Radius at InputAperture (cm)

No collimation 63 13 0.90 95 110Gaussiancollimation

49,300 1400 85 13 75

Gaussian spot 988,000 1900 112 3.1 67


material(s) (obscurants). This represents amaximumpractical bracketing performance for an object of thissize, using nearly realistic system parameters with a1m main aperture diameter.The curve sets in Fig. 7 represent performance pre-

dictions from several model simulations to show theimpact that main aperture size and target-to-back-ground contrast ratio have on IDperformance. Inbothcurve sets, the performance predictions are for thecase where there is no system noise, no atmosphericattenuation, and no target-concealing material(s)(obscurants). In Fig. 7(a), the target-to-backgroundcontrast ratio and the system focal length are heldconstant at values of 0.3 and 1:0m, respectively. InFig. 7(b), the main aperture size and the system focallength are held constant at values of 0.33 and 1:0m,respectively. Other simulations (not examined here)show that range performance can also be strongly af-fected by the detector IFOV.

The following two sets of performance simulationsexplore the effects of active-illumination beam shap-ing on ID performance for the single-element,scanned imaging system configuration; the thirdset of performance simulations explores the effectof active scene illumination on ID performance as re-quired for FPA detector-based imaging systems. Thefollowing simulation parameter(s) remained fixed forall three of the following sets: basic system para-meters, main aperture diameter 0:3048m (f -number3.3), detector size 1:8mm; target parameters, targetreflectivity 0.9, background reflectivity 0.3. [Thetarget parameter values were chosen to approximatea highly reflective metal target (weapon) and a lessreflective background (human skin)].

Fig.8givestheprobabilityofIDversusrangeresultsusing a 22dB gain horn antenna (beam divergence70mrad) on the output of the active-illuminationsource.For these simulations, theNEPwasset to5:0 ×

Table 2. Summary of Passive-Emission Radiometric Results

ConditionTarget Exitance

μW=m2Image Plane

Irradiance μW=m2Power onto

Detector (μW)Beam Radiusat Target (cm)

Beam Radiusat Input Aperture (cm)

Passive, no atmosphere 59,100 1330 22 × 10−3 Lambertian LambertianPassive 55,300 810 Lambertian Lambertian

(effective std.) (35,900)Passive 55,300 580 1:6 × 10−3 Lambertian Lambertian

(effective fog) (25,900)Passive Narrow Band 856 16.7 45 × 10−6 Lambertian Lambertian

(effective std.) (742)

Fig. 6. (Color online) Example graphical output from the MATLAB-based imaging system performance model.


10−13 W=Hz1=2 (the estimated NEP for the VirginiaDiodesheterodyne receiver), and thedetector integra-tion time was set to 10ms. Note that, for the rangesshown, atmospheric attenuation has little impact onrange performance.Figure 9 gives the probability of ID versus range

results using collimated active illumination (beamdivergence 2× the detector IFOV). Again, the detec-tor NEP was set to 5:0 × 10−13 W=Hz1=2.Figure 10 gives the probability of ID versus range

results using scene active illumination (beam diver-gence 90mrad, just larger than the system field ofview). For these simulations, the detector NEP wasset to 1:0 × 10−12 W=Hz1=2, the detector size was setto 0:5mm (each side), and the antenna couplingefficiency was set to 10% (values are estimates forpresent FPA technology).One of the interesting results from the performance

model simulations is that a scanning, active-illumination, THz imaging system that focuses mostof the source radiation into the detector’s IFOV is op-timal; for ranges less than approximately 25m, essen-tially all of the effects of systemnoise andatmosphericand target-concealment-material attenuation can be

eliminated [refer to Fig. 9(a)]. When the source radia-tion is defocused in amanner such that it just fills thesystem field of view (as required for a FPA-detector-based system), and lower-performance, FPA-technology system parameters are utilized, thepresent simulations predict a significant loss of rangeperformance [primarily due to low detector signal-to-noise ratios (SNR’s)]. It should be noted that these lat-ter predictions are expected to change toward betterrange performance when the specular componentsof the target and background reflective propertiesare included in the simulations using optimal tar-get–background orientations. For nonoptimally or-iented target–background scenarios, ID rangeperformance would be expected to decrease becausea significant amount of illumination power would bereflected in a specular fashion away from the system’sreceiver–aperture.

5. Model Calibration and Validation

As a first step toward validating the subject THz ima-ging system performance model, the model needs tobe calibrated with human perception testing. Percep-tion testing is required for determining the discrimi-

Fig. 7. (Color online) ID range performance as a function of (a) aperture size (f -number), (b) target-to-background contrast ratio.

Fig. 8. (Color online) Probability of ID versus range results using a horn output antenna: atmospheric attenuation set to (a) 30:0dB=km,(b) 60:0dB=km.


nation task difficulty parameter V50. This parameteris very similar to the previous Johnson’s criteria (N50)and is measured by human perception testing of tar-get ID in the spectral band of interest. Previous ex-perience shows that this calibration is different fordifferent bands. It is more difficult to identify objectsin the infrared than in the shortwave or visible bandsandmaybe evenmore difficult in theTHz regime. It isexpected that this calibration in the THz band will besufficiently different from the criteria in the infraredand visible, that humanperception testing is requiredfor proper calibration. The procedure for deriving thecalibration parameter involves collection of high-resolution radiometric images, segmentation of theseimages for contrast determination, blurring theseimages to limit the available spatial frequencies,and measuring the 50% probability-of-ID point asso-ciated with the collections of perceived frequencies.The V50 values are the calibration coefficients for ap-plication of the sensormodel to the concealed-weaponID problem in the THz regime.

6. Conclusions and Future Plans

AMATLAB-based imaging systemperformancemod-el for concealed-weaponIDintheTHzregimehasbeendeveloped. Themodel accounts for the effects of imageblur, image noise, the human response to displayedimagery, atmospheric attenuation, and target-concealment-material attenuation. The model hasalso been designed to account for the specular andLambertian reflective properties of targets and back-grounds in this frequency region. Results from theradiometric calculations show a strong SNR advan-tageforsystemsthatutilizeactive illuminationversuspassive-only systems. Results from the performancemodel simulations performed at 0:650THz indicatethat themaximum range that a target with a criticaldimension of approximately 3 in: can be identified(using a 1m receiving aperture) is approximately55m (with a 50% probability of success). Analysis ofsimulation data shows that range performance is astrong function of the size of the main imaging aper-ture, the target-to-background contrast ratio, and

Fig. 9. (Color online) Probability of ID versus range results using a collimated output beam: detector integration time set to (a) 10ms,(b) 52 μs. In (b) an entire image frame could be captured in 1 s.

Fig. 10. (Color online) Probability of ID versus range results using a scene-collimated, active-illumination output beam: detector inte-gration time set to (a) 10ms, (b) 1 s.


thedetectorIFOV.Otherresults fromtheperformancemodel simulations indicate that a scanning, active-illumination, THz imaging system that focuses mostof the source radiation into the detector’s IFOV is op-timal; for ranges less thanapproximately25m(with asource output power of 0:5mW), all of the effectsof system noise and atmospheric and target-concealment-material attenuation can be eliminatedwith such focusing. Alternatively, when the source ra-diation is defocused in a manner such that it just fillsthe system field of view, and lower-performance, FPA-technologysystemparametersareutilized,present si-mulations predict a significant loss of range perfor-mance due to low detector SNRs. These FPA-basedpredictions are expected to change toward betterrange performance when the specular componentsof the target and background reflective propertiesare included in the simulations using optimaltarget–background orientations. For nonoptimally-oriented target–background scenarios, ID rangeperformance would be expected to decrease due to asignificant amount of illumination power being re-flected in a specular fashion away from the system’sreceiver–aperture. Future work is to include the cali-bration and validation of the subject performancemodel through systematic human perception testingand the incorporation of the specular characteristicsof various targets and backgrounds into performancemodel simulations as the phenomenological data be-come available. Target–background orientation ef-fects will also be addressed in future work.

The authors recognize and thank Ron Driggers(NVESD) and Mark Rosker (Defense Advanced Re-search Projects Agency) for their programmatic andtechnical guidance during the course of this work.

References1. W. R. Tribe, D. A. Newnham, P. F. Taday, and M. C. Kemp,

“Hidden object detection: security applications of terahertztechnology,” Proc. SPIE 5354, 168–176 (2004).

2. C. Baker, W. R. Tribe, T. Lo, B. E. Cole, S. Chandler, andM.C. Kemp, “People screening using terahertz technology,”Proc. SPIE 5790, 1–10 (2005).

3. M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald,and W. R. Tribe, “Security applications of terahertz technol-ogy,” Proc. SPIE 5070, 44–52 (2003).

4. D. Zimdars, “Fiber-pigtailed terahertz time domain spectro-scopy instrumentation for package inspection and securityimaging,” Proc. SPIE 5070, 108–116 (2003).

5. F. C. De Lucia,“THz þ X—A search for new approaches to sig-nificant problems,” Proc. SPIE 5790, 219–230 (2005).

6. T. W. Crowe, D. W. Porterfield, J. L. Hesler, W. L. Bishop,D. S. Kurtz, and K. Hui, “Terahertz sources and detectors,”Proc. SPIE 5790, 271–280 (2005).

7. MATLAB is a mathematical engineering software product ofMathworks, Inc. (Natick, Mass.)

8. P. G. J. Barten, “Evaluation of subjective image quality withthe square-root integral method.” J. Opt. Soc. Am. A 7, 2024–2031 (1990).

9. R. Vollmerhausen, “Incorporating display limitations intonight vision performance models,” in Proceedings of the1995 Meeting of the Infrared Information Symposium (IRIS)Specialty Group on Passive Sensors (Infrared InformationAnalysis Center, 1995) Vol. 2, pp. 11–31.

10. NVTherm, www.ontar.com.11. P. G. J. Barten, Contrast Sensitivity of the Human Eye and Its

Effects on Image Quality (SPIE, 1999).12. J. Johnson, “Analysis of image forming systems,” in Proceed-

ings of the Image Intensifier Symposium (Warfare ElectricalEngineering Department, U.S. Army Research and Develop-ment Laboratories, 1958), pp. 249– 273.

13. R. H. Vollmerhausen, E. L. Jacobs, and R. G. Driggers, “Newmetric for predicting target acquisition performance,” Proc.SPIE 5076, 28–40, 2003.

14. G. D. Boreman, Basic Electo-Optics for Electrical Engineers(SPIE, 1998), pp. 23–30.

15. R. H. Vollmerhausen and R. G. Driggers, Analysis of SampledImaging Systems (SPIE, 2000), Chap. 2.

16. J. W. Goodman, Introduction to Fourier Optics (McGraw Hill,1996), Chap. 2.

17. W. C. Jakes Jr., “Gain of electromagnetic horns,” Proc. IRE, 39,160–162 (1951).

18. R. H. Vollmerhausen and E. L. Jacobs, “The Targeting TaskPerformance (TTP)Metric: A NewModel for Predicting TargetAcquisition Performance,” AMSEL-NV-TR-230 (U.S. ArmyNight Vision and Electronic Sensors Directorate, 2004),pp. 29–40, 66.

19. F. T.Ulaby, R. K. Moore, and A. K. Fung, in Microwave RemoteSensing: Active and Passive (Addison-Wesley, 1982), Vol. 2,pp. 457–463.

20. http://www.virginiadiodes.com/.


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Terahertz imaging system performance model for concealed-weapon identification