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Far field 3D localization of radioactive hot spots using a coded aperture camera
Applied Radiation and Isotopes 107 (2016) 177–182
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Far field 3D localization of radioactive hot spots using a coded aperture camera Sun Shifeng a,b,c, Zhang Zhiming a,b, Shuai Lei a,b, Li Daowu a,b, Wang Yingjie a,b, Liu Yantao a,b, Huang Xianchao a,b, Tang Haohui a,b, Li Ting a,b, Chai Pei a,b, Zhang Yiwen a,b, Zhou Wei a,b,c, Yang Mingjie a,b,c, Wei Cunfeng a,b, Ma Chuangxin a,b, Wei Long a,b,n a
Division of Nuclear Technology and Applications, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Beijing Engineering Research Center of Radiographic Techniques and Equipment, Beijing 100049, China c University of Chinese Academy of Sciences, Beijing 100049, China b
H I G H L I G H T S
A method is presented to remotely estimate source activity. The method allows determination of source location from a single projection. A tungsten–copper alloy coded aperture mask is used to modulate the incoming gamma-rays. The method was successfully tested for point and line sources.
art ic l e i nf o
a b s t r a c t
Article history: Received 20 July 2015 Received in revised form 19 October 2015 Accepted 19 October 2015 Available online 20 October 2015
This paper presents a coded aperture method to remotely estimate the radioactivity of a source. The activity is estimated from the detected counts and the estimated source location, which is extracted by factoring the effect of aperture magnification. A 6 mm thick tungsten–copper alloy coded aperture mask is used to modulate the incoming gamma-rays. The location of point and line sources in all three dimensions was estimated with an accuracy of less than 10% when the source-camera distance was about 4 m. The estimated activities were 17.6% smaller and 50.4% larger than the actual activities for the point and line sources, respectively. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Source localization Source activity determination Coded aperture Far-filed measurements Gamma camera Modified Uniformly Redundant Array (MURA)
1. Introduction Gamma cameras are widely used in nuclear facilities to locate radiation sources within a given field of view, to help with decontamination, maintenance, repair or decommissioning (Woodring et al., 1999; Santo et al., 2006; Gamage et al., 2012; Sun et al., 2015). Measurements are always performed many meters away from the hot spots, to lower personal exposure. With the current commercially available coded aperture gamma camera (Woodring et al., 2003; Gal et al., 2006; Gmar et al., 2011; Lemaire n Corresponding author at: Division of Nuclear Technology and Applications, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China. Fax: þ86 10 88236413. E-mail addresses: [email protected] (S. Shifeng), [email protected] (W. Long).
http://dx.doi.org/10.1016/j.apradiso.2015.10.021 0969-8043/& 2015 Elsevier Ltd. All rights reserved.
et al., 2014), multiple sources can be located and identified quickly. However, the decoded gamma image of conventional imaging systems has only two dimensions projecting the radioactivity on the imaging plane of a camera, i.e., it does not measure the sourcecamera distance. Knowing this distance along with the measured radiation intensity can be used to determine the source activity. In nearby conditions, such as those encountered in medical applications, image reconstruction methods for three-dimensional (3D) distribution of radioactive isotopes are used (Ito and Fujimura, 1996; Berrim et al., 1996; Hong et al., 2006; Mu and Liu, 2006; Mu et al., 2009). However, these reconstruction methods require multiple projections acquired at different angles or positions. In industrial applications, it is impractical to acquire such multiple projections. Therefore, Raffo-Caiado et al. (2010) investigated the use of a 3D laser imaging system, combined with a
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coded aperture camera, for accountancy of nuclear materials in enrichment plants. The system was able to predict the location and geometry of gram quantities of uranium with good accuracy, at a standoff distance of about 4 m (Boehnen et al., 2011). However, such scheme is only suited for surface sources, and is not usable for sources shielded from the laser beam, such those located inside pipes or containers. In this paper, a method for determining the source-camera distance without the aid of 3D laser scanners is introduced. The method uses aperture magnification to determine the sourcecamera distance. Once the source-camera distance is determined, the source’s activity can be determined. The paper begins by a review of the coded aperture approach and its use to determine the source-camera distance. The approach is then applied to determine the location and activity of the line and point sources.
2. Determination of source-camera distance A coded aperture imaging system consists of a mask and a detector. The mask has holes distributed in a predictable pattern within a sheet made of material opaque to radiation. Sources within the field-of-view project a shadow of the aperture on to the detector. A coded aperture imaging system can be modeled by convolution (Fenimore and Cannon, 1978). When imaging objects at a finite distance, the mask pattern will be magnified at the detector plane. Let O(x,y;z) be a planar object located at distance z from the aperture plane, and D(x,y) be the coded image on the detector plane. Then, the coded aperture image modulated by aperture A(x,y) can be expressed as (Caroli et al., 1987)
D(x, y) = O(x, y ; z ) ⊗ A(x, y)
(1)
where ⊗ indicates convolution. To reconstruct the planar object O (x,y;z0) at distance z0, the coded pattern DZ0(x,y), taken from the coded image, must consider a magnification factor M(z0) ¼(z0 þf)/ z0. Here z0 is the distance between the object source and the aperture plane, and f is the distance between the aperture and detector plane. The image can be directly reconstructed by correlating the coded pattern with a decoding array G(x,y), which has a property such that A(x,y)⊗G(x,y) is a delta, δ, function. Then,
Dz 0 (x, y) ⊗ G(x, y) = O(x, y ; z 0) ⊗ A(x, y) ⊗ G(x, y) = O(x, y ; z 0) ⊗ δ(x, y) = O(x, y ; z 0)
(2)
The size of the aperture projection depends on the source-detector distance. Therefore, the source-detector distance can be determined by reconstructing the images at a number of presumed magnification factors. This process is demonstrated with
Fig. 2. A plot of max value, RMS, and SNR value of reconstructed image sequences as a function of assumed magnification factor.
the aid of a light source with a coded-aperture mask made of stainless steel sheet. A visible light coded aperture mask, rank 11 Modified Uniformly Redundant Arrays (MURAs) (Gottesman and Fenimore, 1989), as shown in Fig. 1(a), was used to demonstrate the feasibility of source-camera distance estimation. We first conducted the measurements of a point source. The mask-detector distance was fixed at f¼ 90 mm, and the mask-source distance was changed from 0.5 to 5 m, corresponding to a system magnification in the range of 1.018–1.180. When the mask-source distance changed from 0.1 to 0.5 m, the corresponding magnification factor ranged from 1.180 to 1.900. The point source light was placed near the center of the field of view (FOV) at 2.43 m; the acquired mask projection is nearly ideal, as can be seen by comparing Fig. 1(a) to (b). We reconstructed the images at a number of presumed magnification factors and evaluated the reconstructed image sequences; the result is shown in Fig. 2. The maximum intensity value in the image varied slowly as the magnification factor increased. The larger root-mean-square (RMS) fluctuations in non-source pixels, and the smaller signal-tonoise (SNR) values, occurred when the assumed magnification factor is not the actual mask magnification. The distance to the source can be inferred from the data by finding the minimum in the plot of RMS or the maximum of SNR. The minimal value of RMS and maximum value of SNR both correspond to the magnification m ¼ 1.037. As the mask-detector distance was fixed at
Fig. 1. Measurement of a light point source at 2.43 m. (a) Mask configuration. (b) Mask projection with the source located near the center of the field of view. (c) Reconstructed image of the mask projection (b) at magnification m ¼1.037.
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179
Fig. 3. Rank 11 and rank 19 MURA mask. (a) Rank 11 MURA, the mask's dimensions are 168 168 6 mm3 with a pixel pitch 8 mm. (b) Rank 19 MURA, the mask's dimensions are 222 222 6 mm3 with a pixel pitch 6 mm.
Fig. 4. Large area NaI(Tl) detector. (a) Photograph. (b) Two-dimensional flood image.
Fig. 5. A plot of SNR value of reconstructed gamma image sequences as a function of assumed magnification factor.
f ¼90 mm, the source-camera distance corresponding to m ¼ 1.037 is 2.432 m. The estimated distance is very close to the actual source position of 2.430 m. The peak width of SNR is narrower
Fig. 6. Estimated source-camera distance plotted against the measured gamma source position.
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Fig. 7. Rank 19 MURA reconstructed image of line source (a) reconstructed at magnification m ¼1.001. (b) Reconstructed at magnification m¼ 1.0383. (c) Reconstructed at magnification m¼ 1.100.
α Z2. Relatively accurate source-camera distance could be extracted when α Z3. 3. Activity estimation of a point source
Fig. 8. A plot of SNR value of reconstructed gamma image sequences of line source and point source as a function of assumed magnification factor.
For a certain point source, the detector's count rate dependents on the source position. For a single point detector, the count rate has an inverse square relationship with the source-detector distance. The count rate is also affected by the detection efficiency, the blocking of the mask, and the attenuation of gamma-rays in the air. The detection efficiency is independent of the actual source position. Since the measurement range may be several meters or more, the attenuation of gamma-rays in air cannot be ignored. For example, for gamma-rays of 662 keV, when the source-detector distance is 10 m, the attenuation of gamma-rays in the air is about 10%. The intensity, I, of gamma-rays measured by the detector is related to the actual intensity, I0, from a point radiation source by the relationship
I0 = than the valley width of RMS. Therefore, SNR is used as the main distance estimation parameter. Originally, the projection on the detector of each hole in the aperture covered 200 200 pixels, which means a sampling rate α ¼200. In order to figure out how sampling rate will impact on source-camera distance estimation, we decreased the projection resolution by combing N N pixels into one pixel. It was found that source-camera distance estimation requires a sampling rate
4π r 2 × I P (θ , r ) × Ω(r ) × e−μair r
(3)
where r is the source-detector distance, P(θ,r) is the positional parameter of gamma sources at distance r and incident angle θ, Ω (r) is the solid angle of the field-of-view of the detector, and μair is the linear attenuation coefficient of air. The parameter, P(θ,r), was determined in advance through a series of measurements, by recording the detector’s count rates when a known point source was placed at some discrete distances and incident angles. Then, P(θ,r),
Fig. 9. Two-dimensional activity distributions of a point source and line source. Values on the sidebars indicate the activity (MBq/pixel). (a) 9.66 107 point source. (b) 2.31 108 Bq line source.
S. Shifeng et al. / Applied Radiation and Isotopes 107 (2016) 177–182
was linearly interpolated from the lookup table at a certain distance and incident angle.
4. Experimental testing The mosaic arrays of rank 11 and 19 MURAs were employed as the masks (Fig. 3). The primary components of the masks are 6 mm thick tungsten–copper alloy sheets. As shown in Fig. 4, the detector consists of a 75 75 array of 1.8 1.8 6 mm3 (pitch 2 mm) NaI(Tl) elements. The scintillation array is optically coupled to a 3 3 group of Hamamatsu H8500 position-sensitive photomultiplier tubes (PSPMTs). The central 71 71 scintillator pixels are well separated. The energy resolution obtained is better than 12% FWHM at 140 keV in the PSPMT centers. The sampling rate for rank 11 and 19 MURAs are 4 and 3, respectively. As the MURA is antisymmetric on a 90° rotation, the data were all collected in equal-time mask/anti-mask configurations to improve performance. The mask-detector distance was fixed at f ¼ 0.15 m. For the rank 11 and 19 MURAs, the FOV is 29.9° and 39.6°, respectively. The mask-detector distance was adjustable between a minimum of 50 mm and a maximum of 0.90 m, and the gross weight of the imaging system is approximately 50 kg. A Tc-99m point source (9.66 107 Bq) was centrally located 3.910 m from the mask plane. The data were collected with a total acquisition time of 240 s. The reconstructed gamma image sequences of rank 11 and 19 MURAs were evaluated, and the results are shown in Fig. 5. Compared to rank 11, the SNR peak width of rank 19 is wider. Further, the value of the rank 19 SNR is more unstable, which may be mainly due to its lower sampling rate. Fig. 6 shows the estimated source-camera distances of the rank 11 and 19 MURAs when the source-mask distances changed from 0.9 to 8 m. The root mean squared errors of the calibrated reconstructed source positions of the rank 11 and rank 19 MURAs were 0.163 and 0.175 m respectively. In addition to the point source, a 0.9 m long Tc-99m line source (2.31 108 Bq) was placed horizontally near the center of the FOV, at 3.910 m from the mask. The data were collected with a total acquisition time of 400 s. The rank 19 MURA reconstructed images of the line source are shown in Fig. 7. The reconstructed gamma image sequences of the rank 19 MURA were evaluated; the rank 19 MURA results for the line source and point source are shown in Fig. 8. For comparison, the result of the point source at 3.910 m is also shown. The SNR peak width of the line source is wider, and the maximum values of SNR for the line source and point source correspond to the magnifications m¼ 1.0350 and m ¼1.0392. The corresponding source-camera distances are 4.286 m and 3.830 m. The estimated source-camera distance of the line source could be a weighted average source-camera distance of the line. The rank 11 MURA results were not shown as the correct source-camera distance was not extracted. This may mainly be due to its low resolution. A threshold was set to distinguish the source from the background noise in the reconstructed images. Incident angles of the gamma sources were obtained through the discrete pixelization of the field of view. The detected counts were distributed according to the reconstruction values. Each image's pixel activity was estimated using Eq. (3). Fig. 9 shows the evaluated results of the source activities, based on the estimated source-camera distances and reconstructed images of the rank 19 MURA. Measurements were acquired with the camera at a standoff distance of 3.910 m. With the mask-detector distance fixed at 150 mm, the image pixel size is 80 80 mm2. At a length of 0.90 m, the line source was expected to extend horizontally through 11 pixels. Due to the limited resolution, the point source and line source extended to a 3 3
181
pixels region and a 3 11 pixels region, respectively. The total activities of these regions are 7.96 107 Bq and 3.47 108 Bq, which are 17.6% smaller and 50.4% larger than the actual activities. In order to analyze the standard uncertainty in inferring the source activity, ten replication measurements were performed. A Tc-99m point source (1.055 108 Bq) was centrally located 3.91 m from the rank 19 MURA mask. The data were all collected with a total acquisition time of 240 s. After radioactive decay rate correction, the mean source activity was 1.018 108 Bq with an estimated standard error of 71.369 107 Bq.
5. Conclusions This paper introduced a method of estimating the radioactivity of a source remotely using a coded aperture camera. Without the aid of 3D laser scanners, source-camera distance is estimated by factoring the effect of aperture magnification. The estimated source-camera distance along with the measured radiation intensity is used to determine the source activity. For the point source, source-camera distances were determined within an error of 6%. At a standoff distance of about 4 m, the gamma camera was able to predict the location of point and line sources in all three dimensions with an accuracy of less than 10%. For a point source and a source-camera distance 4 m, source activity was estimated with an accuracy of less than 20%.
Acknowledgments This work was supported by the National Key Scientific Instrument and Equipment Development Project of China (Grant no. 2011YQ120096), and by the National Natural Science Foundation of China (Grant nos. 11205170, 11175200).
References Berrim, S., Lansiart, A., Moretti, J.L., 1996. Implementing of maximum likelihood in tomographical coded aperture. Proc. Int. Conf. Image Process. IEEE 2, 745–748. Boehnen, C., Paquit, V., Ziock, K., et al., 2011. Field trial of a highly portable coded aperture gamma ray and 3D imaging system. Future of Instrumentation International Workshop (FIIW), IEEE. pp. 75–78. Caroli, E., Stephen, J.B., et al., 1987. Coded aperture imaging in X-and gamma-ray astronomy. Space Sci. Rev. 45 (3–4), 349–403. Fenimore, E.E., Cannon, T.M., 1978. Coded aperture imaging uniformly redundant arrays. Appl. Opt. 17 (3), 337–347. Gal, O., Gmar, M., Ivanov, O.P., et al., 2006. Development of a portable gamma camera with coded aperture. Nucl. Instrum. Meth. Phys. Res. A 563, 233–237. Gamage, K.A.A., Joyce, M.J., Taylor, G.C., 2012. A digital approach to neutron–γ imaging with a narrow tungsten collimator aperture and a fast organic liquid scintillator detector. Appl. Radiat. Isot. 70, 1223–1227. Gmar, M., Agelou., M., Carrel, F., et al., 2011. GAMPIX: a new generation of gamma camera. Nucl. Instrum. Meth. Phys. Res. A 652, 638–640. Gottesman, S.R., Fenimore, E.E., 1989. New family of binary arrays for coded aperture imaging. Appl. Opt. 28 (20), 4344–4352. Hong, B., Mu, Z., Liu, Y.H., 2006. A new approach of 3D SPECT reconstruction for near-field coded aperture imaging. Medical Imaging 2006: Physics of Medical Imaging, edited by Michael J. Flynn, Jiang Hsieh, Proceedings of SPIE. Vol. 6142, 61424D, 1605-7422/06/$15. http://dx.doi.org/10.1117/12.653300. Ito, T., Fujimura, S., 1996. Improvement on depth resolution and reduction of Poisson noise in coded aperture emission CT. Proc. Int. Conf. Image Process. IEEE 1, 757–760. Lemaire, H., Khalil, R.A., Amgarou, K., et al., 2014. Implementation of an imaging spectrometer for localization and identification of radioactive sources. Nucl. Instrum. Meth. Phys. Res. A 763, 97–103. Mu, Z., Liu, Y.H., 2006. Aperture collimation correction and maximum-likelihood image reconstruction for near-field coded aperture imaging of single photon emission computerized tomography. IEEE Trans. Med. Imaging 25 (6), 701–711. Mu, Z., Hong, B., Li, S., et al., 2009. A novel three-dimensional image reconstruction method for near-field coded aperture single photon emission computerized tomography. Med. Phys. 36 (5), 1533–1542. Raffo-Caiado, A.C., Ziock, K.P., Hayward, J.P., et al., 2010. Combining Measurements with Three-Dimensional Laser Scanning System and Coded-Aperture Gamma-
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Ray Imaging Systems for International Safeguards Applications. In: IAEA Symposium on International Safeguards. Santo, J.T., Maul, M., Lucero, R., et al., 2006. Application of Remote Gamma Imaging Surveys at the Turkey Point PWR Reactor Facility. In: Institute of Nuclear Materials Management, INMM 47th Annual Meeting. Sun, S., Zhang, Z., Shuai, L., et al., 2015. Development of a panorama coded-aperture
gamma camera for radiation detection. Radiat. Meas. 77, 34–40. Woodring, M., Souza, D., Tipnis, S., et al., 1999. Advanced radiation imaging of lowintensity gamma-ray sources. Nucl. Instrum. Meth. Phys. Res. A 422, 709–712. Woodring, M., Beddingfield, D., Souza, D., et al., 2003. Advanced multi-dimensional imaging of gamma-ray radiation. Nucl. Instrum. Meth. Phys. Res. A 505, 415–419.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Far field 3D localization of radioactive hot spots using a coded aperture camera Sun Shifeng a,b,c, Zhang Zhiming a,b, Shuai Lei a,b, Li Daowu a,b, Wang Yingjie a,b, Liu Yantao a,b, Huang Xianchao a,b, Tang Haohui a,b, Li Ting a,b, Chai Pei a,b, Zhang Yiwen a,b, Zhou Wei a,b,c, Yang Mingjie a,b,c, Wei Cunfeng a,b, Ma Chuangxin a,b, Wei Long a,b,n a
Division of Nuclear Technology and Applications, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Beijing Engineering Research Center of Radiographic Techniques and Equipment, Beijing 100049, China c University of Chinese Academy of Sciences, Beijing 100049, China b
H I G H L I G H T S
A method is presented to remotely estimate source activity. The method allows determination of source location from a single projection. A tungsten–copper alloy coded aperture mask is used to modulate the incoming gamma-rays. The method was successfully tested for point and line sources.
art ic l e i nf o
a b s t r a c t
Article history: Received 20 July 2015 Received in revised form 19 October 2015 Accepted 19 October 2015 Available online 20 October 2015
This paper presents a coded aperture method to remotely estimate the radioactivity of a source. The activity is estimated from the detected counts and the estimated source location, which is extracted by factoring the effect of aperture magnification. A 6 mm thick tungsten–copper alloy coded aperture mask is used to modulate the incoming gamma-rays. The location of point and line sources in all three dimensions was estimated with an accuracy of less than 10% when the source-camera distance was about 4 m. The estimated activities were 17.6% smaller and 50.4% larger than the actual activities for the point and line sources, respectively. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Source localization Source activity determination Coded aperture Far-filed measurements Gamma camera Modified Uniformly Redundant Array (MURA)
1. Introduction Gamma cameras are widely used in nuclear facilities to locate radiation sources within a given field of view, to help with decontamination, maintenance, repair or decommissioning (Woodring et al., 1999; Santo et al., 2006; Gamage et al., 2012; Sun et al., 2015). Measurements are always performed many meters away from the hot spots, to lower personal exposure. With the current commercially available coded aperture gamma camera (Woodring et al., 2003; Gal et al., 2006; Gmar et al., 2011; Lemaire n Corresponding author at: Division of Nuclear Technology and Applications, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China. Fax: þ86 10 88236413. E-mail addresses: [email protected] (S. Shifeng), [email protected] (W. Long).
http://dx.doi.org/10.1016/j.apradiso.2015.10.021 0969-8043/& 2015 Elsevier Ltd. All rights reserved.
et al., 2014), multiple sources can be located and identified quickly. However, the decoded gamma image of conventional imaging systems has only two dimensions projecting the radioactivity on the imaging plane of a camera, i.e., it does not measure the sourcecamera distance. Knowing this distance along with the measured radiation intensity can be used to determine the source activity. In nearby conditions, such as those encountered in medical applications, image reconstruction methods for three-dimensional (3D) distribution of radioactive isotopes are used (Ito and Fujimura, 1996; Berrim et al., 1996; Hong et al., 2006; Mu and Liu, 2006; Mu et al., 2009). However, these reconstruction methods require multiple projections acquired at different angles or positions. In industrial applications, it is impractical to acquire such multiple projections. Therefore, Raffo-Caiado et al. (2010) investigated the use of a 3D laser imaging system, combined with a
178
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coded aperture camera, for accountancy of nuclear materials in enrichment plants. The system was able to predict the location and geometry of gram quantities of uranium with good accuracy, at a standoff distance of about 4 m (Boehnen et al., 2011). However, such scheme is only suited for surface sources, and is not usable for sources shielded from the laser beam, such those located inside pipes or containers. In this paper, a method for determining the source-camera distance without the aid of 3D laser scanners is introduced. The method uses aperture magnification to determine the sourcecamera distance. Once the source-camera distance is determined, the source’s activity can be determined. The paper begins by a review of the coded aperture approach and its use to determine the source-camera distance. The approach is then applied to determine the location and activity of the line and point sources.
2. Determination of source-camera distance A coded aperture imaging system consists of a mask and a detector. The mask has holes distributed in a predictable pattern within a sheet made of material opaque to radiation. Sources within the field-of-view project a shadow of the aperture on to the detector. A coded aperture imaging system can be modeled by convolution (Fenimore and Cannon, 1978). When imaging objects at a finite distance, the mask pattern will be magnified at the detector plane. Let O(x,y;z) be a planar object located at distance z from the aperture plane, and D(x,y) be the coded image on the detector plane. Then, the coded aperture image modulated by aperture A(x,y) can be expressed as (Caroli et al., 1987)
D(x, y) = O(x, y ; z ) ⊗ A(x, y)
(1)
where ⊗ indicates convolution. To reconstruct the planar object O (x,y;z0) at distance z0, the coded pattern DZ0(x,y), taken from the coded image, must consider a magnification factor M(z0) ¼(z0 þf)/ z0. Here z0 is the distance between the object source and the aperture plane, and f is the distance between the aperture and detector plane. The image can be directly reconstructed by correlating the coded pattern with a decoding array G(x,y), which has a property such that A(x,y)⊗G(x,y) is a delta, δ, function. Then,
Dz 0 (x, y) ⊗ G(x, y) = O(x, y ; z 0) ⊗ A(x, y) ⊗ G(x, y) = O(x, y ; z 0) ⊗ δ(x, y) = O(x, y ; z 0)
(2)
The size of the aperture projection depends on the source-detector distance. Therefore, the source-detector distance can be determined by reconstructing the images at a number of presumed magnification factors. This process is demonstrated with
Fig. 2. A plot of max value, RMS, and SNR value of reconstructed image sequences as a function of assumed magnification factor.
the aid of a light source with a coded-aperture mask made of stainless steel sheet. A visible light coded aperture mask, rank 11 Modified Uniformly Redundant Arrays (MURAs) (Gottesman and Fenimore, 1989), as shown in Fig. 1(a), was used to demonstrate the feasibility of source-camera distance estimation. We first conducted the measurements of a point source. The mask-detector distance was fixed at f¼ 90 mm, and the mask-source distance was changed from 0.5 to 5 m, corresponding to a system magnification in the range of 1.018–1.180. When the mask-source distance changed from 0.1 to 0.5 m, the corresponding magnification factor ranged from 1.180 to 1.900. The point source light was placed near the center of the field of view (FOV) at 2.43 m; the acquired mask projection is nearly ideal, as can be seen by comparing Fig. 1(a) to (b). We reconstructed the images at a number of presumed magnification factors and evaluated the reconstructed image sequences; the result is shown in Fig. 2. The maximum intensity value in the image varied slowly as the magnification factor increased. The larger root-mean-square (RMS) fluctuations in non-source pixels, and the smaller signal-tonoise (SNR) values, occurred when the assumed magnification factor is not the actual mask magnification. The distance to the source can be inferred from the data by finding the minimum in the plot of RMS or the maximum of SNR. The minimal value of RMS and maximum value of SNR both correspond to the magnification m ¼ 1.037. As the mask-detector distance was fixed at
Fig. 1. Measurement of a light point source at 2.43 m. (a) Mask configuration. (b) Mask projection with the source located near the center of the field of view. (c) Reconstructed image of the mask projection (b) at magnification m ¼1.037.
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179
Fig. 3. Rank 11 and rank 19 MURA mask. (a) Rank 11 MURA, the mask's dimensions are 168 168 6 mm3 with a pixel pitch 8 mm. (b) Rank 19 MURA, the mask's dimensions are 222 222 6 mm3 with a pixel pitch 6 mm.
Fig. 4. Large area NaI(Tl) detector. (a) Photograph. (b) Two-dimensional flood image.
Fig. 5. A plot of SNR value of reconstructed gamma image sequences as a function of assumed magnification factor.
f ¼90 mm, the source-camera distance corresponding to m ¼ 1.037 is 2.432 m. The estimated distance is very close to the actual source position of 2.430 m. The peak width of SNR is narrower
Fig. 6. Estimated source-camera distance plotted against the measured gamma source position.
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Fig. 7. Rank 19 MURA reconstructed image of line source (a) reconstructed at magnification m ¼1.001. (b) Reconstructed at magnification m¼ 1.0383. (c) Reconstructed at magnification m¼ 1.100.
α Z2. Relatively accurate source-camera distance could be extracted when α Z3. 3. Activity estimation of a point source
Fig. 8. A plot of SNR value of reconstructed gamma image sequences of line source and point source as a function of assumed magnification factor.
For a certain point source, the detector's count rate dependents on the source position. For a single point detector, the count rate has an inverse square relationship with the source-detector distance. The count rate is also affected by the detection efficiency, the blocking of the mask, and the attenuation of gamma-rays in the air. The detection efficiency is independent of the actual source position. Since the measurement range may be several meters or more, the attenuation of gamma-rays in air cannot be ignored. For example, for gamma-rays of 662 keV, when the source-detector distance is 10 m, the attenuation of gamma-rays in the air is about 10%. The intensity, I, of gamma-rays measured by the detector is related to the actual intensity, I0, from a point radiation source by the relationship
I0 = than the valley width of RMS. Therefore, SNR is used as the main distance estimation parameter. Originally, the projection on the detector of each hole in the aperture covered 200 200 pixels, which means a sampling rate α ¼200. In order to figure out how sampling rate will impact on source-camera distance estimation, we decreased the projection resolution by combing N N pixels into one pixel. It was found that source-camera distance estimation requires a sampling rate
4π r 2 × I P (θ , r ) × Ω(r ) × e−μair r
(3)
where r is the source-detector distance, P(θ,r) is the positional parameter of gamma sources at distance r and incident angle θ, Ω (r) is the solid angle of the field-of-view of the detector, and μair is the linear attenuation coefficient of air. The parameter, P(θ,r), was determined in advance through a series of measurements, by recording the detector’s count rates when a known point source was placed at some discrete distances and incident angles. Then, P(θ,r),
Fig. 9. Two-dimensional activity distributions of a point source and line source. Values on the sidebars indicate the activity (MBq/pixel). (a) 9.66 107 point source. (b) 2.31 108 Bq line source.
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was linearly interpolated from the lookup table at a certain distance and incident angle.
4. Experimental testing The mosaic arrays of rank 11 and 19 MURAs were employed as the masks (Fig. 3). The primary components of the masks are 6 mm thick tungsten–copper alloy sheets. As shown in Fig. 4, the detector consists of a 75 75 array of 1.8 1.8 6 mm3 (pitch 2 mm) NaI(Tl) elements. The scintillation array is optically coupled to a 3 3 group of Hamamatsu H8500 position-sensitive photomultiplier tubes (PSPMTs). The central 71 71 scintillator pixels are well separated. The energy resolution obtained is better than 12% FWHM at 140 keV in the PSPMT centers. The sampling rate for rank 11 and 19 MURAs are 4 and 3, respectively. As the MURA is antisymmetric on a 90° rotation, the data were all collected in equal-time mask/anti-mask configurations to improve performance. The mask-detector distance was fixed at f ¼ 0.15 m. For the rank 11 and 19 MURAs, the FOV is 29.9° and 39.6°, respectively. The mask-detector distance was adjustable between a minimum of 50 mm and a maximum of 0.90 m, and the gross weight of the imaging system is approximately 50 kg. A Tc-99m point source (9.66 107 Bq) was centrally located 3.910 m from the mask plane. The data were collected with a total acquisition time of 240 s. The reconstructed gamma image sequences of rank 11 and 19 MURAs were evaluated, and the results are shown in Fig. 5. Compared to rank 11, the SNR peak width of rank 19 is wider. Further, the value of the rank 19 SNR is more unstable, which may be mainly due to its lower sampling rate. Fig. 6 shows the estimated source-camera distances of the rank 11 and 19 MURAs when the source-mask distances changed from 0.9 to 8 m. The root mean squared errors of the calibrated reconstructed source positions of the rank 11 and rank 19 MURAs were 0.163 and 0.175 m respectively. In addition to the point source, a 0.9 m long Tc-99m line source (2.31 108 Bq) was placed horizontally near the center of the FOV, at 3.910 m from the mask. The data were collected with a total acquisition time of 400 s. The rank 19 MURA reconstructed images of the line source are shown in Fig. 7. The reconstructed gamma image sequences of the rank 19 MURA were evaluated; the rank 19 MURA results for the line source and point source are shown in Fig. 8. For comparison, the result of the point source at 3.910 m is also shown. The SNR peak width of the line source is wider, and the maximum values of SNR for the line source and point source correspond to the magnifications m¼ 1.0350 and m ¼1.0392. The corresponding source-camera distances are 4.286 m and 3.830 m. The estimated source-camera distance of the line source could be a weighted average source-camera distance of the line. The rank 11 MURA results were not shown as the correct source-camera distance was not extracted. This may mainly be due to its low resolution. A threshold was set to distinguish the source from the background noise in the reconstructed images. Incident angles of the gamma sources were obtained through the discrete pixelization of the field of view. The detected counts were distributed according to the reconstruction values. Each image's pixel activity was estimated using Eq. (3). Fig. 9 shows the evaluated results of the source activities, based on the estimated source-camera distances and reconstructed images of the rank 19 MURA. Measurements were acquired with the camera at a standoff distance of 3.910 m. With the mask-detector distance fixed at 150 mm, the image pixel size is 80 80 mm2. At a length of 0.90 m, the line source was expected to extend horizontally through 11 pixels. Due to the limited resolution, the point source and line source extended to a 3 3
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pixels region and a 3 11 pixels region, respectively. The total activities of these regions are 7.96 107 Bq and 3.47 108 Bq, which are 17.6% smaller and 50.4% larger than the actual activities. In order to analyze the standard uncertainty in inferring the source activity, ten replication measurements were performed. A Tc-99m point source (1.055 108 Bq) was centrally located 3.91 m from the rank 19 MURA mask. The data were all collected with a total acquisition time of 240 s. After radioactive decay rate correction, the mean source activity was 1.018 108 Bq with an estimated standard error of 71.369 107 Bq.
5. Conclusions This paper introduced a method of estimating the radioactivity of a source remotely using a coded aperture camera. Without the aid of 3D laser scanners, source-camera distance is estimated by factoring the effect of aperture magnification. The estimated source-camera distance along with the measured radiation intensity is used to determine the source activity. For the point source, source-camera distances were determined within an error of 6%. At a standoff distance of about 4 m, the gamma camera was able to predict the location of point and line sources in all three dimensions with an accuracy of less than 10%. For a point source and a source-camera distance 4 m, source activity was estimated with an accuracy of less than 20%.
Acknowledgments This work was supported by the National Key Scientific Instrument and Equipment Development Project of China (Grant no. 2011YQ120096), and by the National Natural Science Foundation of China (Grant nos. 11205170, 11175200).
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