TWI407097B - Structural analysis system and method - Google Patents
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本發明是有關於一種結構分析系統及方法，特別是指一種利用寬帶(broadband)電磁波來分析一待測物之結構的結構分析系統及方法。The present invention relates to a structural analysis system and method, and more particularly to a structural analysis system and method for analyzing the structure of an object to be tested by using broadband electromagnetic waves.
參閱圖1與圖2，在習知的X射線結晶學(X-ray crystallography)中，是利用單頻(monochromatic)X射線來分析一晶體(lattice)的結構，即原子的排列方式。首先，一X射線源11發射一具有單一頻率成分(即單頻)的入射X射線到待測物2。入射X射線會通過待測物2並傳送到一觀察平面3，且在通過待測物2時會產生繞射(diffraction)。接著，一強度偵測器12在觀察平面3上移動，且在觀察平面3上的多個位置偵測X射線之強度(intensity)，以產生一反應入射X射線在觀察平面3上之遠場繞射圖(far-field diffraction pattern)的強度資料。最後，一處理模組13根據強度資料計算與待測物2的結構相關的資訊。值得注意的是，強度偵測器12可以被替換為一設置在觀察平面3上的底片(圖未示)，以記錄X射線之強度，強度資料可以根據底片而被產生。Referring to Figures 1 and 2, in conventional X-ray crystallography, monochromatic X-rays are used to analyze the structure of a crystal, i.e., the arrangement of atoms. First, an X-ray source 11 emits an incident X-ray having a single frequency component (i.e., a single frequency) to the object 2 to be tested. The incident X-rays pass through the object to be tested 2 and are transmitted to an observation plane 3, and a diffraction is generated when passing through the object 2 to be tested. Next, an intensity detector 12 moves on the observation plane 3, and the intensity of the X-rays is detected at a plurality of positions on the observation plane 3 to generate a far field of the incident incident X-rays on the observation plane 3. The intensity data of the far-field diffraction pattern. Finally, a processing module 13 calculates information related to the structure of the object 2 based on the intensity data. It should be noted that the intensity detector 12 can be replaced with a negative film (not shown) disposed on the viewing plane 3 to record the intensity of the X-rays, and the intensity data can be generated according to the negative film.
在二維的情況下，假設待測物2的結構函數是g (x' ,y' )，且其經傅利葉轉換的結果是F (g (x' ,y' ))，則從傅利葉光學可知，單頻的入射X射線在觀察平面3上的遠場繞射圖與|F (g (x' ,y' ))|2 相關，其中，x' 是待測物2在一第一軸X上的座標變數，y' 是待測物2在一第二軸Y上的座標變數。In the case of two-dimensional, assuming that the structure function of the object 2 is g ( x ' , y ' ), and the result of the Fourier transform is F ( g ( x ' , y ' )), it is known from Fourier optics. The far-field diffraction pattern of the single-frequency incident X-ray on the observation plane 3 is related to | F ( g ( x ' , y' ))| 2 , where x ' is the object to be tested 2 on a first axis X The coordinate variable on the upper side, y' is the coordinate variable of the object 2 to be tested on a second axis Y.
由於|F (g (x' ,y' ))|2 經反傅利葉轉換的結果等於待測物2的結構函數g (x' ,y' )及其反對稱函數的迴旋積，如式(1)所示：Since | F ( g ( x ' , y' ))| 2 is inversely Fourier transformed, the result is equal to the structural function g ( x ' , y ' ) of the object 2 and its convolution product of the antisymmetric function, as in equation (1) ) shown:
F -1 |F (g (x' ,y' ))2 =g (x' ,y' )*g (-x' ,-y' ) 式(1) F -1 | F ( g ( x' , y' )) 2 = g ( x' , y' )* g (- x' , - y' ) (1)
其中，F -1 表示反傅利葉轉換，g(-x' ,-y' )是g (x' ,y' )的反對稱函數，*表示迴旋運算(convolution operation)，g (x' ,y' )*g (-x' ,-y' )被稱為哈克圖(Harker pattern)，因此，處理模組13只要對與|F (g (x' ,y' ))|2 相關的強度資料進行反傅利葉轉換，就可以計算出待測物2的結構函數及其反對稱函數的迴旋積g (x' ,y' )*g (-x' ,-y' )(即哈克圖)，然後利用從分子的物理化學導出的額外資訊，就可以從哈克圖計算出待測物2的結構函數g (x' ,y' )。Where F -1 denotes the inverse Fourier transform, g(- x' , - y' ) is the antisymmetric function of g ( x ' , y ' ), * denotes the convolution operation, g ( x ' , y ' * g (- x' , - y ' ) is called a Harker pattern, so the processing module 13 only needs to correlate the intensity data associated with | F ( g ( x ' , y' )) | 2 By performing the inverse Fourier transform, we can calculate the convolution product g ( x ' , y ' ) * g (- x' , - y ' ) of the structure function of the object 2 and its antisymmetric function (ie, the Huck diagram). The structural function g ( x ' , y ' ) of the analyte 2 can then be calculated from the Huck graph using additional information derived from the physical chemistry of the molecule.
上述這種習知的X射線結晶學的缺點是：在使用強度偵測器12的情況下，需要在觀察平面3上的多個位置偵測X射線之強度，因此偵測時間較長；而在使用底片的情況下，則無法節省底片的成本及顯影時間(development time)。A disadvantage of the above-described conventional X-ray crystallography is that in the case of using the intensity detector 12, it is necessary to detect the intensity of the X-rays at a plurality of positions on the observation plane 3, so that the detection time is longer; In the case of using a film, the cost of the film and the development time cannot be saved.
因此，本發明之目的即在提供一種結構分析系統，可以縮短偵測時間，並節省底片的成本及顯影時間。Accordingly, it is an object of the present invention to provide a structural analysis system that can reduce detection time and save film cost and development time.
於是，本發明結構分析系統適用於分析一待測物的結構，且包含一電磁波源、一頻譜偵測器及一處理模組。該電磁波源用於發射一具有多數頻率成分的電磁波到該待測物。該頻譜偵測器用於在空間中一位置偵測從該電磁波源發出、通過該待測物且傳送到該位置的電磁波之頻譜，以產生一頻譜資料。該處理模組用於根據該頻譜資料計算與該待測物的結構相關的資訊。Therefore, the structural analysis system of the present invention is suitable for analyzing the structure of an object to be tested, and includes an electromagnetic wave source, a spectrum detector and a processing module. The electromagnetic wave source is used to emit an electromagnetic wave having a plurality of frequency components to the object to be tested. The spectrum detector is configured to detect a spectrum of electromagnetic waves emitted from the electromagnetic wave source, passing through the object to be tested, and transmitted to the position in a position in the space to generate a spectrum data. The processing module is configured to calculate information related to the structure of the object to be tested according to the spectrum data.
其中，該處理模組根據該頻譜資料計算該待測物的結構函數經傅利葉轉換的結果之平方，及對該待測物的結構函數經傅利葉轉換的結果之平方進行反傅利葉轉換，以計算該待測物的結構函數及其反對稱函數的迴旋積。The processing module calculates a square of the result of the Fourier transform of the structure function of the object to be tested according to the spectrum data, and performs inverse Fourier transform on the square of the result of the Fourier transform of the structure function of the object to be tested to calculate the square The structural function of the object to be tested and its convolution product of the antisymmetric function.
而本發明之另一目的即在提供一種結構分析方法，可以縮短偵測時間，並節省底片的成本及顯影時間。Another object of the present invention is to provide a structural analysis method which can reduce the detection time and save the cost and development time of the film.
於是，本發明結構分析方法適用於以包括一電磁波源、一頻譜偵測器及一處理模組的一結構分析系統來實現，以分析一待測物的結構。該結構分析方法包含：(a)利用該電磁波源發射一具有多數頻率成分的電磁波到該待測物；(b)利用該頻譜偵測器在空間中一位置偵測從該電磁波源發出、通過該待測物且傳送到該位置的電磁波之頻譜，以產生一頻譜資料；及(c)利用該處理模組根據該頻譜資料計算與該待測物的結構相關的資訊，包括以下子步驟(c-1)利用該處理模組根據該頻譜資料計算該待測物的結構函數經傅利葉轉換的結果之平方，及(c-2)利用該處理模組對該待測物的結構函數經傅利葉轉換的結果之平方進行反傅利葉轉換，以計算該待測物的結構函數及其反對稱函數的迴旋積。Therefore, the structural analysis method of the present invention is applicable to a structural analysis system including an electromagnetic wave source, a spectrum detector and a processing module to analyze the structure of an object to be tested. The structural analysis method comprises: (a) using the electromagnetic wave source to emit an electromagnetic wave having a plurality of frequency components to the object to be tested; and (b) using the spectrum detector to detect and emit a position from the electromagnetic wave source in space; And measuring (c) using the processing module to calculate information related to the structure of the object to be tested, including the following substeps ( C-1) using the processing module to calculate a square of the result of the Fourier transform of the structure function of the object to be tested according to the spectrum data, and (c-2) using the processing module to perform a structure function on the object to be tested by Fourier The square of the result of the conversion is subjected to inverse Fourier transform to calculate the gyro product of the structure function of the object to be tested and its antisymmetric function.
有關本發明之前述及其他技術內容、特點與功效，在以下配合參考圖式之一個較佳實施例的詳細說明中，將可清楚地呈現。The foregoing and other technical aspects, features and advantages of the present invention will be apparent from the following description of the preferred embodiments.
參閱圖3與圖4，本發明結構分析系統4之較佳實施例適用於分析一待測物5的結構，且包含一電磁波源41、一頻譜偵測器42及一處理模組43。電磁波源41發射一具有多數頻率成分(即多頻(polychromatic)或寬帶)的入射電磁波(例如：光)到待測物5。入射電磁波會通過待測物5並傳送到一觀察平面6，且在通過待測物5時會產生繞射。頻譜偵測器42在觀察平面6上的一位置p 偵測電磁波之頻譜(spectrum)，以產生一頻譜資料。處理模組43根據頻譜資料計算與待測物5的結構相關的資訊。Referring to FIG. 3 and FIG. 4, the preferred embodiment of the structural analysis system 4 of the present invention is suitable for analyzing the structure of an object to be tested 5, and includes an electromagnetic wave source 41, a spectrum detector 42 and a processing module 43. The electromagnetic wave source 41 emits an incident electromagnetic wave (for example, light) having a plurality of frequency components (i.e., polychromatic or broadband) to the object to be tested 5. The incident electromagnetic wave passes through the object to be tested 5 and is transmitted to an observation plane 6, and a diffraction is generated when passing through the object to be tested 5. The spectrum detector 42 detects the spectrum of the electromagnetic waves at a position p on the observation plane 6 to generate a spectrum of data. The processing module 43 calculates information related to the structure of the object to be tested 5 based on the spectrum data.
值得注意的是，本實施例可以分析週期性的結構(例如：晶體中原子的排列方式)及非週期性的結構，也可以分析各種尺度的的結構。另外，本實施例可以分析一維、二維及三維的結構，以下則是以二維為例進行說明。It is worth noting that this embodiment can analyze periodic structures (for example, the arrangement of atoms in a crystal) and non-periodic structures, and can also analyze structures of various scales. In addition, the present embodiment can analyze one-dimensional, two-dimensional, and three-dimensional structures, and the following is an example of two-dimensional.
假設待測物5的結構函數是g
(x'
,y'
)，且其經傅利葉轉換的結果是F
(g
(x'
,y'
))，則在位置p
偵測到的頻譜S
(p
,ω
)如式(2)所示：
其中，x' 是待測物5在一第一軸X上的座標變數，y' 是待測物5在一第二軸Y上的座標變數，ω 是角頻率，S' (ω )是入射電磁波的頻譜。Where x' is the coordinate variable of the object 5 on a first axis X, y' is the coordinate variable of the object 5 on a second axis Y, ω is the angular frequency, and S' ( ω ) is the incident The spectrum of electromagnetic waves.
在式(2)中，由於ω 及S' (ω )是已知的，加上S (p ,ω )可以被 偵測到，所以|F (g (x' ,y' ))|2 可以被計算出。In equation (2), since ω and S' ( ω ) are known, plus S ( p , ω ) can be detected, | F ( g ( x ' , y ' )) | 2 can It is calculated.
由於|F (g (x' ,y' ))|2 經反傅利葉轉換的結果等於待測物5的結構函數及其反對稱函數的迴旋積g (x' ,y' )*g (-x' ,-y' )，如式(1)所示，因此，處理模組43只要根據頻譜資料計算出|F (g (x' ,y' ))|2 ，並對|F (g (x' ,y' ))|2 進行反傅利葉轉換，就可以計算出待測物5的結構函數及其反對稱函數的迴旋積g (x' ,y' )*g (-x' ,-y' )(即哈克圖)，然後，利用額外的資訊(例如：從分子的物理化學導出的資訊，或結構的對稱性)，就可以從哈克圖計算出待測物5的結構函數g (x' ,y' )。Since | F ( g ( x ' , y' ))| 2 is inversed by the Fourier transform, the result of the inverse of the structure function of the object 5 and its antisymmetric function g ( x ' , y ' ) * g (- x ' , - y ' ), as shown in equation (1), therefore, the processing module 43 only needs to calculate | F ( g ( x ' , y' ))| 2 according to the spectral data, and | F ( g ( x ) ' , y' ))| 2 Performing the inverse Fourier transform, we can calculate the structure of the object 5 and its convolution product g ( x ' , y ' ) * g (- x ' , - y ' ) (ie, Huck diagram), and then, using additional information (eg, information derived from the physical chemistry of the molecule, or structural symmetry), the structural function g of the analyte 5 can be calculated from the Huck graph ( x' , y' ).
在本實施例中，處理模組43能以軟體或硬體來實現。當處理模組43以軟體實現時，其可以被載入一處理器，以使處理器執行所述動作。In this embodiment, the processing module 43 can be implemented in software or hardware. When the processing module 43 is implemented in software, it can be loaded into a processor to cause the processor to perform the actions.
值得注意的是，雖然已有多篇論文揭露了式(2)，例如：2002年Optics Letters第27卷第14期”Spectral anomalies in a Fraunhofer diffraction pattern”論文，但是在這些論文中，都是先根據待測物5的結構推導出F (g (x' ,y' ))，再配合已知的ω 及S' (ω )，來得知S (p ,ω )，且僅是學術上的研究，而無產業上的應用。本申請案的發明人則首先將式(2)應用在本實施例的結構分析系統4中，先偵測出S (p ,ω )，再配合已知的ω 及S' (ω )，以求出|F (g (x' ,y' ))|2 ，接著據此求出與待測物5的結構相關的資訊，如此一來，本實施例只需要在觀察平面6上的一個位置偵測電磁波之頻譜，而不用像習知的X射線結晶學一樣需要在觀察平面3上的多個位置偵測X射線之強度或在觀察平面3上設置底片，因此，本實施例可 以縮短偵測時間，並節省底片的成本及顯影時間，故確實能達成本發明之目的。It is worth noting that although many papers have revealed the formula (2), for example: 2002 Optics Letters, Vol. 27, No. 14, "Spectral anomalies in a Fraunhofer diffraction pattern" paper, but in these papers, According to the structure of the object to be tested 5, F ( g ( x ' , y ' )) is derived, and the known ω and S′ ( ω ) are used to know S ( p , ω ), and only academic research Without industrial applications. The inventor of the present application first applies the formula (2) to the structural analysis system 4 of the present embodiment, first detecting S ( p , ω ), and then combining the known ω and S' ( ω ) to Finding | F ( g ( x ' , y' ))| 2 , and then obtaining information related to the structure of the object 5 to be tested, so that this embodiment only needs a position on the observation plane 6 The spectrum of the electromagnetic waves is detected without the need to detect the intensity of the X-rays at a plurality of positions on the observation plane 3 or to set the film on the observation plane 3 as in the conventional X-ray crystallography. Therefore, the present embodiment can shorten the detection. The time is measured, and the cost of the film and the development time are saved, so that the object of the present invention can be achieved.
參閱圖3、圖4與圖5，本實施例所使用的結構分析方法包含以下步驟：Referring to FIG. 3, FIG. 4 and FIG. 5, the structural analysis method used in this embodiment includes the following steps:
步驟71是電磁波源41發射寬帶的入射電磁波到待測物5。Step 71 is that the electromagnetic wave source 41 emits a wide-band incident electromagnetic wave to the object 5 to be tested.
步驟72是頻譜偵測器42在空間中一位置(即觀察平面6上的位置p )偵測電磁波之頻譜，以產生頻譜資料。Step 72 is to detect the spectrum of the electromagnetic wave by a spectrum detector 42 at a position in space (i.e., position p on the observation plane 6) to generate spectral data.
步驟73是處理模組43根據頻譜資料計算與待測物5的結構相關的資訊，且包括以下子步驟：子步驟731是處理模組43根據頻譜資料計算待測物5的結構函數經傅利葉轉換的結果之平方|F (g (x' ,y' ))|2 。Step 73 is that the processing module 43 calculates information related to the structure of the object to be tested 5 according to the spectrum data, and includes the following sub-steps: sub-step 731 is that the processing module 43 calculates the structure function of the object to be tested 5 according to the spectrum data by Fourier transform. The square of the result | F ( g ( x' , y' ))| 2 .
子步驟732是處理模組43對待測物5的結構函數經傳利葉轉換的結果之平方|F (g (x' ,y' ))|2 進行反傅利葉轉換，以計算待測物5的結構函數及其反對稱函數的迴旋積g (x' ,y' )*g (-x' ,-y' )。Sub-step 732 is a square of the result of the transfer function of the structure function of the object 5 to be processed by the processing module 43 | F ( g ( x ' , y' ))| 2 to perform inverse Fourier transform to calculate the structure of the object 5 to be tested The convolution product g ( x' , y' )* g (- x' , - y' ) of the function and its antisymmetric function.
子步驟733是處理模組43根據待測物5的結構函數及其反對稱函數的迴旋積g (x' ,y' )*g (-x' ,-y' )，計算出待測物5的結構函數g (x' ,y' )。Sub-step 733 is that the processing module 43 calculates the object to be tested 5 according to the structure of the object 5 and the gyro product g ( x ' , y ' ) * g (- x ' , - y ' ) of the anti-symmetric function. The structure function g ( x' , y' ).
惟以上所述者，僅為本發明之較佳實施例而已，當不能以此限定本發明實施之範圍，即大凡依本發明申請專利範圍及發明說明內容所作之簡單的等效變化與修飾，皆仍屬本發明專利涵蓋之範圍內。The above is only the preferred embodiment of the present invention, and the scope of the invention is not limited thereto, that is, the simple equivalent changes and modifications made by the scope of the invention and the description of the invention are All remain within the scope of the invention patent.
4‧‧‧結構分析系統4‧‧‧Structural Analysis System
41‧‧‧電磁波源41‧‧‧Electromagnetic source
42‧‧‧頻譜偵測器42‧‧‧ spectrum detector
43‧‧‧處理模組43‧‧‧Processing module
5‧‧‧待測物5‧‧‧Test object
6‧‧‧觀察平面6‧‧‧ observation plane
71~73‧‧‧步驟71~73‧‧‧Steps
731~733‧‧‧子步驟731~733‧‧‧substeps
圖1是一方塊圖，說明習知的X射線結晶學在分析一晶體的結構時所需的元件；圖2是一示意圖，說明習知的X射線結晶學在分析晶體的結構時的位置關係；圖3是一方塊圖，說明本發明結構分析系統之較佳實施例；圖4是一示意圖，說明較佳實施例與待測物的位置關係；及圖5是一流程圖，說明較佳實施例所使用的結構分析方法。BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a block diagram showing the elements required for conventional X-ray crystallography in analyzing the structure of a crystal; and Figure 2 is a schematic view showing the positional relationship of conventional X-ray crystallography in analyzing the structure of a crystal. Figure 3 is a block diagram showing a preferred embodiment of the structural analysis system of the present invention; Figure 4 is a schematic view showing the positional relationship between the preferred embodiment and the object to be tested; and Figure 5 is a flow chart showing the preferred embodiment The structural analysis method used in the examples.
4．．．結構分析系統4. . . Structural analysis system
41．．．電磁波源41. . . Electromagnetic wave source
42．．．頻譜偵測器42. . . Spectrum detector
43．．．處理模組43. . . Processing module
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| TW98130075A TWI407097B (en) | 2009-09-07 | 2009-09-07 | Structural analysis system and method |
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| TW98130075A TWI407097B (en) | 2009-09-07 | 2009-09-07 | Structural analysis system and method |
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| TWI407097B true TWI407097B (en) | 2013-09-01 |
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| TW200516236A (en) * | 2003-11-05 | 2005-05-16 | Jordan Valley Applied Radiation Ltd | X-ray scattering with a polychromatic source |
| US20060165218A1 (en) * | 2003-07-11 | 2006-07-27 | Masayuki Uda | Energy dispersion type x-ray difraction/spectral device |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US20060165218A1 (en) * | 2003-07-11 | 2006-07-27 | Masayuki Uda | Energy dispersion type x-ray difraction/spectral device |
| TW200516236A (en) * | 2003-11-05 | 2005-05-16 | Jordan Valley Applied Radiation Ltd | X-ray scattering with a polychromatic source |
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