1、<p><b>　　畢業(yè)論文</b></p><p><b>　　英文文獻(xiàn)及中文翻譯</b></p><p>　　學(xué)生姓名： 學(xué)號(hào)： 10051041 </p><p>　　學(xué) 院： 信息與通信工程學(xué)院 </p><

2、;p>　　專(zhuān) 業(yè)： 光電信息工程 </p><p>　　指導(dǎo)教師： </p><p>　　2014年 6 月</p><p>　　Three Dimensional photo-thermal Deflection of Solids Us

3、ing</p><p>　　Modulated CW Lasers : Theoretical Development</p><p>　　M. Soltanolkotabi and M. H. Naderi</p><p>　　Physics Department ， Faculty of Sciences ， University of Isfahan， Isf

4、ahan， Iran</p><p><b>　　Abstract</b></p><p>　　In this paper，a detailed theoretical treatment of the three dimensional photo-thermal deflection ，under modulated cw excitation ， is pres

5、ented for a three layer system( backing-solid sample-fluid). By using a technique based on Green’s function and integral transformations we find the explicit expressions for laser induced temperature distribution functio

6、n and the photo-thermal deflection of the probe beam. Numerical analysis of those expressions for certain solid samples leads to some interesti</p><p>　　I. Introduction</p><p>　　photo-thermal te

7、chniques evolved from the development of photoacoustic</p><p>　　spectroscopy in the 1970s. They now encompass a wide range of techniques and</p><p>　　phenomena based upon the conversion of absor

8、bed optical energy into heat . When an</p><p>　　source is focused on the surface of a sample ， part or all of the incident energy is absorbeenergy d by the sample and a localized heat flow is produced in the

9、 medium</p><p>　　following a series of nonradiative deexcitation transitions . Such processes are the</p><p>　　origins of the photo-thermal effects and techniques . If the energy source is modul

10、ated，a periodic heat flow is produced at the sample . The resulting periodic heat flow in the material is a diffusive process that produces a periodic temperature distribution called a thermal wave .</p><p>

11、　　Several mechanisms are available for detecting ，directly or indirectly ， thermal waves . These includes gas-microphone photoacoustic detection of heat flow from the sample to the surrounding gas; photo-thermal measurem

12、ents of infrared radiationemitted from the heated sample surface ; optical beam deflection of a laser beamtraversing the periodically heated gaseous or liquids layer just above the sample surface ; laser detection of the

13、 local thermoelastic deformations of the surface; and interfer</p><p>　　The photo-thermal deformation technique is simple and straightforward. A laser beam (pump beam) of wavelength within the absorption ran

14、ge of the sample is incident on the sample and it is absorbed . The sample gets heated and this heating leads ， through thermoelastic coupling ， to an expansion of the interaction volumewhich in turn causes the deformati

15、on of the sample surface. The resulting thermoelastic deformation of the surface is detected by the deflection of a second ，weaker laser beam (pr</p><p>　　Ameri and his colleagues were among those who have u

16、sed first ， both the laser interferometric and laser deflection techniques for spectroscopic studies onamorphous silicon.Their method restricted to low to moderate modulation frequencies. Opsal et al have used thermal wa

17、ve detection for thin film thickness measurements using laser beam deflection technique. They have obtained temperature distribution function for what is called 1-D temperature distribution function. In their analysis th

18、ey assum</p><p>　　In this paper ， we present a detailed theoretical analysis of the deflection process in three dimensions，for a three layer system consisting of a transparent fluid ，an optically absorbing s

19、olid sample ， and a backing material . It is assumed that the system is irradiated by a modulated cw laser beam .The theoretical treatment of photo-thermal deflection can be devided into two parts. In Sec II.A we will fi

20、nd the 3D laser-induced temperature distribution within the three region of the system ， du</p><p>　　II. Theory of CW photo-thermal Deflection</p><p>　　Let us consider the geometry as shown in F

21、ig.1 . The solid sample is assumed to be deposited on a backing and is in contact with a fluid . lf ，， and lb are the thicknesses of the fluid ，sample ，and the backing ，respectively . The fluid can be air or another medi

22、um . It is assumed that the solid sample is the only absorbing medium ; the fluid and the backing are transparent. For simplicity ，we also assume that all three regions extend to infinity in radial directions. A modulate

23、d cw cylindrical l</p><p>　　III. Numerical Results and Discussions</p><p>　　In this section we will describe the results obtained for the temperature distribution within the three layer system a

24、nd photo-thermal deflection of the probe beam. The temperature profile Tf and the thermal deflection signals θt and θn can not be evaluated in closed form ， so numerical methods must be used.</p><p>　　Figur

25、es 5a and 5b show the temperature distribution Tf (0，z，t) as a function of z</p><p>　　for several values of time in one modulation cycle and for f = 10 Hz and f= 100 Hz ，</p><p>　　respectively .

26、 The surface temperature is sinousoidally modulated as found in Fig.4 ，</p><p>　　and a thermal wave propagate in the fluid . The thermal wave is strongly attenuated</p><p>　　with the decay lengt

27、h of the order of f σ .</p><p>　　Figure 6 shows the peak values of the temperature in the fluid Tf0 as a function of the distance z for three different values of the modulation frequency f . Two effects shou

28、ld be noted . First ， the temperature of the sample surface decreases with increasing modulation frequency because of the thermal inertia of the sample.In other words ，the sample is unable to respond to the intensity cha

29、nges to a lesser and lesser degree as the modulation frequency of the pump laser increases. Second ， the e</p><p>　　Figure 7a shows the dependence of the peak values of the temperature at sample surface on r

30、 for three different types of solid samples . As the thermal diffusivity Dsincreases the temperature decreases because the heat is able to diffuse further .Moreover ， the profile of the temperature distribution gets broa

31、der with increasing Ds .Here the optical absorption coefficient α for each of the three samples is much larger than the corresponding values of 1sσ ? . This case corresponds to the situatio</p><p>　　Figure 8

32、 shows the temperature profile as a function of r in the fluid for the</p><p>　　parameters shown on the figure . The temperature profile is seen to broaden with</p><p>　　increasing z ，as expecte

33、d .</p><p>　　We now proceed to evaluate numerically the deflection signal . For this purpose ，as before ， we have used Gaussian quadrature of 64-points. The deflection takes place in three dimensions ; the p

34、robe beam propagates in the x-direction and is deflected normally away from the sample surface into the z direction， and tangential to the sample surface into the y-direction，θt in</p><p>　　Eq.， as was shown

35、 in Figs.1 and 3 . As before ，we assume that the fluid and</p><p>　　backing are nitrogen gas and Corning glass ，respectively . It is also assumed that</p><p>　　pump power P=1W ，?n / ?T = 9.4

36、5;10?7K?1 (at room temperature) and η=1 .</p><p>　　For the glass-Ge-nitrogen system ， Figures 9a and 9b give θt and θn ， respectively，</p><p>　　as functions of y at z=0 for different values of t

37、ime in one modulation cycle and for</p><p>　　f=10 Hz. As before ， the initial value of the time ， θ = ωt is chosen such that Tf =0 at</p><p>　　y=0 at this time . The normal deflection is maximum

38、 at y = 0 but in the tangential</p><p>　　deflection there is no signal when the pump is centered on the probe at y= 0 ， the</p><p>　　probe beam is pulled equally in each direction . To either si

39、de of this point ， the probe beam is deflected in opposite directions ， up or down ， thus the change in sign on either side. In both figures the distribution is reflective of the Gaussian pump profile.</p><p&g

40、t;　　In figures 10a and 10b the peak values of the tangential and normal photo-thermal</p><p>　　deflection are plotted against the y coordinate ， for several different values of z and</p><p>　　fo

41、r f = 10Hz. These are the signals that are generally measured using the lock-in</p><p>　　techniques. As the distance from the surface increases the deflection signal intensity</p><p>　　decreases

42、 and the width increases since the heat is dispersed throughout more of the</p><p>　　fluid. It is interesting to note that the gradient of θn0， for the values of the parameters</p><p>　　chosen h

43、ere， is ~2 orders of magnitudes smaller than that that of θt0 . In fact the</p><p>　　gradient of photo-thermal deflection ( curvature of refractive index ) characterizes the</p><p>　　inverse of

44、the focal length of the thermal lens that is produced by the heating</p><p>　　action of the Gaussian laser beam. Therefore we find that the peak value of the</p><p>　　inverse focal length of th

45、e photo-thermal lens in the z direction is ~2 orders of</p><p>　　magnitude smaller than that of in y direction .</p><p>　　The effect of changing the sample diffusivity/conductivity on the tangen

46、tial deflection signal is shown in Fig.11. The peak value decreases as the sample diffusivity is increased. This is the behavior that was seen in the fluid temperature of figures 7a and 7b. As modeled the absorption coef

47、ficient of the sample is very large and the radiation absorption is taking place at the surface. The heat then diffuses preferentially into and throughout the sample due to the relatively low thermal conducti</p>

48、<p>　　Figure 12 shows the effect of the modulation frequency on the tangential deflection</p><p>　　signal. The signal and its width decrease with increasing frequency ， as expected.</p><p>

49、　　Decreasing the signal width with increasing modulation frequency shows that for</p><p>　　larger frequency the focal length of photo-thermal lens in y direction decreases . The</p><p>　　plot of

50、 peak value of normal deflection signal as a function of y for different values</p><p>　　of modulation frequency (not shown) also reveals similar dependence on frequency as</p><p>　　the peak val

51、ue of tangential deflection signal.</p><p>　　IV. Conclusions</p><p>　　We have presented a detailed theoretical description of the three dimensional</p><p>　　photothermal deflection，

52、 induced by modulated cw laser excitation， for a three layer</p><p>　　system consisting of a transparent fluid ， an optically absorbing solid sample and a</p><p>　　backing material. Some of the

53、important results are the following : (i) the laser</p><p>　　induced temperature of the sample surface decreases with increasing modulation</p><p>　　frequency of the pump laser. (ii) The effecti

54、ve thermal length decreases with</p><p>　　increasing modulation frequency ， thereby making the decay of photo-thermal signal</p><p>　　with z faster. (iii) As the modulation frequency increases t

55、he temperature distribution</p><p>　　Tf0 decreases and gets narrower. (iv) As the distance from the surface of solid sample</p><p>　　increases the deflection signalintensity decreases and its w

56、idth increases. (v) The</p><p>　　focal length of the photo-thermal lens ， produced by the heating action of the pump</p><p>　　laser ， in the z direction is much greater than that of in y directi

57、on. (vi) The increasing of diffusivity/ conductivity of solid sample results in a decrease in the deflection signal intensity and slight increase in the signal width. (vii) The normal deflection is greater than the tange

58、ntial deflection ， while its gradient is much smaller than that of tangential deflection. (viii) The deflection signal and its width decrease with increasing modulation frequency.</p><p>　　Figure CaptionFig.

59、1 Geometry of the three layer system of photo-thermal deflection effect. Each region is taken to be of infinite extent in the x-y plane.</p><p>　　Fig.2 An illustration of the photo-thermal deflection spectro

60、scopy .</p><p>　　Fig.3 Probe beam deflection normal and tangential to the sample surface. The box is</p><p>　　within the fluid region ， with the sample surface parallel to the nearest box face.&

61、lt;/p><p>　　Fig.4a Surface temperature T (r，0，t) as a function of r for five different times in</p><p>　　one modulation cycle and f=10Hz .</p><p>　　Fig.4b Surface temperature T(r，0，t)

62、 as a function of r for five different times in one</p><p>　　modulation cycle and f=100Hz .</p><p>　　Fig.5a Temperature distribution Tf as a function of z at r=0 for different times and</p>

63、;<p><b>　　f= 10Hz.</b></p><p>　　Fig.5b Temperature distribution Tf as a function of z at r=0 for different times and</p><p>　　f= 100Hz .</p><p>　　Fig.6 Temperatur

64、e distribution Tf0 (peak value) as a function of z at r=0 for</p><p>　　different values of modulation frequency.</p><p>　　Fig.7a Temperature distribution Tf0 (peak value) as a function of r at z

65、=0 for three</p><p>　　sample diffusivities and f=10Hz.</p><p>　　Fig.7b Temperature distribution Tf0 (peak value) as a function of r at z=0 for three</p><p>　　sample diffusivities an

66、d f=100Hz.</p><p>　　Fig.8 Temperature distribution Tf0 (peak value) as a function of r for different values</p><p>　　of z and f=10Hz.</p><p>　　Fig.9a Transverse deflection θ as a fu

67、nction of y for three different times in one</p><p>　　modulation cycle and f= 10Hz.</p><p>　　Fig.9b Normal deflection as a function of y for three different times in one n θ</p><p>

68、　　modulation cycle and f= 10Hz.</p><p>　　Fig. 10a Transverse deflection θt0(peak value) as a function of y for three different</p><p>　　values of z .</p><p>　　Fig. 10b Normal deflec

69、tion (peak value) as a function of y for three different n0 θ</p><p>　　values of z .</p><p>　　Fig. 11 Transverse deflection θ (peak value) as a function of y at z=0 and for</p><p>　

70、　three different values of sample diffusivity/conductivity.</p><p>　　Fig. 12 Transverse deflection θ (peak value) as a function of y at z=0 and for</p><p>　　three different values of modulation

71、frequency.</p><p><b>　　中文翻譯：</b></p><p>　　基于調(diào)制連續(xù)激光器的三維固體光熱偏轉(zhuǎn)的理論研究。</p><p>　　M. Soltanolkotabi and M. H. Naderi大學(xué)物理系、科學(xué)學(xué)院、伊斯法罕大學(xué)、伊斯法罕、伊朗</p><p><b>　　摘要

72、</b></p><p>　　本課題，提出了一個(gè)三層系統(tǒng)，該系統(tǒng)在調(diào)制激光器的激勵(lì)下研究了立體光熱偏轉(zhuǎn)的詳細(xì)理論方法。通過(guò)使用一種基于格林函數(shù)和積分轉(zhuǎn)換的方法，我們發(fā)現(xiàn)激光誘導(dǎo)溫度分布函數(shù)的顯式表達(dá)式和光熱光譜分析探測(cè)光束的偏轉(zhuǎn)。這些表達(dá)式的數(shù)值分析會(huì)產(chǎn)生重要的結(jié)果。</p><p><b>　　1 介紹</b></p><p>　

73、　1970年代光熱光譜分析技術(shù)從光聲光譜學(xué)的發(fā)展演變而來(lái)。在吸收光能量轉(zhuǎn)化為熱量方面，他們現(xiàn)在包含各種各樣的技術(shù)和現(xiàn)象。當(dāng)一個(gè)能源集中在樣品表面時(shí)，部分或全部的入射能量被樣品吸收并且隨著一系列非輻射的退激轉(zhuǎn)換在媒介中產(chǎn)生一個(gè)局部熱流。這樣的過(guò)程是光熱效應(yīng)和技術(shù)的基本原理。如果能量源是已調(diào)的，那么就會(huì)在樣品中形成一個(gè)周期熱流。材料產(chǎn)生的周期性熱流是一個(gè)擴(kuò)散過(guò)程，產(chǎn)生周期性的溫度分布稱(chēng)為熱波。</p><p>　　一

74、些機(jī)制會(huì)直接或間接的對(duì)熱波檢測(cè)有用。這些機(jī)制包括熱流從樣本到周?chē)臍怏w的光聲檢測(cè)；紅外輻射加熱樣品表面的光熱探測(cè)；在樣品表面上方進(jìn)行周期性激勵(lì)的光熱偏轉(zhuǎn)檢測(cè)；樣品表面熱彈性形變的激光檢測(cè)；樣品表面的熱彈性位移的干涉檢測(cè)。尤其是，熱波檢測(cè)的最后兩個(gè)方案被廣泛應(yīng)用，他們形成了光熱光譜檢測(cè)的基礎(chǔ)，主要原因是，他們提供了一個(gè)寶貴測(cè)量光學(xué)材料和熱參數(shù)的方法，如光學(xué)吸收系數(shù)和熱擴(kuò)散率。</p><p>　　光熱變形原理是簡(jiǎn)單

75、明了的。一束在樣品可吸收范圍內(nèi)波長(zhǎng)的激光照射在樣品上且被他吸收。樣品加熱 ，通過(guò)熱彈性耦合交互量的擴(kuò)大反過(guò)來(lái)使樣品表面的變形。產(chǎn)生的熱彈性變形的表面被一束弱激光(探測(cè)光束)檢測(cè)。</p><p>　　Ameri和他的同事們第一次使用激光干涉和激光偏轉(zhuǎn)光譜研究非晶硅。他們的方法限制在低到中等程度的調(diào)制頻率。Opsal等使用激光光束偏轉(zhuǎn)技術(shù)對(duì)薄膜厚度進(jìn)行熱波檢測(cè)。他們已經(jīng)獲得被稱(chēng)為一維溫度分布函數(shù)的溫度分布函數(shù)。在&

76、lt;/p><p>　　他們的分析中，假定探測(cè)光和泵浦光垂直于樣品表面。Miranda通過(guò)忽略溫度分函數(shù)的瞬時(shí)值和直流分量得到了樣品的溫度分布。另一方面，Li已經(jīng)給出了脈沖激光器在準(zhǔn)靜態(tài)近似下光熱位移的原理。張和合作者研究了更一般的情況下短激光脈沖激勵(lì)下的動(dòng)態(tài)熱彈性響應(yīng)。此外，陳和張已經(jīng)在考慮用光熱信號(hào)來(lái)分析半導(dǎo)體中光生載流子的擴(kuò)散。</p><p>　　在本文中，我們提出一個(gè)詳細(xì)的偏轉(zhuǎn)過(guò)程的

77、理論分析，他是基于立體的，有關(guān)透明流體，可吸收固體樣品和基地材料的三層系統(tǒng)。它假定系統(tǒng)被已調(diào)連續(xù)激光光束照射。光熱偏轉(zhuǎn)的理論方法可以分為兩部分。由于吸收泵浦的光束，我們會(huì)發(fā)現(xiàn)3 d激光系統(tǒng)的溫度分布在三個(gè)地區(qū)，。我們的數(shù)學(xué)方法是基于格林函數(shù)和積分變換。流體的溫度分布會(huì)被推導(dǎo)出來(lái)。探測(cè)光束通過(guò)流體來(lái)計(jì)算光熱偏轉(zhuǎn)。在第三部分典型的固體樣品會(huì)得出數(shù)值結(jié)果，并且第四部分會(huì)畫(huà)出結(jié)論。</p><p>　　2 連續(xù)的光熱偏

78、轉(zhuǎn)原理</p><p>　　讓我們考慮一下幾何結(jié)構(gòu)。固體樣品被認(rèn)為是堆積在襯墊且和液體接觸。L1，L2，L3分別是液體，固體，和襯底的厚度。液體可以是空氣或另一種介質(zhì)。假定固體樣品是唯一吸收介質(zhì);流體和襯底是透明的。為簡(jiǎn)單起見(jiàn)， 我們假定所有三個(gè)區(qū)域擴(kuò)展到無(wú)窮大徑向方向。連續(xù)的調(diào)制圓柱激光束垂直地照射在樣品的表面。首要任務(wù)是獲得由于加熱流體在樣品表面形成的溫度分布。</p><p>　　3

79、 數(shù)值結(jié)果和討論</p><p>　　在本節(jié)中，我們將描述三層系統(tǒng)內(nèi)的溫度分布和用光熱光譜分析探測(cè)光束的偏轉(zhuǎn)。溫度 Tf，光熱偏轉(zhuǎn)信號(hào)θt和θn不能被近似估算，所以必須使用數(shù)值方法。</p><p>　　圖5 a和5 b分別顯示在一個(gè)調(diào)制周期內(nèi)，頻率f = 10赫茲和f = 100赫茲的溫度分布 Tf (0，z，t)關(guān)于z的函數(shù)。這個(gè)表面溫度是在圖4的基礎(chǔ)上進(jìn)行調(diào)制的，且熱波在流體中傳遞

80、。熱波隨著衰減長(zhǎng)度σ強(qiáng)烈的衰減。</p><p>　　圖6顯示了在三個(gè)不同的調(diào)制頻率情況下，液體Tf0對(duì)于距離z的峰值溫度函數(shù)。</p><p>　　兩個(gè)影響應(yīng)該被注意。首先， 由于樣品的熱慣性，樣品表面的溫度隨著調(diào)制頻率增加而降低。換句話說(shuō)樣品不能對(duì)泵浦激光器調(diào)制頻率緩慢的增加進(jìn)行響應(yīng)。第二，有效熱長(zhǎng)度σ隨著頻率增加而減少，從而使光熱光譜分析信號(hào)比z衰減得更快。</p>&

81、lt;p>　　圖7顯示了樣品表面的峰值溫度在三種不同類(lèi)型的固體樣品中對(duì)r的值依賴(lài)。因?yàn)闊崃磕軌蜻M(jìn)一步擴(kuò)散，溫度會(huì)隨著熱擴(kuò)散系數(shù)d的增加而降低。此外，隨著數(shù)據(jù)的增加，溫度分布會(huì)更加廣泛。這里三個(gè)樣本的光學(xué)吸收系數(shù)α遠(yuǎn)遠(yuǎn)大于相應(yīng)的值σ。大部分的激光能量被樣品表面吸收符合本課題的研究情況?？磥?lái)在負(fù)z方向的熱擴(kuò)散支配者反方向的。我們還發(fā)現(xiàn)流體在表面上的溫度變化情況對(duì)熱擴(kuò)散率沒(méi)有顯著影響。，圖7b描繪了 在z=0，r的Tf0函數(shù)。這里的調(diào)制

82、頻率被認(rèn)為是100 Hz。另一些參量和圖7a相同。比較圖7a可以得出Tf0隨著f的增加而減少。事實(shí)上隨著調(diào)制頻率的增加，樣本和液體熱波的透射系數(shù)的邊界增加，因此Tf0減少。正如預(yù)期，隨著頻率的增加溫度分布更加窄。</p><p>　　圖8顯示了函數(shù)r的溫度曲線，函數(shù)的參數(shù)顯示在圖上。正如所預(yù)測(cè)的，溫度剖面隨著z的增加不斷擴(kuò)大。</p><p>　　現(xiàn)在我們進(jìn)行評(píng)估數(shù)值偏差信號(hào)。為此，和之前

83、一樣，我們使用64點(diǎn)的高斯求積法。如圖1和3，偏轉(zhuǎn)發(fā)生在立體空間；探測(cè)光束經(jīng)過(guò)X軸，遠(yuǎn)離樣品表面發(fā)生偏轉(zhuǎn)，偏離垂直的樣品表面到z方向，并且切向樣品表面到y(tǒng)方向。和之前一樣，我們假設(shè)流體和襯底分別是氮?dú)夂涂祵幉Ａ?。也假定，泵浦功率P = 1 w，?n /?T = 9.4×10?7 k?1(室溫)和η= 1。</p><p>　　對(duì)于這個(gè)系統(tǒng)，圖9a和9b分別給出了θt 和 θn作為y的函數(shù)，他們是在z=0

84、，10Hz的調(diào)制周期，對(duì)于不同時(shí)間而得出來(lái)的。在初始時(shí)間，θ = ωt ， Tf =0 ，</p><p><b>　　y=0 。 </b></p><p>　　標(biāo)準(zhǔn)信號(hào)在y=0處達(dá)到最大，但無(wú)正切信號(hào)，因?yàn)樘綔y(cè)光束被平分到另一方向。這個(gè)點(diǎn)的兩側(cè)，因?yàn)樾盘?hào)的變化，探測(cè)光束向相反的方向偏轉(zhuǎn)，或上或下。兩個(gè)圖的分布都是高斯光束的反射形成的。</p><

85、p>　　圖10a和10b顯示了，對(duì)于不同的z值，在f=10Hz的調(diào)制頻率內(nèi)，法相和正切信號(hào)的峰值畫(huà)在了y軸的反向。這些信號(hào)通常使用鎖相放大測(cè)量技術(shù)。隨著表面距離增加，偏轉(zhuǎn)信號(hào)強(qiáng)度減少和增加寬度，熱量會(huì)自更多的分散在液體里。事實(shí)上，光熱偏轉(zhuǎn)信號(hào)的梯度(折射率)具有使熱透鏡焦距反轉(zhuǎn)的特征，它是由高斯激光束加熱產(chǎn)生的。因此，我們知道熱透鏡在z方向的峰值焦距比在y方向上的小。</p><p>　　圖11顯示了在切線

86、方向改變樣品的熱擴(kuò)散系數(shù)的影響。峰值隨著樣品的熱擴(kuò)散系數(shù)的增加而減少。圖7 a和7 b顯示了流體的溫度的反應(yīng)。在建模中樣品的吸收率很大，輻射率主要發(fā)生在樣品表面。由于液體相對(duì)低的熱導(dǎo)率，熱量會(huì)優(yōu)先通過(guò)樣品。對(duì)于小樣品的熱擴(kuò)散率，信號(hào)會(huì)更大因?yàn)闊崃繒?huì)徘徊在樣品表面很長(zhǎng)時(shí)間，當(dāng)考慮到更多的熱量通過(guò)液體時(shí)。增加的熱量導(dǎo)致更大的溫度梯度和更大的偏轉(zhuǎn)信號(hào)。隨著樣品的熱擴(kuò)散率變大，熱量會(huì)很快傳遍整個(gè)樣品，而只有當(dāng)初樣品表面的熱量會(huì)傳到液體中。這導(dǎo)致

87、信號(hào)強(qiáng)度減少和信號(hào)寬度的輕微增加。法相偏轉(zhuǎn)信號(hào)的峰值函數(shù)顯示了對(duì)垂直偏轉(zhuǎn)信號(hào)的峰值函數(shù)的相似依賴(lài)。由于熱量中心距離的增加，法相偏轉(zhuǎn)的信號(hào)比垂直偏轉(zhuǎn)信號(hào)更大。此外它的梯度比切向偏轉(zhuǎn)信號(hào)更小。熱透鏡在z方向的焦距比在y方向的更小。</p><p>　　圖12顯示了在切向偏轉(zhuǎn)信號(hào)調(diào)制頻率的影響。正如預(yù)期，此信號(hào)及其寬度隨著頻率增加而減少。信號(hào)寬度隨著調(diào)制頻率增大而減少顯示出在y方向熱透鏡焦距的減少。不同的調(diào)制頻率時(shí)垂直

88、偏轉(zhuǎn)信號(hào)的峰值函數(shù)(沒(méi)有顯示)顯示出對(duì)類(lèi)似的頻率切向偏轉(zhuǎn)信號(hào)峰值的依賴(lài)。</p><p><b>　　4 結(jié)論</b></p><p>　　我們已經(jīng)提出了一個(gè)詳細(xì)的三維光熱偏轉(zhuǎn)的理論描述，由調(diào)制連續(xù)激光激發(fā)，三層系統(tǒng)由透明液體，光吸收固體和材料襯墊組成的。一些重要結(jié)果如下:(1)激光誘導(dǎo)的樣品表面溫度隨泵浦激光器的調(diào)制頻率增加而降低。(2)有效熱長(zhǎng)度隨調(diào)制頻率增加而

89、減少，從而使光熱光譜分析信號(hào)的衰減比z更快。(3)隨著調(diào)制頻率的增加溫度分布Tf0減少且越來(lái)越窄。(4)當(dāng)固體樣品表面的距離增加時(shí)偏轉(zhuǎn)信號(hào)強(qiáng)度降低但增加了它的寬度。(5) 由泵浦激光的加熱產(chǎn)生的熱透鏡的焦距 z方向的遠(yuǎn)遠(yuǎn)大于在y方向的。(6) 增加固體樣品的擴(kuò)散系數(shù)或電導(dǎo)率導(dǎo)致偏差信號(hào)強(qiáng)度的減少和信號(hào)寬度少量的增加。(7)垂直的偏轉(zhuǎn)大于切向偏轉(zhuǎn)，而其梯度比切向偏轉(zhuǎn)小得多。(8)偏轉(zhuǎn)信號(hào)及其寬度隨著調(diào)制頻率增加而減小。</p>

90、;<p><b>　　5 圖片說(shuō)明</b></p><p>　　圖 1用光熱光譜分析偏轉(zhuǎn)效應(yīng)的三層系統(tǒng)的幾何結(jié)構(gòu)。每個(gè)地區(qū)是在x - y平面是無(wú)限擴(kuò)展的。</p><p>　　圖 2光熱偏轉(zhuǎn)光譜的說(shuō)明。</p><p>　　圖3探測(cè)光束偏轉(zhuǎn)與樣品表面的切向。盒子是液體的區(qū)域，樣品表面平行于盒子的最近端面。</p>

91、<p>　　圖4a 在一個(gè)調(diào)制頻率為10Hz的周期內(nèi)五個(gè)不同時(shí)刻的表面溫度函數(shù) T (r，0，</p><p><b>　　t)。</b></p><p>　　圖 4b 在一個(gè)調(diào)制頻率為100Hz的周期內(nèi)五個(gè)不同時(shí)刻的表面溫度函數(shù) T (r，0，t)。</p><p>　　圖 5a 頻率為10Hz，r=0，關(guān)于z的溫度分布函數(shù)Tf。&

92、lt;/p><p>　　圖 5b 頻率為100Hz，r=0，關(guān)于z的溫度分布函數(shù)Tf。</p><p>　　圖 6 r=0，不同的調(diào)制頻率時(shí)溫度分布峰值的函數(shù)</p><p>　　圖 7a z=0，頻率為10Hz三個(gè)不同熱擴(kuò)散率樣品的溫度峰值函數(shù)。</p><p>　　圖 7b z=0，頻率為100Hz三個(gè)不同熱擴(kuò)散率樣品的溫度峰值函數(shù)。<

93、;/p><p>　　圖 8 頻率為10Hz，不同z的溫度峰值函數(shù)。</p><p>　　圖 9a 在一個(gè)調(diào)制周期內(nèi)，頻率為10Hz，三個(gè)不同時(shí)刻關(guān)于y的橫向偏轉(zhuǎn)函數(shù)。</p><p>　　圖 9b 在一個(gè)調(diào)制周期內(nèi)，頻率為10Hz，三個(gè)不同時(shí)刻關(guān)于y的直角偏轉(zhuǎn)函數(shù)。</p><p>　　圖10a 三個(gè)不同z時(shí)，關(guān)于y的橫向偏轉(zhuǎn)峰值函數(shù)。</