Exponential Interpolation Technique for Scanning Electron Microscope Signal-to-Noise Ratio Estimation.

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1 184 Int'l Conf. IP, Comp. Vision, an Pattern Recognition IPCV'16 Exponential Interpolation Technique for Scanning Electron Microscope Signal-to-Noise Ratio Estimation. Z.X.Yeap1, K.S.Sim 1 1 Faculty of Engineering an Technology, Multimeia University, Ayer Keroh, Melacca, Malaysia Abstract - This paper introuces a new technique to estimate the value of the focuse SEM images from a efocus images. Basically SEM user took hours to make ajustment on the SEM an prouce a focuse image. Therefore, in orer to solve the time consuming problem, a solution is propose. Base on the experiments on 100 images, a metho use an exponential equation is evelope to estimate the noise-free zero offset point of a focuse image by using a efocuse image. This metho uses less than a minute to process an it can overcome the time consuming problem while taking image repeately to get the most focus one. Keywors: estimation, focus, efocus, SEM 1 Introuction Scanning Electron Microscopy (SEM) is a evice to capture high-resolution imaging of surfaces. SEM is particularly use for unerstaning of nano materials base on topographic an composition elements [1]. It is wiely use in science, such as metallurgy, geology, biology an IC failure analysis. A high resolution, noiseless an focuse SEM images are helpful in the analysis process. However, it is time consuming to capture such high quality images [2]. Besies, filtering process might make the image blur [3]. Therefore, a metho to estimate the original noise free image is neee. Basically, signal-to-noise ratio () is use to quantify the image quality. In this paper, a metho to estimate the of the SEM image using an out of focus image is propose. This metho is base on the focus etection which propose by Ong in 1997 an single image estimation technique which propose by Sim in 2002 [3][4][5]. This metho works by performing the Fast Fourier transform (FFT) of the image, obtains the autocorrelation curve (ACF) an etermines the relationship of focus an the center of the FFT. From the estimation, the can be calculate by using the single image approach. 2 Problem Formulation is an important parameter to characterize the quality of images taken by using SEM. However, it is a ifficult process to get a high resolution an focus SEM image. Manual focusing is very time-consuming even for the experience SEM operator especially in low-ose an highresolution task. Although there is an auto focus feature in the SEM itself, it oes not perform well in the samples which containing highly irectional features. In orer to estimate the of the SEM images, Frank an L.Al Ali evelope two images estimation base on the cross correlation function (CCF) of two images acquisition of the same object [6][7][8]. The equation is shown in Eq.1. (1) where, is of the CCF function, is the mean an is the variance of the respective two aligne images. Then equation of is shown in Eq.2. (2) However, this metho nees to capture the images of the same sample. The perfect alignment of the two images becomes critical issue. Besies, this metho is not applicable on the existe images store in the ata base. In 2002, Sim propose a single image estimation technique [5]. In Sim s single image approach, he assume that the two images were ientical. Therefore from Eq.1, the mean an variance of two images are the same which is, Eq.2 can be simplifie into Eq.5 (3) (4) (5) where, is signal component an is noise component. Fig.1 represents the equation in graphical way.

2 Int'l Conf. IP, Comp. Vision, an Pattern Recognition IPCV' Noise Signal X where c is a scaling constant an r is the intensity of each pixel. Fig.2 shows the FFT isplaye an its respective image. Top left image is a focuse SEM image of IC an top right image is its processe FFT image. In the other han, the bottom left image is a efocuse SEM image of IC an bottom right image is its processe FFT image. A focus image has large amount of white ots an efocus image has lesser white ots. Figure 1: ACF of image with white noise [9] Since noise-free zero offset point is an unknown in this single image approach, an estimation technique to estimate the point is neee [10]. 3 Estimation of point in ACF curve from efocus image In 1979, Tee propose auto-focus metho by etermining the point of the best focus from the erivative or graient of the signal [11]. This metho has a major isavantage. It is sensitive to noise as the metho is base on the ifferentiation of the signal. Therefore in 1982, Erasmus an Smith propose another metho which was base on the power spectrum [12]. The power spectrum of an image an the Fourier transform of the covariance function (CF) of the same image are the same [5]. So the CF can be use irectly in the metho where the CF contains also the focus information. By observing the center point on the CF without concerning the shape, the focusing correction can be one. However, this metho requires certain number of of image variance versus the focus currents to maintain the accuracy of the algorithm. If the number of are too less, the accuracy will ecrease. However, it is time consuming to take more in orer to increase the accuracy of the algorithm. Besies, this metho requires three curves. So more time is neee to compare to other algorithm using only one curve. Furthermore, this metho is prove that it has a best result when using 3,000 x magnifications. But, in orer to get a high-resolution SEM image, Ong suggeste to have magnification more than 3,000x [4]. In 1996, Postek verifie that FFT can be use in etecting the efocus of images [13]. Later in 1997, Ong propose an algorithm which can etect the focus or efocus of the images by observing the change in the FFT while changing the focus [4]. The algorithm changes the FFT of an image into the range of 0 to 255 for isplay purpose so that important information oes not lost while isplay. Then the intensity of every pixel is transforme using Eq.6. Figure 2: Comparison of focus an efocus image an its FFT. However, this metho might not perform well while the images are too much out of focus as the information contains in FFT is not enough. Even though Ong has propose a solution which is to repeat the algorithm from low magnification until the esire magnification is reache, this solution is time consuming [2][5]. Base on the theory propose by Ong, this paper proposes a metho which can etermine the relationship of focus an of the images an create an equation to estimate the noise-free zero off set point of the noise-free focuse original image. From the observation, we can see that the ACF curve of focus image has sharper tren line on the center of ACF. Fig.3 shows the comparison of focus an efocus image in term of ACF curve. (6)

3 186 Int'l Conf. IP, Comp. Vision, an Pattern Recognition IPCV'16 From the ata collecte using 100 images with ifferent level of focus, the relationship between the focus an the ifference between noisy an noise-free zero offset are plotte on graph. From the graph plotte, an equation which best fitte the line on the graph is shown in Eq.8. (8) where is the focus point of the image. is the ifference between focus noise-free zero offset point an efocus noise-free zero offset point Figure 3: Comparison of ACF curve of focus an efocus SEM image. Top left: focus SEM image, top right: ACF curve of focus image, bottom left: efocus SEM image, bottom right: ACF of efocus SEM image. There are two versions of the propose metho. These methos are evelope base on 100 images with ifferent level of focus sets. One set of image contains of many images of the same specimen area with ifferent focus level. First version is one by observing the relationship between the focus an the ifference between noisy an noise-free zero offset point. The relationship information is then plotte on a graph. The first metho give poor accuracy ue to the non-stanarize number of focus. Eq.7 shows the equation which best fitte the graph of focus an the ifference between noisy an noise-free zero offset point. (7) where is the non- focus point of the image. is the ifference between focus noise-free zero offset point an efocus noise-free zero offset point is calculate the FFT of that particular image. The image is first resize into 512x512 for the ease of the process. Then it will be converte into ouble format an performs the FFT. From the FFT, the image ata is into range of 1 to 255. Then the threshol is set to 0.5 accoring to Ong an the ata is converte into white as 1 an black as 0 [4]. The focus are the white ots insie the In orer to the focus of ifferent images into the same stanar, the focus are ivie by to get the is the total number of pixels in the image with size of 512x512. Next, a graph of the ifference of value of focuse an efocuse image versus is plotte. Estimation tren line is plotte on the graph an the equation to estimate the noisefree zero offset point of the focuse image is efine in Eq.7. Eq.7 is applie on a set of SEM images with ifferent level of focus an gets the value respectively. The ifference is ae into the efocus noise-free zero offset point respectively an average is calculate to get the focus noise-free zero offset point. can be calculate using Eq.5. 4 Results an iscussion 4 sets of images are chosen to test this propose estimation technique. The 4 selecte images are shown in Fig.4. From the analyzation an observation of the first version, the error percentage is high for some images. It is because the number of focus of the most focus image in a set is ifferent ue to the nature of image. Therefore, we the focus by iviing all the number of focus of images with the largest number of focus among set. After the normalization, the most focus image among the set will have focus point of 1.

4 Int'l Conf. IP, Comp. Vision, an Pattern Recognition IPCV' Figure 4: 4 selecte images use to test the estimation metho. Top left: set 1, top right: set 2, bottom left: set 3, bottom right: set 4. Tables 1 to 4 show the estimate an estimate zerooffset noise free using 3 sets of images. Eq.9 is use to calculate the percentage error by comparing to no.0 image (focuse image). (9) Table 1: Results of estimate using set 1 images. 0 to 8 inicates image no.1 to image no.8. Labeling inicates the Average estimate point= By comparing the average of estimate point an the point of image no.0 (focuse image) point, the ifference of the estimate an real zero-offset noise free point is equal to. Percentage ifference is Table 2: Results of estimate using set 2 images. 0 to 8 inicates image no.1 to image no.8. Labeling inicates the Average estimate point= By comparing the average of estimate point an the point of no.0 (focuse image) point, the ifference of the estimate an real zero-offset noise free point is equal to. Percentage ifference is By applying Eq.8, the percentage error of set 3 is: From the results shown in Table 1 to Table 3, the error percentage is less than 10% which is acceptable result. By applying Eq.8, the percentage error of set 4 is: From the results shown in Table 1 to Table 3, the error percentage is less than 10% which is acceptable results. By observing the results of Table 1 to Table 4, the estimation metho is applicable in both high focus images an low focus images. From Table 2 an Table 4, a focus image has white an a efocus image has only white, the percentage error is less than 10% an this means that this metho can estimate the zero offset point accurately. Using the results get from 4 sets of images, the of the focus image can be estimate. Table 5 shows the comparison of real value an estimate value. In this test, noise variance is set to

5 188 Int'l Conf. IP, Comp. Vision, an Pattern Recognition IPCV'16 Table 3: Results of estimate using set 3 images. 0 to 8 inicates image no.1 to image no.8. Labeling inicates the Average estimate point= Table 4: Results of estimate using set 4 images. 0 to 8 inicates image no.1 to image no.8. Labeling inicates the Table 5: Comparison of real an estimate. Image Real Real in B in B set set set set From the result in Table 5, the estimate in B are similar to the real in B. The estimate of set 3 has bigger ifference compare to real ue to the noise existe in the image is more than other images. Table 6 shows the comparison results of two versions of the propose metho. Table 6: Comparison of results of using focus an non- focus Image without without in B with with in B set set set set From the result in Table 6, we can see the application using focus give a better result compare to the version which use the non- focus. Table 7 shows the percentage error using the non- focus to preict the zero offset noise-free point Average estimate point=

6 Int'l Conf. IP, Comp. Vision, an Pattern Recognition IPCV' Table 7: Percentage error of using the non- focus. Image Real zero offset noise-free point using non Percentage error (%) Set % Set % Set % Set % From the result of Table 7 an the calculation in Table 1 to Table 4, the percentage error reuce for average of 14% overall. 5 Conclusion In conclusion, this propose metho can estimate the focus SEM images using efocus image. Besies, this metho only use up to few secons to process. It saves more time as compare to time taken for repeating ajusting on SEM machine to capture a focuse image. From the results an iscussion part, the normalization part plays an important role to make the solution more accurate. This metho can estimate the noise-free zero offset point more accurately if using more images with ifferent focus level as the final result is from the average result of images with ifferent focus level. 6 References [1] K.S. Sim, M.A. Kiani, M.E.Nia an C.P. Tso, Signalto-noise ratio enhancement on SEM images using a cubic spline interpolation with Savitzky Golay filters an weighte least squares error, in Journal or Microscopy, 2014, vol.00(0), pp1-11. [5] K.S.Sim, Signal-to-noise ratio estimation in scanning electron microscope imaging system, M.S.thesis, National University if Singapore, Singapore, (2002). [6] J. Frank, Three imensional electron microscopy of macromolecular assemblies, San Diago: Acaemic. [7] J.Frank an L.Al-Ali, Signal-to-noise ratio of electron micrograph obtaine by cross correlation in Nature. Vol.256, pp , [8] J.Frank, The role if correlation technique in computer image processing in computer processing of electron microscope images, Berlin: Springer-Verlag, pp , [9] K.S.Sim, M.Y.Wee an W.K.Lim. Image signal-tonoise ratio estimation using shape-preserving piecewise cubic Hermite autoregressive moving average moel, in Journal of Microscopy Research an Technique, vol. 71(10), pp , [10] V. Teh & K.S. Sim, Image signal-to-noise ratio estimation using aaptive slope nearest-neighborhoo moel. in Journal of Microscopy vol.260, pp , [11] W.J. Tee, K.C.A. Smith an D.M.Holburn, Automatic focusing an stigmatizing system for the SEM, in Journal of Physics E: Scientific Instrument, vol.12, pp.35-38, [12] S. J. Erasmus an K. C. A. Smith, An automatic focusing an astigmatism correction system for the SEM an CTEM, in Journal of Microscopy, vol.127, pp [13] M.T. Postek an A.E.Vlaar, SEM performance evaluation using the sharpness criterion, in Stanars an calibration metho for critical imension metrology, Santa Clara, CA, 1996, vol.2725, pp [2] E. Oho an K. Suzuki, Highly accurate measurement using the covariance of two SEM images with the ientical view, in Scanning, vol.34, pp.43-50, Feb [3] K.S. Sim, V. Teh an M.E.Nia. Aaptive noise Wiener filter for scanning electron microscope imaging system in Scanning vol.38, pp , [4] K.H. Ong, J.C.H.Phang an J.T.L.Thong, A Robust ing an Astigmatism Correction Metho for the Scanning Electron Microscope, in Scanning, 1997, vol.19, pp