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            09法布里-珀罗(F-P)干涉


            工程光学实验

            F-P 干涉仪

            实验九 法布里-珀罗(F-P)干涉仪测钠双线的波长差
            [实验目的]
            1.了解法布里-珀里(F-P)干涉仪的结构,掌握调节与使用 F-P 干涉仪的方法; 2.用 F-P 干涉仪观察钠双线的实验现象。

            [仪器和装置]
            法布里-珀里(F-P)干涉仪,钠光灯,测量望远镜 法布里-珀里(F-P)干涉仪是由两块间距为 h,相互平行的平板玻璃 G1 和 G2 组成,如图 1 所示。为了获 得明亮细锐的干涉条纹,两板相对的内表上镀有高反射铝膜或多层介质膜,两反射面的平面度要达到 1/20 ~ 1/100 波长,同时,两板还应保持平行。为了避免 G1、G2 外表面反射光的干扰,通常将两板做成有一小 楔角。将 G2 固定,G1 可连续地在精密导轨上移动,以调节两板间距 h。

            图 1 F-P 干涉仪光路原理图 F-P 干涉仪属于分振幅多光束等倾干涉装置。可用有一定光谱宽度的扩展光源照明,在透镜 L 的焦平 面上将形成一系列很窄的等倾亮条纹。与迈克耳逊干涉仪产生的双光束等倾干涉条纹比较,F-P 干涉仪的 等倾圆纹要细锐得多,如图 2 所示。

            图 2 两种干涉仪产生的干涉图 a) F-P 干涉仪产生的多光束干涉图 b) 迈氏干涉仪产生的双光束干涉图 一般情况下,测量迈氏仪产生的圆条纹时读数精度为 1/10 条纹间距左右;对 F-P 干涉仪产生的圆条 纹,其读数精度可高达条纹间距的 1/100 ~ 1/1000。因此,F-P 干涉仪常用于高精度计量技术与光谱精细结 构分析。

            [实验原理]
            如果投射到 F-P 干涉仪上的光波中含有两个光谱成分 λ1、2, λ 其平均波长为 ? , 则在 L 的焦平面上,可以得到分别用实线(λ2)和虚线(λ1)表示的两组同心圆条 纹(λ2>λ1) ,如图 3 所示。两波长同级条纹的角半径稍有差别。 对于靠近条纹中心的某点(θ ? 0) ,两波长干涉条纹的级次差 ? 2h ? ? ? 2h ? ? 2h?? 2 ? ?1 ? (9-1) ?m ? m1 ? m2 ? ? ? ? ? ? ? ?? ?? ? ? ? ?1? 2 ? 1 ? ? ? ?2 ? ? 图 3 波长 λ1 和 λ2 另外,由图 3 可知 的两组等倾圆纹
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            工程光学实验

            F-P 干涉仪

            ?m ?

            ?e e

            (9-2)

            式中,Δe 是两波长同级条纹的相对位移量,e 是同一波长的条纹间距。 比较上两式,当 λ1 ? λ2 时,可得到

            ?e?2 (9-3) 2he 式中,平均光波长 λ 由分辨本领较低的分光仪预先测定。因此,只要测出 e、Δe 和 h 就可按式(9-3)计 算出波长差 Δλ。 应该注意的是,利用上述方法测量 Δλ 时,不允许使两组条纹的相对位移 Δe 大于条纹间距 e,即不允 许发生干涉级次的交错现象。 ?? ? ? 2 ? ? 1 ?

            [内容和步骤]
            1. 调试仪器 (1) 转动手轮 1 将 G1 与 G2 间的间距调至 2mm 左右,再分别调节 G1、G2 背面的螺钉 3 使之松紧程度大致 相同。 (2) 点亮钠灯,调节光窗位置,使之处于 G1 板的正前方。 (3) 在钠灯光窗的毛玻璃上画一个十字线,则在 G2 的透射光中可看到十字线的多个象,分别调节螺钉 3 和 微调旋钮 4,使各个十字线象完全重合。此时,视场中应有条纹出现,将圆纹中心调至视场中央。左右移 动眼睛,仅圆条纹中心随眼睛移动,而环径大小不变,这表示 G1 和 G2 内表面平行。换用望远镜观察,略 微调节旋钮 4,便可得到图 2 所示的圆纹。 2.观察现象 旋转微调手轮 2,缓慢减小 G1 和 G2 的间距。注意用力均匀轻缓,不能使两者相碰。然后反方向旋转 微调手轮 2,增大 h。必须沿一个方向旋转手轮,不得中途逆转,以避免回程误差。这时视场中条纹数逐 渐增加,并且开始分离出双线。注意观察实验现象继续增大 h,当 Δe=e 时,λ1 的第 m 级条纹与 λ2 的第 m -1 级条纹重合,称此为重级现象。若再继续增大 h,将出现 Δe>e,发生级次交错。在测试中是不允许出 现级次交错。

            [思考题]
            1. 分振幅双光束干涉条纹与多光束干涉条纹的强度分布有什么不同?原因是什么? 2. 开始调节 F-P 干涉仪时,圆纹中心往往偏在一边甚至不在视场内;或者圆纹中心虽在视场中央,但移动 眼睛时,圆纹中心不仅移动,环径也随之改变,这些现象如何解释?如何纠正?

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            工程光学实验

            F-P 干涉仪

            Experiment 9

            Use of Fabry-Perot interferometer to measure wavelength difference between sodium doublet lines

            [Experimental Objectives]
            1. To understand the configuration of Fabry-Perot interferometer and master the operating technique of F-P interferometer 2. To observe sodium doublet lines interferogram by F-P interferometer.

            [Apparatus and Setup]
            Fabry-Perot interferometer, sodium lamp, and measuring telescope As shown in Fig. 1, Fabry-Perot interferometer consists of two glass plates, which are parallel to each other with the separation of h. In order to obtain bright and sharp fringes, high-reflection aluminum film or multilayer dielectric film is coated onto the internal surfaces of the plates. The flatness of two reflection surfaces is of 1/20 ~ 1/100 wavelength. In addition, the two plates must be kept strictly parallel. Usually, the plates are wedge-shape to prevent the disturbance of reflection lights from external surfaces. G 2 is fixed, and G1 can be moved continuously along a precision track to adjust the separation h.

            Reflection film

            Fig. 1 Principle of Fabry-Perot interferometer F-P interferometer is an amplitude-splitting multiple-beam equal-inclination interferometer. When a light source with certain spectrum width is used, a series of very narrow equal-inclination bright fringes will be produced on the focal plane of the lens L in F-P interferometer. As shown in Fig. 2, these fringes are much narrower than those produced by double-beam equal-inclination interference of a Michelson interferometer. In most of cases, the reading accuracy for Michelson interferometer is about 1/10 fringe separation, whilst that for F-P interferometer can reach 1/100 ~ 1/1000 fringe separation. Therefore, F-P interferometer is usually used for high-accuracy measurement and fine-spectrum analysis.

            Fig. 3-2 Interferograms produced by two interferometers
            a) Interferogram produced in F-P interferometer b) Interferogram produced in Michelson interferometer

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            工程光学实验

            F-P 干涉仪

            [Experimental Principle] For the light projected to F-P interferometer, there are two wavelengths of λ1 and λ2, whose average value is ? . On the focal plane of L, two concentric circular fringes (λ2>λ1) appear, denoted with solid line (λ2) and broken line (λ1) in Fig. 3. Please note that there are slightly differences in angular radius for the same order fringes produced by two wavelengths.

            Fig. 3 Two equal-inclination circular fringes for wavelength λ1 and λ2 For a certain point close to the center (θ ? 0), the order difference of two fringes is ? 2h ? ? ? 2h ? ? 2h?? 2 ? ?1 ? . (9-1) ?m ? m1 ? m2 ? ? ? ? ? ? ? ?? ?? ? ? ? ?1? 2 ? 1 ? ? ? ?2 ? ? In addition, from Fig. 3, we have ?e ?m ? e (9-2) where, Δe is the relative displacement for the same order fringes, and e is the fringe separation for certain wavelength. Comparing the above two equations, when λ1 ? λ2, we have ?e?2 ?? ? ? 2 ? ? 1 ? (9-3) 2he where, the average wavelength ? is pre-determined by a spectrometer with relatively low resolution. Therefore, once e, Δe and h are determined, the wavelength difference Δ? can be calculated using Eq. (9-3). Please note that, when using this method to determine Δ?, it is not allowed that the relative displacement Δe is larger than the fringe separation e, i.e., order overlapping not allowed.

            [Experimental Procedure]
            1. Adjust the system (1) Turn Hand-wheel 1 until the separation between G1 and G2 is about 2mm. And then adjust Screws 3 behind G1 and G2 to the same tightness. (2) Turn on the sodium lamp and adjust the position of the light window to make it right ahead G1. (3) Draw a cross line on the sodium lamp’s window and several cross-line images may appear. Adjust Screws 3 and Knob 4 consequently to make the images entirely superimposed. At this moment, fringes can be seen in the field of view. Move the fringe center to the center of the field. If move the eyes right and left, only the fringe center shifts with eye movement, and the size of circular fringes keeps unchanged, which indicates the internal planes of G1 and G2 are parallel. Circular fringes, as shown in Fig. 2, can be observed through the measuring telescope. Adjust Knob 4 slightly, if necessary.
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            工程光学实验

            F-P 干涉仪

            2. Observe the phenomenon Turn Hand-wheel 2 to reduce the separation between G1 and G2. Then turn Hand-wheel 2 to increase h continuously (to avoid hysterisis error), more fringes are produced and doublet lines are present. If continue to increase h until Δe=e, the mth fringe of λ1 will be superimposed with the (m-1)th fringe of λ2, which is called superimposing phenomenon. Increasing h further, Δe>e, resulting in interference order overlapping, which is not allowed during the test.

            [Questions]
            1. What is the difference in intensity contribution between amplitude-splitting multi-beam fringes and double-beam fringes? Why? 2. When adjusting F-P interferometer, the fringe center is slanting or even out of the field of view; or the fringe center is in the field center, but the fringe center moves and the cyclic fringe size also changes when moving the eyes. How to explain this phenomenon? And how to correct it?

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