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Abstract
The refractive index of the scintillation crystal is a key parameter in the design of Positron Emission Tomography (PET) devices. However, existing methods to measure the refractive index always suffer from problems such as the complexity of optical path adjustment, long time cost, or high equipment consumption. To overcome these problems, we propose a method that can obtain the refractive index of the scintillation crystal with high accuracy in real time. In this method, we employ the Mach-Zehnder interferometer to generate the interference pattern when one beam of light passes through the scintillation crystal, which encodes the value of refractive index into the width of pattern. To obtain the width of interference pattern, we calculate the width pixels of dark/bright stripes in pattern with threshold, respectively, and finally get the average number of pixels of the pattern; this strategy can eliminate the coherent interference signal and random noise effectively. The optical path need not adjust during the whole measurement. Thus, the refractive index of scintillation crystals can be measured with reliability and efficiency. To validate the effectiveness of the proposed method, we measure different batches of BGO crystal and Ce:LYSO crystal samples. The results show that the proposed method can measure refractive indices with high accuracy and high efficiency, providing a reliable crystal refractive index measurement procedure for the PET detector module design. The proposed method is also suitable for refractive index measurements of transparent materials in visible light bands.
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1. Introduction
Positron Emission Tomography (PET), as a sensitive and quantitative functional molecular imaging technology, has been widely used in the pre-monitoring of cardiovascular diseases such as cancer and tumor [1,2]. The main components of PET equipment include front-end detector, image reconstruction and display, data filtering and processing system. When high-energy rays are incident on the scintillation crystal, low-energy visible photons would generate radially inside the crystal [3–5]. After one or more reflections on the inner wall surface of the photonic crystal, the visible scintillation photons will emit from the light emitting surface of the crystal end. The terminal photodetector converts the detected visible photons into electrical signals. After computer processing, we can get the specific position of the high-energy ray reaction crystal [6,7]. BGO crystal has many advantages such as high density, high mechanical strength, and high energy resolution. It is widely used in high-energy physics experiments such as PET field or CERN large electron-positron collider [8,9]. Ce: LYSO crystal is a kind of inorganic scintillation crystal with excellent comprehensive properties. By virtue of its short luminescence decay time and high light yield, it has been widely used in the PET field, nuclear radiation measurement or safety detection [10–12]. The performance of the PET detector largely depends on the number of scintillation photons detected by the photosensitive elements. The more scintillation photons detected by photosensitive elements, the better the energy resolution and the more accurate the decoding [13,14]. When high-energy rays are transmitting in scintillation crystals, in order to reduce the light loss, it is necessary to coat a highly reflective film on the crystal surface. Therefore, it is important to accurately measure the surface refractive index of scintillation crystals to prepare the reflective film on the outer surface layer [15,16].
There are many methods for measuring refractive index, which can be summarized as follows: (1) Geometrical optical measurement methods. The geometric method is to calculate the refractive index from the light deflection angle by the refraction law and reflection law of light. Such as minimum deflection angle [17], Fresnel reflection method [18], V prism method [19]. (2) Digital image processing method. This computer vision and image recognition method combines image sensing technology with computer automatic data processing, and modulates the information of emitted light to obtain refractive index [20,21]. (3) Interferometry. Interferometry is on the basis of the relationship between refractive index and interference optical path difference. The refractive index can be measured by the difference of measured interference fringes caused by the change of optical path difference. Such applications include Michelson interferometer [22,23], Fabry-Perot interferometer [24], Mach-Zehnder interferometer [25,26]. McKee et al. [27] proposed a method for measuring the refractive index of crystals using Michelson interferometer in 1995. In 2015, Wu et al. [28] proposed a method to measure the refractive index of bulk materials using a Michelson interferometer, and obtained good measurement results. Geometric measurement methods generally have problems of complicated debugging of optical paths and small measurement range. Digital image processing methods are often limited by the resolution of imaging results, and the measuring accuracy is not high enough. Interferometry is more convenient than the two kinds of methods relatively. However, interferometry is limited by the accuracy of the optical path. Moreover, the optical path needs to be adjusted frequently during measurement so that it is impossible to analyze the crystal interferometric fringe images in real time.
In this study, we propose a Mach-Zehnder interferometer based optical system, which integrates optical interference measurement theory and digital image processing algorithm, to measure the refractive index of scintillation crystal. The phase shift of interference pattern caused by scintillation crystal encodes the information of refractive index. In the proposed method, we adopt the Mach-Zehnder interferometer to generate the interference pattern when one beam of light passes through the scintillation crystal, which encodes the value of refractive index into the width of pattern. To obtain the width of interference pattern, we calculate the width pixels of dark/bright stripes in pattern with threshold respectively and finally get the average number of pixels of the pattern, this strategy can eliminate the coherent interference signal and random noise effectively. The optical path need not adjust during the whole measurement. Thus, the refractive index of scintillation crystals can be measured with reliability and efficiency. In order to verify the effectiveness of the proposed method, we measured samples of BGO crystal and Ce: LYSO crystal in different production batches. The results show that the proposed method can measure refractive indices with high accuracy and high efficiency, providing a reliable crystal refractive index measurement procedure. Furthermore, compared with the traditional refractive index measurement methods, our proposed method does not require extra crystal processing, nor does it need to frequently adjust the system. It has the advantages of low cost, simple operation and high measurement accuracy, and is suitable for refractive index measurement of various transparent materials.
2. Materials and methods
2.1 Principle of measuring device
Figure 1 shows a collimated laser which is split into two plane waves and then recombined by using two mirrors (M) and two beam splitters (BS). One path of light is used to illuminate the object, and the other is used to directly illuminate the recording film, which captures the interference pattern. Assuming that the wavelength of the incident light is $\lambda $. At a certain point between ${M_2}$ and $B{S_2}$, the virtual phase difference between the two outgoing beams is expressed as:
The measured thickness of the medium is h, and the refractive index is n. When $nh = m\lambda $, $|m |= 0,1,2, \cdots $, a bright stripe appears in the pattern; when $nh = m\lambda $, $|m |= \frac{1}{2},\frac{3}{2},\frac{5}{2}, \cdots $, a dark stripe appears in the pattern. A typical interference pattern is shown in Fig. 2.
2.2 Calculation of refractive index
In Mach-Zehnder interferometer system, the relationship between medium refractive index and medium length can be deduced from Eq. (1):
where $\varDelta \varphi $ is the phase difference between the two interference patterns, and d is the length of the medium. It is difficult to obtain the value of $\varDelta \varphi $, but the variation amplitude of fringes can be measured directly and accurately. According to the physical relationship between optical path difference and stripe width, optical path difference $\delta $ can be calculated as: where $s(r )$ is the fringe variation, D is the stripe width. Then, the fringe phase difference $\varDelta \varphi $ caused by fringe variation can be expressed as: simultaneous Eq. (3) and Eq. (4), Eq. (5) can be deduced: according to Eq. (2) and Eq. (5), the refractive index n is expressed as:Equation (6) shows that if the wavelength $\lambda $ of incident light and the measured thickness d of medium are known, the refractive index n of scintillation crystal can be obtained from the measurement values of the stripe width D and fringe variation $s(r )$.
2.3 Fringe width estimation
In recent years, interference fringe information extraction is mainly based on photoelectric sensor and image processing [29,30]. Nevertheless, the counting accuracy of the photoelectric sensor would be significantly decreased by noise. The image processing method directly identifies the central dark and bright count of stripes, ignoring the change details between dark and bright stripes. We propose a threshold judgment method based on the combination of Otsu threshold algorithm [31]. For the interference pattern captured by CCD, we calculate the maximum value of the average gray variance of the pattern by Otsu threshold algorithm, this value is selected as the detection threshold. In each line of pattern, the gray value of every pixel is compared with the threshold, the pixel with the gray value larger than threshold is defined as bright pixel, the pixel with the gray value smaller than threshold is defined as dark pixel. The number of bright pixels and dark pixels in each line are recorded. If the number of bright pixels is more than the number of dark pixels, the line is judged as bright stripe, otherwise, the line is judged as dark stripe. Then, the average pixel number of stripes is calculated to provide parameters for refractive index calculation.
Otsu threshold algorithm has the advantages of being convenient calculation, not affected by the brightness and the contrast of input image [32]. The calculation process can be expressed as:
For an interference pattern, we regard a single pixel as an area, and the gray value of this point is regarded as the quality of this point, then we can find the centroid point. Assume that there are m pixels in the image captured by CCD, where $\textrm{i} \times j$ is the size of the image ($m = \textrm{i} \times j$) and the gray value is ${g_{ij}}$. We can get the centroid coordinates of the image:
By setting the threshold value, we calculate the average number of pixels of the bright and dark stripes and get the number of pixels of the stripe width. According to Eq. (6), we can calculate the refractive index from the number of pixels in the stripe width and the camera pixel size.
The corresponding interference pattern processing method steps are as follows:
- (1) acquiring interference pattern by CCD;
- (2) the detection thresholds of dark/bright stripes are calculated by Otsu threshold algorithm. Judging whether all pixels in each row are greater than or equal to the detection threshold, if the gray value is larger than threshold, its corresponding pixel is recorded as bright, otherwise the pixel is recorded as dark. Thus, we can count the width pixels of dark/bright stripes respectively. For each line, if the number of bright pixels is more than the number of dark pixels, the line is judged as bright stripe, otherwise, the line is judged as dark stripe;
- (3) dividing all pixels corresponding to the width of dark/bright stripes by the number of dark/bright stripes to get the average number of pixels in the stripes;
- (4) according to Eq. (8), calculate the fringe variation $s(r )$;
- (5) the stripe width D is the product of average stripe pixels and CCD camera pixels;
- (6) calculating the refractive index from Eq. (6).
3. Experimental method and results
Based on the Mach-Zehnder interferometer, we use a CCD camera to acquire the deformed interference pattern of the scintillation crystal, and then calculate the refractive index of the scintillation crystal with the proposed algorithm. The system at room temperature of 20°C and the atmospheric pressure. Experimental setup is illustrated in Fig. 3. The laser light emitted by He-Ne laser ($\lambda $=632.8 nm) passes through the beam expander and reaches the 50/50 beam splitter, which is divided into two object light and reference light with equal intensity. The reference light is reflected to another 50/50 beam splitter by the mirror. The scintillation crystal with thickness d and refractive index n is fixed on the device platform, so that the laser is incident vertically into the crystal. The object light will form a series of parallel interference fringes with the reference light.
Fig. 3. Diagram of the experimental setup for measuring the refractive index of scintillation crystals.
In the experiment, we only need to fix the bottom of the crystal to ensure that the laser is vertically incident on the upper middle part of the crystal. Figure 4 displays a scene where the scintillation crystal is vertically incident by incident light. This placement way ensures that the crystal will not be damaged during measurement. The interference pattern is recorded by CCD camera (BFLY-U3-23S6M-C). The camera has a resolution of 1920*1200 and a pixel size of 5.86 $\mu m$. Different batches of BGO and Ce:LYSO scintillation crystals, which are commonly used in PET detector modules [33,34]. The specific dimension of scintillation and production time are shown in Table 1, where the production time represents different batches.
Table 1. Dimension of the experimental crystals
Due to different production batches of crystal growth, processing, transportation and other reasons, there may be some deviations in crystal dimension. It will increase the un-certainty of crystal thickness measurement. According to section 2.2, the crystal thickness has a great influence on the value of refractive index. Repeated measurement of crystal dimension with micrometer can confirm that there is no obvious difference in the crystal thickness of each batch. The inspection values and average values are shown in Table 2. The maximum deviation is 0.003 mm. Due to the small thickness deviation, the refractive index measurement is reliable.
Table 2. Experimental crystal thickness check results
The refractive index of BGO1, BGO2, Ce:LYSO1, Ce:LYSO2 crystals at 632.8 nm wavelength was measured by the proposed method. The experiment performed multiple measurements on this scintillation crystal, the measurement diagrams with representative characteristics were shown in Fig. 5. It can be seen that the theoretical refractive index of BGO crystal at 632.8 nm is 2.0974, and the theoretical refractive index of Ce:LYSO crystal at 632.8 nm is 1.8010 by calculation [35,36]. The measured refractive index is shown in Table 3. It shows that the deviations of refractive index the four crystals from the theoretical value are 0.046%, 0.134%, 0.064%, and 0.056%. Different relative errors of the same crystal may be caused by different crystal growth and different batch production. After the experiment, scintillation crystals are not damaged. The proposed refractive index calculation algorithm runs for 5 s.
Fig. 5. Experimental measurement chart with representative characteristics. (a)The interference pattern without BGO1 crystal; (b) The interference pattern with BGO1 crystal; (c)The interference pattern without Ce:LYSO1 crystal; (d) The interference pattern with Ce:LYSO1 crystal.
Table 3. Refractive index of several crystals at the laser wavelength ${\boldsymbol \lambda }$=632.8 nm.
From the theoretical analysis of the measurement error, the errors in the system are mainly caused by the measurement errors of the optical length ${D_o}$ and the physical length (thickness) d of the crystal. The refractive index n can be expressed as:
in which d is consistent with Eq. (6). Optical length ${D_o}$ is determined by the incident light wavelength, stripe width and fringe variation, ${D_o} = \frac{{\lambda s(r )}}{d}$. The error transmission formula of this system is:From the precision of micrometer, optical imaging system and pattern analysis, we can know the error of optical length of four crystal measurement experiments, $\varDelta {D_{o1}} = 1\; \mu m$, $\varDelta {D_{o2}} = 1\; \mu m$, $\varDelta {D_{o3}} = 0.54\; \mu m$, $\varDelta {D_{o4}} = 0.54\; \mu m$. The errors of physical length calculated according to Table 2 are as follows: $\varDelta {d_1} = 1\; \mu m$, $\varDelta {d_2} = 89\; \mu m$, $\varDelta {d_3} = 13\; \mu m$, $\varDelta {d_4} = 20\; \mu m$. The average errors caused by measurement errors are 0.1222%, 0.1223%, 0.1152% and 0.1154%. If only considering the optical length measurement error caused by the system, $\varDelta n$ can be calculated as:
Calculated by Eq. (11), the average error caused by the optical length measurement of the system are 0.1192%, 0.1193%, 0.0995%, and 0.1005%. It can be seen from the error analysis that the systematic error mainly comes from the thickness measurement of the measured crystal. Optical system and fringe image analysis have little influence on the measurement. Using a micrometer with higher accuracy, or measuring with a high-precision spectral confocal sensor is a good choice to improve the accuracy. It can reduce the measurement error of physical length caused by measuring the thickness of the crystal.
4. Conclusions
In this paper, we designed a new method that can quickly measure the refractive index of various transparent dielectric materials. Interference pattern generated by Mach-Zehnder interferometry with the scintillation crystal is captured with CCD camera. According to the interference pattern, the proposed algorithm detects the average number of dark and bright stripes of the fringe to determine the average width of interference pattern. The refractive index of scintillation crystal can be calculated from the width of interference pattern. In the experiment, we measured different batches of BGO crystal and Ce:LYSO crystal samples. The results show that the relative errors of the refractive index of BGO and Ce:LYSO scintillating crystals are 0.046%∼0.13%. The calculation time of the proposed algorithm is controlled within 5 s, the measurement accuracy reaches 10−3. The optical path need not adjust during the whole measurement. At the same time, the scintillation crystals are not damaged. Therefore, the proposed method can measure scintillation crystals with high precision, real-time and non-destructive, providing a reliable refractive index value for the PET detector module. The proposed method is applicable to refractive index measurements of trans-parent materials in visible light bands.
Funding
National Natural Science Foundation of China (62075168); Key scientific research platforms and projects of ordinary universities in Guangdong Province (2021KCXTD051); Key Projects of Basic and Applied Basic Research of Jiangmen (2021030103730007331).
Acknowledgments
The authors would like to thank Huazhong University of Science and Technology for research support.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. Quanquan Sun, Qiyu Peng, Zhongding Wu, Qiu Huang, and JianFeng Xu, “Ultra-thin high-reflector film designed for LYSO scintillators,” In Proceedings of the 2016 IEEE Nuclear Science Symposium, Medical Imaging Conference and Room-Temperature Semiconductor Detector Workshop (NSS/MIC/RTSD), Strasbourg, France, 29 October–6 November 2016, 1–2 (2016).
2. F. Gramuglia, S. Frasca, E. Ripiccini, E. Venialgo, V. Gâté, H. Kadiri, N. Descharmes, D. Turover, E. Charbon, and C. Bruschini, “Light Extraction Enhancement Techniques for Inorganic Scintillators,” Crystals 11(4), 362 (2021). [CrossRef]
3. Q. Sun, Q. Peng, Z. Wu, S. Xie, Q. Huang, and J. Xu, “Design of ultra-thin anti-reflection films directly coated on LYSO scintillators,” 2017 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC). IEEE, Atlanta, USA, 21-28 October 2017, 1–3 (2017).
4. N. P. Giha, W. M. Steinberger, L. Q. Nguyen, J. S. Carlson, P. L. Feng, S. D. Clarke, and S. A. Pozzi, “Organic glass scintillator bars with dual-ended readout,” Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip. 1014, 165676 (2021). [CrossRef]
5. S. Xie, X. Zhang, Y. Zhang, G. Ying, Q. Huang, J. Xu, and Q. Peng, “Evaluation of Various Scintillator Materials in Radiation Detector Design for Positron Emission Tomography (PET),” Crystals 10(10), 869 (2020). [CrossRef]
6. S. Xie, J. Xu, M. Yang, G. Ying, X. Zhang, Q. Huang, and Q. Peng, “Methods to improve light transport efficiency in LYSO crystals based on characteristics of optical reflectance,” IEEE Trans. Nucl. Sci. 66(9), 2100–2106 (2019). [CrossRef]
7. Y. Chen, Z. Song, Y. Deng, X. Cao, and Z. Deng, “Research Progress of Scintillation Crystals for Positron Emission Tomography,” Journal of the Chinese Ceramic Society. 49(09), 1898–1906 (2021).
8. Y. Liu, J. Jiang, and Y. Wang, “High-granularity crystal calorimetry: conceptual designs and first studies,” J. Instrum. 15(04), C04056 (2020). [CrossRef]
9. N. Kratochwil, S. Gundacker, P. Lecoq, and E. Auffray, “Pushing Cherenkov PET with BGO via coincidence time resolution classification and correction,” Phys. Med. Biol. 65(11), 115004 (2020). [CrossRef]
10. G. Tamulaitis, E. Auffray, A. Gola, M. Korzhik, A. Mazzi, V. Mechinski, and A. Vasil’ev, “Improvement of the timing properties of Ce-doped oxyorthosilicate LYSO scintillating crystals,” J Phys Chem Solids. 139, 109356 (2020). [CrossRef]
11. Q. Wei, T. Ma, N. Jiang, T. Xu, Z. Lyu, Y. Hu, and Y. Liu, “A side-by-side LYSO/GAGG phoswich detector aiming for SPECT imaging,” Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip. 953, 163242 (2020). [CrossRef]
12. B. Wan, F. Yang, D. Ding, S. Zhao, J. Xie, L. Chen, and J. Shi, “Effects of yttrium content on intrinsic radioactivity energy spectra of LYSO: Ce crystals,” Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip. 1001, 165263 (2021). [CrossRef]
13. S. Xie, X. Zhang, H. Peng, J. Yang, Q. Huang, J. Xu, and Q. Peng, “PET detectors with 127 ps CTR for the Tachyon-II time-of-flight PET scanner,” Nucl. Instrum. Methods. Phys. Res. B 933, 48–55 (2019). [CrossRef]
14. F. Loignon-Houle, S. Gundacker, M. Toussaint, F. C. Lemyre, E. Auffray, R. Fontaine, S. A. Charlebois, P. Lecoq, and R. Lecomte, “DOI estimation through signal arrival time distribution: a theoretical description including proof of concept measurements,” Phys. Med. Biol. 66(9), 095015 (2021). [CrossRef]
15. F. Loignon-Houle, M. Bergeron, C. M. Pepin, S. A. Charlebois, and R. Lecomte, “Simulation of scintillation light output in LYSO scintillators through a full factorial design,” Phys. Med. Biol. 62(2), 669–683 (2017). [CrossRef]
16. J. Xu, Q. Sun, Z. Wu, L. Guo, S. Xie, Q. Huang, and Q. Peng, “Development of broad-band high-reflectivity multilayer film for positron emission tomography system,” J. Instrum. 13(09), P09016 (2018). [CrossRef]
17. Y. Sun, Y. Chen, B. Han, and Y. Li, “Precision test technology of liquid refractive index using the method of minimum deviation angle,” Chinese Optics 12(4), 826–832 (2019). [CrossRef]
18. R. Martínez-Manuel, M. del Rosario Bautista-Morales, D. López-Cortés, C. Pineda-Arellano, M.G. Shlyagin, and O. Esteban, “Multi-point fiber refractometer using Fresnel reflection and a coherent optical frequency-domain multiplexing technique,” Appl. Opt. 58(3), 684–689 (2019). [CrossRef]
19. J. Yan, Y. Che, and S. Geng, “Dispersion coefficient measuring system of automatic alignment based on novel mathematical model,” Infrared Laser Eng. 44, 2858–2862 (2015).
20. J. Jung, S.-J. Hong, H.-B. Kim, G. Kim, M. Lee, S. Shin, S. Lee, D.-J. Kim, C.-G. Lee, and Y. Park, “Label-free non-invasive quantitative measurement of lipid contents in individual microalgal cells using refractive index tomography,” Sci. Rep. 8, 1–10 (2018). [CrossRef]
21. A. Abou Khalil, W. Gebremichael, Y. Petit, and L. Canioni, “Refractive index change measurement by quantitative microscopy phase imaging for femtosecond laser written structures,” Opt. Commun. 485, 126731 (2021). [CrossRef]
22. D. Wang, J. Cui, F. Zhang, S. Min, and K. Chen, “Review of Michelson Laser Interferometer for Micro Displacement Measurement,” Acta Metrolo. Sin. 42(1), 1–9 (2021). [CrossRef]
23. Yifeng Tang and Wanrong Gao, “Effects of orientation deviation of a beam splitter and a reference mirror on the stability of a two-interferometer-based handheld FFOCT imaging probe,” Appl. Opt. 60(20), 5942–5952 (2021). [CrossRef]
24. J. Wang, B. Liu, Y. Wu, Y. Mao, L. Zhao, T. Sun, T. Nan, and Y. Han, “Temperature insensitive fiber Fabry-Perot/Mach-Zehnder hybrid interferometer based on photonic crystal fiber for transverse load and refractive index measurement,” Opt. Fiber Technol. 56, 102163 (2020). [CrossRef]
25. B. Azizi, M. A. G. Shabankareh, and A. Farmani, “Simulation of a refractive index sensor based on the Vernier effect and a cascaded PANDA and Mach–Zehnder interferometer,” J. Comput. Electron. 20(4), 1599–1610 (2021). [CrossRef]
26. F. Zhao, Z. Tian, Z. Liu, B. Yang, and H. Zhou, “Measurement of Dispersion Characteristics of Atomic Medium Utilizing Mach-Zehnder Interferometer,” Acta Photon. Sin. 47, 268–277 (2018). [CrossRef]
27. D. J. McKee, J. F. H. Nicholls, and I. S. Ruddock, “Interferometric measurement of refractive index,” Eur. Phys. J. C 16(3), 127–134 (1995). [CrossRef]
28. X. Wu and Y. Miao, “Experiment Study on Measurement of the Refractive Index of Bulk Material,” Acta Metrolo. Sin. 36, 588–591 (2015). [CrossRef]
29. C. S. Lin, S. W. Yang, H. L. Lin, and J. W. Li, “Measurement of surface profile and surface roughness of fibre-optic interconnect by fast fourier transform,” Metrol. Meas. Syst. 24(2), 381–390 (2017). [CrossRef]
30. V.C. Mawardi, Y. Yoferen, and S. Bressan, “Sketch-Based Image Retrieval with Histogram of Oriented Gradients and Hierarchical Centroid Methods,” E3S Web of Conferences188, 00026 (2020).
31. W. Xue-guang and C. Shu-hong, “An improved image segmentation algorithm based on two-dimensional Otsu method,” Information Sciences Letters. 1.3, 2 (2012).
32. S. M. ElBayoumi Harb, N. A. MatIsa, and S. A. Salamah, “Improved image magnification algorithm based on Otsu thresholding,” Comput. Electr. Eng. 46, 338–355 (2015). [CrossRef]
33. S. Gundacker, R. M. Turtos, N. Kratochwil, R. H. Pots, M. Paganoni, P. Lecoq, and E. Auffray, “Experimental time resolution limits of modern SiPMs and TOF-PET detectors exploring different scintillators and Cherenkov emission,” Phys. Med. Biol. 65(2), 025001 (2020). [CrossRef]
34. F. E. Enríquez-Mier-y-Terán, A. S. Ortega-Galindo, T. Murrieta-Rodríguez, M. Rodríguez-Villafuerte, A. Martínez-Dávalos, and H. Alva-Sánchez, “Coincidence energy spectra due to the intrinsic radioactivity of LYSO scintillation crystals,” EJNMMI physics 7(1), 1–17 (2020). [CrossRef]
35. P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35(19), 3562–3569 (1996). [CrossRef]
36. K. F. Chen and D. F. Xue, “Fast growth of cerium-doped lutetium yttrium orthosilicate single crystals and their scintillation properties,” J. Rare Earths. 39(12), 1527–1532 (2021). [CrossRef]
