【導(dǎo)讀】厚度和折射率在一個比較廣的范圍內(nèi)。特別是，在二邊緣位置的未測量的基礎(chǔ)上。我們將展示如何計算兩個表面分離距離（膜厚度）。我們討論了測量精度，盡管。在表面力裝置試驗(yàn)中，通常使用3或5層的干擾儀。適用于任何數(shù)量的層次，但是在這里我們使用3層干涉儀。當(dāng)透明的基質(zhì)層（通。常是云目表）接觸時，pth-order的邊緣位置0p?通常在可見光的波長范圍內(nèi)。板表面后，相隔的距離為d的位置形成三層干涉。邊緣轉(zhuǎn)移到更長的波長，他們。γ或μβ）和μmed分別是云母和中間介質(zhì)的折射率，在式中。的方程使其成為最常用的方法。除了實(shí)施不變以外，這也限制了可衡量的分離范圍，因?yàn)槟壳暗姆?。生微米尺度的誤差。順序條紋的距離。射率μ未知，這時需要計算出兩個帶有兩個位置量的方程，D和μmed。的基板制成的，遵守下列關(guān)系，觸邊緣位置和任何其他聯(lián)系邊緣位置有關(guān)聯(lián)。是不可見的，一種能夠計算出（p-m）（在完成mth邊緣的。的折射率非常的依賴薄弱。不考慮色散，例如，結(jié)果為：

　　

【正文】 ow the relation for the refractive index of the fringe (β or γ) that is being measured as a function of ―brownish mica,‖ this is [17] 5 ?? ?? ? ? (12) where λ is the wavelength in 197。. We ?rst calculate the refractive indices at the three contact wavelengths, and obtain Now, using Eq. (5), we obtain 0021 .5 9 2 9 5 6 0 4 .1 8 5 9 2 7 .2 41 .5 9 3 7 5 6 0 4 .1 81 .5 9 4 6 1 2 ( 1 )1 .5 9 4 6 5 7 6 1 .0 7p A? ? ?????????? (13) which is in excellent agreement with the measured value of 177。 197。, indeed, within the experimental error. Actually, one could use the measured value of 02P?? to determine one of the constants in Eq. (12) or, if we also measured 01p?? and 03p?? ,to get both constants. Note that it is not necessary to know the value of p, nor does it matter if p is odd or even—the equations are identical. Only for the separation measurements of the threelayer interferometer is it important to know whether p is odd or even (it happened to be odd for this speci?c example).We also note that this method can be used to calculate the contact wavelength of any fringe order, not just 02P?? . . Example 2 Calculating distances D from 0p? and 01p?? , and the measured positions Dm? and 1Dm?? of any two adjacent fringes of unknown order m and m? 1. A measured contact position of a fringe of unknown order p is at 0 ? ? and that of order p ? 1 is at 00 1 A? ? ? The substrate is brownish mica, whose refractive index is given by Eq. (12). The surfaces are well separated and we want to calculate the distance D between the two surfaces. We know that the medium between the two mica substrates has a refractive index of [14], and we perform simultaneous measurements of 0p? , 01p?? , Dm? , 1Dm?? in this example). For a quick estimate of D, one can use Eq. (6) to calculate the contact positions of various fringes p + 1,p + 2,... (see Example 1) and Eq. (1a) to calculate the distances of our threelayer interferometer until p + (p ? m) is found. A more accurate approach is to use Eqs. (5) and (6) for the calculation of the positions p + 1,p + 2,..., as described in Example 1, and Eq. (9) for the distances. In this example we show a case where Eq. (5) is used with Eq. (1a) [14]. Obviously m p。 hence our ?rst guess is m = p. Using this guess, we put the values for 0p? , 01p?? and Dm? (which we guess to be DP? ) in the odd version of Eq. (1a) and obtain D = 1363 197。. We then perform the same calculation using 1Dm?? (which weguess to be 1DP?? ) and the values for 01p?? and 02P?? usingthe even version of Eq. (1a), and obtain D = 1310 197。. Since , our guess was wrong. Our second guesswould be m = p + 1 (where m is now even), and we use the even version of Eq. (1a) with the calculated value of 01p?? , measured 0p? and n Dm? (which we guess to be 1DP?? ).We obtain D = 3288 197。. The odd version of Eq. (1a) with 0p? , 01p?? , and 1Dm?? (which we guess to be DP? ), now resultsin D = 3280 197。. Since , we conclude thatm = p + 1. The difference of 8 197。 is in part because therefractive index of the medium was assumed to be nondispersive, and in part because the mica–silver phase change was also assumed to be nondispersive. We should also note that for m = p + 2, we obtain D = 5217 197。 using the odd version of Eq. (1a) with 02p?? , 01p?? , and Dm? (guessed to be 2DP?? ), and D = 5248 197。 using the even version of Eq. (1a) with 01p?? , 0p? , and 1Dm?? (guessed to be 1DP?? ), and we get 0 0 0 02 1 1 1( , , ) ( , , )DDm D D m D pDD? ? ? ? ? ?? ? ? ??. Indeed, for all guesses above p + 1 the second estimate is higher than the first, while for all guesses below p + 1 the reverse is true, and this observation is general. In other words, the separation calculated using a higher order contact fringe couple is bigger than that using a lower order contact fringe couple for (m?p) guesses which are smaller than the real (m?p), whereas the separation calculated using a higher order contact fringe couple is smaller than that using a lower order contact fringe couple for (m ? p) guesses which are bigger than the real (m?p). Formulating this would look like this 0 0 0 01 1 1 2( , , ) ( , , )DDm p i p i m p i p iDD? ? ? ? ? ?? ? ? ? ? ? ? ??for ()i m p?? 0 0 0 01 1 1 2( , , ) ( , , )DDm p i p i m p i p iDD? ? ? ? ? ?? ? ? ? ? ? ? ??for ()i m p?? 0 0 0 01 1 1 2( , , ) ( , , )m p i p i m p i p i? ? ? ? ? ?? ? ? ? ? ? ? ??for ()i m p?? The above example uses only m = p + 1 (i = 1) and would work for most cases only for very small values of (m?p). Thus, in general it is advised to count the number of passing fringes in order to determine (m?p). Theoretically, it should be possible to include the dispersive refractive index of the medium and the dispersive phase change at the reflector–substrate interface. However, as we discuss below, incorporating a dispersive phase change, while theoretically desirable, is difficult in practice. Since the above did not include the dispersive phase change, the similarity obtained for the two calculations of D does not suggest that this is the ―error‖ in the separation, which could be larger. As we shall see, incorporation of the phase change gives a formally accurate solution。 however, there are good reasons to use only the substrate dispersive refractive index and neglect the dispersive phase chang 指導(dǎo)教師評語： 簽名： 年 月 日