Evaluation of a 2D diode array for IMRT quality assurance

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Separable Kernel for Image Deblurring

Separable Kernel for Image Deblurring
Separable Kernel for Image Deblurring
Lu Fang1 ∗, Haifeng Liu1 , Feng Wu1 , Xiaoyan Sun2 , Houqiang Li1 1 University of Science and Technology of China, Hefei, China {fanglu, lemt, fengwu, 2 Microsoft Research Asia, Beijing, China xysun@
where K is a non-negative blur kernel, whose support is small compared to the image size, I is the latent sharp image, N is noise, and ⊗ denotes convolution. Image deblurring is to solve the deconvolution of Eq. (1) [14, 16]. The blur kernel K needs to be recovered simultaneously with the latent sharp image I from the observed blurry image B . Currently, the kernel K is represented by a 2D matrix. But if carefully analyzing the process of photography, we can find that it actually consists of three aspects: trajecwork was supported in part by Natural Science Foundation of China (NSFC) under contract No. 61303151, 61331015 and 61390514.

高性能PtS2

高性能PtS2

第42卷 第1期吉林大学学报(信息科学版)Vol.42 No.12024年1月Journal of Jilin University (Information Science Edition)Jan.2024文章编号:1671⁃5896(2024)01⁃0074⁃07高性能PtS 2/MoTe 2异质结红外光电探测器收稿日期:2023⁃01⁃12基金项目:上海市自然科学基金资助项目(15ZR1627300)作者简介:潘生生(1995 ),男,合肥人,上海理工大学硕士研究生,主要从事二维光电材料研究,(Tel)86⁃187****3664(E⁃mail)2351948787@;通讯作者:袁涛(1983 ),女,上海人,上海理工大学教授,博士,主要从事新能源材料研究,(Tel)86⁃181****3228(E⁃mail)4673250167@㊂潘生生1,袁 涛1,周孝好2,王 振2(1.上海理工大学理学院,上海200093;2.中国科学院上海技术物理研究所,上海200092)摘要:由于光电探测器的工作性能直接关系到系统数据采集质量,为此,对高性能PtS 2/MoTe 2异质结红外光电探测器进行了研究㊂通过选取材料㊁试剂和设备制作了PtS 2/MoTe 2异质结红外光电探测器㊂搭建探测器性能测试环境,并利用光响应度㊁探测率㊁响应时间和光电导增益4个指标,分析探测器性能㊂结果表明,随着测试时间的推移,PtS 2/MoTe 2异质结红外光电探测器的光响应度数值始终处于5A /W 限值以上;无论对采集何种材质反射的红外光,探测器探测率均大于10cm㊃Hz1/2W -1;无论光生电流是处于上升还是下降时间,其响应时间始终在限值150μs 以下;光电导增益值保持在80%以上㊂关键词:PtS 2/MoTe 2异质结红外光电探测器;光响应度;探测率;光电导增益中图分类号:TP365.66文献标志码:AHigh Performance PtS 2/MoTe 2Heterojunction Infrared PhotodetectorPAN Shengsheng 1,YUAN Tao 1,ZHOU Xiaohao 2,WANG Zhen 2(1.College of Science,Shanghai University of Technology,Shanghai 200093,China;2.Shanghai Institute of Technical Physics,Chinese Academy of Sciences,Shanghai 200092,China)Abstract :As one of the important components of the detection system,the performance of photoelectric detector is directly related to the quality of system data acquisition.In order not to affect the final detection result,it is essential to ensure the detector performance.The performance of high performance PtS 2/MoTe 2heterojunction infrared photodetector is studied.First,the materials,reagents and equipment are prepared to make PtS 2/MoTe 2heterojunction infrared photodetectors.The detector performance test environment,the four indicators of light response,detection rate,response time and photoconductivity gain are set up,and the detector performance is analyzed.The results show that the optical responsivity of PtS 2/MoTe 2heterojunction infrared photodetector is always above the 5A /W limit with the passage of test time.The detection rate of the detector is greater than 10cm㊃Hz1/2W -1regardless of the infrared light reflected from any material.Whether the photocurrent is in the rising time or the falling time,its response time is always below the limit of 150μs;The photoconductivity gain value has been kept above 80%.Key words :PtS 2/MoTe 2heterojunction infrared photodetector;optical responsivity;detection rate;photoconductivity gain0 引 言目标检测是一个确定目标缺陷㊁故障㊁属性㊁类型的过程,其是很多领域的研究重点课题㊂在目标检测过程中,基础数据采集是首要环节,其质量直接关系到目标检测结果的准确性[1]㊂针对目标的不同,基础数据的采集手段也各不相同,如振动传感㊁雷达㊁光电探测系统等㊂其中,光电探测系统根据发射光的颜色不同,又分为紫外光㊁可见光及红外光等[2]㊂而其中红外光由于探测范围较为广泛,使其成为光电探测系统中的重要组成部分㊂其工作原理是反射光照射到半导体材料上后,会吸收光能量,则会触发光电导效应,从而将红外光转换为电信号[3]㊂红外光电探测器是整个探测系统的 核心”,因此其性能会直接影响数据采集质量,进而影响整个探测工作质量㊂基于上述分析,人们对红外光电探测器性能进行了大量分析研究㊂周国方等[4]以石墨烯材料为基础并利用碱刻蚀法合成金字塔状硅,形成异质结,制备近红外光探测器,并针对其响应速度㊁比探测率㊁光电流等性能进行了检测㊂秦铭聪等[5]首先选取探测器制备所需要的材料并制备了各个组成元件,然后将这些元件组合,构成了高性能近红外有机光探测器件,最后针对响应度和比探测率㊁线性动态范围LDR(Low Dynamic Range)㊁光开关特性和响应时间等性能进行了分析㊂皇甫路遥等[6]以二硫化钼和二硒化钨为基础,利用蒸镀机热蒸镀法制备成异质结光电探测器,然后针对该设备进行了拉曼荧光㊁输出㊁光电特性的分析㊂在上述研究基础上,笔者制备高性能PtS 2/MoTe 2异质结红外光电探测器并对其性能进行研究,以期为红外光电探测器设计和应用提供参考㊂1 高性能PtS 2/MoTe 2异质结红外光电探测器设计1.1 材料制备二硫化铂(PtS 2)是一种过渡金属硫族层间化合物,其光响应特性优秀,因此广泛用于光电探测器的设计中;二碲化钼(MoTe 2)是一种N 型半导体材料,具有良好的光吸收性㊁半导体特性以及同质结效率,可保证电子在其中迅速运动[7]㊂这两种材料是形成探测器光电导效应的主要原料㊂其基础性质如表1所示㊂表1 PtS 2和MoTe 2的性质 2和MoTe 2两种主要材料外,还需要衬底材料,以承载PtS 2和MoTe 2氧化硅,来自浙江精功科技股份有限公司,该硅片基础参数如下:氧化层厚度:50~200μm;晶向:〈100〉;掺杂类型:P;电阻率:1~3Ω㊃cm㊂1.2 试剂制备PtS 2/MoTe 2异质结红外光电探测器制备所需试剂如表2所示㊂表2 探测器制备所需试剂57第1期潘生生,等:高性能PtS 2/MoTe 2异质结红外光电探测器1.3 设备选取PtS 2/MoTe 2异质结红外光电探测器制备所需设备如表3所示㊂表3 探测器制备所需设备Tab.3 Equipment required for detector preparation设备名称型号生产厂家旋涂仪SPIN200i⁃NPP 北京汉达森机械技术有限公司电子束蒸发系统FC /BCD⁃2800上海耀他科技有限公司扫描电子显微镜WF10X /23上海锦玟仪器设备有限公司鼓风干燥箱xud 东莞市新远大机械设备有限公司超声清洗机SB⁃50江门市先泰机械制造有限公司无掩模光刻机Micro⁃Writer ML3英国DMO 公司氮气枪沈阳广泰气体有限公司双温区管式炉MY⁃G3洛阳美优实验设备有限公司紫外曝光系统UVSF81T007356复坦希(上海)电子科技有限公司三维转移平台SmartCART北京昊诺斯科技有限公司1.4 红外光电探测器制作工艺基于表1~表3给出的制备材料㊁试剂和设备,制备出高性能PtS 2/MoTe 2异质结红外光电探测器用于性能测试[9]㊂具体过程如下㊂步骤1) 制作衬底㊂①氧化硅片切割成直径为1cm 的圆形硅片;②将圆形硅片放入准备好的烧杯容器中;③在其中加入丙酮溶液,浸泡10min;④取出硅片后,放入乙醇溶液中,再次浸泡10min;⑤将硅片放入去离子水中并同时利用超声清洗机清洗5min,用氮气枪吹干表面的水分,完全去除附着在硅片表面的有机物和杂质;⑥利用氢氟酸溶液去除氧化层;⑦通过外延生长技术得到p 型硅;⑧进行紫外臭氧处理20min,得到衬底[10]㊂步骤2) 利用热辅助硒化法制备PtS 2和MoTe 2薄膜㊂步骤3) 将PtS 2薄膜贴到衬底上,得到薄层PtS 2样品㊂步骤4) 在薄层PtS 2样品上均匀旋涂上聚甲基丙烯酸甲酯㊂步骤5) 在显微镜和三维转移平台下将MoTe 2薄膜进行精确定位,然后对准并贴合在一起㊂步骤6) 利用鼓风干燥箱干燥处理㊂步骤7) 浸泡氢氟酸溶液㊁捞取㊁烘烤㊁去胶和退火,完成PtS 2/MoTe 2异质结制备[11]㊂图1 PtS 2/MoTe 2异质结红外光电探测器示意图Fig.1 Schematic diagram of PtS 2/MoTe 2heterojunction infrared photodetector步骤8) 在PtS 2/MoTe 2异质结上光刻出图形,形成微结构㊂步骤9) 利用紫外曝光和湿法刻蚀工艺制备出晶体管栅极㊂步骤10) 利用电子束曝光结合电子束蒸发系统制备出源漏电极㊂步骤11) 完成高性能PtS 2/MoTe 2异质结红外光电探测器的制作如图1所示㊂67吉林大学学报(信息科学版)第42卷2 光电探测器性能测试对制备好的PtS 2/MoTe 2异质结红外光电探测器进行性能测试㊂其测试工作分为两部分,一是设定测试环境,二是确定测试指标[12]㊂2.1 设定测试环境图2 红外光电探测器测试环境Fig.2 Test environment of infrared photodetector 红外光电探测器是光电探测系统中的重要组成部分,光电探测系统主要用于目标检测,因此为测试所制备的PtS 2/MoTe 2异质结红外光电探测器性能,需要搭配其他系统构成测试环境,如图2所示[13]㊂应用所设计的PtS 2/MoTe 2异质结红外光电探测器采集反射信号,测试持续10min㊂记录期间内探测器的相关工作参数,以便性能指标的计算[14]㊂2.2 性能测试指标针对所设计的PtS 2/MoTe 2异质结红外光电探测器,选用以下4个指标进行性能评定,即光响应度㊁探测率㊁响应时间和光电导增益[15]㊂1)光响应度㊂描述探测器光电转换能力的指标,该指标越大,说明探测器的光电转换能力越好㊂计算如下:A =a 1/B ,(1)其中A 表示光响应度,a 1表示光照射下产生的光生电流,B 表示入射光功率㊂光响应度大于5A /W 为高性能标准㊂2)探测率㊂反射的光信号中部分信号是十分微弱的,并不容易被采集到,因此要求探测器具有良好的针对微弱信号的探测能力,探测率就是描述该能力的最直观指标,该指标越大,说明探测器的针对微弱信号的探测能力越好[16]㊂计算如下:C =a 2L /D ,(2)其中D =G 1/A ,(3)其中C 表示探测率,大于10cm㊃Hz1/2W -1为高性能标准,a 2表示器件有效面积,L 表示带宽,D 表示噪声等效功率,G 1表示1Hz 带宽的噪声电流㊂红外光电探测器常用于不同材质目标的检测,因此保证其适用性是非常重要的㊂为此,在文中设置3种材质或属性的探测目标,即混凝土材质㊁金属材质以及人体㊂针对这3种材质或属性的探测目标,测试其探测率变化情况㊂3)响应时间㊂其反映了光电探测器对入射光信号响应的快慢,包括上升和下降时间㊂上升时间是指光生电流从10%上升到90%的这段时间,而下降时间则相反㊂实际应用中对光照快速响应的需求为小于等于150μs,且时间越短,表示器件响应越快㊂计算如下:E =~A[1+(2πeg )2]1/2T ,(4)其中E 表示响应时间,~A表示静态光照下的光响应度,e 表示电子电荷的数值,T 表示时间长度㊂4)光电导增益㊂其指标描述了光作用下外电路电流的增强能力㊂计算如下:H =(a 1/N )MP×100%,(5)其中H 表示光电导增益,该值越大,说明探测器工作越稳定,以80%为标准,大于该值认为探测器达到高性能标准;N 表示光电子的电荷量,P 表示探测器的电子转移效率,M 表示光电子数目㊂77第1期潘生生,等:高性能PtS 2/MoTe 2异质结红外光电探测器3 性能测试结果与分析3.1 光响应度图3为光响应度测试结果㊂从图3可看出,随着测试时间的推移,光响应度波动较小,基本保持稳定㊂并且光响应度数值始终处于5A /W 限值以上,说明所设计的PtS 2/MoTe 2异质结红外光电探测器达到了高性能标准㊂3.2 探测率图4为探测率测试结果㊂从图4可看出,无论是采集何种材质反射的红外光,所设计的探测器探测率均大于10cm㊃Hz1/2W -1,说明该探测器针对微弱信号具有较强的检测能力,达到高性能标准㊂ 图3 光响应度测试结果 图4 探测率测试结果 Fig.3 Optical responsivity test results Fig.4 Detection rate test results3.3 响应时间图5为响应时间测试结果㊂从图5可看出,无论光生电流处于上升还是下降时间,其响应时间始终在限值150μs 以下,说明所设计的探测器能快速检测入射光信号,完成信号采集工作㊂图5 响应时间测试结果Fig.5 Response time test results图6 光电导增益测试结果Fig.6 Photo conductivity gain test results3.4 光电导增益图6为光电导增益测试结果㊂从图6可看出,随着时间的推移,光电导增益值并没有随之下降,虽然有所波动,但也一直保持在80%以上,证明了所设计探测器的性能㊂4 结 语红外探测器是光电探测系统中的最重要组成部分,起到数据收集的重要作用,而收集的数据质量越高,探测结果越准确㊂因此,保证探测器的工作性能87吉林大学学报(信息科学版)第42卷对于数据收集工作具有重要作用㊂为此,进行了高性能PtS 2/MoTe 2异质结红外光电探测器性能研究㊂并以PtS 2/MoTe 2为基础设计一款探测器,同时测定了探测器的4个指标,分析了其探测性能㊂实验结果表明,tS 2/MoTe 2异质结红外光电探测器的光响应度㊁探测率㊁光电导增益均较高,响应时间在限值150μs以下㊂通过本研究以期为PtS 2/MoTe 2异质结红外光电探测器的研究和应用提供参考㊂参考文献:[1]林亚楠,吴亚东,程海洋,等.PdSe 2纳米线薄膜/Si 异质结近红外集成光电探测器[J].光学学报,2021,41(21):184⁃192.LIN Y N,WU Y D,CHENG H Y,et al.Near⁃Infrared Integrated Photodetector Based on PdSe 2Nanowires Film /Si Heterojunction [J].Acta Optica 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/CuZnSHeterojunction [J].Acta Physica Sinica,2022,71(21):382⁃390.[10]王月晖,张清怡,申佳颖,等.ε⁃Ga 2O 3/SiC 异质结自驱动型日盲光电探测器[J].北京邮电大学学报,2022,45(3):44⁃49.WANG Y H,ZHANG Q Y,SHEN J Y,et al.Self⁃Driven Solar⁃Blind Photodetector Based on ε⁃Ga 2O 3/SiC Heterojunction [J].Journal of Beijing University of Posts and Telecommunications,2022,45(3):44⁃49.[11]何峰,徐波,蓝镇立,等.基于石墨烯/硅微米孔阵列异质结的高性能近红外光探测器[J].红外技术,2022,44(11):1236⁃1242.HE F,XU B,LAN Z L,et al.High⁃Performance Near⁃Infrared Photodetector Based on a Graphene /Silicon Microholes Array97第1期潘生生,等:高性能PtS 2/MoTe 2异质结红外光电探测器08吉林大学学报(信息科学版)第42卷Heterojunction[J].Infrared Technology,2022,44(11):1236⁃1242.[12]张翔宇,陈雨田,曾值,等.自供能Bi2O2Se/TiO2异质结紫外探测器的制备与光电探测性能[J].激光与光电子学进展,2022,59(11):177⁃182.ZHANG X Y,CHEN Y T,ZENG Z,et al.Preparation and Photodetection Performance of Self⁃Powered Bi2O2Se/TiO2 Heterojunction Ultraviolet Detectors[J].Laser&Optoelectronics Progress,2022,59(11):177⁃182.[13]朱建华,容萍,任帅,等.ZnO纳米棒/Bi2S3量子点异质结的制备及光电探测性能研究[J].光学精密工程,2022,30 (16):1915⁃1923.ZHU J 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Chapter7_Optical transducers

Chapter7_Optical transducers
Chapter 7: Optical transducers
Contents
1. 2. 3. 4. 5. 6. Principles of optical measurements Optical components Surface plasmon resonance biosensors Optical chemical sensors Optical physical sensors SAQ‟s
C x
Reflectance Mirror or specular reflection occurs at a boundary surface when there is no light transmission through it Diffuse reflection requires that the light penetrates the boundary, is partially absorbed and scattered, and reappears at the surface Changes in the intensity of the reflected light may accurately represent physical as well as chemical events that occur Kubelka-Munk theory relates the total diffuse reflection from a material to its scattering and absorption

Example

Bioluminescence and chemiluminescence
Phosphorescence When photons of energy, such as visible light, are absorbed by a certain material, the electrons orbiting the atoms can move to orbits of higher energies. When the electron in the outer orbit falls back to the original state a photon of energy is emitted, usually in the form of visible light Slow decay by emission of photons continues long after the illumination is over Fluorescent decay is very fast, ending when light is extinguished

二维核磁共振谱在多糖结构研究中的应用_李波

二维核磁共振谱在多糖结构研究中的应用_李波

二维核磁共振谱在多糖结构研究中的应用李 波1,2*,陈海华2,许时婴2(1.河南科技学院食品学院,新乡453003;2.江南大学食品学院,无锡214036)摘 要:二维核磁共振谱(2D NMR )是获取多糖结构信息,尤其是在多糖序列分析方面的有力工具。

本文重点介绍了在多糖结构解析中常用的几种2D NMR 谱以及2D NM R 解析多糖结构的方法。

关键词:核磁共振;二维核磁共振;多糖;结构中图分类号:O65 Application of Two Dimension Nuclear Magnetic Resonance in the StructuralDetermination of PolysaccharideLI Bo 1,2*,C HE N Hai -hua 2,XU Shi -ying 2(1.Food School ,Henan Institute of Science and Technology ,Xinxian g 453003,China ;2.School of Food Science and Technology ,Southern Yangt ze Univers ity ,Wuxi 214036,China )A bstract :Two dimension nuclear magnetic resonance (2D NMR )is a powerful tool acq uiring structural information of pol ysac -charide ,especiall y in the sequence analysis of polysaccharide .Several 2D NM R spectra often used in polysaccharide structural analysis and the method for studying polysaccharide structure usin g 2D NMR are introduced in this paper .Key words :nuclear magnetic resonance ;2D NMR ;polysaccharide ;structure 天然产物研究与开发 2005 Vol .17 No .4NA TUR AL PROD UCT RESEARCH AND DEVELOP M ENT 收稿日期:2004-04-06 接受日期:2004-05-12 *通讯作者Tel :86-373-3040977;E -mail :libowuxi @yahoo .co m .cn 近年来,多糖类化合物由于具有多方面的功能性质,因而成为研究领域的一个热点,多糖的结构及其构效关系也越来越引起人们的重视。

基于最小冗余线阵的二维DOA估计方法

基于最小冗余线阵的二维DOA估计方法

第22卷 第3期2009年3月传感技术学报CHIN ES E JOURNAL OF S ENSORS AND ACTUA TORSVol.22 No.3Mar.2009Minimum 2R edundancy Linear Array B ased Two 2Dimensional DOA Estimation Approach 3Z H A N G Con g ,Q I U Peng 2y u ,L U H uan 2z hang3(School of Elect ronic Science and Engineering ,N ational Universit y.of Def ense Technology ,Changsha 410073,China )Abstract :To overcome t he low sensor utilization rate problem existing in most two 2dimensional (22D )di 2rection 2of 2arrival (DOA )estimation algorit hms ,a new met hod wit h low array redundancy is proposed in t his paper.The p roposed array configuration consist s of a minimum redundancy linear array (MRLA )and two guiding sensors.Wit h t he help of t hese guiding sensors ,t he application of MRL A is extended to 22D DOA estimation.U sing multiple lag conjugate cyclic correlation f unctions of different sensor outp ut s ,two p seudo 2data mat rices are const ructed.Since t he p seudo 2data mat rices can be regarded as t he outp ut s of t he two parallel arrays wit h rotational invariance p roperty ,t he DOA Matrix idea is t hen applied to estimate t he DOAs.The p ropo sed met hod not only inherit s t he advantages of t he DOA Matrix met hod ,but also avoids t he optimal lag choo sing problem.Besides ,t his met hod obtains larger array apert ure wit h fewer sensors.Simulation result s verify t hat t he propo sed algorit hm achieves better performance and better robust ness t han CCDM met hod.K ey w ords :array signal processing ;minimum redundancy linear array ;two 2dimensional DOA ;cyclosta 2tionarity ;conjugate cyclic correlation EEACC :7200基于最小冗余线阵的二维DOA 估计方法3张 聪,邱鹏宇,卢焕章3(国防科学技术大学电子科学与工程学院,长沙410073)基金项目:国家863基金项目资助(2007AA703428);国家重点实验室基金项目资助(J C05204212)收稿日期:2008209230 修改日期:2008212213摘 要:针对传感器阵列二维DOA 估计中阵元数较多且阵元利用率较低的问题,提出了一种低阵元冗余的二维DOA 估计方法。

Symmetric2DLDA

Symmetric2DLDA

Symmetric Two Dimensional Linear Discriminant Analysis(2DLDA)Dijun Luo,Chris Ding,Heng HuangUniversity of Texas at Arlington701S.Nedderman Drive Arlington,TX76013dijun.luo@,{chqding,heng}@AbstractLinear discriminant analysis(LDA)has been success-fully applied into computer vision and pattern recognition for effective feature extraction.High-dimensional objects such as images are usually transform as1D vectors be-fore the LDA transformation.Recently,two-dimension LDA (2DLDA)methods have been proposed which reduced the dimensionality of images without transforming the matrices into vectors.However,the objective function for2DLDA re-mains an unresolved problem.In this paper,we(1)propose a symmetric LDA formulation which resolves the ambigu-ity problem,and(2)propose an effective algorithm to solve the symmetric2DLDA objective.Experiments on UMIST, CMU PIE,and YaleB images databases show that our ap-proach outperforms the other2DLDA methods in terms of both classification accuracy and objective function results.1.IntroductionFisher linear discriminant analysis(LDA)has been suc-cessfully applied to computer vision and pattern recogni-tion applications in the past few years.As a subspace analysis approach to learn the low-dimensional structure of high-dimensional data,LDA seeks for a set of vectors that maximized Fisher Discriminant Criterion.It simulta-neously minimized the within-class scatter while maximiz-ing the between-class scatter in the projective feature vec-tor space.Typical transform-based methods include Fish-erfaces[1]and its variations[8].Belhumeur et al.dis-cussed the comparison between Fisherface and Eigenface in[1]and also showed that LDA was better than Principle Component Analysis(PCA).Recently several two-dimensional LDA(2DLDA)meth-ods have been presented recently.Liu et al.[6],Li and Yuan[5],and Xiong et al.[9]formulated the image based between-class scatter matrix and within-class scatter matrix calculation.Those methods didn’t convert the images into vectors so that reduced the dimensionality of image matri-ces.Song et al.[7]and Yang et al.[10]used the column by column correlations to reduce the number of columns. Yang et al.[12]improved and gave out an algorithm to re-duce the number of columnsfirst and reduce the number of rows later.This method is an order dependent algorithm. Ye et al.[14]introduce an order independent2DLDA with an iterative solution algorithm.They consider the projec-tion of the data onto a space which is the tensor product of two vector spaces.In Inoue and Urahama’s paper[4], they pointed out Ye’s iterative algorithm does not necessar-ily increase objective function monotonically.Because one more objective function exists for2DLDA and it can de-crease when we maximize another one.Inoue and Urahama [4]proposed a method for selecting the transformation ma-trices which give higher value of the generalized Fisher cri-terion than both Yang’s and Ye’s2DLDAs.They also gave out a non-iterative algorithm in which the rows and columns matrices are treated independently.However,a fundamental problem with2DLDA remains unresolved.For1D vectors,the between-class and within-class scatter matrices are uniquely defined.For2D matrices such as images,the between-class and within-class scatter matrices are not unique.There is a large number of possible choices,see Eqs.(10-14).In other words,the2DLDA ob-jective functions used in all previous work are incomplete.In this paper,we present a novel approach that re-solves this ambiguity problem of2DLDA.We begin with a key observation:if the2D matrix objects are symmet-ric,then the between-class and within-class scatter matrices are uniquely defined.Motivated from this observation,we propose a new data representation which(1)enforces sym-metry and(2)are equivalent to the standard transforms in 2DLDA.This symmetric data representation therefore de-fines a unique2DLDA objective function,which is consis-tent generalization from1DLDA(see Section3).In Section4,we propose an effective algorithm to solve the new2DLDA objective function.In Section5, we perform experiments on three well-known face images databases to evaluate the performance of other2DLDA methods and2DSVD(representing the methods from unsu-pervised learning family).Our experimental results demon-strate that our approach outperforms other2DLDA meth-ods.2.Review of LDA and Existing2DLDA2.1.Classic LDAThe classical LDA transforms the original data into a much lower dimensional space where the classification task is much easier to perform.Let the original be a set of1D vectors:X=(x1,···,x n)∈R m×n,with the knowl-edge that they are partitioned into k pattern classesΠ={π1,···,πk},withπi contains n i data points in the i-th class.In LDA,the transformation to the lower dimensional (sub)-space isy i=G T x i,(1) where G is the transformation to the subspace.We often write(y1,···,y n)=G T(x1,···,x n)or Y=G T X The goal of LDA is tofind the G such that different classes are more separated in the transformed space and thus more eas-ily distinguished from each other.Define the between-class scatter matrix S b and within-class scatter matric S wS b(x)=kj=1n j(m j−m)(m j−m)T,(2)S w(x)=kj=1x i∈πj(x i−m j)(x i−m j)T,(3)where m j=1njx i∈πjx i is its class mean and m=1 n ni=1x i is the global mean.In the transformed space,S b and S w are transformed intoS b(Y)=G T S b(X)G,S w(Y)=G T S w(X)G.The optimization criteria of LDA is that G is chosensuch that different classes are more separated from other(max S b(Y))and each class is more compact(min S w(Y)). This leads to the standard LDA optimization objective func-tion:max G J(G)=trS b(Y)S w(Y)=trG T S b(X)GG T S w(X)G.(4)Note that tr(A/B)=tr(B−1A)=tr(AB−1).2.2.2DLDAIn2DLDA,we deal with a set of images X= (X1,···,X n),X i∈ r×c.With similar intuition of clas-sical LDA,2DLDA tries to seek a bilinear transformationY i=L T X i R,(5)such that different classes are more separated.The key issue is how to select the subspace L and R based on between-class and within-class scatter matrices.We immediately see there is a fundamental ambiguity problem:There are two ways to define the within-class scat-ter matric S wS w(XX T)=kj=1x i∈πj(X i−M j)(X i−M j)T,(6) S w(X T X)=kj=1x i∈πj(X i−M j)T(X i−M j),(7)and there two ways to define the between-class scatter ma-tric S bS b(XX T)=kj=1n j(M j−M)(M j−M)T,(8) S b(X T X)=kj=1n j(M j−M)T(M j−M).(9) Therefore,in the transformed space,we have correspondingS b(Y Y T),S b(Y T Y),S w(Y Y T),S w(Y T Y).In general,images are not symmetric:X i=X T i.ThusS b(Y Y T)=S b(Y T Y),S w(Y Y T)=S w(Y T Y).For this reason,the LDA objective function is ambiguous. We have a large number of choices:J1=trS b(Y Y T)S w,(10) J2=trS b(Y T Y)S w(Y T Y),(11) J3=trS b(Y Y T)S w(Y Y T)+S b(Y T Y)S w(Y T Y),(12) J4=trS b(Y T Y)S w(Y Y)S b(Y T Y)S w(Y Y),(13) J5=trS b(Y Y T)+S b(Y T Y)S w w Y),(14) etc.Which is the right one?Why?3.Symmetric2DLDAOur main contribution in this paper is to introduce a new data representation to resolve the ambiguity problem of the existing2DLDA.Our approach is motivated by a key observation:if theimages is symmetric,i.e.,X i =X Ti,then S w (XX T)=S w (X TX ),S b (XX T )=S b (X T X ).Then the ambiguity problem in Eqs.(10-14)will be re-solved.For this reason,we introduce a new data represen-tation (bilinear transformation).3.1.Symmetric Bilinear TransformationHere we introduce a symmetric bilinear transformation:Y T i Y i =ΓT X iX Ti Γ,Γ= L R.(15)Using this symmetric transformation,the scatter matri-ces become unique and the ambiguity problem of existing2DLDA is resolved.We now show that the bilinear transformation of Eq.(15)is equivalent to the linear transformation of Eq.(5).We have the following equalities:ΓTX i X Ti Γ= R T X Ti L L T X i R (16)Thus Y i =L TX i R holds identically.We also haveX T iX i−ΓY iY TiΓT 2=2||X i −LY i R T ||2(17)Therefore,optimizations using (L,R )are equivalent to op-timizations using Γ.3.2.Symmetric 2DLDAUsing the symmetric bilinear transformation of Eq.(15)we have the following theorem:Theorem 1:The unique LDA objective function for 2DLDA isJ 2DLDA=trS b (Y Y T)S w (Y Y T )=trS b (Y TY )S w (Y T Y )(18)=tr R T S L b R R S w R +L T S R b LL S w L (19)whereS Rw=k j =1 X i ∈πj (X i −M j )RR T (X i −M j )T ,(20)S L w=k j =1 X i ∈πj(X i −M j )T LL T (X i −M j ).(21)S Rb=k j =1n j (M j −M )RR T (M j −M )T ,(22)S L b =k j =1n j (M j −M )T LL T (M j −M ).(23)The proof is rather lengthy and is given in Appendix A.4.Related Work on 2DLDAWith the notation introduced in Theorem 1,it is now con-venient to discuss earlier work relating to 2DLDA.Yang et al.[10]first propose to useJ 2=trS b (Y T Y )S w (Y T Y )=tr L T S b L L T S w L.This idea is the further development of 2DPCA [11].Ye etal.[14]usesJ 1=tr S b (Y Y T )S w (Y Y T )=tr R T S L b R R T S L wR ,(24)J2=tr S b (Y T Y )S w (Y T Y )=tr L T S R b L L T S R wL .(25)This idea is the further development of GLRAM [13].Inoueet al.[4]emphasized the inconsistency of the optimization approach of Ye et al.[14]and provide several alternatives.This issue is explained more carefully below.4.1.Inconsistency of Independent Alternating Op-timization ApproachIn both Ye’s [14]and Inoue et al.’s [4]approaches,they optimize the two objectives Eqs.(24,25)max RJ 1(R,L ),max LJ 2(R,L ),in an independent and alternating way.They obtain R bymaximizing J 1(ignoring J 2)and then obtain L by maxi-mizing J 2(ignoring J1).A fundamental drawback of this approach is the inconsistency of optimization.When maxi-mizing J 1(without considering J 2),J 2could be and is often decreased.Similarly,when maximizing J2(without consid-ering J 1),J1could be and is often decreased.Inoue and Urahama [4]noticed and emphasized this in-consistency.They provided some quick fixes,but did not provide a satisfactory solution.A satisfactory solution to this problem has two technicalchallenges.First,when maximizing J1,we need to takeinto account of J2.But in order to do so,we need to knowhow J 1and J 2should be combined.One choice is simpleadditive combination:J =J 1+J2.Another choice should beJ =tr R T S L b R +L T S R b LR T S L w R +L T S R wL ,(26)There are many other choices.Clearly,this requires a rig-orous definition of the objective function for 2DLDA.Oursymmetric LDA is motivated by this challenge.The second challenge is how to optimize the result-ing objective function.The solution for max R J1is sim-ply given by the eigenvectors of (S L w )−1S Lb ,as in stan-dard LDA.For the objectives such as Eq.(26)or Eq.(19)the functional dependency on R,L via Eqs.(20,21,33,23)are rather complicated.The required algorithm could be far more complicated than the eigenvector solution in the independent-alternating approach.Our work resolves this challenge by developing the derivative based approach as described in the next section.putational Algorithms for Symmetric2DLDAThe objective of Symmetric 2DLDA in Eq.(19)is no longer the trace of a single ratio two scatter matrices.As discussed in §4.1,this objective can not be solved directly by calculating eigenvectors (as in standard LDA).Fortu-nately we are able to develop an efficient algorithm to solve this problem by using gradient-ascend approach.This ap-proach requires the derivatives of the objective.The deriva-tives of matrix functions be worked out using basic matrix algebra such as in the book [2].We skip the rather lengthy derivation and present the results in the following Lemma:Lemma 1.Let P L =L T S R bL ,Q L =L T S R w L ,P R =R T S L bR ,and Q R =R T S L w R .The derivatives of the objec-tive function J 2DLDA of Eq.(19)are the following.For ∂J∂R ,we have∂∂R tr R T S Lb R R T S L w R=2S L b RQ −1R −2S Lw RQ −1R P Q −1R ,(27)and∂∂R tr L T S Rb L L T S R w L=2K k =1 A i ∈πk (A i −M k )T LQ −1L L T(A i −M k )R−2Kk =1(M k −M )T LQ −1L P L Q −1L L T(M k −M )R.(28)For∂J ∂L ,we have∂∂L tr L T S R b L L T S R w L=2S R b LQ −1L −2S Rw LQ −1L P L Q −1L ,(29)∂∂L tr R T S LbR R T S L w R=2K k =1 A i ∈πk (A i −M k )RQ −1R R T (A i −M k )TL−2Kk =1(M k −M )RQ −1R P R Q −1R R T (M k −M )TL.(30)We present the results in four parts to make them moretransparent.Algorithm 1Solving Symmetric 2DLDA using gradient.Inputa)A set of images {X i }n i =1and their class labels.b)Initial L 0,R 0c)Frequency c for orthogonalization Initializationa)L ←L 0,R ←R 0,b)Calculate M k ,k =1,2,...,K and M ,c)t ←0DoCalculate S L w ,S L b ,S R w ,S R b .R ←R +δ∂J∂RL ←L +δ∂J∂L t ←t +1if (t mod c )=0R ←eigenvectors of (S L w)−1S L b L ←eigenvectors of (S R w )−1S Rb endifUntil stopping criteria is satisfied.Output L,RUsing the explicit formulations of the gradient above,wedevelop Algorithm 1in Table.The step size δis set toδ=0.02<|R |>/<|∂J/∂R |>where <|A |>= m i =1 nj =1|A ij |/nm .The parameter c is to control the frequency for R T S L b R,R T S L wR,L T S R b L,and L T S Rw L to be nearly di-agonal.This implies that in the transformed space,S L b,S L w ,S R b ,and S R w are nearly diagonal,i.e.,data are si-multaneously uncorrelated w.r.t.S L t=S L b +S L w and are uncorrelated w.r.t.S R t =S R b +S Rw .In the experiments,we set c =3.6.Experimental ResultsWe compare performance of symmetric 2DLDA to the method of Ye et al.[13]on three standard face images datasets.6.1.UMISTThefirst benchmark UMIST faces is for multi-view face recognition,which is challenging in computer vision be-cause the variations between the images of the same face in viewing direction are almost always larger than image variations in face identity.A robust face recognition system should be able to recognize the person even though the test-ing image and training images have quite different poses. This dataset contains20persons with18images for each. All these images of UMIST database are cropped and re-sized into28×23images.In this dataset,wefirst visualize the discriminant capa-bility of subspace of our approach.Since typically the dis-tance of two two-dimension object X i is evaluate in the L,R subspace:Y i=L T X i R,we want to see the major components of subspace in two-dimension plot,which are shown Figure1.In thisfigure,we compare PCA,2DSVD, Ye’s2DLDA,and our method.We use3(shown infirst two columns),6(shown in the third and fourth columns),and9 (shown in the last two columns)images per person to train the data across all the persons and pick up three persons,18 images for each,to plot in the selected subspace.For PCA, we plotfirst principle component(as x-axis)versus second principle(y-axis)in(a)columns andfirst principle compo-nent(x-axis)versus third principle component(y-axis)in (b)columns.For2DSVD,Ye’s2DLDA,and our method, we use l T1X i r1as x-axis and l T1X i r2as y-axis to plot im-age X i in(a)columns and l T1X i r1as x-axis and l T2X i r1as y-axis to plot in(b)columns,where l1,l2,r1,r2are thefirst two columns of L and R respectively.In each plot,blue points denote training dataset which are used to seek the subspace,and red points are testing images.From the plots, we can see that unsupervised methods(PCA and2DSVD) are not suitable to generate a discriminative subspace.In-stead,supervised methods(Ye’s2DLDA and our method) are much better.We can also see that the more training im-ages we use,the more discriminative the subspace is.The plots also indicate that our method enjoy much more dis-criminative capability than Ye’s2DLDA since our method directly solve the2DLDA objective.Instead of using cross validation,we systematically eval-uate the classification accuracy and objective function value using a cross validation-like scheme which is much more challenging:The images are equally divided into5parts. Then pick one part as the training dataset and the rest4parts as testing dataset.Repeat it5times by picking up different parts as training dataset.This is scheme only uses20%of the images to train and80%to test.We set k=5,8,12 and compare the classification with subspace of2DSVD, Ye’s2DLDA and original space(direct Nearest Neighbor classication).We plot the average Nearest Neighbor classi-fication accuracy and the corresponding2DLDA objective defined in Eq.(19).For original space and2DSVD,we(a)k=5(b)k=8(c)k=12Figure2.Classification accuracy and objective function value comparison on UMIST.omit the objective function value.Thefigure shows that our method is significantly better in term of objective function since we are explicitly solving the objective function.Our method also generate better subspace(3%-5%better in clas-sification accuracy),see Figure2(a),2(b),and2(c).We also summarize the best results in classification and objective in Table1.6.2.CMU PIE DatasetThe second dataset is CMU PIE(Face Pose,Illumina-tion,and Expression)face database which contains68sub-jects with41,368face images as a whole.Preprocessing to locate the faces was applied.Original images were nor-malized(in scale and orientation)such that the two eyes were aligned at the same position.Then,the facial areas were cropped into thefinal images for matching.The size of each cropped image is64×64pixels,with256grey levels per pixel.No further preprocessing is done.In ourFigure1.Visualization of discriminative capability of PCA,2DSVD,Ye’s2DLDA and our method on UMIST dataset.Shown are3cases for training the subspace using3,6,and9images per person.UMIST k=5k=8k=12Acc Obj Acc Obj Acc Obj KNN0.764–0.764–0.764–Y2DLDA0.81587.60.76469.10.85366.8 S2DLDA0.848148.10.880141.70.885105.6 PIE k=8k=12k=16Acc Obj Acc Obj Acc Obj KNN0.537–0.537–0.537–Y2DLDA0.623459.80.678366.10.691327.2 S2DLDA0.651514.40.678411.70.696339.7 YaleB k=8k=12k=16Acc Obj Acc Obj Acc Obj KNN0.572–0.572–0.572–Y2DLDA0.766418.80.804348.30.791303.2 S2DLDA0.768446.00.799393.20.796336.9 Table 1.Summarization of best classification accuracy and 2DLDA objective function value in UMIST,PIE,and YaleB face datasets.Methods:KNN in original space,Ye’s2DLDA (Y2DLDA),and Symmetric2DLDA(S2DLDA). experiment,we randomly pick10different combinations of pose,face expression,and illumination condition.Finally we have68×10=680images.We use the same scheme discussed above in this dataset except we set k=8,12,16since the image size is larger than UMIST.The results can be found in Figure3(a),3(b),and3(c).In this dataset,we generate a reasonable bet-ter result in classification(about5%better)when k=8 and slightly better in the other cases.Overall,the clas-sification accuracy is much more stable.Our method is also always outperforms Ye’s method in2DLDA objective (roughly30%better).The summarization of the results are shown in Table1.6.3.YaleB DatasetThefinal face images benchmark used in our experiment is the combination of extended and original Yale database B[3].These two databases contain single light source im-ages of38subjects(10subjects in original database and28 subjects in extended one)under576viewing conditions(9 poses x64illumination conditions).Thus,for each subject, we got576images under different lighting conditions.The facial areas were cropped into thefinal images for match-ing[3],including:1)preprocessing to locate the faces was applied;2)original images were normalized(in scale and orientation)such that the two eyes were aligned at the same position.The size of each cropped image in our experi-ments is192×168pixels,with256gray levels per pixel. We randomly pick up20images for each person and also subsample the images down to48×42.In this dataset,the solutions of our method is till stably better than Ye’s2DLDA in2DLDA objective(see the right(a)k=8(b)k=12(c)k=16Figure3.Classification accuracy and objective function value comparison on PIE.part of Figure4(a),4(b),and4(c)).And the classification accuracy is close to each other.In this YaleB dataset,the faces are taken in64different illumination conditions and we only pick up20%of the data to train.Thus both Ye’s 2DLDA and Symmetric2DLDA are easy to overfit in the training set.However,Symmetric2DLDA is still slightly better and more stable overall.We can alsofind the summa-rization of the results in Table1.7.ConclusionThis paperfirst points out the LDA ambiguity problem that was existing in the previous2DLDA objective func-tions.After that,we present a novel symmetric data repre-sentation and resolve the ambiguity problem using the com-plete objective function for2DLDA.Our2DLDA(Sym-metric2DLDA)is thefirst one to define2DLDA using ratio trace formulation with complete between-class scat-ter matrices and within-class scatter matrices.An effective(a)k=8(b)k=12(c)k=16Figure4.Classification accuracy and objective function value comparison on YaleB.computational algorithm is also given out to solve the com-plete objective function of Symmetric2DLDA.The exper-imental results show that our method achieves better face recognition accuracy than other2DLDA methods.The new methodology improves the feature extraction and pattern classification in computer vision and machine learning re-lated research.2DLDA is a kind of bilinear discriminant analysis meth-ods.Tensor based LDA can be generated using the ap-proach presented in this paper.Our future work will exploit the multi-linear discriminant analysis problem. AcknowledgementThis work is partially supported by NSF DMS-0844497, NSF CCF-0830780,and University of Texas Stars Award.Appendix AProof of Theorem1:We write the within-class scatter matrices S w(Y Y)as follows:S w(Y Y)=nj=1Y i∈πj(Y i−M Y j)T(Y i−M Y j)·(Y i−M Y j)T(Y i−M Y j)(31)Substituting Eq.(15)into Eq.(31),we get:S w(Y Y)=nj=1X i∈πjLRT(X i−M j)(X i−M j)TLRLRT(X i−M j)(X i−M j)TLR=nj=1X i∈πjLRTdiag(X i−M j)RR T(X i−M j)T(X i−M j)T LL T(X i−M j)LR=LRTS R wS L wLR.(32)Similarly,we can write the between-class scatter matrices as:S b(Y Y)=LRTS RbS LbLR.(33)The standard LDA objective function isJ2DLDA(L,R)=tr S b(Y Y)S w(Y Y)=trLRTS RbS LbLRLRTS RwS LwLR=trR T S LbR00L T S R b LR T S LwR00L T S R w L=tr(R T S L w R)−100(L T S R w L)−1·R T S LbR00L T S R b L=trR T S LbRR T S LwR+trL T S RbLL T S RwLReferences[1]P.Belhumeur,J.Hespanha,and D.Kriengman.Eigenfacesvsfisherfaces:recognition using class specific linear projec-tion.IEEE Trans.Pattern Analysis and Machine Intelligence, 19(7):711–720,1997.[2]K.Fukunaga.Introduction to statistical pattern recognition.Academic Press Professional,2nd edition,1990.[3] A.Georghiades,P.Belhumeur,and D.Kriegman.From fewto many:Illumination cone models for face recognition un-der variable lighting and pose.IEEE Trans.Pattern Anal.Mach.Intelligence,23(6):643–660,2001.[4]K.Inoue and K.Urahama.Non-iterative two-dimensionallinear discriminant analysis.Proceedings of the18th In-ternational Conference on Pattern Recognition,2:540–543, 2006.[5]M.Li and B.Yuan.2d-lda:A novel statistical linear discrim-inant analysis for image matrix.Pattern Recognition Letters, 26(5):527–532,2005.[6]K.Liu,Y.Cheng,and J.Yang.Algebraic feature extractionfor image recognition based on an optimal discriminant cri-terion.Pattern Recognition,26(6):903–911,1993.[7] F.Song,S.Liu,and J.Yang.Orthogonalizedfisher discrim-inant.Pattern Recognition,38(2):311–313,2005.[8] D.Swets and ing discriminant eigenfeatures forimage retrieval.IEEE Trans.Pattern Analysis and Machine Intelligence,18(8):831–836,1996.[9]H.Xiong,M.Swamy,and M.Ahmad.Two-dimensionalfldfor face recognition.Pattern Recognition,38(7):1121–1124, 2005.[10]J.Yang,J.Yang, A.F.Frangi,and D.Zhang.Uncor-related projection discriminant analysis and its application to face image feature extraction.International Journal of Pattern Recognition and Artificial Intelligence,17(8):1325–1347,2003.[11]J.Yang,D.Zhang,A.F.Frangi,and J.Yang.Twodimen-sional pca:A new approach to appearancebased face rep-resentation and recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence,26(1),2004.[12]J.Yang,D.Zhang,X.Yong,and J.Yang.Two-dimensionallinear discriminant transform for face recognition.Pattern Recognition,38(7):1125–1129,2005.[13]J.Ye.Generalized low rank approximations of matrices.In-ternational Conference on Machine Learning,2004. 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Nature Research Reporting Summary说明书

October 2018Corresponding author(s):Sinem K. Saka, Yu Wang, Peng YinLast updated by author(s):June 05, 2019Reporting SummaryNature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Research policies, see Authors & Referees and the Editorial Policy Checklist .StatisticsFor all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section.The exact sample size (n ) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedlyThe statistical test(s) used AND whether they are one- or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section.A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals)For null hypothesis testing, the test statistic (e.g. F , t , r ) with confidence intervals, effect sizes, degrees of freedom and P value notedGive P values as exact values whenever suitable.For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settingsFor hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomesEstimates of effect sizes (e.g. Cohen's d , Pearson's r ), indicating how they were calculatedOur web collection on statistics for biologists contains articles on many of the points above.Software and codePolicy information about availability of computer codeData collection Commercial softwares licensed by microscopy companies were utilized: Zeiss Zen 2012 (for LSM 710), Leica LAS AF (for Leica SP5), ZeissZen 2.3 Pro Blue edition (for LZeiss Axio Observer Z1), Olympus VS-ASW (for Olympus VS120), PerkinElmer Phenochart (version 1.0.2) .Data analysis Open-source Python (3.6.5), TensorFlow (1.12.0), and Deep Learning packages have been utilized for machine learning-based nucleiidentification (the algorithm and code is available at https:///HMS-IDAC/UNet). We used Matlab (2017b) for watershed-based nuclear segmentation using the identified nuclear contours. Python 3.6 was used for the FWHM calculations, as well as plotting ofhistograms. We used MATLAB and the Image Processing Toolbox R2016a (The MathWorks, Inc., Natick, Massachusetts, United States)for quantifications in mouse retina sections and for Supplementary Fig. 4. We utilized Cell Profiler 3.1.5 for the quantifications of signalamplification in FFPE samples in Figure 2 and 3. FIJI (version 2.0.0-rc-69/1.52n) was utilized for ROI selections and format conversions.HMS OMERO (version 5.4.6.21) was used for viewing images and assembling figure panels.For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors/reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Research guidelines for submitting code & software for further information.DataPolicy information about availability of dataAll manuscripts must include a data availability statement . This statement should provide the following information, where applicable:- Accession codes, unique identifiers, or web links for publicly available datasets- A list of figures that have associated raw data- A description of any restrictions on data availabilityData and Software Availability: The data and essential custom scripts for image processing will be made available from the corresponding authors P.Y.(**************.edu),S.K.S.(***********************.edu),andY.W.(********************.edu)uponrequest.Thedeeplearningalgorithmandtestdataset for automated identification of nuclear contours in tonsil tissues is available on https:///HMS-IDAC/UNet . The MATLAB code for nuclear segmentation isOctober 2018available on: https:///HMS-IDAC/SABERProbMapSegmentation .Field-specific reportingPlease select the one below that is the best fit for your research. If you are not sure, read the appropriate sections before making your selection.Life sciencesBehavioural & social sciences Ecological, evolutionary & environmental sciencesFor a reference copy of the document with all sections, see /documents/nr-reporting-summary-flat.pdfLife sciences study design All studies must disclose on these points even when the disclosure is negative.Sample size Each FFPE experiment batch were performed on consecutive sections from the same source, each containing over 600,000 cells. Due to largenumber of single cells with tens of distinct germinal center morphologies being present in each section, ROIs from different parts of a wholesection was used for quantification of signal improvement for each condition (consecutive sections were used for all the conditions of onequantification experiment). Number of ROIs are noted in the respective figure legends. For quantifications in retina samples, due toconserved staining morphology and low sample-to-sample variability n = 6 z-stacks were acquired from at least 2 retina sections. ForSupplementary Fig. 4, minimum 5 z-stacks were acquired for each condition to collect images of 18-45 cells. Number of cells are reported in the graphs.Data exclusions Parts of the FFPE tissue sections were excluded from analysis due to automated imaging related aberrations (out-of-focus areas) or tissuepreparation aberrations (folding of the thin sections at the edges, or uneven thickness at the edge areas). For FWHM calculations inSupplementary Fig. 2, ROIs that yield lineplots with more than one automatically detected peak were discarded to avoid deviations due tomultiple peaks. For Supplementary Fig. 4 cells in the samples were excluded when an external bright fluorescent particle (dust speck, dye aggregate etc.) coincided with the nuclei (as confirmed by manual inspection of the images). The exclusion criteria were pre-established.Replication Each FFPE experiment batch were performed on consecutive sections from the same source, each containing over 600,000 cells. Forevaluation and quantification of our method, multiple biological replicates were not accumulated in order to avoid the error that would beintroduced by the natural biological and preparation variation, and to avoid unnecessary use of human tissue material. In the case of themouse retina quantifications a minimum of two distinct retinal sections were imaged, and each experiment was performed at least twice. ForSupplementary Fig. 4 dataset, 16 different conditions were prepared and each were imaged multiple times (before linear, after linear, beforebranch, after branch). Although the data was not pooled together for the statistics reported in the figure, low cell-to-cell variability was observed and high consistency was seen across the samples for comparable conditions, suggesting low sample to sample variability.Randomization Randomization was not necessary for this study.Blinding Blinding was not possible as experimental conditions were mostly evident from the image data.Reporting for specific materials, systems and methodsWe require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material, system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response.AntibodiesAntibodies used The full list is also available in Supplementary Information, Supplementary Table 4.Ki-67 Cell Signaling #9129, clone: D3B5 (formulated in PBS, Lot: 2), diluted 1:100-1:250 after conjugationCD8a Cell Signaling #85336 clone: D8A8Y (formulated in PBS, Lot: 4) diluted 1:150 after conjugationPD-1 Cell Signaling #43248, clone: EH33 (formulated in PBS, Lot: 2), diluted 1:150 after conjugationIgA Jackson ImmunoResearch #109-005-011 (Lot: 134868), diluted 1:150 after conjugationCD3e Cell Signaling #85061 clone: D7A6E(TM) XP(R) (formulated in PBS, Lot:2), diluted 1:150 after conjugationIgM Jackson ImmunoResearch #709-006-073 (Lot: 133627), diluted 1:150 after conjugationLamin B Santa Cruz sc-6216 clone:C-20, (Lot: E1115), diluted 1:100Alpha-Tubulin ThermoFisher #MA1-80017 (multiple lots), diluted 1:50 after conjugationCone arrestin Millipore #AB15282 (Lot: 2712407), diluted 1:100 after conjugationGFAP ThermoFisher #13-0300 (Lot: rh241999), diluted 1:50 after conjugationSV2 HybridomaBank, Antibody Registry ID: AB_2315387, in house production, diluted 1:25 after conjugationPKCα Novus #NB600-201, diluted 1:50 after conjugationCollagen IV Novus #NB120-6586, diluted 1:50 after conjugationRhodopsin EnCor Bio #MCA-A531, diluted 1:50 after conjugationCalbindin EnCor Bio #MCA-5A9, diluted 1:25 after conjugationVimentin Cell Signaling #5741S, diluted 1:50 after conjugationCalretinin EnCor Bio #MCA3G9, diluted 1:50 after conjugationVLP1 EnCor Bio #MCA-2D11, diluted 1:25 after conjugationBassoon Enzo ADI-VAM-#PS003, diluted 1:500Homer1b/c ThermoFisher #PA5-21487, diluted 1:250SupplementaryAnti-rabbit IgG (to detect Ki-67 and Homer1b/c indirectly) Jackson ImmunoResearch # 711-005-152 (Multiple lots), 1:90 afterconjugationAnti-mouse IgG (to detect Bassoon indirectly) Jackson ImmunoResearch #715-005-151) (Multiple lots), diluted 1:100 afterconjugationAnti-goat IgG (to detect Lamin B indirectly) Jackson ImmunoResearch # 705-005-147) (Lot: 125860), diluted 1:75 afterconjugationAlternative antibodies used to validate colocalization of VLP1 and Calretinin in Supplementary Fig. 8d-f:Calretinin (SantaCruz #SC-365956; EnCor Bio #CPCA-Calret; EnCor Bio #MCA-3G9 AP), VLP1 (EnCor Bio #RPCA-VLP1; EnCor Bio#CPCA-VLP1; EnCor Bio #MCA-2D11). All diluted 1:100.Fluorophore-conjugated secondary antibodies used for reference imaging:anti-rat-Alexa647 (ThermoFisher #A-21472, 1:200), anti-rabbit-Alexa488 (ThermoFisher #A-21206, 1:200), anti-rabbit-Atto488(Rockland #611-152-122S, Lot:33901, 1:500), anti-mouse-Alexa647 (ThermoFisher #A-31571, 1:400), anti-goat-Alexa647(ThermoFisher # A-21447, 1:200), anti-rabbit-Alexa647 (Jackson ImmunoResearch, 711-605-152, Lot: 125197, 1:300).Validation All antibodies used are from commercial sources as described. Only antibodies that have been validated by the vendor with in vitro and in situ experiments (for IHC and IF, with images available on the websites) and/or heavily used by the community withpublication in several references were used. The validation and references for each are publicly available on the respectivevendor websites that can reached via the catalog numbers listed above. In our experiments, IF patterns matched the distributionof cell types these antibodies were expected to label based on the literature both before and after conjugation with DNA strands. Eukaryotic cell linesPolicy information about cell linesCell line source(s)BS-C-1 cells and HeLa cellsAuthentication Cell lines were not authenticated (not relevant for the experiment or results)Mycoplasma contamination Cell lines were not tested for mycoplasma contamination (not relevant for the experiment or results)Commonly misidentified lines (See ICLAC register)No commonly misidentified cell lines were used.October 2018Animals and other organismsPolicy information about studies involving animals; ARRIVE guidelines recommended for reporting animal researchLaboratory animals Wild-type CD1 mice (male and female) age P13 or P17 were used for retina harvest.Wild animals The study did not involve wild animals.Field-collected samples The study did not involve samples collected from the field.Ethics oversight All animal procedures were in accordance with the National Institute for Laboratory Animal Research Guide for the Care and Useof Laboratory Animals and approved by the Harvard Medical School Committee on Animal Care.Note that full information on the approval of the study protocol must also be provided in the manuscript.Human research participantsPolicy information about studies involving human research participantsPopulation characteristics We have only used exempt tissue sections for technical demonstration, since we do not derive any biological conclusions, thepopulation characteristics is not relevant for this methodological study.Recruitment Not relevant for this study.Ethics oversight Human specimens were retrieved from the archives of the Pathology Department of Beth Israel Deaconess Medical Centerunder the discarded/excess tissue protocol as approved in Institutional Review Board (IRB) Protocol #2017P000585. Informedinform consent was waived on the basis of minimal risk to participants (which is indirect and not based on prospectiveparticipation by patients).Note that full information on the approval of the study protocol must also be provided in the manuscript.October 2018。

理学空气动力学


下面我们用以上的微分形式控制方程推导出准一维
流动的面积-速度关系式(area-velocity relation),并用 面积-速度关系式来研究准一维流动的一些物理特性。
将方程(10.14)d(uA) 0 展开并同除以 uA 得:
d du dA 0 uA
(10.20)
因为我们要得到面积-速度关系式,因此我们要
2
e2
u22 2
h1
u12 2h2来自u22 2•状态方程:
h0 常数
p2 2RT2
•对于量热完全气体焓与温度的关系为:
h2 c pT2
(10.8) (10.9) (10.10) (10.11) (10.12)
将控制方程归纳如下:
1u1A1 2u2 A2 或
uA 常数
(10.1)
p1A1 1u12 A1
A
u
2、For M>1 (supersonic flow), the quantity in parentheses
in Eq.(10.25) is positive. Hence, an increase in velocity
(positive du ) is associated with an increase in area (positive
A2 A1
pdA
p2 A2
2u22 A2
得:
pA u2 A pdA
( p dp)(A dA) ( d)(u du)2 (A dA)
(10.15)
我们忽略所有微分的乘积, 即高阶微分量,得:
Adp Au2d u2dA 2uAdu 0 (10.16)
我们将微分形式的连续方程 d (uA) 0 (10.14)展开,

纹理物体缺陷的视觉检测算法研究--优秀毕业论文


摘 要
在竞争激烈的工业自动化生产过程中,机器视觉对产品质量的把关起着举足 轻重的作用,机器视觉在缺陷检测技术方面的应用也逐渐普遍起来。与常规的检 测技术相比,自动化的视觉检测系统更加经济、快捷、高效与 安全。纹理物体在 工业生产中广泛存在,像用于半导体装配和封装底板和发光二极管,现代 化电子 系统中的印制电路板,以及纺织行业中的布匹和织物等都可认为是含有纹理特征 的物体。本论文主要致力于纹理物体的缺陷检测技术研究,为纹理物体的自动化 检测提供高效而可靠的检测算法。 纹理是描述图像内容的重要特征,纹理分析也已经被成功的应用与纹理分割 和纹理分类当中。本研究提出了一种基于纹理分析技术和参考比较方式的缺陷检 测算法。这种算法能容忍物体变形引起的图像配准误差,对纹理的影响也具有鲁 棒性。本算法旨在为检测出的缺陷区域提供丰富而重要的物理意义,如缺陷区域 的大小、形状、亮度对比度及空间分布等。同时,在参考图像可行的情况下,本 算法可用于同质纹理物体和非同质纹理物体的检测,对非纹理物体 的检测也可取 得不错的效果。 在整个检测过程中,我们采用了可调控金字塔的纹理分析和重构技术。与传 统的小波纹理分析技术不同,我们在小波域中加入处理物体变形和纹理影响的容 忍度控制算法,来实现容忍物体变形和对纹理影响鲁棒的目的。最后可调控金字 塔的重构保证了缺陷区域物理意义恢复的准确性。实验阶段,我们检测了一系列 具有实际应用价值的图像。实验结果表明 本文提出的纹理物体缺陷检测算法具有 高效性和易于实现性。 关键字: 缺陷检测;纹理;物体变形;可调控金字塔;重构
Keywords: defect detection, texture, object distortion, steerable pyramid, reconstruction
II

Bio-Rad ProteoGel IPG Strips 技术手册说明书

ProteoGel IPG StripsStorage Temperature –20 °CTECHNICAL BULLETINProduct DescriptionTwo-dimensional (2D) electrophoresis separatesproteins in the first dimension by their isoelectric point (pI) and by molecular weight in the second dimension. Isoelectric point separation is achieved by electrophoresis (focusing) of solubilized proteins in agel containing an immobilized pH gradient (ProteoGelIPG Strips). Following the first dimension separation,the ProteoGel IPG Strip is equilibrated with ProteoGelIPG Equilibration Buffer (Product Code I 7281) to denature the proteins with a detergent (SDS) and urea. The ProteoGel IPG Strip is then placed in the well of a SDS-PAGE 2D gel and electrophoresed to separate the proteins by molecular weight.ProteoGel IPG Strips are produced using acrylamido buffers to create stable, immobilized pH gradients in a polyacrylamide matrix. The polyacrylamide matrix isdried onto a plastic backing to increase the shelf-life ofthe IPG strips and to allow the strip to be rehydratedwith the protein sample.ProteoGel IPG Strips are available with a wide rangepH gradient (pH 3-10) or 5 different narrow range pH gradients (3-5, 4-7, 5-8, 6-11, and 8-11) to optimize the separation of the proteins. The strips are available in three different lengths (7 cm, 11 cm, and 18 cm). The strips are conveniently labeled with a “+” on the acidic (anode) end of the strip for orientation in the focusing unit.Table 1.ProteoGel IPG Strip Product CodespH RangeLength 3-10 3-5 4-7 5-8 6-11 8-11 7 cm I 2531 I 3031 I 2906 I 3156 I 7406 I 3281 11 cm I 3406 I 3656 I 3531 I 3781 I 7531 I 3906 18 cm I 4031 I 4281 I 4156 I 4406 I 7656 I 4531 Products Required But Not ProvidedUltrapure Water (18 MΩ•cm or equivalent) Rehydration trayForceps (Product Code F 3767)Mineral oil (Product Code M 3516)IPG strip focusing apparatusProteoGel IPG Equilibration Buffer (ProductCode I 7281)SDS-PAGE apparatusGel Protein StainCoomassie Brilliant Blue G-250 stain(EZBlue Gel Staining Reagent, ProductCode G 1041) orSilver Stain(ProteoSilver Silver Stain Kit, Product CodePROT-SIL1) or (ProteoSilver Plus, ProductCode PROT-SIL2 for samples prepared forMALDI-MS analysis.)DuraSeal laboratory stretch film (Product CodeD 3172) or Parafilm (Product Code P 7793) Precautions and DisclaimerThese products are for R&D use only, not for drug, household, or other uses. Please consult the Material Safety Data Sheet for information regarding hazards and safe handling practices.Storage/StabilityThe ProteoGel IPG strips are stable at −20 °C for at least 1 year in an unopened package.Procedure1. Prepare the protein sample in an appropriatesolubilization/extraction solution. Sigma offersthree different ProteoPrep kits (PROT-TOT,PROT-TWO, and PROT-MEM) for2D electrophoresis sample preparation. Each kit contains solubilization/extraction solutions, atributylphosphine solution for reduction of thesample, and iodoacetamide for protein alkylation.22. Dilute an aliquot of the prepared sample to thedesired concentration. Pipette the appropriateamount of sample (see Table 2) along the edge ofthe rehydration tray.Table 2.ProteoGel IPG strip rehydration volumesIPG strip length Sample volume7 cm 125 µl11 cm 200 µl18 cm 320 µl3. Remove the protective plastic from the ProteoGelIPG strip gel surface and place the strip, gel sidedown, on the sample such that the entire gel is incontact with sample.Note: When the gel side is down, the writing on the strip will appear in the correct orientation. Wrap the rehydration tray with laboratory stretch film toprevent evaporation. Allow the strips to rehydrateat room temperature for 5 hours or until essentially all the sample has been absorbed into the gel.Lower temperatures may cause the urea toprecipitate. Less than 3 µl of the sample shouldremain in the tray after rehydration.Note: Water-saturated blotting paper may be added to an empty lane of the rehydration tray to reduceevaporation or overlay mineral oil (Product CodeM 3516) on the strips.4. Assemble the strip into the IPG strip focusingapparatus following the manufacturer's instructions.The acidic end (+) of the ProteoGel IPG stripshould be at the anode (red/+). Ensure that the gel on the IPG strip has made contact with theelectrode or a moist electrode wick. Overlaymineral oil on the strips to minimize evaporationduring the focusing.5. See Table 3 for the recommended electrophoresisprotocols for focusing of the ProteoGel IPG strips.The recommended temperature is 20 °C. Lowertemperatures may cause the urea to precipitate.Increasing the total volt hours may improve thefocusing. The maximum current allowed per strip is50 µA, otherwise damage to the strip fromoverheating may occur. Table 3.ProteoGel IPG Strip Focusing ConditionsStep VoltageTimeVoltHours 7 cm stripConditioningRampFocusing250 V250 – 6000 V6000 V1 hour2 hours60,00011 cm stripConditioningRampFocusing250 V250 – 6000 V6000 V1 hour2 hours80,00018 cm stripConditioningRampFocusing250 V250 – 6,000 V6,000 V1 hour2 hours100,0006. If necessary, the focused ProteoGel IPG strips maybe wrapped with laboratory stretch film and storedbelow –20 °C for up to 1 week, prior to running thesecond dimension gel.7. After focusing, equilibrate the focused IPG Stripwith ProteoGel IPG Equilibration Buffer for 20 to30 minutes at room temperature.8. Fill the well of a SDS-PAGE 2D gel with electrodebuffer and place the ProteoGel IPG Strip into thewell, with forceps, so that the side of the stripmakes complete contact with the top of thepolyacrylamide gel. Avoid air bubbles between thestrip and the top of the gel.Note: An agarose overlay is not necessary.9. Assemble the SDS-PAGE 2D gel into theelectrophoresis unit and electrophorese the gel untilthe blue dye front is within 1 cm of the bottom of thegel.10. Stain the SDS-PAGE gel using Coomassie BrilliantBlue (EZBlue Gel Staining Reagent, Product CodeG 1041) or silver stain (ProteoSilver Silver Stain Kit,Product Code PROT-SIL1) to visualize the proteins.Proteosilver Plus (Product Code PROT-SIL2) isrecommended for samples prepared for MALDI-MSanalysis.3 Related Products Product CodeProteoPrep KitsTotal Extraction SampleMembrane Protein Extraction Universal Extraction PROT-TOT PROT-MEM PROT-TWOProtein Extraction ReagentType 4C 0356 Protein Extraction ReagentType 2C 0606 Dithiothreitol (DTT)D 5545 Iodoacetamide (IAA) A 3221 Tributylphosphine (TBP) T 7567 ProteoGel IPG EquilibrationBufferI 7281 ProteoGel Tris-Tricine-SDSElectrode BufferT 2821 Hi/Lo Profile Rocker Z36,774-5 References1. Gorg, Angelika, Two-Dimensional Electrophoresisof Proteins Using Immobilized pH Gradients. ALaboratory Manual. Technical University of Munich (Munich, Germany: 1998).Coomassie Brilliant Blue is a registered trademark of Imperial Chemical Industries.Duraseal is a trademark of Diversified Biotech. Parafilm is a registered trademark of American National Can Company.Technology developed in partnership with Proteome Systems.GL/MDS/MAM 06/04Sigma brand products are sold through Sigma-Aldrich, Inc.Sigma-Aldrich, Inc. warrants that its products conform to the information contained in this and other Sigma-Aldrich publications. Purchaser must determine the suitability of the product(s) for their particular use. Additional terms and conditions may apply. Please see reverse side ofthe invoice or packing slip.。

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Evaluation of a 2D diode array for IMRT quality assuranceDaniel Le´tourneau *,Misbah Gulam,Di Yan,Mark Oldham,John W.Wong Department of Radiation Oncology,William Beaumont Hospital,3601W.Thirteen Mile Road,Royal Oak,MI 48073,USAReceived 30April 2003;received in revised form 7October 2003;accepted 29October 2003AbstractBackground and purpose :The QA of intensity modulated radiotherapy (IMRT)dosimetry is a laborious task.The goal of this work is toevaluate the dosimetric characteristics of a new 2D diode array (MapCheck from Sun Nuclear Corporation,Melbourne,Florida)and assess the role it can play in routine IMRT QA.Material and methods :Fundamental properties of the MapCheck such as reproducibility,linearity and temperature dependence are studied for high-energy photon beams.The accuracy of the correction for difference of diode sensitivity is also assessed.The diode array is benchmarked against film and ion chambers for conventional and IMRT treatments.The MapCheck sensitivity to multileaf collimator position errors is determined.Results :The diode array response is linear with dose up to 295cGy.All diodes are calibrated to within ^1%of each other,and mostly within ^0.5%.The MapCheck readings are reproducible to within a maximum SD of ^0.15%.A temperature dependence of 0.57%/8C was noted and should be taken into account for absolute dosimetric measurement.Clinical performance of the MapCheck for relative and absolute dosimetry is demonstrated with seven beam (6MV)head and neck IMRT plans,and compares well with film and ion chamber parison to calculated dose maps demonstrates that the planning system model underestimates the dose gradients in the penumbra region.Conclusions :The MapCheck offers the dosimetric characteristics required for performing both relative and absolute dose measurements.Its use in the clinic can simplify and reduce the IMRT QA workload.q 2003Elsevier Ireland Ltd.All rights reserved.Keywords:Intensity modulated radiation therapy;Quality assurance;Diode array1.IntroductionThe potential improvement of tumor local control with dose escalation and decrease of side effects with better sparing of critical organs have contributed to the eager incorporation of intensity modulated radiation therapy (IMRT)techniques by the radiation therapy community.Clinical implementation of IMRT,however,has been hindered by the lack of efficient tools and methods for dosimetry verification and quality assurance (QA).Typi-cally,the QA process consists of verifying the absolute dose delivered to a reference point,and also the relative planar isodose distribution.The latter task is more involved and performed using two general approaches:integrated dosim-etry [11,13,15,17–19,22,27]and individual beam dosimetry [1,3,12,23,27].Integrated dosimetry consists of measuring the relative composite dose distribution in one or moreselected planes of a (often cylindrical)phantom.In the individual beam approach,the relative dose distribution is measured on a plane perpendicular to the central axis of each beam in a flat phantom.The integrated dose approach provides direct information on the composite dose distri-bution and is more efficient.On the other hand,the individual beam approach allows for a more comprehensive analysis and can lead to a better understanding of the sources of error in the planning and delivery process.In both cases,films are generally used as relative 2D dosimeter of choice.IMRT film dosimetry can be very tedious,particularly when repeat QA measurements need to be made.A new 2D diode array has been developed for routine QA of planar IMRT dosimetry (MapCheck from Sun Nuclear)[10].This device contains 445n-type diodes distributed over an area of 22£22cm 2.The diode spacing is 7.07mm in the 10£10cm 2central portion of the detector and increases to 14.14mm outside of this area.Illustration of0167-8140/$-see front matter q 2003Elsevier Ireland Ltd.All rights reserved.doi:10.1016/j.radonc.2003.10.014Radiotherapy and Oncology 70(2004)199–206/locate/radonline*Corresponding author.the diode array is given in Fig.1.The MapCheck can make both relative and absolute dose measurements simul-taneously and therefore greatly simplify and reduce the QA workload.This device is however not designed to achieve composite beam dosimetry at non-normal incidence due to the diode directional response.Many properties of the MapCheck device need to be thoroughly understood before it can be applied for accurate IMRT verification.In this paper,we characterize and validate several of the basic MapCheck dosimetric properties shown by Jursinic and Nelms [10],such as diode linearity with dose,dose rate response,reproducibility with time and temperature fluctu-ations.In addition,measurements of conventional and IMRT relative beam dosimetry were made with the diode array and compared with those made with film and ion chamber.The potential use of MapCheck as an absolute dosimeter is demonstrated.The sensitivity of the MapCheck measurements to multileaf collimator (MLC)positioning errors is also assessed.Finally,we discuss the issues of setting MapCheck tolerance criteria when comparing measurements and calculations for IMRT beams.2.Methods and materials 2.1.Theory of operationThe dose deposited in the MapCheck by a high-energy photon beam is measured by integrating the current generated in each diode over the irradiation period.Each individual MapCheck diode is 0.8£0.8mm 2.The diode plane has a 2cm thick water-equivalent buildup material and a 2.3cm thick water-equivalent backscattering material.This inherent scattering material replaces,to a certain extent,the usual shielding added around diodes to flatten their response to the low energy scattered photons.According to the manufacturer,the MapCheck diodes areradiation hardened and exhibit a sensitivity degradation ofabout 2.6%/kGy delivered with a 10MeV electron beam.The MapCheck is calibrated for radiation measurement with the diode outputs corrected for their variations in radiation sensitivity.This is achieved by a six-step calibration process designed by the manufacturer.The MapCheck calibration can be done in any high-energy photon beam.The result of the calibration is a file containing an individual correction factor for each diode.During a measurement session,the MapCheck is leveled on the accelerator couch and its center is aligned with the center of the beam utilizing the beam crosshair.The output of the MapCheck is sent to a graphical software interface for display and analysis on a PC.A background correction is also required prior to a measurement session,to account for cable and diode noise in the absence of radiation.2.2.Calibration and reproducibilityWe verified the accuracy of the MapCheck calibration method by subtracting measurements of a 6MV photon beam (Elekta Precise,Crawley,UK)acquired at 0and 1808rotation of the detector array.For each detector orientation,six MapCheck readings were acquired and averaged.The field size was 25£25cm 2at 100cm source-to-surface distance (SSD)and 5cm buildup was used.One hundred MUs were delivered per reading.The two matrices of average dose measurements were appropriately rotated for subtraction.The diode array reproducibility over a measurement session was evaluated by calculating the SD of 15consecutive readings made by each MapCheck diode.These measurements were acquired with 5cm of water-equivalent buildup at a SSD of 100cm.Photon beams of 6and 18MV (SL20,Elekta,Crawley,UK)at a field size of 25£25cm 2were used to deliver 60MUs per reading.A Farmer chamber placed in solid water at 1.5cm under the MapCheck was used to measure the stability of the beam on the central axis.The reproducibility of dosimetry using Kodak XV films was also measured in similar conditions for comparison.2.3.Linearity,pulse rate and dose rate responseNote that the measurements of linearity,pulse and dose rates dependence,and output factor were made only with the central diode of the device because the MapCheck exhibits a uniform inter-diode response once calibrated,as will be shown in Section 3.Measurements were made using 6and 18MV photon beams (SL20,Elekta,Crawley,UK)at the standard 5cm buildup and 100cm SSD geometry.The dose linearity response of the MapCheck central diode was evaluated by measuring its output for beam deliveries of 1–450MUs.The Elekta linear accelerators allow the user to select different repetition rates by varying the number ofradiationFig.1.Two-dimensional diode array (MapCheck).D.Le´tourneau et al./Radiotherapy and Oncology 70(2004)199–206200pulses per second.Therefore,the pulse rate dependence of the same diode was determined by measuring its response at a constant dose(100MU)delivered with repetition rate ranging from50to600MU/min.The diode response to the dose per pulse,or dose rate,was also evaluated at a constant machine repetition rate of400MU/min and output of 100MUs.The dose rate was varied by changing the SSD from75to135cm,with5cm buildup.The MapCheck results were referenced to the measurements made with a Farmer ion chamber under the same irradiation conditions.2.4.Output factor comparisonThe MapCheck central diode was used to measure the relative dose output for various squarefield sizes ranging from1£1to25£25cm2for6and18MV beams, respectively.These measurements were done with a buildup of10cm and a source to buildup distance of90cm.The relative output factors derived from these measurements were compared to the measurements made with a Farmer chamber(PTW30006)and a pinpoint chamber(PTW 31006)in the same conditions.2.5.Temperature effectTemperature dependence was measured for two indivi-dual MapCheck n-type diodes provided by the manufac-turer.The diodes were immersed in a cold water bath at a depth of1.5cm.The source to water distance was100cm.A laboratory water heater-circulator attached to the reservoir was used to slowly increase the water temperature from10to408C at a rate of approximately0.258C/min.A thermocouple attached to the diode capsules was used to monitor the diode temperature.A6MV photon beam delivered an output of100MU to the diodes after every58C rise in temperature.Before each irradiation and measure-ment,the water heating system was turned off for 10–15min in order for the temperature in the diode capsule to reach equilibrium.The charges produced by both diodes are collected simultaneously with a two-channel electrometer.2.6.Clinical applicationFor absolute dosimetry,the MapCheck is calibrated,for a given photon energy,by delivering100cGy to the unit with afield size of10£10cm2and a SSD of100cm.The MapCheck software then calculates a(central)diode output to dose conversion factor.The conversion factor and the inter-diode responses are saved infiles that can be loaded when the MapCheck is used for subsequent dose measure-ments at specific photon energy.For relative isodose distribution delivered by any given beam,‘reference’measured or calculated dose maps can be loaded into the MapCheck software for comparison with dose maps measured with MapCheck.The reference dose map can be shifted manually to optimize alignment with the MapCheck dose map.The quality of the match between the two dose maps is evaluated by determining the number of diodes that satisfy a relative dose difference tolerance and a distance to agreement tolerance set by the user.Initial clinical testing of the MapCheck involved simple comparisons of6and18MV open and608wedgedfield profiles measured with an IC10ion chamber(Scanditronix-Wellhofer,Bartell,TN),films and MapCheck.The ion chamber profiles were scanned in a water tank,whereas the film and MapCheck measurements were obtained in solid water.The buildup thickness was5cm and the SSD was 100cm.The MapCheck profiles were obtained with the diagonal diodes aligned with the collimator crosshair to achieve maximum spatial resolution.Thefilms were digitized with a Vidar12-bit scanner and processed using the RIT software(Radiological Imaging Technology, Colorado Springs,CO)at a resolution of0.423mm.A medianfilter(3£3pixels)was used to smooth thefilm data.For the open beam profiles,the MapCheck results were compared to the ion chamber measurements for low gradient areas inside and outside of the beam.The MapCheck results were compared withfilm measurements in the penumbra region where high-spatial resolution was parison of the608wedge profiles was performed to evaluate MapCheck’s response to beam hardened dosimetry.The relative dosimetry performances of the MapCheck for IMRT QA were evaluated by comparing the MapCheck measurements tofilm results for a head and neck IMRT treatment containing seven beams.This plan contained an average of9segments/beam and the averagefield size was 14£17cm2.MapCheck measurements were also compared to the calculated dose maps obtained with Pinnacle3(Philips Medical System—Radiotherapy).Both the MapCheck and thefilm dose maps were obtained with5cm of buildup and at a SSD of90cm.All irradiations were delivered at08gantry angle in order to simplify setup.Bothfilm and calculated dose maps were loaded into the MapCheck software for comparison.The film results were down sampled to a1£1mm2resolution grid by the MapCheck software.The Pinnacle3dose maps were calculated at the same resolution.After the user normalizes the diode array and reference dose maps to a selected dose point,the software application calculates the number of diodes,which satisfy the dose difference tolerance and distance to agreement criteria selected by the user.The accuracy of the MapCheck absolute dose measure-ments was verified by comparing its readings to the doses measured with a pinpoint chamber(PTW31006)for the seven IMRT irradiations in solid water.For each beam, the point of measurement is chosen to coincide with the normalization point used for the relative dose comparison. The absolute calibration of the diode array is performed justD.Le´tourneau et al./Radiotherapy and Oncology70(2004)199–206201prior to these measurements to eliminate all possible temperature dependence effects.The last MapCheck clinical test consisted of verifying its sensitivity to MLC positioning errors.This was achieved by modifying another clinical seven-beam head and neck IMRT plan where all MLC segments were contracted and expanded by1and2mm,respectively.This plan had an average of9segments/beam and with an averagefield size of17£20cm2.Each of the contracted and the expanded beams were delivered to the MapCheck.For a given beam, the unmodified,contracted and the expanded deliveries measured with MapCheck were compared with the calculated dose map.The MapCheck sensitivity to the MLC positioning error was evaluated by the variation of the number of diodes that did not satisfy the dose and distance to agreement tolerances specified by the user.3.Results3.1.Calibration and reproducibilityThe accuracy of the correction for difference in radiation sensitivity of the445MapCheck diodes was verified by subtracting measurements of a6MV photon beam acquired at0and1808rotation of the diode array.The discrepancies observed vary from20.6%to0.8%with more than85%of the diodes within^0.4%.It is important to mention that stability of the calibration is affected by the stability of the radiation beam used for the calibration process.The symmetry stability of the calibration beam was about 0.1%.When the calibration beam stability was arbitrarily degraded to0.3%,the discrepancies between the rotated readings increased to^1.2%.The maximum SD for each MapCheck diode and for15 consecutive measurements is^0.15%.These measure-ments included not only the reproducibility of the detector but also the reproducibility of the beam output between measurements.SD of the15reference ion chamber readings is0.04%compared to that of0.06%of the central MapCheck diode.Almost identical results were obtained for an18MV photon beam.In comparison,the maximum SD of15Kodak XVfilm measurements using45MU exposures is^1.7%in the open portion(80%)of thefield, in agreement with published data[2,14].3.2.Linearity,pulse rate and dose rate responseThe diode response is linear with dose and demonstrates a slightly higher sensitivity for18MV photons than for 6MV.The slopes of the best linearfit for6and18MV photon beams are11094.6and11854.1counts/Gy with regression coefficients of0.99999and0.99995,respec-tively.The diode saturates at2.95and2.76Gy for6and 18MV,respectively,due to the capacitor size used in our MapCheck integrator circuit.The pulse rate dependence of the central diode for a 6MV photon beam and repetition rate ranging from50to 600MU/min is shown in Fig.2.The response of a Farmer ion chamber using the same irradiation conditions is also shown.Both curves are normalized to the measurements at maximum dose rate.The diode exhibits a monotonically increasing sensitivity variation of2% with increasing pulse repetition rate.The Farmer chamber exhibits,0.5%variation,attributable to the variation of dose delivery of the linear accelerator as a function of the selected repetition rate.We have verified that this unexpected diode behavior is not due to a variation of MapCheck integrator response as function of the exposure time by repeating all measurements with constant irradiation time.The results are identical to the ones presented in Fig.2.Similar results are also obtained for the diode and the chamber for18MV photon beam. The basic mechanism of the MapCheck behavior is not resolved at the present time and is under investigation.Pulse rate dependence of the diode should not be a concern for IMRT QA because all treatments are generally delivered with the same repetition rate.The diode’s dependence on dose rate needs to be examined,as dose delivered to a point will vary withfield size or IMRT segments.The ratios of the relative doses measured with the MapCheck central diode and a Farmer ion chamber in the same irradiation conditions(10£10cm2,5cm depth and 2.5cm of backscattering material)for SSD of75–135cm are presented in Fig.3.This change in SSD corresponds to a change in dose rate from6.50to2.10Gy/min.These dose rates are obtained by correcting the nominal dose rate of 4Gy/min(SSD100cm,10£10cm2,d max)with the inverse square law and the proper TMR.The results are normalized to the measurements at95cm SSD.The plotted data are averages of three diode and three Farmer readings, respectively.(The error bars correspond to the sum of the relative diode and Farmer reading errors in quadrature.)The Fig.2.Pulse rate dependence of the central diode of the MapCheck in a 6MV photon beam.The pulse rate dependence of a Farmer ion chamber placed1.5cm under the diode array is also shown.D.Le´tourneau et al./Radiotherapy and Oncology70(2004)199–206 202diode sensitivity varies from 1.05to 20.85%for SSD from 75to 135cm,respectively.These results fall within the range of published data for different n-and p-type silicon diodes [4,6,8–10,25,26].3.3.Output factor comparisonThe output factors of a 6MV photon beam measured for different field sizes with the MapCheck central diode,a Farmer chamber (PTW30006)and a pinpoint chamber (PTW31006)are presented in Fig.4.The results are normalized with respect to that for a 10£10cm 2field.For field sizes equal to 4£4cm 2and larger,MapCheck and Farmer results agree generally to within 1%.At 25£25cm 2,where the field size exceeds the diode array,the MapCheck underestimates the output factor by 1.2%.For field size smaller than 4£4cm 2,the Farmer chamber underestimates the output factor due to the volume averaging effect.The output factors measured with the MapCheck diode and the pinpoint chamber agree to within 2%for field sizes down to 2£2cm 2.For the 1£1cm 2field,the pinpoint chamber output factor is 13.3%lowerthan that measured with the MapCheck.For such small field dimensions,the 2mm diameter by 5mm length of pinpoint chamber seems less suitable than the 0.8£0.8mm 2MapCheck diode for dose measurements.For small field sizes,output factors measured with MapCheck agree to within 2%of published data for 6MV photon beam (Elekta linear accelerator)measured with a diamond detector or calculated with Monte Carlo simulation [7].3.4.Temperature effectThe results for two individual MapCheck diodes demonstrate a linear increase of sensitivity with tempera-ture.The two diodes exhibit a slight difference in temperature dependence,with temperature coefficients equal to 0.52and 0.57%/8C,respectively.These results fall within the range of diode temperature coefficients published in the literature (20.1to 0.6%/8C)[10,16,20,24].For room temperatures from 18to 258C,the diodes show an average sensitivity increase of about 4%.Diode temperature dependence is not corrected for by the MapCheck hardware or software.The absolute calibration of the MapCheck should be repeated if the room temperature differs from the calibration condition by more than ^18C in order to achieve high-accuracy absolute dose measurements.3.5.Clinical applicationProfiles of 10£10and 20£20cm 2field have been measured with an IC10ion chamber,films and MapCheck.The IC10ion chamber and MapCheck results for both field sizes agree to within ^1%in the low-dose gradient regions inside and outside of the field.The film profiles are noisier and agree with the chamber measurements to within ^3%in the low gradient area.The film data were not excessively smoothed in order to preserve the sharpness of the profile in the penumbra region.In the high-dose gradient region,the volume averaging effect degrades the ion chamber profiles.Discrepancies greater than 1.5mm distance to agreement are observed between the ion chamber and the film measurements in the high-gradient regions.The limited resolution of the MapCheck means that often only one or two measurement points will be in the 20–80%penumbra region.The diode readings are accurate also in the high-dose gradient region and match well with the film profiles.The MapCheck results are less sensitive to volume averaging effect or low energy scattered photon.The diode array readings also appear to be insensitive to beam hardening produced by a 608wedge (Fig.5).The ion chamber and MapCheck profiles of the wedged field agree well over the open portion of the field.The discrepancy between both curves reaches 5%at the tip of the profile,mainly due to the poorer spatial resolution of the chamber.The MapCheck performance for relative dosimetry of IMRT fields was evaluated based on a seven beam,6MVFig.3.The ratio of relative doses measured with the MapCheck central diode and a Farmer ion chamber in the same irradiation conditions as function of the source-to-surface distance (SSD).The dose rate seen by the detectors is varied by changing the SSD from 75to 135cm.Fig.4.Output factors of a 6MV photon beam measured with the central diode of the MapCheck,a Farmer (PTW30006)and a pinpoint chamber (PTW31006).The results are normalized for the 10£10cm 2field size.D.Le ´tourneau et al./Radiotherapy and Oncology 70(2004)199–206203head and neck IMRT plan.The agreements between MapCheck with film,and MapCheck with Pinnacle dose maps are evaluated for dose differences of 3and 5%and distances to agreement of 1and 2mm.For the seven IMRT beams,Fig.6shows the average percentage of diodes,which agrees within the specified tolerances.The error bars on the graph represent ^1SD on the percentage of diodes satisfying the tolerances.Fig.7shows a screen capture of a section of the MapCheck interface where the film or the calculated dose map is shown in gray scale in the background overlaid with the failed diodes (blue or red diodes for negative and positive differences,respectively).For a tolerance of 3%dose difference and 2mm distance toagreement (denoted 3%/2mm),99.6%of the diodes agree with the film measurements.The percentage of diodes in agreement with the film decreases to 99.0and 95.6%for tighter tolerances of 5%/1mm and 3%/1mm,respectively.These results demonstrate excellent agreement between MapCheck and film measurements.The percentage of diodes in agreement with the treatment plan calculated dose maps ranges from 96.4,90and 83.4%for the tolerance of 3%/2mm,5%/1mm and 3%/1mm,respectively.The failed diodes are located mainly in regions of high-dose gradient.This disagreement is due in part to the modeling of the penumbra in the planning system.The same type of discrepancies was observed between film measurements and Pinnacle calculations in the high-dose gradient regions.Our Pinnacle 3calculations underestimate the gradient in the penumbra region because its beam model has been based on beam profiles acquired with a 6mm diameter ion chamber.The improvement of the Pinnacle 3model based on profiles measured with a high-resolution scanning diode to achieve better agreement in the beam penumbra is under investigation.Absolute dose measurements are also achieved with the MapCheck and a pinpoint chamber (PTW31006)for the previous IMRT plan.The MapCheck results are system-atically higher than the chamber readings and the dis-crepancy between both detectors ranges from 0to 3.2%.The chamber is believed to underestimate slightly the dose due to a lack of sensitivity.In fact,for segments,which block the measurement point,the small chamber does not record any signal whereas the diode array detectstheFig.5.Inplane profiles of a 20£20cm 2608wedged field (6MV)measuredwith the MapCheck,an IC10ion chamber andfilms.Fig. parison between 2D MapCheck measurements,film and Pinnacle dose maps for a seven-beam head and neck IMRT plan.The histogram shows the number of diodes,which agree with the film and the calculated dose,respectively (within given dose difference and distance to agreementtolerances).Fig.7.Screen capture of a section of the MapCheck interface.The film or the calculated dose map is shown in gray scale in the background with the failing diodes in overlay.Diodes are displayed in red or blue to represent positive or negative discrepancy,respectively.The green diode represents the normalization point.The tolerances used in this example are 3%and 2mm.D.Le´tourneau et al./Radiotherapy and Oncology 70(2004)199–206204radiation transmission through the collimator.For certainbeams where the normalization point is located on a narrow dose peak,the volume averaging effect can also explain in part the lower dose seen by the ion chamber.The sensitivity of the diode array for MLC positioning errors was investigated using another seven-beam head and neck IMRT plan.Fig.8shows the results of the comparison of MapCheck and Pinnacle 3dose maps as percentage of diodes within tolerance.On average,92.3%of the MapCheck diode readings agree with the unmodified dose map for a tolerance set at 3%/2mm.For the 1mm contracted and expanded MLC deliveries,the percentage of diodes in agreement with the unmodified Pinnacle 3dose maps decreases to 83.3and 91.9%,respectively,at 3%/2mm tolerance.The agreement decreases further to 75.4and 80.5%for the 2mm contracted and expanded MLC deliveries,respectively.The error bars on the graph in Fig.8represent ^1SD on the percentage of diodes satisfying the tolerances.In all cases,the failed diodes are mainly located in regions of high-dose gradient.As expected,for the contracted plans,the failed diodes showed lower dose than the unmodified calculated dose maps.The opposite was observed for the expanded plans.In multiple segment delivery,the effect of the systematic MLC position errors is emphasized by the presence of multiple field edges and can be detected by the MapCheck even if the spacing between the diodes is larger than the MLC position error.Fig.8shows that the difference in MapCheck agreement was noticeably smaller for a 1mm MLC expansion than for a 1mm MLC contraction.The results suggest that the MLC itself might have been initially calibrated to produce fields that were smaller than intended such that the expected discrepancies were not observed when the MLC segments were enlarged by 1mm.The magnitude of the calibrationerror also appears to be less than 1mm.Our results demonstrate that,with a properly designed set of QA measurements,the diode array can detect a systematic MLC position error of the order of 1mm in all the MLC leaves.4.Discussion and conclusionsOur results demonstrate that the MapCheck can be used to accurately and efficiently verify the dosimetry of IMRT treatment delivery.The setting of MapCheck comparison tolerance criteria is challenging and needs to take into account the uncertainties of the MapCheck measurements,the MLC calibration,radiation delivery and treatment plan dose calculation.Van Dyke et al.[21]and the AAPM task group 53[5]suggest criteria of 3%of dose difference and 4and 3mm,respectively,for dosimetry of conformal therapy beam.At present,in our institution,the tolerances between measurements and calculations are set at 3%/2mm.The percentage of diode failing these criteria can reach up to 15%and is due mainly to the modeling of the penumbra in our planning system.The disagreement between the measured and calculated dose maps increases generally with the number of segments per beam and with the use of small segments (,2cm 2)delivering an appreciable fraction of the MUs.In our practice,we try to eliminate these small segments during the planning process by limiting the minimum segment size and by reviewing all segments before submitting the plan to the physician for review.After MapCheck measurement,the physician and the physicist inspect the position of the failed diodes with respect to the location of the target and organs at risk.The decision to go ahead with the plan,to modify it or to change the delivery method is then made.Methods to improve the agreement between planned and measured IMRT delivery are currently under investigation.A new image-based procedure has been implemented in our clinic to achieve MLC calibration to within ^0.5mm.The re-modeling of the penumbra in our planning system based on high-resolution measurements should also improve the match between the calculated and the measured dose maps.In the light of our results,we conclude that the diode array presents the required characteristics for performing dosimetry of conventional and IMRT deliveries.The ability of the MapCheck to simultaneously perform both relative and absolute dose measurements can simplify and reduce the IMRT QA workload.Furthermore,its interface makes the comparison to planning data easy and efficient.The definition of the acceptable tolerances for dosimetry comparison is challenging,but provides a meaningful approach to quantify IMRT QA.AcknowledgementsThis work has been funded in part by Sun NuclearCorporation.parison between 2D MapCheck measurements and Pinnacle dose maps for a seven-beam head and neck IMRT plan.The histogram shows the number of diodes,which agree with the calculated dose (within given dose difference and distance to agreement tolerances)for induced MLC positioning errors of ^1and ^2mm.D.Le ´tourneau et al./Radiotherapy and Oncology 70(2004)199–206205。

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