物理專業(yè)英語翻譯141-149.doc

物理專業(yè)英語翻譯姓名：陳云飛學號：09027203頁數(shù)：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.一個波在相干時間運動的距離【lcoh=c*tcoh】被稱為相干長度（波列的長度）。相干長度是一個階段的機會改變達到約的值。以獲得通過分裂成兩部分的自然波干涉圖樣的距離，光程差小于相干長度是必要的。使用Fig.6.2所示的布局時，這項規(guī)定限制可見干擾觀察邊緣。附帶數(shù)m的增加，是表現(xiàn)在增長路徑差異。因此，邊緣銳度變得越來越弱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.讓我們通過光波的非單色性的考慮。假設光相同頻率波列序列組成。期限，當一列波列與另一取代階段的經(jīng)驗無序的變化，因此，波列是相干的。有了這些假設，波列的時間幾乎恰逢相干時間的相干時間。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.在數(shù)學中，傅立葉定理證明，任何有限的和可積函數(shù)F（t），可以在無限多的頻率不斷變化的諧波成分的總和形式表示：F（t）=|F（）e itd（6.16）表達（6.16）被稱為傅立葉積分。函數(shù)內(nèi)的積分（）是有關(guān)的單色成分的振幅。根據(jù)傅立葉積分，函數(shù)A（）的分析形式的理論是表達式A（）=2F（）eI d其中是一個輔助的一體化變量。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.假設函數(shù)F（t），描述了一個在某一點上在時間t，由于單波波列時刻光干擾。因此，它是由條件 F（t）=A0exp（i0t） aat|t | F（t）=0 aa t |t|這個函數(shù)的實部圖是Fig.6.4。波形圖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()=以外的時間間隔從-到+函數(shù)F（t）是零。因此，確定諧波成分的幅值的表達（6.17）的形式 A()=2【A0 exp(i0-)】exp(-i)d=2A0【exp i(0-) 】d=2A0|()引進的整合限制和簡單的轉(zhuǎn)換后，我們到達的方程 A()=A0 諧波組件的強度I（）是振幅的平方成正比，i.e.t.o的表達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所示的函數(shù)曲線圖（6.18）。一個一目了然的數(shù)字顯示，頻率的寬度間隔內(nèi)的元件，其強度W =2/大大超過其余部分的強度。此情況下，使我們能夠與波列期間的傅立葉頻譜的有效頻率范圍： =2/= 1 /v識別與相干時間，我們到達的關(guān)系 tcoh1 /v（符號表示“等于量級”）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，從更廣泛的間隔在一個給定的光波的頻率，規(guī)模較小的，是這一波的相干時間的表達（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 很明顯v=c/0頻率是在真空中的波長有關(guān)。該表達式產(chǎn)生分化V =彗星0/02彗星/2（我們省略了分化得到的減號，還假定，0）。v的方程（6.29）其表達通過和代，我們獲得的相干時間下面的表達式： t coh 因此，我們得到的相干長度為以下值： 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）式的推導結(jié)果表明，在獲得最大的m階的路徑差異是由下列關(guān)系式是決定 m=m0m 當這條道路的差異達到秩序的相干長度的值，邊緣變得沒有什么區(qū)別。，因此，極端的干擾為了觀察是由條件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從式（6.22）在Fig.6.2所示的布局觀察干涉條紋的數(shù)目增長時所使用的光的波長間隔減少。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.空間相干性。根據(jù)方程K=/ V=n/c，散射的頻率在散射光值結(jié)果我們已經(jīng)建立了時間相干性的值決定。因此，時間相干性與散射載體k.空間相干性是相關(guān)聯(lián)的特點就是由數(shù)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.設置在不同的價值觀與EK波產(chǎn)生的振蕩空間的某一點是可能的，如果這些波是由不同的部分，如果一個擴展（不是點）光源發(fā)出的。讓我們假設為簡單起見，源磁盤從一個角度點可見的形式，可以看到從Fig.6.6，角度間隔圍的單位向量ek的特點。我們應考慮這個小角度。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.假設，從源頭上落在后面的兩個屏幕（Fig.6.7）窄的狹縫。我們應考慮源發(fā)出的頻率間隔非常小。這是需要時間相干性的程度，足以獲得一個尖銳的干涉圖樣。波到達Fig.6.7劃“O”的表面部分產(chǎn)生一個零階在屏幕中間最大的“M”零階的最大M“波產(chǎn)生的O節(jié)抵達”將流離失所從屏幕中間距離x。由于狹小的角度的比例我們可以認為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”.零階最大的M“從第0抵達波產(chǎn)生的”流離失所者在向相反的方向，在距離X“X”等于屏幕中間。從零階的最大源的其他部分在最大值M“和”M之間 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).光源的不同部分產(chǎn)生的波段無法與其他聯(lián)系。出于這個原因，出現(xiàn)在屏幕上的干涉圖樣是每個獨立部分產(chǎn)生的波的疊加。如果位移X是遠遠小于干涉條紋的寬度x= 見式（6.10），然后從源的不同部分的最大值幾乎是疊加于另一個光源產(chǎn)生的波。當x=x，極大部分波段將疊加其他最小值，無干擾的部分將被觀察到。因此，干擾的部分將被區(qū)分提供XX，即 或 我們在推出從式（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.一級方程式（6.24）決定所觀測相干源的角度。我們也可以用這個公式找到從干擾源角度仍然可以觀察到狹縫之間的距離最大。以我們到達的條件乘D /不等式 （6.24）： d/點的波不相干。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.如果源單色一個簡潔pseudowave的表面，這可能是一個波之一，我們將調(diào)用一個表面。我們可以減少這個狹縫之間的距離d滿足條件（6.24），ieby偽波面接近點。因此，在充分接近偽波面點波產(chǎn)生的振蕩是一致的。這種相干性是稱為空間。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，振蕩的相位變化無序地傳遞一個pseudowave表面從一個點到另一個時。讓我們介紹的距離coh后，沿著pseudowave表面位移，其中一個階段的隨機變化達到約值。在兩個點的間隔距離，除了一個pesudowave表面振蕩低于coh將約為相干。coh的距離被稱為空間相干長度或相干半徑。從表達（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太陽的角尺寸為約0.01弧度，光波的長度大約是0.5微米。因此，來自太陽的光波的一致性半徑有規(guī)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。波占用整個空間可以分為多個相干部分。這樣一個空間的一部分，在其量級等于時間相干長度和半徑為coh的圓的面積的區(qū)域內(nèi)被稱為相干量。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.附近的加熱體發(fā)光，它是由限制的只有少數(shù)幾個波長的值coh表面光波的空間相干性。從源距離的增加，空間相干度的增長。激光的輻射有一個巨大的時間和空間的連貫性?？臻g相干性激光的出風口，整個光束的整個橫截面觀察。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.這似乎可以觀察在一個不透明的屏幕上，通過兩個狹縫光傳播從任意源的干擾。然而，隨著一個小狹縫的下降波的空間相干性，光線穿過梁然后將相干，和一個干涉圖樣將缺席。英國科學家托馬斯楊（1772年至1829年）在1802年通過把單個波陣面增加兩個狹縫的獲得兩個波陣面來獲得光的空間相干波。楊在一個不透明的屏幕上，首先通過小光圈光取得這樣的增幅。此燈是用來在第二個不透明屏幕照亮狹縫。因此，楊歷史上首次觀測的光波的干擾，并確定了這些波的長度。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觀察光干涉的方法讓我們考慮兩個具體的相干關(guān)系，其中之一使用分裂反射光波分為兩個部分，和其他折射光 菲涅耳雙面鏡。兩平面接觸鏡OM和ON安排，使他們反映，從一個鈍角接近（Fig.6.8）的表面。因此，圖中的角是非常小的的。一個直光源S（例如，一個狹窄的光縫