Deterministic simulation of thermal neutron radiography and tomography

Transcription

1 Sholars' Mine Masters Theses Student Researh & Creative Works Summer 2016 Deterministi simulation of thermal neutron radiography and tomography Rajarshi Pal Chowdhury Follow this and additional works at: Part of the Nulear Engineering Commons Department: Reommended Citation Pal Chowdhury, Rajarshi, "Deterministi simulation of thermal neutron radiography and tomography" (2016). Masters Theses This Thesis - Open Aess is brought to you for free and open aess by Sholars' Mine. It has been aepted for inlusion in Masters Theses by an authorized administrator of Sholars' Mine. This work is proteted by U. S. Copyright Law. Unauthorized use inluding reprodution for redistribution requires the permission of the opyright holder. For more information, please ontat sholarsmine@mst.edu.

2 DETERMINISTIC SIMULATION OF THERMAL NEUTRON RADIOGRAPHY AND TOMOGRAPHY by RAJARSHI PAL CHOWDHURY A THESIS Presented to the Faulty of the Graduate Shool of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE in NUCLEAR ENGINEERING 2016 Approved by: Xin Liu, Advisor Hyoung Koo Lee Ayodeji Alajo

3 2016 Rajarshi Pal Chowdhury All Rights Reserved

4 iii ABSTRACT In reent years, thermal neutron radiography and tomography have gained muh attention as one of the nondestrutive testing methods. However, the appliation of thermal neutron radiography and tomography hindered by their tehnial omplexity, radiation shielding, and time-onsuming data olletion proesses. Monte Carlo simulations have been developed in the past to improve the neutron imaging faility s ability. In this present work, a new deterministi simulation approah has been proposed and demonstrated to simulate neutron radiographs numerially using a ray traing algorithm. This approah has made the simulation of neutron radiographs muh faster than by previously used stohasti methods (i.e Monte Carlo methods). The major problem with neutron radiography and tomography simulation is finding a suitable satter model. In this paper, an analyti satter model has been proposed that is validated by a Monte Carlo simulation. Two simulation geometries have been analyzed in this work. One is a highly sattering medium, another is medium sattering media. It has been shown that this algorithm works well in the medium sattering media. The satter model has been verified using Monte Carlo method (MCNP5).There are some empirial parameters that have been determined using urve fitting methods using MATLAB. There are some disadvantages of using the satter orretion algorithm proposed in this work, but the advantages are far more rewarding. This method of simulation redues the time of simulation in 5-10 seonds ompared to several hours using Monte Carlo methods and an be used for rapid prototyping for neutron imaging failities. Filtered bak-projetion with a ramp filter has been used for reonstrution.

5 iv ACKNOWLEDGEMENTS I thank my advisor Dr.Xin Liu for giving me valuable guidane and required funding to work on my masters projet. I also like to thank my olleagues Edward Norris, Huseyin Sahiner and Zhongmin Jin for their valuable inputs and supports. I will also like to thank Dr. Ayodeji Alajo for helping me to solve some issues in MCNP. I will also like to thank Dr. Hyoung Koo Lee for giving me his valuable time to serve as one of the members in my thesis advisory ommittee. This work is supported by the U.S.Nulear Regulatory Commission (NRC) Faulty Development Grant under Grant no. NRC-HQ-12- G Finally I would like to thank my parents, my sister, my brother in-law, and my ute little niee Sreyoshi for their ontinuous support and enouragement. I would not be able to finish my work without them.

6 v TABLE OF CONTENTS Page ABSTRACT...iii ACKNOWLEDGEMENTS iv LIST OF ILLUSTRATIONS.vii LIST OF TABLES..ix SECTION 1. INTRODUCTION MOTIVATION CHARACTERISTICS OF NEUTRONS INTERACTIONS WITH MATTER AND CROSS SECTION PREVIOUS STUDIES OF NEUTRON IMAGING AND ITS SIMULATION THERMAL NEUTRON RADIOGRAPHY AND TOMOGRAPHY Priniples of Neutron Radiography Priniples of Neutron Tomography NEUTRON SOURCES AND FACILITIES DETERMINISTIC SIMULATION METHOD PHYSICS MODEL NOISE MODEL SCATTER MODEL...23

7 vi 3. SIMULATION SETUP RESULTS DISCUSSION CONCLUSION...39 APPENDIX 40 BIBILOGRAPHY...53 VITA..56

8 vii LIST OF ILLUSTRATIONS Figure Page 1.1. Neutron interation with matter Thermal neutron sattering and absorption ross setion distribution Shemati of a standard neutron radiography system Shemati plot of the satter model. Left: Forward-satter and point spread funtion. Right: Convoluted overall satter intensity profile Simulation setup for different geometries. (a) A homogenous water phantom was irradiated by a ollimated thermal neutron soure. (b) Simulation geometry 1. () Simulation geometry Plot of statistial unertainty of the MCNP simulations. The Colorbar represents The absolute value of the unertainty. (a) Homogenous water ylinder. (b) Geometry 1. () Geometry Simulated neutron radiography of geometry 1 under ideal onditions (i.e., noiseless and without satter ontamination) simulated by (a) Monte Carlo method. (b) Deterministi method. () Line profile omparison Simulated neutron radiography of geometry 2 under ideal onditions (i.e., noiseless and without satter ontamination) simulated by (a) Monte Carlo method. (b) Deterministi method. () Line profile omparison Neutron radiography of geometry 1. (a) Under ideal onditions (noiseless and without satter ontamination). (b) With added Poisson noise and without satter ontamination simulated by the deterministi method. () The line profile omparison The Gaussian funtion used in the satter approximation Neutron radiography of geometry 1. (a) With Satter simulated by MCNP5. (b) With satter simulated by the deterministi method. () Line profile omparison Neutron radiography of geometry 2. (a) With Satter simulated by MCNP5. (b) With satter simulated by deterministi method. () Line profile omparison.. 35

9 viii 4.8. Tomographi image of geometry 1. (a) Under ideal onditions. (b) With added Poisson noise. () With added noise and satter Tomographi image of geometry 2. (a) Under ideal onditions. (b) With added Poisson noise. () With added noise and satter....36

10 ix LIST OF TABLES Table Page 1.1. Neutron properties at various energy ranges...4

11 1. INTRODUCTION 1.1. MOTIVATION Neutron radiography is a well-established method of non-destrutive testing (NDT) whih has been there sine 1950 s [1]. In the last few years, neutron imaging has gained muh more attention over other methods of imaging. Neutron interats with materials in a omplementary way ompared to the X-ray imaging. The materials with high atomi numbers are opaque in X-ray imaging, ompared to the neutron. This mode of imaging is preferred in the areas where it is needed to loate a material of low atomi number inside of a material with high atomi number. In many fields of researh and industry it is important to loate moisture, rak, bubble flow, et., inside a system. For example, in the field of arheology, it is sometimes important to determine the ontent of anient sulptures [2], thermal neutron imaging is a ore part of studies involving water ontent determination [3]. In nulear engineering, neutron radiography and tomography is widely used for the inspetion of fuel ells and neutron radiography is also used in thermal hydraulis to determine void fration in pipes [4-5]. Thermal neutrons have high apability to distinguish between different materials as the thermal neutron ross setions are signifiantly different from low atomi number materials to high atomi number materials and even from one isotope to another. The attenuation probabilities of materials in ase of thermal neutrons are not dependent on their atomi numbers. This property of thermal neutrons makes them suitable in non-destrutive testing. So far the tehniques that have been used for simulating neutron radiography are stohasti methods, suh as Monte Carlo methods [6].

12 2 Simulating a neutron imaging faility s performane is of utmost importane. Simulating the images shows whether the imaging set up works effiiently or not. Based on the results of imaging faility, suitable and faster method needs to be developed. Monte Carlo methods need both signifiant time and resoures to solve neutron imaging problem. To make neutron radiography more effetive a faster method needs to be implemented. In this study, a deterministi method has been implemented to simulate thermal neutron radiography whih is signifiantly faster than previously used methods. There is one disadvantage of using thermal neutrons as a mean to image hydrogenous materials suh as, water, or any suh biologial sample. Hydrogen ats as a highly sattering medium in ase of thermal neutrons. In ase of imaging, sattered neutrons an degrade the quality of the image and introdue effet suh as blurring of image at sharp edges. Sattering adds a neutron distribution to the deteted signal, whih makes the reonstrution proedure very hallenging. So, before reonstrution of images, the effet of satter needs to be removed or minimized without affeting signal quality. Therefore, a suitable satter removal algorithm needs to be developed. The satter orretion methods available till date uses Monte Carlo methods suh as MCNP to simulate the satter effet. In ase of neutron imaging MCNP takes a huge time to run. For example, in the geometry of this present study, it takes almost 10 hours to simulate a single radiograph using 5 million partile histories. Moreover, the same geometry needs to be simulated twie, one with satter, and one without satter. This makes the satter orretion algorithm not viable for pratial purposes.

13 CHARACTERISTICS OF NEUTRONS As a fundamental partile, neutron has the ability to provide a stream of unique harateristis whih are proved to be essential in the imaging ommunity. In this setion, those attributes of neutrons are disussed. These properties of neutrons interating with matter give underlying ideas of neutron imaging. As one of the main omponents of an atom, neutron was disovered in 1932 by J. Chadwik [7]. Neutron is eletrially neutral, whih makes it an attrative both in sattering and imaging appliations. It interats primarily with nulei beause of its harge neutrality; it is highly penetrating and is suitable enough to penetrate materials with higher atomi mass. These properties make neutrons suitable for imaging light materials, or investigating the inside of a large assembly in a nondestrutive way. Another important fundamental property of neutron is its mass, (m n = Kg), whih gives the neutron a de Broglie wavelength ompared to the atomi distanes in room temperatures (thermal energy range). The de Broglie wavelength, λ in units of nm, is given by λ = h m n v = 395.6/v (1) Where, h = J s is the Plank s onstant and v is the neutron veloity in ms 1.The neutron energy is given by: E = 1 m 2 nv 2 = v 2 (2) A neutron in thermal energy (room temperature 300K) will have a veloity of approximately 2224 ms 1 and orresponding wavelength of 0.18nm. Neutrons are typially produed either in reators via the nulear fission or in spallation neutron soures (where a high energy proton beam is inident on a heavy metal and produes neutrons).

14 4 These neutrons are in fast energy range (see Table 1.1). Thermal neutrons are more suitable for imaging purpose beause they are easier to be deteted than fast neutrons. The neutrons need to be slowed or ooled down. Moderators are used to onvert fast neutrons to thermal or old energy range. Generally hydrogen or hydrogenous materials, graphite, et., are used for moderation. Table 1.1. Neutron properties at various energy ranges. Energy Energy Veloity Wavelength(nm) lassifiation range (mev) (ms 1 ) Ultra-Cold Cold Thermal Epithermal , INTERACTIONS WITH MATTER AND CROSS SECTION In thermal neutron imaging the priniple lies in neutron interation that attenuates a ray or beam of neutrons oming from a soure. Neutrons an be removed from the inident beam by the objet by two phenomena, absorption and sattering. Figure illustrates the attenuation of neutron beam inident perpendiularly on a thin sample of

15 5 thikness dx whih is plaed at a distane x from the soure. The thikness is small enough so that it is only one atom layer thik and the neutrons an interat with all the atoms involved. Figure Neutron interation with matter. Let I(x) be the inident neutron flux, and I(x + dx) be the transmitted flux. Let N be the number density of atoms in that layer. It is assumed that the atoms are partiles of radius r. The neutron attenuation is given by the frational area oupied by all the atoms in that layer, whih is equal to dx. Nπr 2. This gives: I(x + dx) = I(x)(1 dx. Nπr 2 ) = I(x)(1 dxnσ) (3)

16 6 Where, σ is defined as the mirosopi ross setion. Mirosopi ross setion is defined as the effetive interation area between the neutron and the nuleus. From Eq.3 the rate of hange of I(x) is given by: di(x) dx = NσI(x) (4) And the solution for I(x) is given as below: I(x) = I 0 exp ( Nσx) (5) Where, I 0 is the inident neutron flux. The produt Nσ is known as the marosopi ross setion. For an objet with more than one material, the marosopi ross setion is the sum over all the marosopi ross setions. The neutron-nuleus interation is of quantum mehanial in nature. Neutron interats with an objet either via absorption or sattering. The total mirosopi ross setion is given by σ t = σ a + σ s (6) Where, σ a and σ s are absorption and sattering ross setion respetively. The neutron sattering ross setion an be further divided into oherent and inoherent sattering. In oherent sattering, neutrons that are sattered primarily by different nulei ombine with one another to produe an interferene pattern that depends on the relative loations of the atoms in the material. Inoherent sattering is the ase when there are more than one isotope present in one sample. Neutrons interat with matter in five different ways. (1) Elasti sattering Neutron ollides with the nuleus and loses its kineti energy. Neutron loses more energy to heavier materials than to lighter materials. Elasti sattering is the most important phenomena to produe thermal or old neutron from fast neutron soures.

17 7 (2) Inelasti sattering Inelasti sattering is similar to elasti sattering but here when the neutron ollides with the atomi nuleus it deposits part of its energy to the nuleus and takes it to an exited state. After ollision, the nuleus emits gamma ray(s) to get bak to the ground state. This type of sattering is not preferred in neutron radiography as it auses gamma emission whih is onsidered as noise. (3) Neutron apture A neutron an be absorbed by the atomi nuleus to inrease its atomi number by one. The new nuleus most likely beomes a radioative nuleus and emits radiation. (4) Charged partile emission This phenomena is generally ourred by fast neutrons, where harged partiles are emitted upon the inidene of neutrons. (5) Fission Fission ours when upon inidene of a neutron, the nuleus divides into two nulei and emit more than one neutrons in proess. In this present work, thermal neutrons are used as the soure. Only the sattering and absorption phenomena is dominant in thermal neutron imaging. Elasti sattering is redominant in thermal neutron energy. The orresponding thermal neutron ross setion of different materials (ranging from atomi number 1-100) is shown in Figure.1.2. From Figure.1.2., it is lear that the sattering ross setion and the absorption ross setion does not have any linear relationship with the atomi number of the materials, and the sattering ross setion is very high in ase of lower atomi number materials suh as hydrogen. Monohromati energy soure of energy eV has been used as a soure.

18 8 This is the most probable energy of a thermal neutron energy distribution. In this work, monohromati energy soure is used to ignore the effets of beam hardening. Thermal neutron energy distribution is a Watt distribution. The veloity distribution funtion of thermal neutron energy range is given by the following equation: Φ(v)dv = Φ 2 v4 v 3 exp ( ( v2 T v T 2)) (7) Figure.1.2. Thermal neutron sattering and absorption ross setion distribution.

19 9 Where, Φ(v)is the neutron veloity flux distribution, v is the neutron veloity and v T is the neutron veloity at temperature equal to 293.6K ( 2200m/s). In this experiment, materials suh as hydrogen, nitrogen, oxygen, alium, iron, lead, et., are used. The mirosopi thermal neutron total and absorption ross setions are obtained from the neutron ross setion library ENDF-B/VII.1 [23].There is no thermal neutron sattering ross setion table available. For the imaging of above materials, the ross setions suh as harged partile emission, fission are negligible and almost equal to zero PREVIOUS STUDIES ON NEUTRON IMAGING AND ITS SIMULATION The idea of imaging is to reate a ontrast between different elements based on their inherent and unique properties like mass attenuation oeffiients, ondutivity, and mirosopi ross setions. Neutron radiography uses the mirosopi ross setion property of materials to generate the radiograph. The main soures of image degradation in neutron radiography are sattering degradation, geometri degradation, displaement degradation, neutron spetral degradation and detetor degradation. In neutron radiography the main mathematial equation an be expressed as I = e Σ t (E).x (8) I 0 Where, Σ t (E) is the total ross setion of the material to be imaged. I and I 0 are the neutron intensity after and before inidene. The thikness of the material is defined as x. It is to be noted that the total material ross setion is energy dependent. The sattering effet an be denoted by I s. The main fous of this is to remove the sattering effet from the image. Sattering effet onsists of neutrons sattering. The term point

20 10 sattered funtion has been introdued here. Equation 1 an be modified after eliminating the effets of sattered neutrons. The new equation an be represented as I I s = E0 0 φ(e)e Σt(E).x de I E0 0 0 φ(e)de (9) φ is the neutron flux.the key fous of this work is to simulate the sattered neutrons using MCNP5 and find the probability distribution funtion (pdf) of these sattered neutrons using effiient analytial methods and subtrat the pdf from the distribution of neutrons obtained from the original radiograph. The two key terms that has been disussed here are Point Spread funtion (PSF) and Point Sattered funtion (PsF). The point spread funtion is an image the system produes of a point like objet. The PSF is the image plane response at an arbitrary point at the image axes when the flux oming from a point neutron soure passes through an infinitesimally small hole of an neutron absorbing material. Ideally the PSFs are δ-funtions.[25] Another key term is the point sattered funtion (PSF) whih has been disussed many times in this paper. It is defined as the density distribution of sattered neutrons on the detetors from a point soure from whih the neutrons inident on the target material diretly. The PSF is dependent on the material thikness(x), distane from soure to detetors (d) and the aperture angle of the soure beam. So it an be said that the PSF is an integrated version of all the PSF at the image plane of the radiograph. When the Point Sattered Funtion is obtained it an be subtrated from the neutron distribution to remove the sattering degradation. There has been a lot of work in the area of neutron radiography using MCNP. Early important work was from Segal et al[8] when

21 11 they published their work regarding the alulation of point spread funtion of thermal neutron radiograph. The ontribution of sattered neutron in the of the radiographed objet was alulated using MCNP. But this work was insuffiient as they failed to provide aurate distribution of dimensions and thikness. Murata et al [9] developed a method to to eliminate the effets of sattered neutrons from NR (Neutron radiography) by using a Cd grid. Raine et al [10] developed a orretion algorithm using MCNP whih determines the sattering ontribution. But this work was limited only to high resolution with objets less than 2 entimeters in vertial or horizontal diretions. Kardjilov et al (2005) [11] derived a proedure where they simulated the point sattered funtion for different position and thikness and property of target materials. Then they formulated a Gaussian funtion whih fits the sattered neutron distribution of the target material at different distanes from the soure and different thikness of the material. One the distribution of sattered neutrons was obtained in mathematial terms it was subtrated from the original radiograph to obtain satter free image. The advantage of this work was one the distribution of sattered neutrons were obtained in terms of Gaussian distribution it eliminated the use of MCNP simulation eah time a radiograph needs to be generated. Montaser Tharwat et al [6] devised a methodology using MCNP and MATLAB together for radiograph generation. The sattered neutron distribution was omputed using MCNP and flux distribution of eah pixel was determined individually whih orresponds to the sattered neutrons and then a software tool named ImageJ from MATLAB was used to effiiently subtrat this effet. LIU Shu-Quan et al [12] designed a method for sattering orretion for fast neutrons at the NECTAR (Neutron Computerized Tomography And Radiography) faility at Germany. They alulated the

22 12 sattered fast neutron distribution at different distane and thikness using MCNP and subtrated it from original image to obtain satter free image. The sattering distribution simulation took 10 hours with 64 CPUs parallel omputing to obtain a PSF data with simulating 10^8 neutrons and with error less than 5%. The improvements that an be done from the previous works are first to find a method to run a huge number of partile history within a small amount of time. Generation of sattered neutron distribution using MCNP and subtration is a time onsuming proedure. If it needs to be implemented ommerially a faster simulation method needs to be developed. The variane redution methods in MCNP an be used to run the simulation very fast. The subtration algorithm needs to be improved in suh a way so that not only sattered neutron effets are eliminated other imaging irregularities should also be removed. An optimization between image quality and run time or partile history has to be analyzed so that a ertain quality of image an be obtained with minimal ost. When the image of an objet is generated a spetrum of neutron energy is used. It an be analyzed whih spetrum or range of energy gives the best resolution or image quality. It is also dependent on the thikness of the material and distane from the soure and its material properties (ross setion). So if some work is done as to whih range provides minimum error it will more effetive THERMAL NEUTRON RADIOGRAPHY AND TOMOGRAPHY Thermal neutron radiography and tomography is a powerful tool of non-destrutive imaging tehniques. The images are formed due to attenuation of thermal neutron beam when it is propagated through the material to be visualized. Neutron radiography are in used sine shortly after the disovery of neutrons by Chadwik in 1932[7]. Different

23 13 radioisotopes soures was used for neutron radiography [13]. Later aelerators and nulear reators were used as neutron soure. Different types of position-sensitive detetors are implemented. Even with advaned instrumentation for radiography it laked in one broad area whih was all the information of a three dimensional objet was restrited to two dimensional image. It was hard to distinguish between two materials with similar attenuation property. The issue was solved by the pioneer work of Hounsfield [14], who implemented omputed tomography based on the early mathematial foundation provided by Radon in 1917[15] Priniples of Neutron Radiography. Radiography implements twodimensional detetion of transmitted neutron beam in a plane perpendiular to the diretion of beam propagation (Figure.1.3). This reates a two-dimensional shadow of the objet. The shadow or radiograph properties vary based on the thikness and integral attenuation properties of the material being imaged. The transmission T, is the ratio of the transmitted beam intensity I, and inident beam intensity I 0. radiation T = I I 0 (10) For any path along the transmission, aording to the basi law of attenuation of I = I 0 exp ( μds ) (11) Where, μ is the loal linear attenuation oeffiient, and s is the propagation path. The attenuation o-effiient is a material property and is given by μ = σρn A /M or μ = i σ i ρ i N A /M i (12)

24 14 For single elements and for multiple elements respetively, where σ is the total interation ross setion, ρ is the density of the material, N A is the Avogadro s number, and M is the molar mass. Neutrons passing through the objet an interat with it in three ways: (1) absorption by the material, (2) sattering (oherent and inoherent) and (3) pass through the material without interation (un-ollided neutrons). In ase of absorption the neutrons get lost or attenuated. In ase of sattering, they slow down or hange diretions. Unollided neutrons are the neutrons that reah the detetor. Sattered neutrons also an reah the detetor from a different diretion and degrade image quality and reate blur. In the present work, a method has been reated to minimize the effet of sattering. Figure Shemati of a standard neutron radiography system.

25 Priniples of Neutron Tomography. Computerized tomography is a tehnique whih an reonstrut the three dimensional image of the objet from different radiographi images taken from different angles in small suessive manner. These images an be mathematially manipulated to reonstrut a three dimensional image.one of the fastest and popular method of reonstrution is the filtered bak projetion algorithm (FBP)[16]. In this work FBP algorithm has been used to reonstrut neutron images. All projetions are first arranged into a new set of images suh that the n th pixel row of eah projetion is now stored sequentially in an individual image, also known as a sinogram. Every sinogram ontains all the attenuation information for all possible angles. An implementation of inverse two dimensional Radon transform is then applied to alulate a ross setional slie from eah sinogram. Eah reonstruted slie lies in a plane perpendiular to the axis of rotation. Colleting all slies into an image stak represents the three-dimensional attenuation distribution of the objet. The image stak an be used to emphasis ertain speifi volume based on requirements. The geometry of the imaging set up is influened by the sample size and the pixel width (smallest possible sanning length or spatial resolution). The flux and the wavelength spread are diretly related, the smaller the wavelength spread, the smaller the flux. This is also true for the spatial resolution; the smaller the pixel size (higher spatial resolution), the smaller the integrated flux at the pixel. Therefore, for attenuation based neutron imaging, full spetrum is used to get statistially signifiant results. For monohromati imaging, generally (1-5%) Δλ/λ is required to distinguish between materials. Sattering phenomena auses unwanted image artifats in ase of neutron radiography. They derease the sharpness of the image. The disadvantage of neutron imaging over X-ray imaging is that

26 16 X-ray sattering ross setion is regular and is related to the atomi number of the material being imaged, whereas neutron sattering ross setions are atomi number independent and statistial in nature. While that partiular property makes neutron imaging suitable for loating light materials under heavy materials, it makes the elimination of satter artifats hallenging. For neutron radiography and tomography, ollimators or slits are used to diret the radiation towards the objet and get a point to point image. In order to obtain neutron image in a ertain exposure time minimum number of neutron flux should be available. The exposure period is dependent on the problem and an vary from few seond to several minutes. The exposure time and the neutron flux should be optimized together NEUTRON SOURCES AND FACILITIES There are three main soures of neutrons; nulear reators, spallation neutron soures, and radioative soures emitting neutrons. It might seem that it is not relevant where the neutrons are oming from, but neutron soure spetrum has a massive impat on the imaging modality. The energy distribution of neutron soure and bakground noise of the soure (fast neutrons, gamma rays, delayed neutrons) an alter the quality of the image in a substantial way. They an also interat with the detetor eletronis. Therefore it is very important to hoose whih type of soure to be used based on the requirement of the experiment. Nulear reators use fission to produe neutrons. Spallation neutron soures produe neutrons by hitting a target material with high energy protons. Both nulear reator and spallation soure produe neutrons with the energy range of few mega eletron volts.

27 17 However, in neutron imaging generally thermal or old neutrons are used. A moderator must be used in order to slow down these fast neutrons. Neutrons an be produed from the radioative soures, for example, Cf-252 isotope produe neutrons.

28 18 2. DETERMINISTIC SIMULATION METHOD Neutron radiography is a useful tool for non-destrutive imaging. There are several failities aross the world to ondut neutron imaging [18]. It is required to simulate the neutron images (radiographs) before atually doing the experiment to analyze the effetiveness of the imaging faility. Monte Carlo methods of simulation have been proven to be the most effetive effetive way to simulate the performane of a neutron imaging faility till date. However, Monte Carlo methods suh as MCNP take a onsiderable amount of time to simulate a single radiograph. To form an image several radiographs are needed, therefore this method of simulation is proved to be extremely time onsuming. It is true that with modern day parallel omputation power, the image an be proessed using multi-ore omputers [19]. This makes the omputation proedure very ostly. To make neutron imaging ommerially effetive, a faster and heaper method needed to be developed. The other disadvantage of using stohasti methods to simulate images is that the unertainty of the omputation depends on the number of partiles simulated. MCNP works on the basis of averaging a large number of partile histories over time. In nulear imaging one priniple onern is to redue the dosage on the sample. Therefore, the less number of inident partiles the less is the dose. Monte Carlo methods do not provide statistially signifiant results when there is less number of partile histories. In this present work, a deterministi method has been developed whih solves both time and resoure onsumption problem. It is also effetive way of simulating when there is less number of partiles to be involved. This deterministi method is based ray traing algorithm provided by the pioneer work of L. Siddon in 1985 [20]. This method assumes

29 19 neutrons as rays. One the neutron ray passes through the subjet and inident on the detetor plane, this algorithm effetively traks bak (traes) eah neutron ray whih effetively and omputes the path travelled within the sample to measure the attenuation. This work has been modified over the years by Freud et al, Zhao et al and Li at al [21-23]. This algorithm has a large appliation in the field of X-ray omputed tomography. In this work the same priniple has been applied to attenuation based neutron imaging. This deterministi approah onsists of basi neutron attenuation law and ray-traing tehniques. A set of neutron rays are emitted towards the enter of every pixel at the detetor plane. Eah ray passes through the objet to be imaged. The objet is divided into multiple voxels. Eah ray passes through one voxel. The attenuation is alulated by measuring the length of the path eah neutron ray overs within the objet by determining the o-ordinates of the intersetion points. The number of neutrons I(E), that emerge from the objet and reahes the detetor pixel is given by I(E) = I 0 ΔΩexp ( i μ i d i ) (12) Where, ΔΩ is the solid angle through whih neutron propagates, μ i isneutron attenuation o-effiient of the i th voxel and d i is the distane overed by the ray oming passing through the i th voxel. Based on the theory of neutron radiography, the attenuation of eah ray is dependent on the path traversed by eah ray inside the objet. This objet is most likely to be heterogenous. That means the neutron ray will traverse different path length within different materials. Identifying the path lengths travelled by eah neutron ray within different material is very hallenging. The entry and exit points of eah neutron ray is alulated by measuring the dot produt of diretion vetor of the ray line and the normal direted away from the objet. Ray traing determines all the intersetions of a line or ray

30 20 from the soure to the region of interest. From these intersetions, the ray depth (d i ) an be alulated. The attenuation is given by exp( μ i d i ),where μ i denotes the neutron attenuation o-effiient at the i th voxel. In three dimensional Cartesian o-ordinate system, the ray is defined parametrially as a straight line onneting from point A to B. X = X A + α(x B X A ) Y = Y A + α(y B Y A ) Z = Z A + α(z B Z A ) The value of the parameter α is zero at point A and unity at point B. The plane urve is defined by the X-Z polygon. There are two onditions that the parameter α must satisfy to fulfil the ray-box intersetion algorithm. The first ondition is that Y o-ordinate of an intersetion must lie on or within the Y extent of the objet. The seond ondition is that all intersetion points must lie between point A and B. 0 α PHYSICS MODEL The physis model ray-traing algorithm is given by the following equation: I (β) = I 0 (β) exp( i μ i ρ i d i ) + I s (β) + I n (β) (13) Where, I(β) is the number of neutrons (or the neutron instensity) deteted at the detetor with soure fan angle β, and I 0 (β) is the soure intensity. β denotes the angular position of a ray in the neutron beam. μ i, ρ i, and d i are respetively the mass attenuation oeffiient, density, and path length of the ray whih travels through the i th material. The sum extends over all the materials through whih the neutron beam (ray) passes on the way to a

31 21 partiular detetor pixel. I s (β) and I n (β) are the ontributions to the deteted neutron intensity from sattered neutrons and noise. Ray traing algorithm only takes are of the unollided neutron but in this work we have modified it so that it takes into aount the effets of sattered neutrons and noise. The modified algorithm works in the following way: 1. Ray asting from the soure to a partiular pixel of the detetor system. 2. Traing the primary ray as it penetrates the objet volume and alulating its attenuation. 3. Computing the sattered ray ontribution with appropriate physis model and ross setion. 4. Compute the statistial noise and satter ontribution with suitable physis models. 5. Aumulating the neutron intensity reorder by eah detetor pixel. Steps 1-5 simulate neutron radiographi imaging. To simulate neutron tomography, the objet volume is rotated to the next view angle and steps 1-5 are repeated. For most ommon materials in NDT, the types of thermal neutron interation are absorption, elasti sattering, and inelasti sattering. Mirosopi ross setion data for these interations for different materials an be found in data libraries, suh as ENDF/B- VII.1 [24]. In this work, a neutron mass attenuation oeffiient data library was reated for elements from hydrogen to zin using the following equation: μ = N A M (σ a + σ s + σ in ) (14) Where, μ is the total mass attenuation oeffiient, N A is the Avogadro s number. M is the atomi mass. σ a, σ s, and σ in are the absorption, elasti sattering, and inelasti

32 22 sattering mirosopi ross setions, respetively. The alulation of the ontributions of sattering and noise to the deteted neutron intensity are desribed in the following setions NOISE MODEL As with X-ray imaging, neutron imaging also suffers from inherent statistial noise. This noise is random and is generated due to effets like Poisson statistis on the deteted number of neutrons, flutuation of energy that eah neutron deposits in the detetor, and eletroni readout noise, et [25]. In this work, the neutron noise is modeled using a Poisson noise approximation. The neutron noise is estimated using a Poisson distribution, as shown in the following equation, Pr(N = k) = exp( λt) (λt) k /k! (15) Where, N is the number of neutrons measured by a given detetor element over a time interval t, and λ is the expeted number of neutrons per unit time interval. The unertainty desribed by this distribution is known as statistial noise. Beause the inident neutron ount follows Poisson distribution, it has the property that its variane is equal to its expetation as shown below: E(N) = Var(N) = λt (16) In the ase of neutron imaging, the neutron noise is modeled as the Poisson noise σ (i.e., square root of the mean number of neutrons deteted. Mathematially, it is expressed by the following equation: σ(β) = I 0 (β) exp( i μ i ρ i d i ) (17)

33 SCATTER MODEL To simulate the ontribution of sattered neutron to the deteted density Kardijlov et al [26], Hassanein et al.[27], and later Hai-Feng and Bin[28] have defined a point satter funtion by reating an image formed by a point soure and a homogenous phantom using MCNP5. A satter distribution funtion was developed whih is dependent on the geometry of the phantom, and the fan beam angle of the soure. The simulated data are proessed with MATLAB [29] to form an analyti representation of the satter distribution. The point satter funtion depends on the size and shape of the objet being imaged, as well as the distane between the objet and the soure. The main disadvantage of this method is that it is not a generalized method and needs a Monte Carlo simulation to be arried out to generate the satter data. In the present work, we have developed an approximate model of neutron satter, whih depends only on the inident intensity and the neutron intensity distribution over the detetor. The foundation of this algorithm lies in the work of T.N.Hangartner[30], who formulated a forward satter funtion for X-ray imaging, with later improvement of the work by Ohnesorge et al.[31]. The interations between neutrons and matter reate sattered rays in all possible diretions.these rays, whih an be either attenuated or sattered, reate further asaded satter events. In neutron and X-ray imaging, first order sattering (where only one satter interation was inluded) aounted for the most severe image artifats, sine the first-order satter ontained the high frequeny omponent of the satter profile. This was due to the fat that non-uniformity of the objet had a muh stronger influene on the spatial distribution of the single satter events than on the multiple satter. For single satter events, forward-sattered neutrons were most likely to penetrate

34 24 the objet and reah the detetor, due to a relatively shorter path length,as ompared to the neutrons sattered in other diretions. Multiple sattering in thermal neutron imaging is approximately a diffusion proess, and results in a low frequeny bakground.to aount for both first-order and multiple sattering in neutron imaging simulation, the following assumptions are made: 1. The first-order sattering an be simulated by the forward sattering approximation desribed by the pioneering work of Hangartner and Ohnesorge et al.(1999). 2. Multiple sattering an be simulated using a onvolution proess, and the onvolution kernel is a Gaussian funtion (i.e., a point spread funtion). A shemati plot of the satter model is shown in Figure. 3.1.The forward satter intensity, I s,f (β), oming from interations between soure neutrons (with fan angle β) and materials along the ray path, forms a point spread funtion at the detetor. The total satter distribution in a projetion, I s (β), results from superposition of satter distributions from all soure fan angles. Mathematially, it an be desribed as a onvolution proess, as shown in the following equation, I s (β) = I s,f (β )G(β β ) = I s,f (β) G(β) (18) Where, G(β) is a Gaussian funtion, and represents the onvolution operation.the forward-satter an be approximately expressed by the following equation using MATLAB urve fitting tool[27]. I s,f (β) = K s,f I(β)ln ( I 0(β) I(β) ) (19)

35 25 Where, K s,f is a onstant whih is proportional to the satter ross setion of the materials along the ray path. In the present work, those onstant are determined by benhmarking the satter model against a MCNP5 simulation.

36 26 3. SIMULATION SETUP The Monte Carlo simulation is onsidered to be one of the most aurate methods for simulating neutron transport due to its high fidelity physis model and its apability of handling ompliated geometries. Parameters in the forward-sattering model and the Gaussian multiple sattering funtion are derived from Monte Carlo simulations performed using MCNP5(Figure.3.1) As shown in Figure.3.2a, a water ylinder that is 5m high with a diameter of 5 m is modeled as a uniform phantom. This uniform phantom an also be used for different ases by replaing water with a different type of material. An isotropi thermal neutron soure with monoenergeti nergy of ev and strength of 1x10 11 neutrons/se has been assumed so that the effet of inaurate resonane ross setions an be ignored. Gadolinium is used to ollimate the isotropi soure.a neutron flux tally (FIR 5, Appendix A) has been used, whih measures the normalized flux disrtribution in eah detetor pixel. The data are simulated separately for both unollided and total (unollided plus sattered) neutron ontributions. The physis ard NOTRN has been used to find only the unollided neutron distribution in the detetor grid. The detetor grid has a dimension of 10m 10m.There are pixels in the detetor grid with pixel size equal to1mm 1mm. The distane between the enter of the phantom to the soure is 10 m and the distane between the middle point of the detetor grid to the enter of the phantom is 5 m. The sattered neutron distribution is obtained by subtrating unollided neutrons from the total neutron ontribution.as desribed in the next setion, the satter (inluding single and multiple satter) effet (I s (β)) is modeled as a onvolution proess of forward satter ( I s,f (β)) with a Gaussian funtion G(β).

37 27 Figure.3.1. Shemati plot of the satter model. Left: Forward-satter and point spread funtion. Right: Convoluted overall satter intensity profile. The Gaussian funtion is estimated by omparing the results of the deterministi simulation and the MCNP5 simulation. To expand the satter model to a more general ase with heterogenous materials, the same deterministi methodology was used. Two simulation geometries were used. For the first one(referred to as geometry 1), a water ylinder (with the same dimensions as the previous homogenous water ylinder) was used with four smaller ylinders (1m diameter eah) filled with different materials inserts, inluding iron, lead, alium, and air as shown in Figure.3.2b.As water is a highly sattering medium for thermal neutrons, the proposed simulation represented a very diffiult problem for thermal neutron imaging. For the seond simulation geometry (referred to as geometry 2 and shown in Figure.3.2 ), an iron ylinder, with the same dimensions (height=5m,diameter=5m) was used; it was filled with four smaller ylinder of the same height and diameter(1m eah).the materials for these smaller ylinders were air,water,alium,and lead respetively. Geometry 2 represented a thermal neutron

38 28 imaging ase with a smaller sattering effet where iron (instead of water) was the main type of material in the phantom. The MCNP5 simulation was run for five million partile histories to obtain the unollided and total neutron ontributions, whih resulted in less than 10% statistial unertainties in the region of the phantom for all ases. Then, the satter distribution was obtained by subtrating the unollided neutrons from the sattered plus the unollided neutron distribution. In the deterministi simulation, to aount for the material non-uniformity, a modified satter model was used: I s,f (β) = K s,f I(β) p ln ( I 0(β) I(β) )q (20) Where, p and q are empirial onstants.tomographi simulation was performed using the deterministi method only, due to the exessively long omputation time that would have been required using MCNP5.To obtain the tomographi reonstruted images, a series of 500 neutron radiography was simulated at different viewing angles with an angular inrement of using the deterministi method for both geometry 1 and geometry 2. The rotation period for geometry 1 and for geometry 2 are different due to the differene in neutron attenuation of these two geometries. The rotation time is 500 s per rotation for geometry 1 (due to high attenuation aused by water) and for geometry 2 it is 50 s per rotation. Three different ases were onsidered with the simulation: (1) Simulation under ideal onditions(i.e. noiseless and no satter ontamination (2) Poisson noise was added (3) Both noise and satter were added into the simulation. Then the filtered bak projetion algorithm was used to reonstrut the tomographi images [32].

39 Figure.3.2. Simulation setup for different geometries. (a) A homogenous water phantom was irradiated by a ollimated thermal neutron soure. (b) Simulation geometry 1. () Simulation geometry 2. 29

40 30 4. RESULTS First, the ideal 2D radiography images of the heterogenous phantoms(geometry 1 and 2) were simulated by both the Monte Carlo and the deterministi method; these inluded only the flux ontributions of unollided neutrons.the Monte Carlo simulations by MCNP5, using FIR5 tally are shown in Figure. 4.2a and Figure.4.3a. The deterministi simulations of the radiography at the same viewing angle are shown in Figure. 4.2b and Figure. 4.3b. The small ylinder inserts are learly seen in all of the images. To quantitatively ompare the Monte Carlo and deterministi simulations, a line profile omparisons are shown in Figure.4.2 and Figure.4.3. The omputation time for the deterministi simulation was signifiantly less than that for the Monte Carlo simulation. Figure Plot of statistial unertainty of the MCNP simulations. The Colorbar represents the absolute value of the unertainty.(a) Homogenous water ylinder. (b) Geometry 1. () Geometry 2.

41 31 Figure.4.2. Simulated neutron radiography of geometry 1 under ideal onditions (i.e., noiseless and without satter ontamination) simulated by (a) Monte Carlo method. (b) Deterministi method. () Line profile omparison. The next simulation shows the effet of the noise inserted into the simulated radiography images. As shown in Figure.4.4a, the ideal image is noiseless and without any satter ontamination. With the added Poisson noise, the deterministi simulated neutron radiography is shown in Figure.4.4b. The line profile omparison is shown in Figure.4.4. To deterministially simulate the satter effet, a Gaussian funtion was first estimated (shown in Figure.4.5). Using Eqs.18 and 20, the sattered intensity ontributed to eah pixel was alulated. In Eq.20, the parameters p and q were determined to be 0.18 and 1.0 respetively after many trials and errors respetively.. This pair of values worked out well

42 32 with different geometries. The value of K s,f was strongly dependent on the major types of material in the simulated geometries. Figure.4.3. Simulated neutron radiography of geometry 2 under ideal onditions (i.e., noiseless and without satter ontamination) simulated by (a) Monte Carlo method. (b) Deterministi method. () Line profile omparison. For geometry 1, K s,f was strongly determined to be equal to 0.3, where water was the main type of material. The value of K s,f was redued to 0.03 for geometry 2, where iron was the main type of material. The deterministi simulations with added satter were ompared to the Monte Carlo simulations. The results are shown in Figures. 4.6 and 4.7.

43 33 The neutron radiography, with added satter simulated by MCNP5 are show in Figures.4.6b and 4.7b. Beause water is a material with a high elasti sattering ross setion, the sattered neutron ontribution was signifiant. The line profile omparison is shown in Figures.4.6 and 4.7. Figure.4.4. Neutron radiography of geometry 1. (a) Under ideal onditions (noiseless and without satter ontamination). (b) With added Poisson noise and without satter ontamination simulated by the deterministi method. () The line profile omparison.

44 34 Figure.4.5. The Gaussian funtion used in the satter approximation. Figure.4.6. Neutron radiography of geometry 1. (a) With Satter simulated by MCNP5. (b) With satter simulated by the deterministi method. () Line profile omparison.

45 35 Figure.4.7. Neutron radiography of geometry 2. (a) With satter simulated by MCNP5. (b) With satter simulated by the deterministi method. () Line profile omparison. As a omparison, the line profile of the Monte Carlo simulation without satter is also plotted. Finally, the deterministi simulations of the neutron tomographi reonstrution are shown in Figures and 4.9. First, a tomographi image of geometry 1 and 2 under ideal imaging onditions (i.e. noiseless and without satter ontamination) are shown in Figures. 4.8a and 4.9a. The tomographi images (shown is Figures.4.8b and 4.9b) were reonstruted from neutron images with added Poisson noise. In Figures.4.8 and 4.9, the tomographi images were reonstruted from neutron images with both added Poisson noise and satter.

46 36 Figure.4.8. Tomographi image of geometry 1. (a) Under ideal onditions. (a) With added Poisson noise. () With added noise and satter. Figure Tomographi image of geometry 2. (a) Under ideal onditions. (b) With added Poisson noise. () With added noise and satter.