Measurements of CP-Violating Asymmetries in B Decays to omegaKs

HANDYSURF+Mobile Surface Measuring InstrumentWith a sleeker design, new 2.4-inch color LCD screen, and improved user interface for intuitiveoperations, HANDYSURF+ offers a simple quality assurance option for measuring surface parameters throughout production. It is an ideal solution for the automotive, mechanical engineering and medical technology industries.Flexible useHANDYSURF+ is flexible and robust, with horizontal, vertical and overhead surface measurement capabilities that travel to the workpieceUser-friendlinessHANDYSURF+ meets all common surface standards (ISO, DIN, CNOMO, ASME and JIS), features 20 languages and can be connected to a PC, printer or flash drive via built-in USBWider measuring rangeHANDYSURF+ covers a 370 μm measuring range — the widest in its class — without compromising its 0.0007 μm resolutionEnhanced analysisHANDYSURF+ offers graphic representations of measurements for on-site verification with paramater and waveform, and is capable of a variety of analyses including BAC, ADC, peakcount and motifsTechnical Data & Specifications:Available in three models: 35, 40 and 45, with stylus tip radiuses of 2 or 5 μm (45 only available with 5 μm stylustip radius)Z measuring range: -210 to +160 μm Z measuring resolution: 0.0007 μm Stylus tip material: Diamond©2019 Carl Zeiss Industrial Metrology, LLC P: +1 800 327-9735 | E: *************************** | W: /metrologyTechnical Data HANDYSURF+EN_60_020_0021I Printed in USASubject to change in design and scope of delivery and as a result of ongoing technical development.ModelHANDYSURF+3535404045Tip radius 5 μmTip radius 2 μmTip radius 5 μmTip radius 2 μmTip radius 5 μmMeasurement range Z direction -210 to +160 μm -210 to +160 μm -210 to +160 μm -210 to +160 μm -210 to +160 μm -210 to +160 μm Drive axis X direction 16 mmX direction 16 mmX direction 16 mmX direction 16 mmY direction 16 mmTracing Driver Movement type Standard type Standard type Retraction type Retraction type Horizontal tracing type Evaluation Length 0.2 to 16 mm0.2 to 16 mm0.2 to 16 mm0.2 to 16 mm0.2 mm to 4.0 mm Measurement speed 0.5, 0.6, 0.75, 1.0 mm/s0.5, 0.6, 0.75, 1.0 mm/s0.5, 0.6, 0.75, 1.0 mm/s0.5, 0.6, 0.75, 1.0 mm/s0.6 mm/sPickup Sensing typeDifferential inductance Differential inductance Differential inductance Differential inductance Differential inductance Measurement Method SkidSkidSkidSkidSkidZ direction resolution 0.0007 μm/-210 to +160 μm 0.0007 μm/-210 to +160 μm 0.0007 μm/-210 to +160 μm 0.0007 μm/-210 to +160 μm 0.0007 μm/-210 to +160 μm Model E-DT-SM10A E-DT-SM49A E-DT-SM10A E-DT-SM49A E-DT-SM39A StylusMeasurement force 4 mN 0.75 mN 4 mN 0.75 mN 4 mN Tip radius r tip = 5 μm r tip = 2 μm r tip = 5 μm r tip = 2 μm r tip = 5 μm Tip angle 90°cone 60°cone 90°cone 60°cone 90°cone Tip materialDiamondDiamondDiamondDiamondDiamondAnalysis item Calculation Standards Comply with JIS2013/2001, JIS1994, JIS1982, ISO1997/2009, ISO13565, DIN1990, ASME2002/2009, ASME1995, CNOMO ParameterProfile Curve Pt, Rmax, Rz, Rk, Rpk, Rvk, Mr1, Mr2, Vo, K, tpRoughness Curve Ra, Rq, Rz, Rv, Rc, Rt, RSm, RΔq, Rsk, Rku, Rmr(c), Rmr, Rδc, Rz94, R3z, RΔa, Ry, Sm, S, tp, PC, RPc JIS, RPc ISO, RPc EN, Pc, PPI, Rp, Rmax, Mr1, Mr2, Rpk, Rvk, Rk, Vo, K, A1, A2, Rpm, Δa, Δq, HtpMotifR, Rx, AR, W, Wx, AW, Rke, Rpke, Rvke, NCRX, NR, CPM, SR, SAR, Wte, NW, SAW, SW, Mr1e, Mr2e, Vo, K Evaluation Curve Profile Curve, Roughness Curve, ISO13565 SpecialRoughness Curve, Roughness motif curve, Waviness motif curve, Upper envelope waviness curve Characteristics graph Bearing area curve, Amplitude distribution curve Filter Filter type Gaussian, 2RC (phase compensation), 2RC (non-phase compensation)Cutoff valueλc 0.08, 0.25, 0.8, 2.5 mm λsNone, 2.5, 8 μmAmplification indicator Display 2.4-inch color liquid crystal panelData output USB connectors for USB memory/printer connection x 1, Micro USB connector for USB communication x 1Print output Optional (external printer unit) / Thermal recording paper width: 58 mm (recording width: 48 mm)Language Japanese, English, Chinese (Traditional Chinese/Simplified Chinese), Korean, Thai, Malay, Vietnamese, Indonesian, German, French, Italian, Czech, Polish, Hungarian, Turkish, Swedish, Dutch, Spanish, Portuguese Specifications Power SupplyChargingBuilt-in battery (to be charged using AC adaptor, PC USB port, USB battery), charging period: 4 hours (about 1000 measurements can be take when fully charged)Voltage, frequency AC100 to 240 V ±10%, 50/60 Hz, Single phase (Included AC adapter)Power consumptionMaximum 10 WExternal dimensions (W x D x H) / WeightAmplification indicator: 184.5 x 68 x 57.4 mm/about 500 g for the entire system。

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硕士学位论文论 文 题 目： 拇指血流灌注指数试验与改良Allen试验的比较Evaluation of the patency of the hand collateralarteries with thumb Perfusion Index test:Comparison with the modified Allen’s test研 究 生 姓 名: 吴阳指导教师: 刘松学科专业: 麻醉学研究方向: 麻醉学临床技能训练与研究论文工作时间: 2015年6月至2016年12月目录中文摘要 (1)英文摘要 (2)正 文 (3)前 言 (3)资料与方法 (7)结 果 (10)讨 论 (15)结 论 (22)参考文献 (23)致 谢 (33)附录A (34)附录B (44)拇指血流灌注指数试验与改良Allen试验的比较中文摘要目的：探讨拇指血流灌注指数(Perfusion Index，PI)试验替代改良Allen试验(modified Allen's test，MAT)评价掌部组织侧支循环血流灌注的可行性。

方法：选择1108例拟行择期手术并需要经桡动脉入路进行有创动脉压力监测的患者，在桡动脉穿刺前先后用MAT和拇指PI值试验分别评价患者试验侧掌部组织侧支循环血流灌注的情况，并将两种试验方法结果进行统计学比较和分析。

结果：在1108例患者中MAT阴性患者1035例(93.41%)，阳性患者73例(6.59%)；拇指PI值试验阴性患者1090例(98.38%)，其中包括57例MAT阳性患者,阳性患者18例(1.62%)。

拇指PI值试验阴性患者行经该侧桡动脉入路进行有创动脉压力监测，两种试验方法结果进行卡方检验，差异有统计学意义(x2=51.27, P＜0.05)。

两种试验方法影响因素进行logistic回归分析发现两种试验方法结果阳性率均与年龄和性别有相关性(P＜0.05)。

结论：在本研究中用拇指PI值试验筛选出1.62%的患者不宜行经桡动脉入路进行有创动脉压力监测。

a rX iv:mat h /48328v1[mat h.DS]24Aug24ON THE INTERPLAY BETWEEN MEASURABLE AND TOPOLOGICAL DYNAMICS E.GLASNER AND B.WEISS Contents Introduction 2Part 1.Analogies 31.Poincar´e recurrence vs.Birkhoff’s recurrence 31.1.Poincar´e recurrence theorem and topological recurrence 31.2.The existence of Borel cross-sections 41.3.Recurrence sequences and Poincar´e sequences 52.The equivalence of weak mixing and continuous spectrum 73.Disjointness:measure vs.topological d mixing:measure vs.topological 125.Distal systems:topological vs.measure 196.Furstenberg-Zimmer structure theorem vs.its topological PI version 217.Entropy:measure and topological 227.1.The classical variational principle 227.2.Entropy pairs and UPE systems 227.3.A measure attaining the topological entropy of an open cover 237.4.The variational principle for open covers 287.5.Further results connecting topological and measure entropy 307.6.Topological determinism and zero entropy 31Part 2.Meeting grounds 338.Unique ergodicity 339.The relative Jewett-Krieger theorem3410.Models for other commutative diagrams3911.The Furstenberg-Weiss almost 1-1extension theorem4012.Cantor minimal representations4013.Other related theorems41References442 E.GLASNER AND B.WEISSIntroductionRecurrent-wandering,conservative-dissipative,contracting-expanding,deter-ministic-chaotic,isometric-mixing,periodic-turbulent,distal-proximal,the list can go on and on.These(pairs of)words—all of which can be found in the dictio-nary—convey dynamical images and were therefore adopted by mathematicians to denote one or another mathematical aspect of a dynamical system.The two sister branches of the theory of dynamical systems called ergodic theory(or measurable dynamics)and topological dynamics use these words to describe different but parallel notions in their respective theories and the surprising fact is that many of the corresponding results are rather similar.In the following article we have tried to demonstrate both the parallelism and the discord between ergodic theory and topo-logical dynamics.We hope that the subjects we chose to deal with will successfully demonstrate this duality.The table of contents gives a detailed listing of the topics covered.In thefirst part we have detailed the strong analogies between ergodic theory and topological dynamics as shown in the treatment of recurrence phenomena,equicontinuity and weak mixing,distality and entropy.In the case of distality the topological version camefirst and the theory of measurable distality was strongly influenced by the topo-logical results.For entropy theory the influence clearly was in the opposite direction. The prototypical result of the second part is the statement that any abstract mea-sure probability preserving system can be represented as a continuous transformation of a compact space,and thus in some sense ergodic theory embeds into topological dynamics.We have not attempted in any way to be either systematic or comprehensive. Rather our choice of subjects was motivated by taste,interest and knowledge and to great extent is random.We did try to make the survey accessible to non-specialists, and for this reason we deal throughout with the simplest case of actions of Z.Most of the discussion carries over to noninvertible mappings and to R actions.Indeed much of what we describe can be carried over to general amenable groups.Similarly, we have for the most part given rather complete definitions.Nonetheless,we did take advantage of the fact that this article is part of a handbook and for some of the definitions,basic notions and well known results we refer the reader to the earlier introductory chapters of volume I.Finally,we should acknowledge the fact that we made use of parts of our previous expositions[86]and[35].We made the writing of this survey more pleasurable for us by the introduction of a few original results.In particular the following results are entirely or partially new.Theorem1.2(the equivalence of the existence of a Borel cross-section with the coincidence of recurrence and periodicity),most of the material in Section4 (on topological mild-mixing),all of subsection7.4(the converse side of the local variational principle)and subsection7.6(on topological determinism).MEASURABLE AND TOPOLOGICAL DYNAMICS3 Part1.Analogies1.Poincar´e recurrence vs.Birkhoff’s recurrence1.1.Poincar´e recurrence theorem and topological recurrence.The simplest dynamical systems are the periodic ones.In the absence of periodicity the crudest approximation to this is approximate periodicity where instead of some iterate T n x returning exactly to x it returns to a neighborhood of x.Thefirst theorem in abstract measure dynamics is Poincar´e’s recurrence theorem which asserts that for afinite measure preserving system(X,B,µ,T)and any measurable set A,µ-a.e.point of A returns to A(see[46,Theorem4.3.1]).The proof of this basic fact is rather simple and depends on identifying the set of points W⊂A that never return to A.These are called the wandering points and their measurability follows from the formulaW=A∩ ∞ k=1T−k(X\A) .Now for n≥0,the sets T−n W are pairwise disjoint since x∈T−n W means that the forward orbit of x visits A for the last time at moment n.Sinceµ(T−n W)=µ(W) it follows thatµ(W)=0which is the assertion of Poincar´e’s theorem.Noting that A∩T−n W describes the points of A which visit A for the last time at moment n, and thatµ(∪∞n=0T−n W)=0we have established the following stronger formulation of Poincar´e’s theorem.1.1.Theorem.For afinite measure preserving system(X,B,µ,T)and any measur-able set A,µ-a.e.point of A returns to A infinitely often.Note that only sets of the form T−n B appeared in the above discussion so that the invertibility of T is not needed for this result.In the situation of classical dynam-ics,which was Poincar´e’s main interest,X is also equipped with a separable metric topology.In such a situation we can apply the theorem to a refining sequence of partitions P m,where each P m is a countable partition into sets of diameter at most1m ofitself,and since the intersection of a sequence of sets of full measure has full measure, we deduce the corollary thatµ-a.e.point of X is recurrent.This is the measure theoretical path to the recurrence phenomenon which depends on the presence of afinite invariant measure.The necessity of such measure is clear from considering translation by one on the integers.The system is dissipative,in the sense that no recurrence takes place even though there is an infinite invariant measure.There is also a topological path to recurrence which was developed in an abstract setting by G.D.Birkhoff.Here the above example is eliminated by requiring that the topological space X,on which our continuous transformation T acts,be compact.It is possible to show that in this setting afinite T-invariant measure always exists,and so we can retrieve the measure theoretical picture,but a purely topological discussion will give us better insight.4 E.GLASNER AND B.WEISSA key notion here is that of minimality.A nonempty closed,T-invariant set E⊂X, is said to be minimal if F⊂E,closed and T-invariant implies F=∅or F=E.If X itself is a minimal set we say that the system(X,T)is a minimal system. Fix now a point x0∈X and consider∞ n=1ω(x0)=MEASURABLE AND TOPOLOGICAL DYNAMICS5 that the converse is also valid—namely if there are no conservative quasi-invariant measures then there is a Borel cross-section.Note that the periodic points of(X,T)form a Borel subset for which a cross-section always exists,so that we can conclude from the above discussion the following statement in which no explicit mention is made of measures.1.2.Theorem.For a system(X,T),with X a completely metrizable separable space, there exists a Borel cross-section if and only if the only recurrent points are the peri-odic ones.1.3.Remark.Already in[42]as well as in[21]onefinds many equivalent conditions for the existence of a Borel section for a system(X,T).However one doesn’tfind there explicit mention of conditions in terms of recurrence.Silvestrov and Tomiyama [76]established the theorem in this formulation for X compact(using C∗-algebra methods).We thank zar for drawing our attention to their paper.1.3.Recurrence sequences and Poincar´e sequences.We will conclude this sec-tion with a discussion of recurrence sequences and Poincar´e sequences.First for some definitions.Let us say that D is a recurrence set if for any dynamical system(Y,T) with compatible metricρand anyǫ>0there is a point y0and a d∈D withρ(T d y0,y0)<ǫ.Since any system contains minimal sets it suffices to restrict attention here to minimal systems.For minimal systems the set of such y’s for afixedǫis a dense open set. To see this fact,let U be an open set.By the minimality there is some N such that for any y∈Y,and some0≤n≤N,we have T n y∈ing the uniform continuity of T n,wefind now aδ>0such that ifρ(u,v)<δthen for all0≤n≤Nρ(T n u,T n v)<ǫ.Now let z0be a point in Y and d0∈D such that(1)p(T d0z0,z0)<δ.For some0≤n0≤N we have T n0z0=y0∈U and from(1)we getρ(T d0y0,y0)<ǫ. Thus points thatǫreturn form an open dense set.Intersecting overǫ→0gives a dense Gδin Y of points y for whichρ(T d y,y)=0.infd∈DThus there are points which actually recur along times drawn from the given recur-rence set.A nice example of a recurrence set is the set of squares.To see this it is easier to prove a stronger property which is the analogue in ergodic theory of recurrence sets.1.4.Definition.A sequence{s j}is said to be a Poincar´e sequence if for anyfinite measure preserving system(X,B,µ,T)and any B∈B with positive measure we haveµ(T s j B∩B)>0for some s j in the sequence.6 E.GLASNER AND B.WEISSSince any minimal topological system(Y,T)hasfinite invariant measures with global support,µany Poincar´e sequence is recurrence sequence.Indeed for any presumptive constant b>0which would witness the non-recurrence of{s j}for(Y,T), there would have to be an open set B with diameter less than b and having positiveµ-measure such that T s j B∩B is empty for all{s j}.Here is a sufficient condition for a sequence to be a Poincar´e sequence:1.5.Lemma.If for everyα∈(0,2π)limn→∞1nn1U s k(1B−f0) L2−→0or1nn1µ(B∩T−s k B)= f0 2>0which clearly implies that{s k}is a Poincar´e sequence. The proof we have just given is in fact von-Neumann’s original proof for the mean ergodic theorem.He used the fact that N satisfies the assumptions of the proposition, which is Weyl’s famous theorem on the equidistribution of{nα}.Returning to the squares Weyl also showed that{n2α}is equidistributed for all irrationalα.For rationalαthe exponential sum in the lemma needn’t vanish,however the recurrence along squares for the rational part of the spectrum is easily verified directly so that we can conclude that indeed the squares are a Poincar´e sequence and hence a recurrence sequence.The converse is not always true,i.e.there are recurrence sequences that are not Poincar´e sequences.This wasfirst shown by I.Kriz[60]in a beautiful example(see also[86,Chapter5]).Finally here is a simple problem.MEASURABLE AND TOPOLOGICAL DYNAMICS7 Problem:If D is a recurrence sequence for all circle rotations is it a recurrence set?A little bit of evidence for a positive answer to that problem comes from looking at a slightly different characterization of recurrence sets.Let N denote the collection of sets of the formN(U,U)={n:T−n U∩U=∅},(U open and nonempty),where T is a minimal transformation.Denote by N∗the subsets of N that have a non-empty intersection with every element of N.Then N∗is exactly the class of recurrence sets.For minimal transformations,another description of N(U,U)is obtained by fixing some y0and denotingN(y0,U)={n:T n y0∈U}Then N(U,U)=N(y0,U)−N(y0,U).Notice that the minimality of T implies that N(y0,U)is a syndetic set(a set with bounded gaps)and so any N(U,U)is the set of differences of a syndetic set.Thus N consists essentially of all sets of the form S−S where S is a syndetic set.Given afinite set of real numbers{λ1,λ2,...,λk}andǫ>0setV(λ1,λ2,...,λk;ǫ)={n∈Z:maxj{ nλj <ǫ}},where · denotes the distance to the closest integer.The collection of such sets forms a basis of neighborhoods at zero for a topology on Z which makes it a topological group.This topology is called the Bohr topology.(The corresponding uniform structure is totally bounded and the completion of Z with respect to it is a compact topological group called the Bohr compactification of Z.)Veech proved in[78]that any set of the form S−S with S⊂Z syndetic contains a neighborhood of zero in the Bohr topology up to a set of zero density.It is not known if in that statement the zero density set can be omitted.If it could then a positive answer to the above problem would follow(see also[32]).2.The equivalence of weak mixing and continuous spectrumIn order to analyze the structure of a dynamical system X there are,a priori,two possible approaches.In thefirst approach one considers the collection of subsystems Y⊂X(i.e.closed T-invariant subsets)and tries to understand how X is built up by these subsystems.In the other approach one is interested in the collection of factors Xπ→Y of the system X.In the measure theoretical case thefirst approach leads to the ergodic decomposition and thereby to the study of the“indecomposable”or ergodic components of the system.In the topological setup there is,unfortunately,no such convenient decomposition describing the system in terms of its indecomposable parts and one has to use some less satisfactory substitutes.Natural candidates for in-decomposable components of a topological dynamical system are the“orbit closures”(i.e.the topologically transitive subsystems)or the“prolongation”cells(which often coincide with the orbit closures),see[4].The minimal subsystems are of particular importance here.Although we can not say,in any reasonable sense,that the study of the general system can be reduced to that of its minimal components,the analysis of8 E.GLASNER AND B.WEISSthe minimal systems is nevertheless an important step towards a better understanding of the general system.This reasoning leads us to the study of the collection of indecomposable systems (ergodic systems in the measure category and transitive or minimal systems in thetopological case)and their factors.The simplest and best understood indecomposable dynamical systems are the ergodic translations of a compact monothetic group(a cyclic permutation on Z p for a prime number p,the“adding machine”on ∞n=0Z2, an irrational rotation z→e2πiαz on S1={z∈C:|z|=1}etc.).It is not hard toshow that this class of ergodic actions is characterized as those dynamical systems which admit a model(X,X,µ,T)where X is a compact metric space,T:X→X a surjective isometry andµis T-ergodic.We call these systems Kronecker or isometric systems.Thus ourfirst question concerning the existence of factors should be:given an ergodic dynamical system X which are its Kronecker factors?Recall that a measure dynamical system X=(X,X,µ,T)is called weakly mixing if the product system(X×X,X⊗X,µ×µ,T×T)is ergodic.The following classical theorem is due to von Neumann.The short and elegant proof we give was suggested by Y.Katznelson.2.1.Theorem.An ergodic system X is weakly mixing iffit admits no nontrivial Kronecker factor.Proof.Suppose X is weakly mixing and admits an isometric factor.Now a factor of a weakly mixing system is also weakly mixing and the only system which is both isometric and weakly mixing is the trivial system(an easy exercise).Thus a weakly mixing system does not admit a nontrivial Kronecker factor.For the other direction,if X is non-weakly mixing then in the product space X×X there exists a T-invariant measurable subset W such that0<(µ×µ)(W)<1.For every x∈X let W(x)={x′∈X:(x,x′)∈W}and let f x=1W(x),a function in L∞(µ).It is easy to check that U T f x=f T−1x so that the mapπ:X→L2(µ)defined byπ(x)=f x,x∈X is a Borel factor map.Denotingπ(X)=Y⊂L2(µ),andν=π∗(µ),we now have a factor mapπ:X→(Y,ν).Now the function π(x) is clearly measurable and invariant and by ergodicity it is a constantµ-a.e.;say π(x) =1. The dynamical system(Y,ν)is thus a subsystem of the compact dynamical system (B,U T),where B is the unit ball of the Hilbert space L2(µ)and U T is the Koopman unitary operator induced by T on L2(µ).Now it is well known(see e.g.[35])that a compact topologically transitive subsystem which carries an invariant probability measure must be a Kronecker system and our proof is complete.Concerning the terminology we used in the proof of Theorem2.1,B.O.Koopman, a student of G.D.Birkhoffand a co-author of both Birkhoffand von Neumann introduced the crucial idea of associating with a measure dynamical system X= (X,X,µ,T)the unitary operator U T on the Hilbert space L2(µ).It is now an easy matter to see that Theorem2.1can be re-formulated as saying that the system X is weakly mixing iffthe point spectrum of the Koopman operator U T comprises the single complex number1with multiplicity1.Or,put otherwise,that the one dimensional space of constant functions is the eigenspace corresponding to the eigenvalue1(thisMEASURABLE AND TOPOLOGICAL DYNAMICS9 fact alone is equivalent to the ergodicity of the dynamical system)and that the restriction of U T to the orthogonal complement of the space of constant functions has a continuous spectrum.We now consider a topological analogue of this theorem.Recall that a topo-logical system(X,T)is topologically weakly mixing when the product system (X×X,T×T)is topologically transitive.It is equicontinuous when the family {T n:n∈Z}is an equicontinuous family of maps.Again an equivalent condition is the existence of a compatible metric with respect to which T is an isometry.And,moreover,a minimal system is equicontinuous iffit is a minimal translation on a compact monothetic group.We will need the following lemma.2.2.Lemma.Let(X,T)be a minimal system and f:X→R a T-invariant function with at least one point of continuity(for example this is the case when f is lower or upper semi-continuous or more generally when it is the pointwise limit of a sequence of continuous functions),then f is a constant.Proof.Let x0be a continuity point and x an arbitrary point in X.Since{T n x: n∈Z}is dense and as the value f(T n x)does not depend on n it follows that f(x)=f(x0).2.3.Theorem.Let(X,T)be a minimal system then(X,T)is topologically weakly mixing iffit has no non-trivial equicontinuous factor.Proof.Suppose(X,T)is minimal and topologically weakly mixing and letπ:(X,T)→(Y,T)be an equicontinuous factor.If(x,x′)is a point whose T×T orbit is dense in X×X then(y,y′)=(π(x),π(x′))has a dense orbit in Y×Y.However,if(Y,T) is equicontinuous then Y admits a compatible metric with respect to which T is an isometry and the existence of a transitive point in Y×Y implies that Y is a trivial one point space.Conversely,assuming that(X×X,T×T)is not transitive we will construct an equicontinuous factor(Z,T)of(X,T).As(X,T)is a minimal system,there exists a T-invariant probability measureµon X with full support.By assumption there exists an open T-invariant subset U of X×X,such that cls U:=M X×X.By minimality the projections of M to both X coordinates are onto.For every y∈X let M(y)={x∈X:(x,y)∈M},and let f y=1M(y)be the indicator function of the set M(y),considered as an element of L1(X,µ).Denote byπ:X→L1(X,µ)the map y→f y.We will show thatπis a continuous homomorphism,where we consider L1(X,µ)as a dynamical system with the isometric action of the group{U n T:n∈Z}and U T f(x)=f(T x).Fix y0∈X andǫ>0.There exists an open neighborhood V of the closed set M(y0)withµ(V\M(y0))<ǫ.Since M is closed the set map y→M(y),X→2X is upper semi-continuous and we can find a neighborhood W of y0such that M(y)⊂V for every y∈W.Thus for every y∈W we haveµ(M(y)\M(y0))<ǫ.In particular,µ(M(y))≤µ(M(y0))+ǫand it follows that the map y→µ(M(y))is upper semi-continuous.A simple computation shows that it is T-invariant,hence,by Lemma2.2,a constant.10 E.GLASNER AND B.WEISSWith y0,ǫand V,W as above,for every y∈W,µ(M(y)\M(y0))<ǫandµ(M(y))=µ(M(y0)),thusµ(M(y)∆M(y0))<2ǫ,i.e., f y−f y0 1<2ǫ.This proves the claim thatπis continuous.Let Z=π(X)be the image of X in L1(µ).Sinceπis continuous,Z is compact. It is easy to see that the T-invariance of M implies that for every n∈Z and y∈X, f T−n y=f y◦T n so that Z is U T-invariant andπ:(Y,T)→(Z,U T)is a homomorphism. Clearly(Z,U T)is minimal and equicontinuous(in fact isometric).Theorem2.3is due to Keynes and Robertson[57]who developed an idea of Fursten-berg,[22];and independently to K.Petersen[70]who utilized a previous work of W.A.Veech,[78].The proof we presented is an elaboration of a work of McMahon[66]due to Blanchard,Host and Maass,[13].We take this opportunity to point outa curious phenomenon which recurs again and again.Some problems in topological dynamics—like the one we just discussed—whose formulation is purely topological, can be solved using the fact that a Z dynamical system always carries an invariant probability measure,and then employing a machinery provided by ergodic theory.In several cases this approach is the only one presently known for solving the problem. In the present case however purely topological proofs exist,e.g.the Petersen-Veech proof is one such.3.Disjointness:measure vs.topologicalIn the ring of integers Z two integers m and n have no common factor if whenever k|m and k|n then k=±1.They are disjoint if m·n is the least common multiple of m and n.Of course in Z these two notions coincide.In his seminal paper of 1967[23],H.Furstenberg introduced the same notions in the context of dynamical systems,both measure-preserving transformations and homeomorphisms of compact spaces,and asked whether in these categories as well the two are equivalent.The notion of a factor in,say the measure category,is the natural one:the dynamical system Y=(Y,Y,ν,T)is a factor of the dynamical system X=(X,X,µ,T)if there exists a measurable mapπ:X→Y withπ(µ)=νthat T◦π=π◦T.A common factor of two systems X and Y is thus a third system Z which is a factor of both.A joining of the two systems X and Y is any system W which admits both as factors and is in turn spanned by them.According to Furstenberg’s definition the systems X and Y are disjoint if the product system X×Y is the only joining they admit.In the topological category,a joining of(X,T)and(Y,S)is any subsystem W⊂X×Y of the product system(X×Y,T×S)whose projections on both coordinates are full;i.e.πX(W)=X andπY(W)=Y.(X,T)and(Y,S)are disjoint if X×Y is the unique joining of these two systems.It is easy to verify that if(X,T)and(Y,S)are disjoint then at least one of them is minimal.Also,if both systems are minimal then they are disjoint iffthe product system(X×Y,T×S)is minimal.In1979,D.Rudolph,using joining techniques,provided thefirst example of a pair of ergodic measure preserving transformations with no common factor which are not disjoint[72].In this work Rudolph laid the foundation of joining theory.He introduced the class of dynamical systems having“minimal self-joinings”(MSJ),and constructed a rank one mixing dynamical system having minimal self-joinings of all orders.MEASURABLE AND TOPOLOGICAL DYNAMICS11 Given a dynamical system X=(X,X,µ,T)a probability measureλon the product of k copies of X denoted X1,X2,...,X k,invariant under the product transformation and projecting ontoµin each coordinate is a k-fold self-joining.It is called an off-diagonal if it is a“graph”measure of the formλ=gr(µ,T n1,...,T n k),i.e.λis the image ofµunder the map x→ T n1x,T n2x,...,T n k x of X into k i=1X i.The joiningλis a product of off-diagonals if there exists a partition(J1,...,J m)of {1,...,k}such that(i)For each l,the projection ofλon i∈J l X i is an off-diagonal,(ii) The systems i∈J l X i,1≤l≤m,are independent.An ergodic system X has minimal self-joinings of order k if every k-fold ergodic self-joining of X is a product of off-diagonals.In[72]Rudolph shows how any dynamical system with MSJ can be used to con-struct a counter example to Furstenberg’s question as well as a wealth of other counter examples to various questions in ergodic theory.In[52]del Junco,Rahe and Swanson were able to show that the classical example of Chac´o n[16]has MSJ,answering a question of Rudolph whether a weakly but not strongly mixing system with MSJ exists.In[38]Glasner and Weiss provide a topological counterexample,which also serves as a natural counterexample in the measure category.The example consists of two horocycleflows which have no nontrivial common factor but are nevertheless not disjoint.It is based on deep results of Ratner[71]which provide a complete description of the self joinings of a horocycleflow.More recently an even more strik-ing example was given in the topological category by E.Lindenstrauss,where two minimal dynamical systems with no nontrivial factor share a common almost1-1 extension,[63].Beginning with the pioneering works of Furstenberg and Rudolph,the notion of joinings was exploited by many authors;Furstenberg1977[24],Rudolph1979[72], Veech1982[81],Ratner1983[71],del Junco and Rudolph1987[53],Host1991 [47],King1992[58],Glasner,Host and Rudolph1992[36],Thouvenot1993[77], Ryzhikov1994[73],Kammeyer and Rudolph1995(2002)[55],del Junco,Lema´n czyk and Mentzen1995[51],and Lema´n czyk,Parreau and Thouvenot2000[62],to men-tion a few.The negative answer to Furstenberg’s question and the consequent works on joinings and disjointness show that in order to study the relationship between two dynamical systems it is necessary to know all the possible joinings of the two systems and to understand the nature of these joinings.Some of the best known disjointness relations among families of dynamical systems are the following:•id⊥ergodic,•distal⊥weakly mixing([23]),•rigid⊥mild mixing([27]),•zero entropy⊥K-systems([23]),in the measure category and•F-systems⊥minimal([23]),•minimal distal⊥weakly mixing,•minimal zero entropy⊥minimal UPE-systems([9]),12 E.GLASNER AND B.WEISSin the topological category.d mixing:measure vs.topological4.1.Definition.Let X=(X,X,µ,T)be a measure dynamical system.1.The system X is rigid if there exists a sequence n kր∞such thatlimµ(T n k A∩A)=µ(A)for every measurable subset A of X.We say that X is{n k}-rigid.2.An ergodic system is mildly mixing if it has no non-trivial rigid factor. These notions were introduced in[27].The authors show that the mild mixing property is equivalent to the following multiplier property.4.2.Theorem.An ergodic system X=(X,X,µ,T)is mildly mixing ifffor every ergodic(finite or infinite)measure preserving system(Y,Y,ν,T),the product system(X×Y,µ×ν,T×T),is ergodic.Since every Kronecker system is rigid it follows from Theorem2.1that mild mixing implies weak mixing.Clearly strong mixing implies mild mixing.It is not hard to construct rigid weakly mixing systems,so that the class of mildly mixing systems is properly contained in the class of weakly mixing systems.Finally there are mildly but not strongly mixing systems;e.g.Chac´o n’s system is an example(see Aaronson and Weiss[1]).We also have the following analytic characterization of mild mixing.4.3.Proposition.An ergodic system X is mildly mixing iffφf(n)<1,lim supn→∞for every matrix coefficientφf,where for f∈L2(X,µ), f =1,φf(n):= U T n f,f . Proof.If X→Y is a rigid factor,then there exists a sequence n i→∞such that U T n i→id strongly on L2(Y,ν).For any function f∈L20(Y,ν)with f =1, we have lim i→∞φf(n i)=1.Conversely,if lim i→∞φf(n i)=1for some n iր∞and f∈L20(X,µ), f =1,then lim i→∞U T n i f=f.Clearly f can be replaced by a bounded function and we let A be the sub-algebra of L∞(X,µ)generated by {U T n f:n∈Z}.The algebra A defines a non-trivial factor X→Y such that U T n i→id strongly on L2(Y,ν). We say that a collection F of nonempty subsets of Z is a family if it is hereditary upward and proper(i.e.A⊂B and A∈F implies B∈F,and F is neither empty nor all of2Z).With a family F of nonempty subsets of Z we associate the dual familyF∗={E:E∩F=∅,∀F∈F}.It is easily verified that F∗is indeed a family.Also,for families,F1⊂F2⇒F∗1⊃F∗2, and F∗∗=F.。

英文文献中关于误差棒的描述In scientific literature, error bars are graphical representations of the variability of data points in a graph. They are commonly used in charts and plots to indicate the uncertainty or deviation associated with each data point. Error bars provide a visual understanding of the range within which the true value of the data is likely to lie.When reading English-language scientific papers, you might encounter various terms related to error bars:Standard Deviation: This is one of the most common types of error bars and represents the spread of data around the mean value. It's calculated as the square root of the variance, which measures how far each data point deviates from the average.Standard Error: This term is used when talking about the precision of the sample mean as an estimate of the population mean. The standard error indicates the extent to which the sample means are expected to vary if the experiment is repeated multiple times.Confidence Intervals: These are statistical intervals that indicate the range in which the true population parameter (like a mean) is likely to fall with a certain level of confidence (such as 95%). Error bars based on confidence intervals show the upper and lower bounds of this interval.Margin of Error: Sometimes used interchangeably with confidence intervals, the margin of error refers to half the width of the confidence interval, showing the maximum expected discrepancy between the estimated value and the true value.Mean ± Standard Deviation: This format for error bars shows the mean value with the standard deviation above and below it, indicating the range within which most data points are likely to be found (typically around 68% for a normal distribution).It's important to understand that error bars represent only a measure of the variability of the data and do not imply anything about causation or the accuracy of the measurements. The choice of what type of error bar to use depends on the nature of the data, the underlying statistical assumptions, and the message the researcher wants to convey.。

Optik124 (2013) 2115–2120Contents lists available at SciVerse ScienceDirectOptikj o u r n a l h o m e p a g e:w w w.e l s e v i e r.d e/i j l eoFocal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysisJitendra Dhanotia,Shashi Prakash∗Photonics Laboratory,Department of Electronics&Instrumentation Engineering,Institute of Engineering&Technology,Devi Ahilya University,Khandwa Road,Indore452017,Indiaa r t i c l e i n f oArticle history:Received26January2012 Accepted18June2012Keywords:Focal lengthFourier transformCollimationCoherent gradient sensing a b s t r a c tA procedure for the measurement of focal length and radius of curvature of a lens using coherent gradient sensing system and Fourier transform fringe analysis technique has been demonstrated.Light from the laser illuminates the specimen and the wavefront emerging from the specimen is tested using coherent gradient sensing interferometer.The fringe pattern corresponding to the test wavefront is stored,and analyzed using Fourier fringe analysis technique.The slope of the wavefront in the direction of shear has been evaluated.It provides the information regarding exact location of points corresponding to the focus/center of curvature of the lens.High accuracy and precision has been achieved.© 2012 Elsevier GmbH. All rights reserved.1.IntroductionCoherent Gradient Sensing(CGS)is double grating lateral shearing interferometric technique used extensively in various engineering applications.The technique has been operated in two primary domains,transmission and reflection.Based on these domains,the technique has been employed in thefield of exper-imental mechanics for slope and curvature measurement[1],crack tip deformation study[2,3]stressfield examination[4],etc.The technique has also been used for the measurement of residual stress in thinfilms[5].Focal length is an important optical parameter which needs to be known precisely in various optical systems.Initially clas-sical methods based on geometrical optics were used such as nodal slide,image magnification,focometer,etc.,but in recent times automated measurement using interferometric techniques has been preferably used.Various modern techniques reported for the measurement of focal length/radius of curvature are based on phenomenon of interference,diffraction,etc.Some of the tech-niques reported in this category are based on Talbot effect[6–8], Lau effect[9],digital moiréeffect[10],etc.Nakano and Murata[6]described a method based on Talbot interferometry for the measurement of focal length.They mea-sured the focal length in two ways:by measuring inclination angle of moiréfringes and by measuring the spacing between the moiréfringes.Bhattacharya and Aggarwal[7]determined the focal length∗Corresponding author.Tel.:+917312361116x7/9977186156;fax:+917312764385.E-mail address:sprakash davv@(S.Prakash).of a collimated lens using Talbot effect and moirétechniques.The defocusing of collimating lens is measured as a function of incli-nation angle of the moiréfringes.Sriram et al.[8]used dualfield grating system in Talbot interferometry for the measurement of focal length of a positive lens by placing the test lens in between the two gratings.The direct measurement of focal length of the test lens was undertaken by measuring separation between‘f’and ‘2f’planes corresponding to the test lens.The ease of detecting the exact location of these two planes has been improved based on principles of Talbot interferometry.Lei and Dang[11]reported the method based on grating shearing interferometry for the measurement of focal length of a lens.The lateral shift between the undiffracted zero order and diffractedfirst order has been mea-sured and used for the determination of focal length.Prakash et al.[9]reported the Lau based technique using incoherent light source to improve the accuracy of focal length measurement.Horner [12]used a simple method based on the observation of Fourier transform intensity pattern of a rectangular slit placed in front of the test lens.The focal length is measured in terms of separation between the zeros of the Fourier transform intensity pattern. The measurement is independent of the degree of collimation of incident beam or the principal plane of the test lens.Matsuda et al.[13]used the multiple beam shearing interferometry for the mea-surement of focal length.Xiang[14]developed retrocollimation interferometry based measurement in which focal length has been determined using Newton’s displacement ter,simple technique using diffraction characteristics of a circular Dammann grating has been used to locate the focal point of a lens[15].Lawall [16]used the spectroscopic approach in Fabry–Perot interferom-eter for the determination of radius of curvature of a concave mirror.Recently,Abdelsalam et al.[17]used the multiple beam0030-4026/$–see front matter© 2012 Elsevier GmbH. All rights reserved. /10.1016/j.ijleo.2012.06.0532116J.Dhanotia,S.Prakash/Optik124 (2013) 2115–2120Fig.1.Basic principle of coherent gradient sensing system. interference phenomenon in reflection mode for the measurement of radius of curvature of spherical smooth surfaces.In the above-mentioned techniques the measurement is based on the visual inspection alone;the results obtained are not quan-titative and are subject to vary based on the visual perception of human senses.Also,the measurement characteristics of the tech-niques were relatively poor.As an alternative to these techniques, direct phase measuring techniques,such as phase shifting method and Fourier transform method have been reported.These have tremendously improved the measurement characteristics in terms of accuracy,precision,and sensitivity achievable.Singh et al.[18] combined four-step phase shifting technique with Fourierfiltering method and correlated the slope of the phase map with the focal length of the test lens.Tay et al.[19]reported focal length mea-surement using phase shifted Lau phase interferometry.However, phase shifting test procedure requires specialized hardware(pre-cision controlled translation stage and associated equipment)and recording of several interferograms to determine the phase.This makes the technique tedious and relatively cumbersome.Toward achieving automation and better measurement char-acteristics,the Fourier Transform Method(FTM)has been used extensively in various scientific and engineering applications. Takeda et al.[20]used the Fourier transform method of computer based fringe pattern analysis for topography and interferometry. The method has been used to make clear distinction between ele-vation and depression of the object,even from a single non-contour type of fringe pattern.The Fourier transform method has been used for applications such as the measurement of3D surface profile[21], temperature[22],distance[23],slope[24],etc.In our previous paper[25],the CGS technique has been employed for collimation testing of an optical beam.In present communication,we report our investigation undertaken toward measurement of focal length and the radius of curvature by using CGS technique.The wavefront emerging from the optical element under test is passed through the CGS interferometer.The exact location of the focal point/center of curvature is determined by analyzing the shearing interferometric fringes generated in the CGS interferometer.Direct wavefront phase based data has been retrieved from the shearing interferometric fringes,using Fourier fringe analysis technique.The information regarding the slope of wavefront phase provides improved accuracy and precision in locating the exact focal point/radius of curvature.2.TheoryThe basic principle of coherent gradient sensing based inter-ferometer is shown in Fig.1.The expanded and collimated laser beam is incident on a pair of Ronchi gratings G1and G2having the same pitch‘p’and an arbitrary separation‘d’.Beyond the grat-ing G1emerge several diffraction orders.For simplicity,only the zeroth and thefirst orders(±1)are considered to propagate inthe Fig.2.Schematic of the experimental arrangement for measurement of focal length of the test lens using coherent gradient sensing and FTM.forward direction.The magnitude of the angle between the propa-gation directions of the zeroth and thefirst order beams is given by the diffraction equationÂ=sin−1( /p),where is the wavelength of light and p is the grating period.These beams after being inci-dent on the second grating G2,are further diffracted into orders such as E(0,0),E(+1,0),E(0,+1)and so on.These wavefronts which propagate in different directions are brought to focus at spatially separate diffraction spots at the focal plane of the lens L1.Out of these,the spot corresponding to thefirst order(E+1,0,E0,+1)is seg-regated and allowed to propagate;rest are blocked using a spatial filter placed at the back focal plane of the lens.Under this condi-tion,the interferometer acts as a shearing interferometer,bearing fringes of sinusoidal profile in the common area between the two wavefronts.The basic schematic of experimental arrangement for the mea-surement of focal length is shown in Fig.2.Expanded and collimated light from the laser is made incident onto the test lens.Beyond the test lens is placed a mirror M.Light reflected from the mirror passes through the test lens.The wavefront emerging from the lens is diverted for the purpose of testing using the beam splitter.Testing is undertaken using CGS interferometer.CGS is basically a grat-ing shearing interferometer.Corresponding to orders(E+1,0,E0,+1) propagated beyond the gratings,the original wavefront and the sheared wavefront emerge.The shearing between the test and the sheared wavefront may be varied by varying the grating separation.Toward making suitable adjustments for undertaking the mea-surement of focal length,the mirror is moved along the optic axis with respect to the test lens.Corresponding to the different positions of the mirror,the‘defocus’error gets introduced in the wavefront,if the mirror is not at exact focus of the lens.An addi-tional error‘wavefront tilt’is introduced by tilting the grating by small angle with respect to each other.The wavefront is then inci-dent on the grating shearing interferometer for testing.The output of the grating shearing interferometer yields a particular type of fringe pattern depending upon the gradient of wavefront errors in the direction of shear[26].Hence,corresponding to the type of wavefront emerging from the test lens,the orientation of the fringes appearing at the output of the interferometer is different.When the separation between the test lens and the mirror is equal to the focal length of the test lens,the wavefront emerging from the test lens is plane.Under this condition the horizontal straight line fringe pattern is obtained.For in-focus and out-focus position,the wave-front emerging out is diverging and the converging,respectively. For the converging or the diverging wavefront the fringe orienta-tion gets inclined at a positive or the negative angle with respect to the horizontal.Fig.3(a)–(c)corresponds to the fringes obtained at in-focus,at-focus and out-of-focus position of the mirror with respect to the defocusing lens(test lens),respectively.To increase the measurement accuracy in the determination of focal point of the test lens,the Fourier fringe analysis of the interferograms isJ.Dhanotia,S.Prakash/Optik124 (2013) 2115–21202117Fig.3.Fringe patterns recorded using CCD camera(a)at in-focus position of the mirror with respect to test lens of focal length240mm,(b)at at-focus position of the mirror with respect to test lens of focal length240mm,and(c)at out-of-focusposition of the mirror with respect to test lens of focal length240mm.Fig.4.Flow chart for a Fourier transform algorithms. undertaken and direct phase˚(X,Y)of the wavefront determined. Fig.4shows the algorithm for undertaking Fourier fringe analysis. The theoretical treatment regarding the Fourier transform method has been explained in Ref.[20].The slope of the phase map pro-vides information about the type of the wavefront.The slope in case of at focus,out focus and in focus position is almost zero,pos-itive and negative respectively.The separation between the lens and the mirror is determined,to yield the focal length.Measurement of radius of curvature has also been undertaken. Fig.5shows the schematic of the experimental arrangement for the measurement of radius of curvature of the concave mirror.The measurement is based on the fact that the distance between two positions at which the incident collimated beam retraces its path after reflection from spherical test surface,is equal to its radius of curvature.The Fourier transform algorithm as mentioned above has been used for the interferogram analysis.3.Experimental detailsThe experimental setup for the measurement of focal length using coherent gradient sensing is shown in Fig.2.He–Ne laser of15mW( =632.8nm)was used as a light source.Light fromthe Fig.5.Schematic of the experimental arrangement for measurement of radius of curvature of the concave mirror using coherent gradient sensing and FTM.He–Ne Laser is spatiallyfiltered using a combination of pinhole of5␮m diameter and microscopic objective of magnification45×. The precision achromatic doublet lens PAC088supplied by New-port Corporation,USA,having a focal length of250mm,has been used as collimationg lens L C.In the path of collimated beam,the lens under test has been introduced.Beyond the lens is introduced a mirror M mounted on the precision translating stage(NF5DP20/M) supplied by Thorlabs Inc.,USA,to translate it along the optical axis. The reflected beam from the mirror M back-propagates through the lens.This beam is deflected using a beam splitter BS for detec-tion of the defocusing errors.Two gratings,G1and G2of period 0.08mm each,have been placed in tandem such that grating lines of two makes equal but opposite angle with respect to the ver-tical.The beam corresponding to thefirst order spot is isolated using a spatialfiltering arrangement comprising of the combina-tion of two lenses and an aperture A.Separation of various orders depends on the period of the gratings used.The shear fringes are formed due to superposition of laterally shiftedfirst order beams diffracted from gratings G1and G2.The shearing interferogram was imaged on the phase plate of CCD camera using lenses L1and L2. Aperture A is placed at the focal plane of the lens L1to allow the desired diffracted order to reach the image plane.The CCD is hav-ing1392×1040pixels with each pixel sized4.65␮m×4.65␮m. For image acquisition and display,CCD camera interfaced with the frame grabber card has been used and the results were displayed on-line onto the computer monitor.To experimentally determine the values of accuracy and pre-cision in the measurement of focal length,the plane mirror M (specimen)mounted on the translation stage is translated upscale and downscale,so that one approaches the focal position/radius of curvature in either direction.Initially,the mirror is placed nearer to the test lens.The mirror is then moved away(in+Z direction) from the test lens.As the mirror approaches the focal point of the test lens,the straight line fringes oriented at a positive angle with respect to the horizontal reference appear.This corresponds to the condition when the wavefront emerging from the lens is diverging.Fig.3(a)corresponds to the position when the wave-front is diverging.As the mirror is moved further the inclination angle of the fringes decreases and they rotate in the clockwise direction.The fringes slowly become parallel to the horizontal as the focal position is reached.Fig.3(b)corresponds to this position. For thefine setting of the focal position a series of interferograms were recorded near this position and analyzed using FFT algorithm. Fig.8(a)and(b)shows the phase plots(obtained using FFT analy-sis)of the recorded interferograms in case when the wavefronts are diverging and plane,respectively.As the mirror is further moved along the optic axis,in the direction same as above and the‘in-focus’position is approached,the wavefront emerging from the test lens becomes converging.The inclination angle of the fringes further decreases and rotates in the clockwise direction.At this position,2118J.Dhanotia,S.Prakash/Optik124 (2013) 2115–2120Fig.6.Fourier spectrum of recorded image for(a)in-focus position of the mirror with respect to test lens,(b)at-focus position of the mirror with respect to test lens, and(c)out-of-focus position of the mirror with respect to test lens.the inclined fringes appear at a negative angle with respect to the horizontal.Figs.3(c)and8(c)corresponds to fringe pattern and the phase plot,respectively.Experiments for the measurement of radius of curvature of reflective surface has also been undertaken.In the experimental set-up of Fig.2the plane mirror has been replaced by the con-vex/concave mirror.A typical set-up for the measurement of radius of curvature of concave mirror is shown in Fig.5.Collimated beam is incident on the corrected lens C L.Beyond the converging lens the beam converges and is incident onto the concave mirror under test.As per the test procedure,the concave mirror is translated along the optic axis till it reaches the focal plane of the corrected lens.At this position,the horizontal fringe pattern is obtained at the image plane.Next,the concave mirror is translated along the optic axis(away from the corrected lens)till the horizontal fringe pattern is again obtained.Now,the series of interferograms were recorded near this position and the exact location of the center of curvature determined using the Fourier transform method.The minimum value of the slope of the phase map has been used as the criterion for the exact determination of the center of curvature of the reflecting surface.The difference between the two positions of the concave mirror,F L and D LM,as shown in Fig.5,may be treated as the correct value of radius of curvature.The similar procedure may be repeated for the convex mirror also.4.Results and discussionExperimental results verify that the measurement of focal length using coherent gradient sensing can be performed advan-tageously.For each position of the mirror the interference patterns are recorded and the images were stored in the Computer mem-ory.For the detection of exact focal length of the test lens,a series of interferogram were recorded near the focus position of the test lens.The measurements were undertaken at several positions of the test lens along the axis;however the results were presented for only three positions.Fig.4corresponds to the proposed Fourier transform algorithm used to extract the phase even from the single interferogram.The Fourier transform method involves taking FFT of the interferogram to obtain its Fourier spectra.Fig.6(a)–(c)shows the Fourier spec-tra of the recorded interferograms corresponding to Fig.3(a)–(c), respectively.In the Fourier spectra the central dot having the maxi-mum intensity shows the zero order while the dots immediately on the two sides of the central spot,show the±1order spectra.Next, thefirst order Fourier spectra was selected and shifted to the cen-ter position.The inverse Fourier transform of the centrally shifted spectra provides the necessary phase information of the recorded interferogram.Fig.7(a)–(c)shows the plot of evaluated phase map with respect to the pixel position for‘in-focus’,‘at-focus’and‘out-of-focus’position of the mirror with respect to the test lens.To obtain reliable phase map,thefield corresponding to the wrapped phase map has been scanned and2 is added or subtractedevery Fig.7.Unwrapped Phase map for a fringe pattern corresponding to(a)in-focus position of the mirror with respect to test lens of focal length240mm,(b)at-focus position of the mirror with respect to test lens of focal length240mm,and(c)out-of-focus position of the mirror with respect to test lens of focal length240mm.time an edge is detected.The phase values so obtained are plotted against the pixel values using MATLAB toolbox.Fig.8(a)–(c)shows the two-dimensional plot of the evaluated phase map with respect to the pixel position for‘in-focus’,‘at-focus’and‘out-of-focus’posi-tion of the mirror with respect to test lens.From the results,it is quite evident that the slope of the phase map is positive for the‘in-focus’position of the mirror with respect to test lens.Plot of phase˚with respect to x domain for afixed value of y,gives a positive slope as anticipated and shown in Fig.8(a). The slope of the phase map decreases as we move toward‘at-focus’position and it approaches zero at the‘at-focus’position of the test lens.This corresponds to the exact focal position of the test lens. The plot of phase˚with respect to x domain,for thefixed value of y(plot of˚along the same row for different values of column vector)gives a straight line as anticipated and is shown in Fig.8(b). As the mirror is moved away from focal position of test lens,the slope of phase maps becomes negative.Negative slope indicates the out-focus’position of the mirror with respect to test lens.Plot of phase˚with respect to x domain for afixed value of y,hasaFig.8.Variation of phase with respect to x-axis for the fringe pattern corresponding to(a)in-focus position of the mirror with respect to test lens of focal length240mm;(b)at-focus position of the mirror with respect to test lens of focal length240mm; and(c)out-of-focus position of the mirror with respect to test lens of focal length 240mm.J.Dhanotia,S.Prakash/Optik124 (2013) 2115–21202119Table1Comparison of the measured values of focal lengths with the standard values of focal lengths.Also,variation of f with the focal length f for grating separation of28mm. S.No.f(mm)Measured f(mm) f(mm)( f/f)×1001150149 1.00.66660.886 2180178.5 1.50.83330.65574 3220217.7 2.3 1.0454 1.75214 4240237 3.0 1.25 2.04817 5290286.2 3.8 1.3103 1.58902negative slope as shown in Fig.8(c).Hence,the focal point of the test lens can be determined very precisely and accurately.The distance between the focal point and the test lens is a direct measure of the focal length.The discussion regarding the comparison of accuracy or rela-tive error in the present case with previous reported literature also needs consideration.The accuracy obtainable in the focal length measurement may be defined as the smallest detectable devia-tion from the perfect focal position,‘ f’of the test lens.This value ‘ f’depends on the focal length,‘f’of the test lens.The percent-age accuracy of the focal length measurement technique has been defined as‘( f/f)×100’.The comparison of the accuracy defined as above,for different techniques reported till date looks most pertinent.Nakano and Murata[6]measured the focal length of 400cm lens with an accuracy of2%corresponding to±1◦accu-racy in inclination angle measurement.Bhattacharya and Aggarwal measured the focal length of the collimating lens as a function of inclination angle of the moiréfringes and achieved an accuracy of 2%of true value.Lei and Dang[11]used the plano-convex lens of focal length77mm and cylindrical plano-convex lens of focal length116mm and obtained an accuracy of1.4%.Keren et al.[27] reported0.8%accuracy using the fringe counting approach for a lens of25mm focal length.Prakash et al.[9]demonstrated the measure-ment of focal length for the lenses of different focal lengths using Lau interferometric arrangement and reported an accuracy of0.7%. Singh et al.[18]reported an automated method for the focal length measurement using temporal phase shifting technique in Talbot interferometry.The authors reported the relative comparison of the accuracy achievable in various focal length measuring test pro-cedures.They correlated the focal length of a test lens with the obtained phase map and reported an accuracy of0.246%for the lens having focal length of240mm.Tay et al.[19]reported an accuracy of0.2%in focal length measurement of a50mm convex lens,using three-step phase shifting algorithm in Lau phase interferometry.The results of the measurement undertaken with the lenses of different focal lengths are shown in parison of the results obtained with those using above-mentioned techniques reveal that,we could measure the focal length more accurately using the proposed technique.To check for the precision of tech-nique,standard deviation( )has also been calculated in each case. The smaller values of standard deviation reveals that the focal point position(hence the focal length)can be determined precisely using this method.The technique has also been used to test the concave mirror of radius of curvature200mm.The relative error r/r for the measurement of radius of curvature was determined to be0.25%. Hence,the measured radius of curvature of the concave mirror shows the close agreement with the standard.The discussions regarding the error in the present system also need consideration.The errors may occur in the system due to mis-alignment of the gratings,quality of optics used,imperfections in the gratings,improper collimation of optical beam,aberrations in lens,etc.Care has been taken to minimize these errors.The pre-cision translating device may also be the cause of systematic or human error.Random error may also affect the accuracy of the sys-tem.Random errors are those remaining when all systematic and gross errors have been taken care of.These are attributed tovarious parameters that affect the system in random fashion.We have taken precautions to minimize these errors.There may be errors due to quantization errors in digitizing the data,source instabilities, and detector non-linearity.Since,it is an interferometric technique the influences of environmental factors such as extraneous vibra-tions and air turbulence have to be taken care of.5.ConclusionsThe accurate measurement of focal length and radius of cur-vature using coherent gradient sensing technique coupled with Fourier transform method has been successfully demonstrated.To check for the validity of the technique,the results of the experimen-tal investigation have been compared with the other techniques. There are some major advantages in this method.(i)The method is simple and direct.The components used areinexpensive.(ii)Method is well adoptable to be used in industrial environment because it is a common path interferometer.The automated interferogram analysis using Fourier fringe analysis involves use of single interferogram,and hence the effect of shock and vibration in measurement may be minimized.(iii)Relative to the self-imaging methods devised earlier,the errors due to in accurate grating seperation may be completely elim-inated.(iv)The profile of recorded fringe pattern in CGS is sinusoidal and devoid of grating noise as in case of Talbot/Lau based interfer-ometers.Hence,higher accuracy and precision of measurement as com-pared to other similar techniques has been reported. AcknowledgementThefinancial support of University Grants commission(UGC), New Delhi in terms of research project grants33-395/2007(SR)is gratefully acknowledged.References[1]H.V.Tippur,Simultaneous and real-time measurement of slope and curvaturefringes in thin structures using shearing interferometry,Opt.Eng.43(2004) 1–7.[2]H.V.Tippur,S.Krishnaswamy,A.J.Rosakis,A coherent gradient sensor for cracktip deformation measurements:analysis and experimental results,Int.J.Fract.48(1991)193–204.[3]H.V.Tippur,S.Krishnaswamy,A.J.Rosakis,Optical mapping of crack tip defor-mations using the methods of transmission and reflection coherent gradient sensing:a study of crack tip K,dominance,Int.J.Fract.52(1991)91–117. [4]L.Xu,H.V.Tippur,C.E.Rousseau,Measurement of contact stresses using realtime shearing interferometry,Opt.Eng.38(1999)1932–1937.[5]T.S.Park,S.Suresh,A.J.Rosakis,J.Ryu,Measurement of full-field curvature andgeometrical instability of thinfilm-substrate systems through CGS interferom-etry,J.Mech.Phys.Solids51(2003)2191–2211.[6]Y.Nakano,K.Murata,Talbot interferometry for measuring the focal length ofa lens,Appl.Opt.24(1985)3162–3166.[7]J.C.Bhattacharya,A.K.Aggarwal,Measurement of the focal length of a collimat-ing lens using the Talbot effect and the moirétechnique,Appl.Opt.30(1991) 4479–4480.[8]K.V.Sriram,M.P.Kothiyal,R.S.Sirohi,Direct determination of focal length byusing Talot interferometry,Appl.Opt.31(1992)5984–5988.[9]S.Prakash,S.Singh,A.Verma,A low cost technique for automated measurementof focal length using Lau effect combined with moiréreadout,J.Mod.Opt.53 (2006)2033–2042.[10]S.D.Nicola,P.Ferraro,A.Finizio,G.Pierattini,Reflective grating interferometerfor measuring the focal length of a lens by digital moiréeffect,mun.132(1996)432–436.[11]F.Lei,L.K.Dang,Measuring the focal length of optical systems by grating shear-ing interferometry,Appl.Opt.28(1994)6603–6608.[12]J.L.Horner,Collimation invariant technique for measuring the focal length of alens,Appl.Opt.28(1989)1047–1048.。

托福听力tpo69 lecture1、2、3 原文+题目+答案+译文Lecture1 (2)原文 (2)题目 (5)答案 (8)译文 (8)Lecture2 (10)原文 (10)题目 (14)答案 (17)译文 (17)Lecture3 (20)原文 (20)题目 (23)答案 (26)译文 (26)Lecture1原文So, we've talked about the plates that form the earth crust and their movements and how in some places they're separating. Now, when this happens in the ocean along a middle ocean ridge, some important things can happen, in particular you can get a hydrothermal vent. This is a lot like a geyser except it’s on the ocean floor.A geyser of course is a kind of eruption from underground hot spring. Water that’s been heated up in Earth’s interior, when under pressure, can erupt, sending that water and steam, shooting upwards through crack in the earth. A hydrothermal vent is essentially this same thing, but the water is emitted out of cracks or, or fractures in the ocean floor. If Forms that don't depend on energy from the sun, but depend on chemical energy.But, the vents are also enormous significance for us. From a purely geological perspective, because the chemistry of the oceans is affected by them. To see how, let’s look at the process a little more closely. They typically occur in fields, so you might have an area with a dozen of them, but you need two things to get one of these fields, first, you got haveheat. And you’ve got have fissures in the ocean floor. So, in a vent field, you've got cracks in the ocean floor. And cold water at the bottom of the ocean, we are talking, maybe two degrees Celsius, goes down into them, as it goes underground, it heats up, because in these fields, there are magma chambers, only a few kilometers below the ocean floor.This hot molten rock heats the solid rock above it to as high as five hundred degrees Celsius. And this heated solid rock, then heats the ocean water that flows over it. Now remember, the high pressure of the deep sea, allows water to stay liquid at such a high temperature, so it can reach temperatures of, three or four hundred degrees Celsius.As the water heated, it rises up through other cracks and it shoots up back into the ocean, much like with geyser on land. Now, the important part, is what the water is carrying with it, as it emerges. The heated water draws minerals from solid rock. So, you get dissolved metals in the water, like iron and copper. When the water shoots up and re-enters the cold ocean, it quickly cools and these minerals precipitate out. They’re released and they are deposited into the ocean water, which affects its composition. And it also creates quite a site, these vents have a plume that looks like a smoke, likes smoke that’s coming up out of the vent in the earth.Remember some of the water coming out of the vents is over threehundred degree Celsius. When it’s this hot, it dissolves sulfur, iron and other metals in the rock and it interacts with. when these minerals precipitate out, the water forms of black plume, so these vents are called black smokers. It's the sulfur and metals precipitating out of the water that that's what causes black color.But there are also white smokers, these emit what looks like a white smoke. That's because their water is relatively cool, above one hundred to three hundred degrees. Still pretty warm, but, not warm enough to dissolve sulfur or iron. Instead, they draw off different minerals from rocks. Things like silica and they give off different color, whitish color, when those minerals precipitate out.But in both black and white smokers as the waters emitted in the plume, the mineral that precipitate out, eventually build up around the vent, forming large, tower, like structures or minerals, build up layer upon layer, we call these chimneys, just like a chimney on a house. Different minerals will tend to build up at different places on the chimneys. But, some of the minerals like silica, a form kind of cement, and they hold the whole structure together. So, they can grow quite large and quite quickly. If you can believe it there was one chimney that reached forty-seven meters, that’s like fourteen story It collapsed, but it’s actually now rebuilding.题目1.What does the professor mainly discuss?A. The process by which molten rock can enter the oceanB. The formation of hydrothermal ventsC. The differences between geysers and hydrothermal ventsD. The mineral composition of hydrothermal vent chimneys2.According to the professor, what is the main difference between geysers and hydrothermal vents?A. Where they occurB. What causes themC. The size of their plumesD. The temperature of the water they emit3.What aspect of hydrothermal vents is of most significance to the professor?A. Their role in supporting unusual life formsB. Their role in affecting the chemical composition of the oceansC. Their role in affecting the movement of ocean platesD. Their role in affecting the temperature of ocean water4.What conditions are needed for hydrothermal vents to form?[Click on2 answers.]A. Heated rock beneath the ocean floorB. Rocks on the ocean floor with high mineral contentC. Cracks in the ocean floorD. Strong ocean currents5.What are two differences between black smokers and whitesmokers?[Click on 2 answers.]A. Black smokers emit water at a higher temperature.B. Black smokers are more common than white smokers are.C. Black smokers are found in deeper ocean water.D. Black smokers release different types of minerals than white smokers release.6.What does the professor say about the chimney structures that grow around hydrothermal vents？A. They last only a few years.B. They are formed by a single mineral.C. They can grow very tall.D. Their growth rate depends on the temperature of the water emitted from the vent.答案B A B AC AD C译文我们之前讨论了构成地壳的板块及其运动，以及在某些地方它们如何分离。

综述书写规范要求：总数一般字数在：3000～5000字；论文分三级标题；文中中文采用宋体，英文一般采用Times New Roman正体。

具体如下：1、中文标题（宋体，三号，加粗）英文标题（Times New Roman，三号，加粗）2、作者，单位（宋体五号）3、中文摘要（宋体小四号）中文关键词（宋体小四号）4、英文摘要（Times New Roman小四号）英文关键词（Times New Roman小四号）5、正文第一级标题: 宋体四号加粗正文第二级以下标题：宋体小四号加粗正文内容：宋体小四号，正文中数字序号全部用阿拉伯数字，如：1 1.1 1.1.1……等。

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为保证表格完整，原则上一个表格不占用两张页面，可根据实际情况调整表中字体及行距（但一般为1.5倍行距，字符间距为正常）。

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作者姓名写至第三位，余者写“，等”或“，et al.”。

参考文献数量不少于30篇，外文文献不应少于3篇。

正文中应按顺序在引用参考文献处的文字右上角用［］（上标）标明，［］中序号应与“参考文献”中序号一致。

6.1 参考文献的类型参考文献（即引文出处）的类型以单字母方式标识，具体如下：M——专著；C——论文集；N——报纸文章；J——期刊文章；D——学位论文；R——报告；S——标准。

对于不属于上述的文献类型，采用字母“Z”标识。

对于英文参考文献，还应注意以下两点：①作者姓名采用“姓在前名在后”原则，具体格式是：姓，名字的首字母.如：Malcolm Richard Cowley 应为：Cowley, M.R.，如果有两位作者，第一位作者方式不变，&之后第二位作者名字的首字母放在前面，姓放在后面，如：Frank Norris 与Irving Gordon应为：Norris, F. & I.Gordon.；②书名、报刊名使用斜体字，如：Mastering English Literature，English Weekly。

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技术 应用 Application今日制造与升级 │ 57参考文献[1]张清勇,郭永波，高战朋.摄影位移测量技术在飞机静力试验中的应用[J].测控技术,2015,34(12):26-29.[2]张清勇.摄影测量系统误差分析.结构强度研究.2015(2):36-39[3]王晓鑫，郭永波，高战朋.大尺寸位移测量分析系统标定方法研究.工程与试验.Mar.2019[4]黄桂平.数字近景工业摄影测量关键技术研究与应用[D].天津大学博士论文.2005.[5]GJB67.9A-2008,军用飞机结构强度规范:地面试验[S].[5] Salbut,L. and M. Kujawinska.The optical measurement station for complex testing of microelements[J].Optics and lasers in Engineering,2001,36(2): 225-240.[6] Quan,C.,X.He,C.Wang,et al.Shape measurement of small objects using LCD fringe projection with phaseshifting[J]. Optics Communications,2001,189(1): 21-29.作者简介高战朋（1970—），男，陕西西安人，航空工业飞机强度研究所八室高级工程师，毕业于西安电子科技大学，硕士，主要从事结构强度试验测控与数据分析研究工作。

机械密封泄露原因分析及采取措施杨永康（中铝工业服务有限公司，北京 ）［摘 要］随着社会对企业“节能”的更高要求，机械密封在越来越多的企业中得到运用。

某国内大型氧化铝厂生产中用的离心泵、液封泵、真空泵、底流泵、碱液泵、料浆泵所选用的密封大部分为机械密封，泵的密封性能好坏和使用情况好坏直接关系到企业的生产稳定，关系到氧化铝的产量与成本。

试验研究2021.5魁W l油页岩与沙复配成土的保水特性及其对燕麦苗期生物量的影响周晓莹&关冰2于国庆2赵艳2李杰颖&（1.抚顺矿业集团工程技术研究中心辽宁抚顺113008；2.辽宁省沙地治理与利用研究所阜新123000）摘要：为了研究油页岩与沙复配成土的保水特性及其对燕麦苗期生物量的影响，试验采用室内盆栽试验的方法将油页岩用量设置5个处理（0#15g/kg#30g/kg#60g/kg#100g/kg）,与风沙土混合并种植燕麦,测定和分析不同油页岩添加量对土壤容重、毛管孔隙度、饱和含水量等物理指标和燕麦生物量的影响。

结果表明，油页岩与沙复配成土后能降低土壤容重，改善土壤松紧状况，提高土壤的供水持水能力，还能为土壤提供外源养分，具有良好的供氮作用，促进燕麦苗期植株生物量的积累,对根系、茎、叶片生物量的影响均达到显著水平（P<0.05）。

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Mitigation”FPGA algorithmTwo narrow-band chirps ()each with central frequency and bandwidth ()are combined to form one chirp with bandwidth ()M=2f B=Δf 2B m NATO ASI UXO 2008The correlation is performed for 108ìs Resultsf fA sequence of narrowband pulses is transmitted at each of the observation position in order to obtain a synthetic range profile.The frequencies are spaced by step M LFM centerB MV2The range resolution is:A part of the transmitted wave form in the time domain /Matlab simulation/:MATLAB simulation of the synthetic range profile constructed in the time domain by combining14narrowband chirps according to this algorithm.:A four-layered ground environment is simulated 14narrow-band chirps are combined into one wide-band chirpSynthetic range profile in dBSynthetic range profile that includes envelopes of 3echo signalsreflected from layers 2,3and 4The receiver block diagramThe used platform[]The total synthesis estimation parameters are:number of slices =8937BRAM =30Mult18x18=62After the simulation performing the real time constraints were approximately found 400ìs According to the synthesis report,the usage of the processor was almost 75%.Sample issue of a correlation on the ModelsimsimulatorТМThe experimentThe transmitter outputReferences[1]Behar V.,Chr.Kabakchiev,“,Proc.IRS-07,4-9Sept.,2007,Cologne,pp.635-639“Stepped-Frequency Processing in Low-Frequency GPR [2]Daniels D,Ground penetrating radar,2nd edition,The Institution of Electrical Engineers,London,200[]3Mikhnev V.,Microwave reconstruction approach for stepped-frequency radar,15th World Conf.on Non-Destructive Testing,15-21Oct,Rome,2000.[4]Nel W.,J.Tait,R.Lord and A.Wilkinson,"The use of a frequency domain stepped frequency technique to obtain high range resolution on the CSIR X-Band SAR system,"Proc.6th IEEE AFRICON Conf.,AFRICON'02,George,South Africa,vol.1,2002,327-332.[5]Zhang Q.,Jin Y .,Aspects of radar imaging using frequency-stepped chirp signals,EURASIP Journal on Applied Signal processing,vol.2006,1-8.All blocks are implemented on VHDL via Xilinx ISE development platformXilinx cores are usedIntlectual Properies All blocks are implemented and tested individuallyon the MODELSIM simulatorТМVerification -All blocks are previously simulated in MATLAB and test benches are made.The results from the hardwareimplementation,obtained in MODELSIM ,simulator are compared with the MATLAB test benches.ТМf0,m 0,m+1=f +ff0,min1=fm=1,...,MδD=∆ f∆。