高分辨GEM探测器及读出方法研究
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摘要
1997年,西欧粒子物理研究中心(CERN)的物理学家F.Sauli首次提出了一种在气体介质中电子倍增的新模式：Gas Electron Multiplier (GEM)并把GEM制作的高速粒子径迹探测器称为GEM探测器。典型的GEM结构是在两边镀铜的聚乙烯薄膜(Kapton)上,用化学蚀刻技术将其腐蚀出许多等间距的小孔,孔的中心部分直径在50μm～80μm,加上一定的电压后可以产生104V/cm以上的电场强度。当电子在电场作用下经过小孔时与气体分子发生碰撞和电离产生多个次级电子,通过气体雪崩放大过程实现对原初电子的倍增。
在普通的多丝正比室(MWPC)或者微条气体室(MSGC)中,插入一片GEM薄膜,可以把原初电离预放大102～103倍,使MWPC(或MSGC)可以工作在较低的增益区,从而有效降低阳极丝附近的正离子云的密度,提高探测系统的时间响应和计数能力,以及增益稳定性。使用两层GEM,气体放大倍数可以达到104以上,配合微型电极条读出,可以制作成不对称型气体探测器结构,其优点是：与多丝正比室相比,它不用通常的金属丝布局来构成电场区,可以有效减小气隙和空间电荷效应；与微条气体室相比,不会由于绝缘支撑造成在高技术率情况下的局部电场不稳地；由于不存在阳极丝间距的限制,直接采用GEM微条电极读出仍可以获得很好的位置分辨(<100μm)。若使用若干层GEM器件串接使其倍增系数达到106,在许多射线测量场合,将能替代笨重且价格昂贵的光电倍增管；此外.GEM质量轻,可以加工成较大的尺寸和各种形状。GEM探测器这些特点,使得它不仅是一种独具特色的新型粒子径迹探测器,同时也将是第三代同步辐射光源实验,医用CT诊断,X射线晶体学等领域很具潜力的成像探测器。以医学影像诊断中广泛使用的X-CT为例,如利用GEM-X射线探测器具有的高灵敏度和快时间响应的特点,可以将光束准直成微米量级进行断层扫描,不仅可以获得最佳的图像反差,而且使病人受到的辐照剂量减小
GEM一经提出,就引起了广泛重视,国外许多科研机构和大学先后开展了对多种不对称型GEM+MWPC, GEM+MSGC双层GEM探测器,三层GEM探测器的原理性实验。为解决GEM高分辨读出的需要,开展了各种读出电子学和读出方法研究,例如：HEXA读出,高分辩的延迟线读出,采用集成芯片的重心读出,使用读出电极与读出电子学集成在一起的集成芯片直接读出等。同时,这些实验的结果也表明：GEM探测器的应用和推广存在一些基本理论和技术问题需要解决,如GEM构型与电子倍增系数的关系；GEM材料电阻率与增益稳定性的关系；不同工作气体和GEM工作电压对倍增系数的影响。在高能物理实验中,由于探测面积大,读出路数非常多,因此需要研制特殊的读出电极及专用读出电路,这是解决GEM高分辩读出的关键问题。在成像应用方面,读出方法多使用投影读出,重建方法最常用的是重心法跟延迟线方法。延迟线重建方法可以大幅度降低读出电子学系统费用,在过去几十年中多用于多丝室信号读出,但是由于技术原因,以前的延迟线本身由金属导线绕制而成。这种延迟线占用空间很大,分布参数难以准确控制。它的延迟时间和频率响应取决于导线特性以及绕制时线与框架之间的寄生电容和电感,因此这种延迟线的单位延迟时间和带宽性能受到很大限制,使得探测器的空间分辨能力以及计数率受到很大影响。近年来,随着电子技术发展,各种高频电感,电容元件出现,通过使用高频电感电容元件,根据延迟线的等效电路模型来构建延迟线读出线板成为一种有效的读出方法。我们的研究结果显示：这种用集总元件组成的延迟线读出板,不但小巧灵活,而且可以根据需要选用不同参数的电阻电容,以获得想要的单位延迟时间和带宽。由于集中元件的参数非常精确,使得延迟线的每个单元延时精确,因此应用这种新型的延迟线读出可以得到好的时间分辨和空间分辨。
在该论文研究期间,本人设计研制了两套GEM探测系统原型,第一套系统以双层GEM探测器为基础,使用双面PCB做为读出电极读出。该读出PCB厚0.2mmm,双面都是读出条,上下两层的读出条互相垂直,上层读出条直接收集电子从而输出信号,下层读出条通过感应上层读出条的信号而输出感应信号。经过测试,该探测器的性能指标如下：
●探测器的有效面积：100mm×100mm;
●气体放大倍数：5×104；
●计数率能力：≥105/mm2·s；
●位置分辨能力：<100μm；
●增益稳定性：连续测量两周增益变化<3%。以该系统为基础,开展了GEM微电极结构和读出方法的研究,并建立了一台基于重心重建方法的GEM-X射线成像装置原型。
第二套系统是以三层GEM探测器为基础的射线探测系统,该系统性能指标跟第一套系统大致相同,由于采用了三层GEM薄膜,探测器的气体增益比第一套系统要高。以第二套系统为基础,我们开展了使用延迟线读出的GEM探测器的实验和模拟研究。研究不同电极参数和延迟线参数的信号传输特性,给出实验和计算结果,并研制多种高时间分辨的延迟线读出线路板。在此基础上,我们研制一台基于延迟线重建方法的x射线成像装置原型,实验结果表明,该系统的位置分辨能力好与160μm。
在对GEM及其相关的读出方法进行的研究中,我所做的主要工作如下：
1.计算了不同几何构型的GEM薄膜在正常工作电压下的内部电场分布与电场线透过率,建立了一套完整的静电场计算方法。电场线的透过率直接从静电学的角度反应了GEM电极的几何构型对电荷传输的影响。根据有限元方法计算得到的GEM三维电场分布能够全面反应GEM的实际电场分布,根据得到的场强分布可以进一步模拟GEM探测器的雪崩放大过程和电荷传输过程。
2.建立了测试装置,测量了双层GEM探测器在不同工作气体,不同工作电压下的有效增益变化情况,并且测量了长时间工作情况下,该探测器有效增益的变化情况,并且测量了长时间工作情况下,该探测器有效增益的变化情况。测量结果表明,该双层GEM探测器的有效增益能达到104左右,通过使用X射线管对GEM进行长时间测量,证明GEM探测器工作稳定,效增益变化小于3%。以该探测器为基础,建立了一套使用重心重建方法的X射线成像系统,测量获得了清晰的图像。
3.研制完成了一个基于三层GEM探测器配合延迟线读出的X射线成像系统,并以之为基础,仔细研究了重建方法。经过对探测器输出信号的以及信号传输方面的研究,总结出了一套详细的延迟线的设计方法,以及根据实验要求,对GEM读出PCB的设计与信号模拟的方法。实验测量表明,该方法设计的延迟线读出系统准确有效,模拟结果与实验测量结果符合得非常好。这种延迟线设计方法也可以扩展到其他适合使用延迟线重建方法得探测器上。在此基础上为BNL/STAR实验设计了一种GEM延迟线读出系统模型,获得了初步的研究结果。
GEM是一种新型的粒子探测器,其性能可以满足新的高能物理实验需求,并且有广泛的应用前景,是目前探测技术研究领域的热点,科大高能物理实验室从2000年开始研制GEM探测器,是国内最早开展此项研究的单位,并获得国家自然科学基金的连续资助(10375062,10575101),我从大学三年级开始参与有关的研究。以上研究结果总结了我在博士(2005-2010)期间的工作。
The Gas Electron Multiplier (GEM), introduced in 1997 by F. Sauli, consists of a set of holes, arranged in a hexagonal pattern (typically 80μm diameter at 140μm pitch), chemically etched through copper-kapton-copper thin-foil composite. Application of a potential difference between the two sides of GEM focuses the field lines into the holes on it, electrons released by the ionization in the gas drift into the holes and multiply in the high electric field (50～70kV/cm), which is high enough for the electrons avalanche.
To combine with the Multi-Wire Proportional Chamber (MWPC) or the MicroStrip Gas Chamber (MSGC), the GEM foil can pre-amplify the primary electrons at the order of 102～103, this pre-amplification allows the MWPC (or MSGC) works at the low gain zone, decreases the density of the ion-cloud near the anode wires, improves the response and count ability and the gas gain stability. The gas gain of a double-GEM detector can be larger than 104, there are a lot of advantages of it:1) Compared with the MWPC,the GEM detector uses a set of holes for the the amplification area of instead of the metal wires, this micro-pattern structure can effectively reduce the gas gap and decrease the space charge effect.2) Compared with the MSGC, the readout anode and the foil are independent, the anode keeps staying at the 0V voltage level which can greatly avoid the discharge.3) The pitch and width of the strips on the readout PCB can be much more smaller than the wire space of the MWPC, so that the position resolution (<100μm)of the GEM detector is much more better than that of the MWPC.4) In a larger number of (?)adiation detection environments, it can instead of the Photomultiplier Tube (PMT).5) The GEM foil can be easy manufactured to any size and shape to satisfy the experiment requirement. Because of these outstanding performances, the GEM is not only a big shot in the modern high energy physics area, but also widely used in the synchrotron radiation, medical CT diagnosis, crystallography, etc.
Lots of groups are attracted by the GEM thus various R&D experiments for the GEM+MWPC, GEM+MSGC, double-GEM detector and triple-GEM detector are per- formed and show that there are some basic problems need to be solved before we apply the GEMs or GEM detectors in the area which we are interested in. For example, on the detector side, why does the foil geometry greatly effect the gas gain of it; what is the relationship between the GEM material and the gas gain stability;how do the dif-ferent gas mixtures and working voltages control the effective gain of the detector; on the readout side, how to design a suit readout anode and what reconstruction method should be used are attractive topics.
In High Energy Physics Group (HEPG) at USTC, I have joined the R&D work of two GEM systems. The first prototype is based on a double-GEM detector whose readout anode is a two layer PCB. The thickness of the readout PCB is 0.2mm, there are strips on both side of it. The strips on the top side collect the avalanche electrons and output a negative pulse. At the same time, this negative pulse can induce a small positive pulse on the bottom layer strips, which can be output as the signal on the bottom side. Our test shows the performances of this GEM system are:
·Effective area of the detector:100mm×10mm;
·Effective gas gain:5×104;
·Count ability:≥105/mm2·s;
·Position resolution:<100μm;
·Gas gain stability:the fluctuation in two weeks<3%. Based on this configuration, we investigated the GEM micro-structure and the relative readout method and constructed a GEM X-ray imaging system whose image is recon-structed by the Center-Of-Gravity(COG) method.
The second system is a triple-GEM detector system, the performances of this system are almost the same as those of the first one except its larger effective gas gain. To adopt the cartesian projective readout PCB and DelayLine reconstruction method, we have performed a detailed research on the parameters of the readout PCB and DelayLine PCB and developed several useful DelayLine PCBs. Based on this DelayLine reconstruction method, the test showed that the position resolution of this GEM system is better than 160μm.
The main researches and results are shown and described in this thesis, including:
1. Calculation of the electrostatic field and transfer efficiency of the field lines of 4 kinds of GEM foils, a detailed calculation method has been established. The transfer efficiency of the field lines are able to, stands on way of the electrostatic field, show that how does the foil geometry effect the charge transfer process in the detector. The calculated 3D field is quite close to the real one in the GEM foil, the field data could be used for the advanced simulation, e.g. the avalanche and charge transfer processes.
2. The system setup and the gas gain test of the double-GEM detector. The effec-tive gas gain of the detector has been detailed investigated while the working gas mixture and working voltage changed, the variation of the gas gain in a long time period has also been tested. the test results show that:1) the effective gas gain of a double-GEM detector is able to reach 104;2) the gas gain stability of the detector is very good, the variation of it is less than 3% during its two weeks work. Based on this GEM detector, we have constructed an X-ray imaging system, clear images have been obtained.
3. A triple-GEM X-ray imaging system has been established. Based on this system, a full design method of the Delay-Line PCB and a simulation/design program for the GEM readout anode design have been summarized after the detailed research on the output signal and its propagation of this GEM detector. Our experiments show that this method is accurate and effective, the simulations are quite agree with the experiment results. This Delay-Line design method can be extended to the other detectors which are compatible with it. Based on this Delay-Line readout technology, a GEM detector system for the Muon Telescope Detector (MTD) at BNL/STAR has been designed, the elementary results have been obtained.
The GEM is a new particle detector, the performances of it is good enough for the modern experiments of high energy physics and the other application areas, it is a big shot in current detector area. The High Energy Physics Group (HEPG) in USTC is the first group involved in the GEM research (started at 2000) in China, this research got continuous supports (10375062,10575101) from National Natural Science Foundation of China. I joined in the GEM group in HEPG at 2002, the results mentioned in this thesis summarizes my work in the period of 2003-2010.
在普通的多丝正比室(MWPC)或者微条气体室(MSGC)中,插入一片GEM薄膜,可以把原初电离预放大102～103倍,使MWPC(或MSGC)可以工作在较低的增益区,从而有效降低阳极丝附近的正离子云的密度,提高探测系统的时间响应和计数能力,以及增益稳定性。使用两层GEM,气体放大倍数可以达到104以上,配合微型电极条读出,可以制作成不对称型气体探测器结构,其优点是：与多丝正比室相比,它不用通常的金属丝布局来构成电场区,可以有效减小气隙和空间电荷效应；与微条气体室相比,不会由于绝缘支撑造成在高技术率情况下的局部电场不稳地；由于不存在阳极丝间距的限制,直接采用GEM微条电极读出仍可以获得很好的位置分辨(<100μm)。若使用若干层GEM器件串接使其倍增系数达到106,在许多射线测量场合,将能替代笨重且价格昂贵的光电倍增管；此外.GEM质量轻,可以加工成较大的尺寸和各种形状。GEM探测器这些特点,使得它不仅是一种独具特色的新型粒子径迹探测器,同时也将是第三代同步辐射光源实验,医用CT诊断,X射线晶体学等领域很具潜力的成像探测器。以医学影像诊断中广泛使用的X-CT为例,如利用GEM-X射线探测器具有的高灵敏度和快时间响应的特点,可以将光束准直成微米量级进行断层扫描,不仅可以获得最佳的图像反差,而且使病人受到的辐照剂量减小
GEM一经提出,就引起了广泛重视,国外许多科研机构和大学先后开展了对多种不对称型GEM+MWPC, GEM+MSGC双层GEM探测器,三层GEM探测器的原理性实验。为解决GEM高分辨读出的需要,开展了各种读出电子学和读出方法研究,例如：HEXA读出,高分辩的延迟线读出,采用集成芯片的重心读出,使用读出电极与读出电子学集成在一起的集成芯片直接读出等。同时,这些实验的结果也表明：GEM探测器的应用和推广存在一些基本理论和技术问题需要解决,如GEM构型与电子倍增系数的关系；GEM材料电阻率与增益稳定性的关系；不同工作气体和GEM工作电压对倍增系数的影响。在高能物理实验中,由于探测面积大,读出路数非常多,因此需要研制特殊的读出电极及专用读出电路,这是解决GEM高分辩读出的关键问题。在成像应用方面,读出方法多使用投影读出,重建方法最常用的是重心法跟延迟线方法。延迟线重建方法可以大幅度降低读出电子学系统费用,在过去几十年中多用于多丝室信号读出,但是由于技术原因,以前的延迟线本身由金属导线绕制而成。这种延迟线占用空间很大,分布参数难以准确控制。它的延迟时间和频率响应取决于导线特性以及绕制时线与框架之间的寄生电容和电感,因此这种延迟线的单位延迟时间和带宽性能受到很大限制,使得探测器的空间分辨能力以及计数率受到很大影响。近年来,随着电子技术发展,各种高频电感,电容元件出现,通过使用高频电感电容元件,根据延迟线的等效电路模型来构建延迟线读出线板成为一种有效的读出方法。我们的研究结果显示：这种用集总元件组成的延迟线读出板,不但小巧灵活,而且可以根据需要选用不同参数的电阻电容,以获得想要的单位延迟时间和带宽。由于集中元件的参数非常精确,使得延迟线的每个单元延时精确,因此应用这种新型的延迟线读出可以得到好的时间分辨和空间分辨。
在该论文研究期间,本人设计研制了两套GEM探测系统原型,第一套系统以双层GEM探测器为基础,使用双面PCB做为读出电极读出。该读出PCB厚0.2mmm,双面都是读出条,上下两层的读出条互相垂直,上层读出条直接收集电子从而输出信号,下层读出条通过感应上层读出条的信号而输出感应信号。经过测试,该探测器的性能指标如下：
●探测器的有效面积：100mm×100mm;
●气体放大倍数：5×104；
●计数率能力：≥105/mm2·s；
●位置分辨能力：<100μm；
●增益稳定性：连续测量两周增益变化<3%。以该系统为基础,开展了GEM微电极结构和读出方法的研究,并建立了一台基于重心重建方法的GEM-X射线成像装置原型。
第二套系统是以三层GEM探测器为基础的射线探测系统,该系统性能指标跟第一套系统大致相同,由于采用了三层GEM薄膜,探测器的气体增益比第一套系统要高。以第二套系统为基础,我们开展了使用延迟线读出的GEM探测器的实验和模拟研究。研究不同电极参数和延迟线参数的信号传输特性,给出实验和计算结果,并研制多种高时间分辨的延迟线读出线路板。在此基础上,我们研制一台基于延迟线重建方法的x射线成像装置原型,实验结果表明,该系统的位置分辨能力好与160μm。
在对GEM及其相关的读出方法进行的研究中,我所做的主要工作如下：
1.计算了不同几何构型的GEM薄膜在正常工作电压下的内部电场分布与电场线透过率,建立了一套完整的静电场计算方法。电场线的透过率直接从静电学的角度反应了GEM电极的几何构型对电荷传输的影响。根据有限元方法计算得到的GEM三维电场分布能够全面反应GEM的实际电场分布,根据得到的场强分布可以进一步模拟GEM探测器的雪崩放大过程和电荷传输过程。
2.建立了测试装置,测量了双层GEM探测器在不同工作气体,不同工作电压下的有效增益变化情况,并且测量了长时间工作情况下,该探测器有效增益的变化情况,并且测量了长时间工作情况下,该探测器有效增益的变化情况。测量结果表明,该双层GEM探测器的有效增益能达到104左右,通过使用X射线管对GEM进行长时间测量,证明GEM探测器工作稳定,效增益变化小于3%。以该探测器为基础,建立了一套使用重心重建方法的X射线成像系统,测量获得了清晰的图像。
3.研制完成了一个基于三层GEM探测器配合延迟线读出的X射线成像系统,并以之为基础,仔细研究了重建方法。经过对探测器输出信号的以及信号传输方面的研究,总结出了一套详细的延迟线的设计方法,以及根据实验要求,对GEM读出PCB的设计与信号模拟的方法。实验测量表明,该方法设计的延迟线读出系统准确有效,模拟结果与实验测量结果符合得非常好。这种延迟线设计方法也可以扩展到其他适合使用延迟线重建方法得探测器上。在此基础上为BNL/STAR实验设计了一种GEM延迟线读出系统模型,获得了初步的研究结果。
GEM是一种新型的粒子探测器,其性能可以满足新的高能物理实验需求,并且有广泛的应用前景,是目前探测技术研究领域的热点,科大高能物理实验室从2000年开始研制GEM探测器,是国内最早开展此项研究的单位,并获得国家自然科学基金的连续资助(10375062,10575101),我从大学三年级开始参与有关的研究。以上研究结果总结了我在博士(2005-2010)期间的工作。
The Gas Electron Multiplier (GEM), introduced in 1997 by F. Sauli, consists of a set of holes, arranged in a hexagonal pattern (typically 80μm diameter at 140μm pitch), chemically etched through copper-kapton-copper thin-foil composite. Application of a potential difference between the two sides of GEM focuses the field lines into the holes on it, electrons released by the ionization in the gas drift into the holes and multiply in the high electric field (50～70kV/cm), which is high enough for the electrons avalanche.
To combine with the Multi-Wire Proportional Chamber (MWPC) or the MicroStrip Gas Chamber (MSGC), the GEM foil can pre-amplify the primary electrons at the order of 102～103, this pre-amplification allows the MWPC (or MSGC) works at the low gain zone, decreases the density of the ion-cloud near the anode wires, improves the response and count ability and the gas gain stability. The gas gain of a double-GEM detector can be larger than 104, there are a lot of advantages of it:1) Compared with the MWPC,the GEM detector uses a set of holes for the the amplification area of instead of the metal wires, this micro-pattern structure can effectively reduce the gas gap and decrease the space charge effect.2) Compared with the MSGC, the readout anode and the foil are independent, the anode keeps staying at the 0V voltage level which can greatly avoid the discharge.3) The pitch and width of the strips on the readout PCB can be much more smaller than the wire space of the MWPC, so that the position resolution (<100μm)of the GEM detector is much more better than that of the MWPC.4) In a larger number of (?)adiation detection environments, it can instead of the Photomultiplier Tube (PMT).5) The GEM foil can be easy manufactured to any size and shape to satisfy the experiment requirement. Because of these outstanding performances, the GEM is not only a big shot in the modern high energy physics area, but also widely used in the synchrotron radiation, medical CT diagnosis, crystallography, etc.
Lots of groups are attracted by the GEM thus various R&D experiments for the GEM+MWPC, GEM+MSGC, double-GEM detector and triple-GEM detector are per- formed and show that there are some basic problems need to be solved before we apply the GEMs or GEM detectors in the area which we are interested in. For example, on the detector side, why does the foil geometry greatly effect the gas gain of it; what is the relationship between the GEM material and the gas gain stability;how do the dif-ferent gas mixtures and working voltages control the effective gain of the detector; on the readout side, how to design a suit readout anode and what reconstruction method should be used are attractive topics.
In High Energy Physics Group (HEPG) at USTC, I have joined the R&D work of two GEM systems. The first prototype is based on a double-GEM detector whose readout anode is a two layer PCB. The thickness of the readout PCB is 0.2mm, there are strips on both side of it. The strips on the top side collect the avalanche electrons and output a negative pulse. At the same time, this negative pulse can induce a small positive pulse on the bottom layer strips, which can be output as the signal on the bottom side. Our test shows the performances of this GEM system are:
·Effective area of the detector:100mm×10mm;
·Effective gas gain:5×104;
·Count ability:≥105/mm2·s;
·Position resolution:<100μm;
·Gas gain stability:the fluctuation in two weeks<3%. Based on this configuration, we investigated the GEM micro-structure and the relative readout method and constructed a GEM X-ray imaging system whose image is recon-structed by the Center-Of-Gravity(COG) method.
The second system is a triple-GEM detector system, the performances of this system are almost the same as those of the first one except its larger effective gas gain. To adopt the cartesian projective readout PCB and DelayLine reconstruction method, we have performed a detailed research on the parameters of the readout PCB and DelayLine PCB and developed several useful DelayLine PCBs. Based on this DelayLine reconstruction method, the test showed that the position resolution of this GEM system is better than 160μm.
The main researches and results are shown and described in this thesis, including:
1. Calculation of the electrostatic field and transfer efficiency of the field lines of 4 kinds of GEM foils, a detailed calculation method has been established. The transfer efficiency of the field lines are able to, stands on way of the electrostatic field, show that how does the foil geometry effect the charge transfer process in the detector. The calculated 3D field is quite close to the real one in the GEM foil, the field data could be used for the advanced simulation, e.g. the avalanche and charge transfer processes.
2. The system setup and the gas gain test of the double-GEM detector. The effec-tive gas gain of the detector has been detailed investigated while the working gas mixture and working voltage changed, the variation of the gas gain in a long time period has also been tested. the test results show that:1) the effective gas gain of a double-GEM detector is able to reach 104;2) the gas gain stability of the detector is very good, the variation of it is less than 3% during its two weeks work. Based on this GEM detector, we have constructed an X-ray imaging system, clear images have been obtained.
3. A triple-GEM X-ray imaging system has been established. Based on this system, a full design method of the Delay-Line PCB and a simulation/design program for the GEM readout anode design have been summarized after the detailed research on the output signal and its propagation of this GEM detector. Our experiments show that this method is accurate and effective, the simulations are quite agree with the experiment results. This Delay-Line design method can be extended to the other detectors which are compatible with it. Based on this Delay-Line readout technology, a GEM detector system for the Muon Telescope Detector (MTD) at BNL/STAR has been designed, the elementary results have been obtained.
The GEM is a new particle detector, the performances of it is good enough for the modern experiments of high energy physics and the other application areas, it is a big shot in current detector area. The High Energy Physics Group (HEPG) in USTC is the first group involved in the GEM research (started at 2000) in China, this research got continuous supports (10375062,10575101) from National Natural Science Foundation of China. I joined in the GEM group in HEPG at 2002, the results mentioned in this thesis summarizes my work in the period of 2003-2010.
引文
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