Application of a lidar-type gamma-ray tomography approach for detection and identification of buried plastic landmines Tanja N. Dreischuh∗a, Ljuan L. Gurdeva, Dimitar V. Stoyanova, Christo N. Protochristovb, and Orlin I. Vankova a Institute of Electronics, 72 Tzarigradsko shosse blvd., 1784 Sofia, Bulgaria b Institute of Nuclear Research and Nuclear Energy, 72 Tzarigradsko shosse, 1784 Sofia, Bulgaria ABSTRACT The efficiency is studied of some applications of a recently developed lidar-type gamma-ray tomography approach for non-destructive evaluation of dense media. The approach consists in time-to-range resolved detection of the Compton returns from the probed object (irradiated by annihilation gamma-photon sensing beams) and data processing based on a lidar-type equation and intended for determination of the extinction and backscattering profiles along the line of sight. The concrete purpose of the work is to reveal by statistical modeling the capabilities, under Poisson noise conditions, of investigating underground layers and detecting low-contrast ingredients such as plastic landmines in soil. The results from simulations show that the method is capable of finding and identifying down to 5 % density-contrast ingredients in soil, at depths to 20 cm, with spatial resolution of 1 to 10 mm, for measurement time of 10 to 1000 s and activity of the gamma-ray source of 50 - 300 mCi. So, the method could be successfully used for examination of ground for landmines. Keywords: lidar, gamma-ray, landmine detection, non-destructive evaluation.

1. INTRODUCTION AND FORMULATION OF THE PROBLEM There are various methods developed for gamma-ray non-destructive probing and characterization of dense optically opaque media. They are usually intended for determination of the electron density distribution inside the probed objects and based on the dependence of the energy of the Compton single-scattered photons on the angle of scattering. A common difficulty of these methods is the lack of any clear approach for taking into account the internal distribution of the linear attenuation coefficient. Recently we developed a novel approach1 for single-sided gamma-ray probing and tomography based on lidar (Light Detection And Ranging) principle2, that is, time-to-range resolved detection of the backscattering-due radiative returns from the probed object irradiated by pulsed gamma-photon beams. In the case of gamma-radiation one should obviously employ the term "graydar" (Gamma RAY Detection And Ranging) principle. This approach allows one to determine simultaneously the distribution of the linear attenuation and Compton-backscattering coefficients within the investigated object and as a final result - the distribution inside the object of different ingredients and their mass densities. For this purpose, the return-signal (graydar) equation, describing the relation between the measured time-to-range resolved return signal profile and the parameters of the radiation-transceiving system, the energy of the sensing gamma photons, and the line-of-sight (LOS) distribution of the physical characteristics of the medium under investigation, is solved. The solutions obtained reveal possibilities to develop some methods1 for determination of the material content and location of different inhomogeneities within the probed objects. The main purpose of the present work is to study by statistical modeling the applicability, under Poisson noise conditions, of the approach concerned here to investigate underground layers and detecting low-contrast ingredients (plastic landmines) in soil. Landmines are a serious calamity created by the human being. There are about 110 million units spread in 90 countries all over the world that claim about 24 000 victims annually. Therefore their detection and obliteration is a problem of primary importance for the human community.

∗

E-mail: [email protected] 14th International School on Quantum Electronics: Laser Physics and Applications, edited by Peter A. Atanasov, Tanja N. Dreischuh, Sanka V. Gateva, Lubomir M. Kovachev, Proc. of SPIE Vol. 6604, 660420, (2007) 0277-786X/07/$15 doi: 10.1117/12.727122 Proc. of SPIE Vol. 6604 660420-1

2. THEORETICAL NOTES Let us consider a monostatic pulsed sensing system emitting narrow pulsed beam of gamma photons of energy Ef and detecting the Compton backward scattered gamma photons of energy Eb at each moment t=2z/c after the pulse emission; z=ct/2 is the one-to-one corresponding coordinate of the act of backscattering along the LOS 0z. A principle blockscheme of such a system is shown in Fig.1. For the mean number of signal gamma-photon counts NT(Eb, t, ∆t) accumulated during the measurement period T per one resolution cell, between the moments t and t+∆t after the pulse emission (respectively, backscatterred between the points z and z+∆z), we can write1 N T ( E b , t , ∆t ) ≡ N T ( E b , z , ∆z ) = dq 0 ∆zTz −2η ( z ) β ( z ) exp{−

∫

z

z0

α ( z ' ) dz '} ,

(1)

where d is an experimental constant, q0 is the mean sensing photon flux during the measurement process; ∆t is the temporal sampling interval, and ∆z=c∆t/2 is the corresponding spatial sampling interval; η(z) is the receiving efficiency of the experimental setup, β(z) is the volume backscattering coefficient, z0 is the longitudinal coordinate of the "entrance" into the investigated object, and α(z)=αf(z)+αb(z) is the two-way extinction index, αf(z) and αb(z) are the volume extinction (linear attenuation) coefficients for the sensing and signal photons, respectively. We have supposed here that the photon registration system is sufficiently fast and precise, having nearly ideal energy and time-to-range resolution. Eq.(1) is the maximum-resolved (δ -pulse) single-scattering graydar equation. It is valid when one use δ -like gamma-ray sensing pulses, narrow-enough field of view of the signal-photon receiver, and (energy) selection of the detected onceonly backscattered photons. For achieving a regime of δ -pulse sensing an approach is proposed1 based on using sensing photon beams resulting from electron-positron annihilation within a converter irradiated by positrons from a radioactive source. As a result of annihilation, two gamma photons of well known energy (Ef = 511 KeV) are simultaneously emitted in opposite directions. A portion of the continuously emitted photons is angle-selected by the collimator to form a narrow sensing beam. The backpropagating photon of each "sensing" pair through the collimator reaches a detector, thus generating a start light pulse. The corresponding backscattered Compton photon of energy Eb ~ Ef /3 3 hits the sensitive layer of the detector and produces a stop light pulse. Thus, two time-resolved light pulses illuminate the photocathode of a joint photomultiplier and produce a couple of two time-shifted electronic pulses corresponding to the start and stop pulses. The output pulses are further amplified and processed additionally to determine simultaneously both the energy and the arrival time of each gamma photon. As a final result one has to obtain a set (along parallel LOSs) of energyselected time-to-range resolved return signal (graydar) profiles NT(Eb, t, ∆t).

Collimator S tart

Ef = 511 KeV

Stand-off z0

Eb ≈ 170 KeV

Converter

Detector

Detector

Detector

Emitter

Positron source

Burial depth

S top Object

Data acquisition and processing system

Mine Soil

Fig.1.Principle block-scheme of experimental set-up for lidar-type single-sided gamma-ray sensing of dense media.

Fig.2. Illustration of mine detection by graydar.

The graydar equation (1) concerns two unknown functions, the profiles β(z) and α(z), containing information about the material properties along each LOS. Certainly, to extract this information one have first to solve Eq.(1) with respect to β(z) and α(z), i.e. to determine the extinction and backscattering distributions within the investigated object, on the basis of the measured graydar profiles. We consider the case when the incident gamma photon beams penetrate alternating homogeneous regions of different ingredients within the probed object. Let us denote the corresponding intersection intervals along the LOS and their lengths and the inside values of α and β, respectively, by ∆i = [zi-1, zi], li = zi-zi-1, αi = α(z ∈ ∆i)=const and βi=β(z ∈∆i)=const, i=1,2,… To determine the extinction and backscattering coefficients within each region, Eq.(1) can be written in the form N T ( E b , t , ∆t ) / W ( z ) = S ( z ) = β i exp{−

∫

zi −1

z0

α ( z ' ) dz '} exp[−( z − z i −1 )α i ] ,

Proc. of SPIE Vol. 6604 660420-2

(2)

where W(z) = dq0∆zTz-2η(z), and S(z) is the so-called (in the lidar practice) S-function2. After taking the logarithm of (2) we obtain the relation ln S ( z ) = ln β i −

∫

z i −1

z0

α ( z ' )dz '−( z − z i −1 )α i ,

(3)

that outlines each homogeneous region ∆i where lnS(z) falls linearly with a slope αi. When the experimental data suggest a linear tendency in the behaviour of lnS(z) within some interval ∆i, one can use linear regression analysis for approximation of lnS(z) and determination of αi. In this case one may expect a high accuracy in the determination of αi even at relatively strong fluctuations (low number) of the stored signal photon counts NT(Eb, t, ∆t). The error in the determination of αi through two-parametric linear regression analysis (straight-line least-square approximation) of lnS is obtained in the form (see, e.g., in 1,4):

δα i = l i−1 {∑ pi= 0 N p p 2 / q i2 − (∑ pi= 0 N p p / q i ) 2 / (∑ pi= 0 N p )} −1 / 2 q −1

q −1

q −1

,

(4)

where qi = li/∆z, and Np is the number of accumulated photon counts in the pth voxel within ∆i. Assuming that the extinction coefficients αj for all homogeneous regions ∆j before the considered one ∆i ( j < i ) are determined in the same way as αi, on the basis of Eq.(3) one can determine the backscattering coefficient βi 1 . A general conclusion following from the considerations in this section is that the gamma-ray sensing would allow one to accurately locate and characterize different inhomogeneities within the investigated object due to the fact that the gamma-ray backscattering and extinction coefficients of the most frequently met materials are determinable.1,5

3. SIMULATIONS Here we represent results from simulations we have conducted to examine the possibilities of detecting and recognizing landmines buried in different depths in soils with different densities. The photon count fluctuations are simulated on the basis of the assumption that they have Poissonian statistics. Then the only parameter of importance is the mean number of photon counts NT(Eb, t, ∆t) accumulated for the measurement time T and corresponding to acts of backscattering between z and z+∆z. At given profiles α(z) and β(z) the mean graydar profile NT(Eb,t,∆t) is calculated according to Eq.(1) and then its realizations are generated.1 A schematic drawing illustrating the simulations is shown in Fig.2. The parameters used are chosen to have the following constant values: ∆z=2 mm, stand-off distance z0=20 cm, Ef=511 KeV, Eb=170,33 KeV and the receiving efficiency η(z)=1. It is also assumed that the angle divergence of the incident photon beam is 1°. Then, if the activity of the radionuclide employed is 300 mCi, the mean sensing photon flux will be q0 = 1.68x106 s-1. Also, the diameter of the sensing beam in the soil will be about 15 mm. Correspondingly, the sampling step of the lateral scan employed to obtain 2D images of the probed medium is chosen to be 15 mm. Three types of soil are considered. Their characteristics (composition, density, extinction and backscattering coefficients) are given in Table 1, Table. 1. Characteristics of soil, TNT and Bakelite used in the simulations. Element H C N O Na Al Si K Ca Fe Density ρ [g/cm3] α [m-1] βc[m-1/sr]

Soil A [Ref.6]

Soil B [Ref.7]

2.8 14.4

2.2

49.7 0.8 8.9 21.3 0.6 0.5 1 0.9 20.2 0.407

57.5 8.5 26.2

5.6 1 22.5 0.449

Soil C [Ref.8] Fraction by weight (%) 2.1 1.6

TNT

Bakelite 5.7 77.5

57.7

2.2 37.0 18.5 42.3

16.8

5 27.1 1.3 4.1 1.1 1.6 35.87 0.720

1.6 36.603 0.748

1.25 28.54 0.584

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2

2

10

3

1

10

0

10

0 2 4 6 8 10 12 14 16 18 20 22 24 Depth (cm)

-1

24 20 16 12 8 4 0

2

4

6 8 10 12 14 16 18 20 Burial depth (cm)

0

8

Relative rms error and deviation (%)

4

(b) 28

Deviation and rms error (m )

3

10

11 10 9 8 7 6 5 4 3 2 1 0

Relative rms error and deviation (%)

1

-1

(a)

4

10

Deviation and rms error (m )

Graydar profile (photon counts)

where Soil A is a carbon-rich loam soil, while Soil C is a typical silty soil. The evaluation of α and β showed that their values are practically insensitive to the soil composition and are determined mainly by the soil density. In the simulations performed we mostly deal with Soil B. The landmine is assumed to be a plastic casing, containing pure TNT as explosive, with sizes approximating those of real mines of Type 72: 7.5 cm in diameter and 4 cm in height. The characteristics of the plastic (bakelite) and TNT are also given in Table 1. The detection and recognition of such a type of mines is relatively most difficult because of their non-metallic casing and minimum sizes, and the lower density of TNT (1.6 gcm-3) compared to that of RDX (1.8 gcm-3). The chosen mine sample is considered as buried in different depths D in Soil B, gradually increasing with step of 1 cm from D=0 cm to D=20 cm. The results from simulations concerning this case are represented in Fig.3. It is seen that at T=100s one can detect a mine (as an inhomogeneity) buried to a depth of 20 cm (Fig.3a). The deviation αir -αi between the recovered αir and model αi values of the extinction is mostly within the evaluated rms interval ±δαi [(Eq.4)]; the relative deviation obtained (αir -αi)/αi is usually bellow 8%, with rare exceptions when it reaches 23 % or 31 % (Fig.3b). At T=10s the mine is detectable to a depth of 10 cm (Fig.3a). The deviation of αir with respect to αi is again mainly within ±δαi; the values of the relative deviation (for D ≤10) are noticeably higher as a whole compared to the case when T=100s (Fig.3c). At T=1000s the accuracy in the determination of αi is naturally higher. For instance, the relative deviation obtained in this case is 0.6 % and 2% for depths of 10 cm and 20 cm, respectively; the corresponding evaluated relative rms errors δαi/αi are 1.6% and 6.6%. In general, one may conclude that for a measurement period T=10 to 1000s the value of αi for TNT could be determined with a sufficient accuracy allowing one to recognize the explosive when buried to depth of 20 cm. 7

(c) 20

6

16

5

12

4 3

8

2

4

1 0

0

2

4 6 8 Burial depth (cm)

10

0

6 5 4

(a) |αsoil-αTNT|

2

0

(b) 3

10

3

1

Graydar profile (photon counts)

-1

rms error and contrast (m )

Fig.3. (a) Graydar profiles obtained for T = 100 s (curves 1, 2, and 3) and 10 s (curve 4), at mine burial depths of 4 cm (1 and 4), 10 cm (2), and 17 cm (3). Theoretically estimated Poisson rms error in the determination of the extinction (circles) and deviation of the results from simulations from the true values of α (triangles) versus mine burial depth at T=100 s (b) and 10 s (c); the right y axis represents the corresponding relative rms error and deviation.

1 2

2

10

rms error 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 3 Soil density (g/cm )

1

10

0

2

4

6 8 10 Depth (cm)

12

14

Fig.4. (a) RMS error in the determination of the extinction of a TNT plastic mine (buried in depth of 6 cm in type-C-like soils with different densities) compared with the corresponding absolute contrast. (b) Realizations of the graydar profiles (compared with the expected ones given by solid curves) obtained at soil densities of 1.4 g/cm3 (1) and 1.75 g/cm3 (2).

The following important question concerns the detectable contrast between soil and explosive. In this case, to distinguish and identify the mine, the contrast should exceed the rms error in the determination of the extinction. This problem concerns mainly soils like Soil C whose density is near that of TNT. To investigate the recognition threshold we have simulated the detection of the above-chosen (TNT) mine buried in a fixed depth of 6 cm at different porosity-conditioned Soil-C densities; the measurement time supposed is T=100s. The theoretical estimation shows (Fig.4a) that under the described conditions the mine is certainly not discernible for soil densities near that of TNT, in the interval from 1.550 to

Proc. of SPIE Vol. 6604 660420-4

1.725 g/cm3. Out of the mentioned density interval, at an extinction contrast above 5 %, the region of explosive is quite (visibly) discernible (Fig.4b). As shown above (see Fig.3b) its kind is also accurately determinable. Let us finally note that the explosive RDX is sufficiently contrastive to be accurately found and recognized in all types of soil having density from 0.8 to 1.6 g/cm3.

10

Depth (sample number)

Depth (sample number)

35 20 30 40 50 60 70

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Width (sample number)

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60 70

5 1

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0

Graydar profile (photon counts)

At last, we have simulated the procedure of obtaining a 2D image (vertical diametrical section) of a mine buried in depth of 5 cm in Soil B. For this purpose a lateral scan is reproduced with T=100s per one position of the line of sight. The results obtained are illustrated in Fig.5, where it is seen that the mine shape is well distinguishable. 4

10

2 1

3

10

2

10

0

2

4

6 8 10 Depth (cm)

12

14

Width (sample number)

(a) (b) (c) Fig.5. Model (a) and recovered (b) 2D extinction image (vertical diametrical section) of a mine buried in Soil B. The grey level bar is in units of m-1. (c) LOS graydar profiles obtained in absence (1) and presence (2) of mine.

4. CONCLUSION The results from simulations, in accordance with the theoretical predictions, show that under Poisson noise conditions one could successfully sound the ground by gamma-photon pencil beams and establish the presence, the disposition, and the explosive of buried plastic landmines. In general, the considered approach is capable of finding and identifying down to 5 % density contrast ingredients (explosives) in soil, at depth to 10-20 cm, with spatial resolution of 1 to 10 mm, for measurement time of 10 to 1000 s and activity of the gamma-ray source of 50 to 300 mCi.

ACKNOWLEDGEMENTS This research was supported by the Bulgarian National Science Fund under grant F-1511.

REFERENCES 1. L.L. Gurdev, D.V Stoyanov, T.N. Dreischuh, Ch.Protochristov, and O. Vankov, “Gamma-ray backscattering tomography approach based on the lidar principle”, IEEE Trans. Nucl. Sci. 54, accepted (2007). 2. R.M. Measures, Laser Remote Sensing, Wiley, New York, 1984. 3. J.M. Jauch and F. Rohrlich, The Theory of Photons and Electrons, Springer, New York, 1976. 4. W. Galbraith and W.S.C. Williams (Eds.), High Energy and Nuclear Physics Data Handbook, National Institute for Research in Nuclear Science and Rutherford High Energy Laboratory, Chilton, 1964. 5. J.H. Hubbell and S.M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients (version 1.4). [Online] Available: http://physics.nist.gov/xaamdi, Gaithersburg, MD: National Institute of Standards and Technology, 2004. 6. J.R. Tickner, “PACSI—A low-cost 3D gamma-ray camera,” in Proc. of the 2nd RCM for the CRP Application of Nuclear Techniques to Humanitarian Demining, St. Petersburg, 2001, pp. 68-78. 7. K. Saito, P. Jakob, “Gamma ray fields in the air due to sources in the ground,“ Radiation Protection Dosimetry 58(1), 29-45 (1995). 8. K.F. Eckerman and J.C. Ryman, External Exposure to Radionuclides in Air, Water, and Soil, Federal Guidance Report No. 12, Washington, D.C: U.S. Environmental Protection Agency, 1993.

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