物理专业英语翻译141-149.doc

物理专业英语翻译姓名：陈云飞学号：09027203页数：141149The distance lcoh=c* tcoh over which a wave travels during the tcoh is called the coherence length （or the train length ）. The coherence length is the distance over which a chance change in the phase reach a value of about 。To obtain an interference pattern by splitting a natural wave into two parts, it is essential that the optical path difference be smaller than the coherence length. This requirement limits the number of visible interference fringes observed when using the layout shown in Fig.6.2. An increase in the fringe number m is attended by a growth in the path difference. As a result, the sharpness of fringes becomes poorer and poorer.一个波在相干时间运动的距离【lcoh=c*tcoh】被称为相干长度（波列的长度）。相干长度是一个阶段的机会改变达到约的值。以获得通过分裂成两部分的自然波干涉图样的距离，光程差小于相干长度是必要的。使用Fig.6.2所示的布局时，这项规定限制可见干扰观察边缘。附带数m的增加，是表现在增长路径差异。因此，边缘锐度变得越来越弱Let us pass over to a consideration of the part of the non-monochromatic nature of light wave. Assume that light consists of a sequence of identical trains of frequency 。 and duration 。When one train is replaced with another one, the phase experiences disordered changes .As a result, the trains are mutually incoherent. With these assumptions, the duration of a train virtually coincides with the coherence time tcoh.让我们通过光波的非单色性的考虑。假设光相同频率波列序列组成。期限，当一列波列与另一取代阶段的经验无序的变化，因此，波列是相干的。有了这些假设，波列的时间几乎恰逢相干时间的相干时间。In mathematics, the Fourier theorem is proved, according to which any finite and integrable function F(t) can be represented in the form of the sum of an infinite number of harmonic components with a continuously changing frequency:F(t) =|A()eit d (6.16)Expression (6.16) is known as Fourier integral. The function A() inside the integral is the amplitude of the relevant monochromatic component. According to the theory of Fourier integrals, the analytical form of the function A() is determined by the expressionA(w)=2|F()e(-i)d （6.16）Where is an auxiliary integration variable.在数学中，傅立叶定理证明，任何有限的和可积函数F（t），可以在无限多的频率不断变化的谐波成分的总和形式表示：F（t）=|F（）e itd（6.16）表达（6.16）被称为傅立叶积分。函数内的积分（）是有关的单色成分的振幅。根据傅立叶积分，函数A（）的分析形式的理论是表达式A（）=2F（）eI d其中是一个辅助的一体化变量。Assume that the function F(t) describes a light disturbance at a certain point at the moment of time t due to a single wave train. Hence, it is determined by the conditionsF(t)=A0exp(i0t) aa t |t|F(t) =0 aa t |t|A graph of the real part of this function is given in Fig.6.4.假设函数F（t），描述了一个在某一点上在时间t，由于单波波列时刻光干扰。因此，它是由条件 F（t）=A0exp（i0t） aat|t | F（t）=0 aa t |t|这个函数的实部图是Fig.6.4。波形图Outside the interval from /2 to +/2, the function F(t) is zero. Therefore, expression (6.17) determining the amplitude of the harmonic components has the formA()=2【A0exp(i0)】exp(-i)d=2A0【exp i(0-) 】d=2A0|()After introducing the integration limits and simple transformations ,we arrive at the equation A()=A0 The intensity I() of a harmonic wave component is proportional to the square of the amplitude, i.e.to the expressionf()=以外的时间间隔从-到+函数F（t）是零。因此，确定谐波成分的幅值的表达（6.17）的形式 A()=2【A0 exp(i0-)】exp(-i)d=2A0【exp i(0-) 】d=2A0|()引进的整合限制和简单的转换后，我们到达的方程 A()=A0 谐波组件的强度I（）是振幅的平方成正比，i.e.t.o的表达f()=A graph of function (6.18 ) is shown in Fig.6.5. A glance at the figure shows that the intensity of the components whose frequencies are within the interval of width w=2/ considerably exceeds the intensity of the remaining components . This circumstance allows us to relate the duration of a train to the effective frequency range of a Fourier spectrum: =2/=1/vIdentifying with the coherence time, we arrive at the relationtcoh1/v(The sign stands for ”equal to in the order of magnitude”) 在Fig.6.5所示的函数曲线图（6.18）。一个一目了然的数字显示，频率的宽度间隔内的元件，其强度W =2/大大超过其余部分的强度。此情况下，使我们能够与波列期间的傅立叶频谱的有效频率范围： =2/= 1 /v识别与相干时间，我们到达的关系 tcoh1 /v（符号表示“等于量级”）It can be seen from expression (6.19) that the broader the interval of frequencies present in a given light wave, the smaller is the coherence time of this wave.可以看出，从更广泛的间隔在一个给定的光波的频率，规模较小的，是这一波的相干时间的表达（6.19）。The frequency is related to the wavelength in a vacuum by the expressly v=c/0. Differentiations of this expression yields v=c0/02c/2(we have omitted the minus sign obtained in differentiation and also assumed that 0). Substituting for v in the E.q.(6.29) its expression through and , we obtain the following expression for the coherence time:t coh Hence, we get the following value for the coherence length:l coh=c tcoh 很明显v=c/0频率是在真空中的波长有关。该表达式产生分化V =彗星0/02彗星/2（我们省略了分化得到的减号，还假定，0）。v的方程（6.29）其表达通过和代，我们获得的相干时间下面的表达式： t coh 因此，我们得到的相干长度为以下值： l coh=c tcoh Examination of Eq.(6.5)shows that the path difference at which a maximum of the m-th order is obtained is determined by the relation m=m 0m When this path difference reaches values of the order of the coherence-length, the fringes become indistinguishable .Consequently, the extreme interference order observed is determined by the condition FIG.6.6mextr lcoh （6.5）式的推导结果表明，在获得最大的m阶的路径差异是由下列关系式是决定 m=m0m 当这条道路的差异达到秩序的相干长度的值，边缘变得没有什么区别。，因此，极端的干扰为了观察是由条件FIG.6.6mextr lcoh Whence mextr It follows from Eq.(6.22) that the number of interference fringes observed according to the layout shown in Fig.6.2 grows when the wave length interval in the light used diminishes.因此 mextr从式（6.22）在Fig.6.2所示的布局观察干涉条纹的数目增长时所使用的光的波长间隔减少。Spatial Coherence. According to the equation k=/v=n/c, scattering of the frequencies results in scattering of the values of k. We have established that the temporal coherence is determined by the value of . Consequently, the temporal coherence is associated with scattering of the value of the magnitude of the wave vector K. Spatial coherence is associated with scattering of the directions of the vector K that is characterized by the quantity ek.空间相干性。根据方程K=/ V=n/c，散射的频率在散射光值结果我们已经建立了时间相干性的值决定。因此，时间相干性与散射载体k.空间相干性是相关联的特点就是由数量ek矢量k方向散射波的幅度值。The setting up at a certain point of space of oscillations produced by waves with different values of ek is possible if these waves are emitted by different sections if an extended (not a point) light source. Let us assume for simplicitys sake that the source has the form of a disk visible from a given point at the angle 。It can be seen from Fig.6.6 that the angle characterizes the interval confining the unit vector ek. We shall consider that this angle is small.设置在不同的价值观与EK波产生的振荡空间的某一点是可能的，如果这些波是由不同的部分，如果一个扩展（不是点）光源发出的。让我们假设为简单起见，源磁盘从一个角度点可见的形式，可以看到从Fig.6.6，角度间隔围的单位向量ek的特点。我们应考虑这个小角度。Assume that the light from the source falls on two narrow slits behind which there is screen (Fig.6.7). We shall consider that the interval of frequencies emitted by the source is very small. This is needed for the degree of temporal coherence to be sufficient for obtaining a sharp interference pattern. The wave arriving from the section of the surface designated in Fig.6.7 by O produces a zero-order maximum M at the middle of the screen .The zero-order maximum M produced by the wave arriving from section O will be displaced from the middle of the screen by the distance x. Owing to the smallness of the angle and of the ratio we can consider that x=l/2.假设，从源头上落在后面的两个屏幕（Fig.6.7）窄的狭缝。我们应考虑源发出的频率间隔非常小。这是需要时间相干性的程度，足以获得一个尖锐的干涉图样。波到达Fig.6.7划“O”的表面部分产生一个零阶在屏幕中间最大的“M”零阶的最大M“波产生的O节抵达”将流离失所从屏幕中间距离x。由于狭小的角度的比例我们可以认为X=。The zero-order maximum “M” produced by the wave arriving from section “O”is displaced in the opposite direction from the middle of the screen over the distance X equal to X. The zero-order maximum from the other sections of the source will be between the maxima” M” and” M”.零阶最大的M“从第0抵达波产生的”流离失所者在向相反的方向，在距离X“X”等于屏幕中间。从零阶的最大源的其他部分在最大值M“和”M之间 The separate sections of the light source produce waves whose phases are in no way related to one another. For this reason the interference pattern appearing on the screen will be a superposition of the patterns produced by each section separately. If the displacement X is much smaller than flip width of an interference fringe x= see Eq.(6.10), then the maxima from different sections of the source will practically be superposed on one another, and the pattern will be like one produced by a point source. When x=x, the maxima from some sections will coincide with the minima from others, and no interference pattern will be observed. Thus, an interference pattern will be distinguishable provided that xx, i.e. OrWe have omitted the factor 2 when passing over from expression (6.22) to (6.24).光源的不同部分产生的波段无法与其他联系。出于这个原因，出现在屏幕上的干涉图样是每个独立部分产生的波的叠加。如果位移X是远远小于干涉条纹的宽度x= 见式（6.10），然后从源的不同部分的最大值几乎是叠加于另一个光源产生的波。当x=x，极大部分波段将叠加其他最小值，无干扰的部分将被观察到。因此，干扰的部分将被区分提供XX，即 或 我们在推出从式（6.22）（6.24）省略了因子2。Formula（6.24）determines the angular dimensions of a source at which interference is observed. We can also use this formula to find greatest distance between the slits at which interference from a source with the angular dimension can still be observed. Multiplying inequality (6.24) by d/ we arrive at the condition： d/ are incoherent.一级方程式（6.24）决定所观测相干源的角度。我们也可以用这个公式找到从干扰源角度仍然可以观察到狭缝之间的距离最大。以我们到达的条件乘D /不等式 （6.24）： d/点的波不相干。We shall call a surface which could be a wave one if source were monochromatic a pseudowave surface for brevity. We could satisfy condition(6.24) by reducing the distance d between this slits, i.e.by taking closer points of the pseudo wave surface. Consequently, oscillations produced by a wave at adequately close points of a pseudo wave surface are coherent. Such coherence is called spatial.如果源单色一个简洁pseudowave的表面，这可能是一个波之一，我们将调用一个表面。我们可以减少这个狭缝之间的距离d满足条件（6.24），ieby伪波面接近点。因此，在充分接近伪波面点波产生的振荡是一致的。这种相干性是称为空间。Thus, the phase of an oscillation changes chaotically when passing from one point of a pseudowave surface to another. Let us introduce the distance coh， upon displacement by which along a pseudowave surface a random change in the phase reaches a value of about . Oscillations at two points of a pesudowave surface spaced apart at a distance less than coh will be approximately coherent. The distance coh is called the spatial coherence length or the coherence radius. It can be seen from expression (6.25) that 因此，振荡的相位变化无序地传递一个pseudowave表面从一个点到另一个时。让我们介绍的距离coh后，沿着pseudowave表面位移，其中一个阶段的随机变化达到约值。在两个点的间隔距离，除了一个pesudowave表面振荡低于coh将约为相干。coh的距离被称为空间相干长度或相干半径。从表达（6.25）可以看出cohThe angular dimension of the Sun is about 0.01 radian, and the length of its light waves is about 0.5 m. Hence, the coherence radius ot the light waves arriving from the Sun has a value of the order of太阳的角尺寸为约0.01弧度，光波的长度大约是0.5微米。因此，来自太阳的光波的一致性半径有规律性的coh = =5m=0.05mmThe entire space occupied by a wave can be divided into parts in each of which the wave approximately retains coherence. The volume of such a part of space, called the coherence volume, in its order of magnitude equals the products of temporal coherence length and the area of a circle of radius coh。波占用整个空间可以分为多个相干部分。这样一个空间的一部分，在其量级等于时间相干长度和半径为coh的圆的面积的区域内被称为相干量。The spatial coherence of a light wave near the surface of the heated body emitting it is restricted by a value of coh of only a few wavelengths. With an increasing distance from the source, the degree of spatial coherence grows. The radiation of a laser has an enormous temporal and spatial coherence. At the outlet opening of a laser, spatial coherence is observed throughout the entire cross section of the light beam.附近的加热体发光，它是由限制的只有少数几个波长的值coh表面光波的空间相干性。从源距离的增加，空间相干度的增长。激光的辐射有一个巨大的时间和空间的连贯性。空间相干性激光的出风口，整个光束的整个横截面观察。It would seem possible to observe interference by passing light propagating from an arbitrary source through two slits in an opaque screen. With a small spatial coherence of the wave falling on the slits, however, the beams of light passing through then will be incoherent, and an interference pattern will be absent. The English scientist Thomas Young (1772-1829) in 1802 obtained interference from two slits by increasing the spatial coherence of the light falling on the slits. Young achieved such an increase by first passing the light through a small aperture in an opaque screen. This light was used to illuminate the slits in a second opaque screen. Thus, for the first time in history, Young observed the interference of light waves and determined the length of these waves.这似乎可以观察在一个不透明的屏幕上，通过两个狭缝光传播从任意源的干扰。然而，随着一个小狭缝的下降波的空间相干性，光线穿过梁然后将相干，和一个干涉图样将缺席。英国科学家托马斯杨（1772年至1829年）在1802年通过把单个波阵面增加两个狭缝的获得两个波阵面来获得光的空间相干波。杨在一个不透明的屏幕上，首先通过小光圈光取得这样的增幅。此灯是用来在第二个不透明屏幕照亮狭缝。因此，杨历史上首次观测的光波的干扰，并确定了这些波的长度。6.3 WAYS OF OBSERVING THE INTERFERENCE OF LIGHTLet us consider two concrete interference layouts of which one uses reflection for splitting a light wave into two parts, and the other refraction of light Fresnels Double Mirror. Two plane contacting mirrors OM and ON are arranged so that their reflecting surfaces from an obtuse angle close to (Fig.6.8). Hence, the angle in the figure is very small. A straight light source S(for example, a narrow luminous slit) is placed parallel to the line of intersection of the mirrors O(perpendicular to the plane of the drawing) at a distance r from it . The mirrors reflect two cylindrical coherent waves onto screen Sc. They propagate as if they were emitted by virtual sources S1 and S2 , Opaque screen Sc1 prevents the direct propagation of the light from source S to screen Sc.6.3观察光干涉的方法让我们考虑两个具体的相干关系，其中之一使用分裂反射光波分为两个部分，和其他折射光 菲涅耳双面镜。两平面接触镜OM和ON安排，使他们反映，从一个钝角接近（Fig.6.8）的表面。因此，图中的角是非常小的的。一个直光源S（例如，一个狭窄的光缝