全像光學元件之表面特徵診斷

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(1)國立台灣師範大學光電科技研究所碩士論文. National Taiwan Normal University Institute of Electro-Optical Science and Technology Master Thesis. 全像光學元件之表面特徵診斷 Optical diagnosis of surface features in holographic optical element. 指導教授 : 郭文娟博士研究生 : 莊富傑中華民國九十七年七月 July 2008. I.

(2) 致謝. 畢業，這只是代表完成階段性的任務，並不是意味著結束。所代表的意義更不是手中緊握的畢業證書，而是心中那份曾經努力付出的感動與負責任的悸動。因為在畢業之後，即將面臨的將會是一個全新的挑戰、全新的開始。在研究所的生活中，我學習到、也體悟了「發現問題」、「找出問題」、「解決問題」的重要性。短短的二年內所得到的收獲與感謝，更是無法輕意地沉靜心弦，經由指尖，透過筆尖，標楷字面，滿滿深刻紙面…。遙想當初剛進實驗室之際，文竑學長與勝宗學長不只協助建立實驗方面良好的根基，也引導著我們一步步成長，有秩序、有規劃的前進，更讓我們看見面對事情該有的條理與心思的細膩。也感謝彥宇學長，曾在百忙之中抽空前來指導；奐章學長，實驗寶貴經驗的傳授；宏任學長，在程式方面不厭其煩的指教；義勝學長，專業領域知識的交流。也謝謝同學柄成和學弟格偉，常在實驗上提供我所需的要素；同學憶緣和億昇，不時在宿舍共同談天、說地、聊實驗、暢說喜悅。也感恩所辦公室的助教瑞蓉姊、工讀生世興、雅婷、沙沙，幫助我們處理許多大大小小的行政事務，也常一起分享許多快樂時光。更感謝實驗室中的成員們：有著爽朗笑聲又很謙虛客氣的博年學長，這些日子以來多虧有你的指導；同學瑋晨、明諭，一起分擔並扛起實驗室的重任；哲泓，一位一起共患難、同進退的好伙伴；學弟妹協誠、惠雯和夢翰，讓實驗室生氣盎然，也分擔了不少實驗室的事務；瓊瑀，讓我感覺就像多了一位好姐姐、親妹妹般的溫馨感動。大學同學，士晉、昊宇、浩洋、彥男、承遠、冠賀、喆閎…；高中同學，于銓、銘煒、柏揚、世煒、文俊、君怡、雅惠、苑菁…；高中老師，國文老師天祥、英文老師玉梅、物理兼導師的婉玲…。國中同學，富洋…。很謝謝有你們的支持與鼓勵!因為好朋友就像是天上的星星，雖然不能天天看見你們、但我深深的知道你們永遠都在那裡!! 其中，最要最要感謝的是不論如何，永遠都會在背後默默支持我、關心我、擔心我、照顧我、呵護我的家人，因為我知道，不管時間過得再長再久，在你們的眼中，我永遠是個長不大的孩子—莊弟弟!. II.

(3) 最後，也要感恩謝美莉老師，提供我實驗上所需要的樣品；賴志明老師，協助我討論與解決實驗上的問題；緊接著，壓軸要感謝的就是生醫光電實驗室的靈魂人物郭文娟老師。自從老師確定當我指導教授的那一刻起，我就很珍惜唸研究所的日子—讓一位剛從大學畢業乳臭未乾的小子，在茫茫然無所適從的研究所中，找到並確立了方向。這些日子以來，我都一直很欣賞郭老師的領導風格，除了訓練我們獨立自主的執行實驗面對挑戰外，事事又會站在學生的立場替我們著想、力挺我們到底，親切到感覺上就像是一位學姐般，這種亦師亦友的感動更是實驗室動力的來源。這兩年來，我知道我的表現不盡完美，不時讓老師勞心費神，但我也總是盡我最大的努力，盡可能的做到最好。所以對我而言，真的真的很謝謝老師!雖然這兩年來有不少風雨，但卻有著更多一起打拼、努力、歡笑過的痕跡，深深烙印…。在未來的日子裡，我希望老師這股教育、育才的熱忱能永不熄滅，因為，畢業後的我，會很驕傲的對人家說：「我是郭文娟老師生醫光電實驗室畢業的!!!」. 衷心感謝所有愛我的人和我愛的人!!!. 富傑 2008 年八月. III.

(4) 摘要. 本論文以正立式的架構搭建一套差動共焦顯微鏡，此系統的架構、元件和儀器的規格，及架構的設計文中也有詳細描述。系統以波長為 632.8nm 之光源、數值孔徑為 0.8 之物鏡為主，其縱向與橫向解析度分別可至 4.2nm 及 422nm，並且動態範圍為 500nm。由於差動共焦顯微術的軸向解析率限制主要來自系統的雜訊，經排除機械震動、光學雜訊與電性擾動等因素，可得到 75.7dB 的差動共焦訊雜比。利用差動共焦顯微術對奈米級表面起伏的敏感性、及非侵入性、非破壞性、非接觸性等優勢，量測出幾種樣品的表面輪廓(例如：微透鏡、高分子膜、一維光柵和二維光子晶體)。並藉由最大可能估計法(maximum-likelihood estimation algorithm，MLE)來提升影像的橫向解晰度。. IV.

(5) ABSTRACT. In this thesis, a homemade differential confocal microscopy (DCM) in upright configuration was constructed successfully. The setup of the system, specification of the elements, optical beam path configurations are described in this thesis. Using light wavelength of 632.8nm, objective lens of 0.8 numerical aperture, axial and lateral resolution can reached to 4.2nm and 422 nm respectively, and dynamic range reached to 500 nm. The axial resolution of DCM is mainly limited by system noises, including mechanical vibration, optical background and electric noises. After noise was well excluded, the measured signal to noise ratio (SNR) reached to 75.7dB. Using the nanometer depth sensitivity of DCM, we measured the surface profile of several devices (e.g. microlens, polymer membrane, one-dimensional phase grating and two-dimensional photonic crystal) in non-invasive, non-contact, and non-destroy method. The lateral resolution of the topographic images is further enhanced by maximum-likelihood estimation (MLE) algorithm.. V.

(6) Contents Chapter 1 Introduction................................................................................................1. Chapter 2 Material & Method....................................................................................4 2.1 Optical Setup ..................................................................................................4 2.2 Measurement principle................................................................................11 2.3 Maximum likelihood estimation (MLE) algorithm ..................................17. Chapter 3 System calibration ...................................................................................19 3.1 The correction of the piezoelectric device..................................................19 3.2 Axial resolution.............................................................................................23 3.3 Lateral resolution.........................................................................................26 3.4 Signal-to-noise ratio .....................................................................................28. Chapter 4 Results.......................................................................................................29 4.1 Microlens ......................................................................................................29 4.2 Polymer Membrane .....................................................................................30 4.3 1-D Phase Grating........................................................................................31 4.4 2-D Photonic crystal.....................................................................................34 4.5 lateral resolution improvement...................................................................36. Chapter 5 Discussion and conclusion.......................................................................39. References...................................................................................................................41. VI.

(7) List of figures. Fig.1. The optical setup of DCM. ..................................................................................5 Fig.2. The diagram of the beam expander......................................................................6 Fig.3. Diagram of Confocal Microscopy .......................................................................7 Fig.4. Circuit Block Diagram.........................................................................................9 Fig.5. The programmable controller interface .............................................................10 Fig.6. Axial response curve of the confocal microscope. ............................................12 Fig.7-1. To obtain the axial response curve by scanning the PZT in Z direction. .......12 Fig.7-2. To obtain a 2D image by scanning the PZT along the X and Y direction. .....13 Fig.7-3. To found the maximum and minimum intensity from recorded 2D dataset. .13 Fig.7-4. To choose the suitable dynamic range from the axial response curve according to the maximum and minimum value..........................................................14 Fig.7-5. To calculate the slope of the chosen linear area. ............................................14 Fig.7-6. Let the minimum of the two dimension matrix shift to zero..........................15 Fig.7-7. To obtain the variable information of sample height after all the element of the data divided by the slope........................................................................................15 Fig.7-8. The structural information and surface image were shown. ..........................16 Fig.8. The axial response curve for the command of position control and voltage control.. ........................................................................................................................20 Fig.9. The test target image from optical microscope (4x objective). .........................20 Fig.10. The test target image from optical microscope(50x, 100x objective). ............21 Fig.11. The image of test target obtained from the DCM. ...........................................21 Fig.12. Measured axial response curve of a mirror......................................................23 Fig.13. Linear signal of our differential confocal microscope.....................................25 Fig.14. Scanning the edge of a cover glass to measure the lateral resolution..............26 Fig.15. By altering the scanning program, the image was improved from blurred to clear. .............................................................................................................................27 Fig.16. The spectrum of the confocal reflectional signal obtained from a dynamic signal analyzer..............................................................................................................28 Fig.17. The image of microlens.. .................................................................................29 Fig.18. The DCM image of microlens. ........................................................................30 Fig.19. The image of polymer membrane....................................................................30 Fig.20. The DCM image of polymer membrane..........................................................31 Fig.21. The AFM and DCM image of the 1-D phase grating.. ....................................32 Fig.22. The AFM and DCM image of the 1-D phase grating.. ....................................33 VII.

(8) Fig.23. Show the SEM image of 2-D Photonic crystal................................................34 Fig.24. The AFM image of 2-D Photonic crystal ........................................................35 Fig.25. The DCM image of 2-D Photonic crystal........................................................35 Fig.26. The MLE image of microlens..........................................................................36 Fig.27. The MLE image of polymer membrane. .........................................................37 Fig.28. The MLE image of 1-D phase grating.............................................................37 Fig.29. The MLE image of 2-D Photonic crystal ........................................................38. VIII.

(9) List of tables. Table.1. The specification of the digital PZT controller………………………...….8 Table.2. The specification of the piezoelectric device…………...………………….8. IX.

(10) Chapter 1 Introduction. Holographic optical elements (so-called HOE) were widely studied and used in many optical applications due to the advantages of the small volume and easy to integrate in optical systems. With the progressing of the fabricating technique, the scale of HOE devices become smaller, which could make the optical system more compactable and useful. In addition, the HOE devices with phase modulation will provide better performance than with amplitude modulation. Usually the phase modulation can be generated by the surface structure of the HOE devices with the uniform material when the light pass through or reflected by the devices. Hence, it is necessary and important to characterize the surface shape of the phase-modulated HOE devices, which will affect the optical properties and performance of the HOE devices. In general, the maximum depth of the surface structure is smaller than the wavelength of the incident light. For example, if the wavelength of the incident light is 532 nm, then the maximum depth of the surface structure for transmission type HOE device with 1.5 refraction index is 532 nm. According to the theoretical analysis, the accuracy of the depth will significantly influence the diffraction efficiency of the HOE devices. The diffraction efficiency of the HOE devices will drop down 10 % when the variation of the depth with 10 % error after the fabrication. Therefore, it is. 1.

(11) very important if the measuring technique have the nanometer sensitivity for the depth resolution during the fabricating procedure of the transmission or reflection types HOE devices. There are many techniques to measure the surface profile of the optical devices, as scanning electron microscopy (SEM), atomic force microscopy (AFM), scanning probe microscopy (SPM), differential confocal microscopy (DCM), and so on. However, among those measuring techniques, SEM requires a conductive surface for good contrast and must operate in a vacuum, which is not suitable for measuring the transmission type HOE devices. SPM has a risk of scratching sample surface with its probe. In contact-mode AFM, non-uniform surface stiffness generates contrast as well as surface-height variation does. A far-field imaging technique is thus desirable for fast and non-invasive diagnosis of surface features. Fortuitously, the differential confocal microscopy (DCM), presented by Lee in 1997, utilizes the linear variance ratio of intensity at the slopes of the axial response curve in confocal microscopy [1]. It has been demonstrated to provide an axial resolution of about 2 nm that was used for surface imaging [2] and monitoring the thermal fluctuations and the deformation of the bilayer membranes of lipid vesicles [3]. Therefore, in this study, we use DCM technique and improve its lateral resolution by the Maximum likelihood estimation (MLE) algorithm to characterize the one dimensional phase grating and two. 2.

(12) dimensional photonic crystal which produce by using the holographic interference technique. According to our experimental setup, the lateral resolution can be reached to 422nm and the depth resolution is 4.2nm. The thesis is organized as follows:. Chapter two introduces the experimental setup, measurement principle, and the lateral resolution improvement technique of the DCM system. Chapter three shows the results of system calibration. Chapter four demonstrates several surface profile measurements in holographic optical elements, and restored DCM image after MLE iteration. Chapter five discusses the advantages of our proposed method, and summary of the thesis.. 3.

(13) Chapter 2 Material & Method. 2.1 Optical Setup The techniques and principle behind the DCM has been previously described in detail in references [4, 5, 6, 7]. The optical setup of the DCM system in this study is shown in Fig.1. A collimated beam from a Helium Neon laser (Melles Griot, 05-STP-901, λ= 632.8nm) was used as the light source. The incident beam is horizontally polarized by adjusting a half-wave plate (HWP) placed in the DCM system. A quarter wave plate (QWP) and a polarization beam splitter (PBS) are placed in the beam path to isolate the laser light from optical feedback. Neutral Density filter (ND filter) is also used to attenuate the intensity of the light. After passing the QWP, the horizontal polarization state transforms into right-hand circular polarization. Then, the beam focused on a sample through an objective lens (Olympus, LMPlanFI 100X, NA = 0.8) which has a working distance of 3.4 mm. Finally, the light reflected from the sample surface passes a 5-μm diameter pinhole by another objective lens (Olympus, LMPlanFI 20X, NA = 0.4), then is collected and detected by a photodiode detector (Thorlab, DET-210). The above setup is similar to those of conventional confocal microscopes, except that the sample surface is placed at the linear region of the confocal axial response curve not at the focal point.. 4.

(14) Fig.1. The optical setup of DCM. ND, Neutral Density filter; L, lens; PZT, piezoelectric transducer; PC, personal computer; HWP, half-wave plate; QWP, quarter-wave plate.. The important components in our optical setup are introduced as follows：. (1) Light source The axial resolution is decided from the noise of system and the stability of the light source. We adopted a stabilized helium neon laser (Melles Griot, 05-STP-901) with 632.8 nm wavelength, 1.0 mW output power, and± 0.1% power stability.. 5.

(15) (2) Beam expander In order to obtain the optimum resolution, the diameter of the incident beam and the diameter of the entrance pupil of the objective must be matched. In our setup, the entrance pupil of the objective is about 4mm, and the diameter of the incident beam is about 1 mm. So, the beam expander which composed of two piece of plano-convex lens (Newport, KPX076 and KPX094) with focal length of 25.4mm and 100mm were chose in our setup (as shown in Fig.2). Then, the magnification for this expander is,. After passing the beam expander, the beam diameter is amplified about four times.. Fig.2. The diagram of the beam expander.. (3) Polarizing beam splitter We adopted the Glan Thompson PBS (CVI, CPBS-10.0-425-675) which has extinction ratio about 105：1, and its transmission efficiency is more than 95%.. 6.

(16) (4) Spatial filter In confocal microscope (Fig.3), the spatial filter is composed of a focusing lens and a pinhole. In order to achieve the optimum resolution, the distance between the focusing lens and the pinhole is important. In addition, focus of the focusing lens and the size of the pinhole also must be matched. Therefore, we chose a pinhole with diameter of 5μm (Newport, 900PH-5) and a focusing lens (Olympus, LMPlanFl 20X) in our system.. Fig.3. Diagram of Confocal Microscopy. (5) Piezoelectric transducer In our setup, we use a digital PZT controller (Physik Instrumente, E-710.4CL) to control the movement of a XY piezoelectric device (Physik Instrumente, P-731.8C) and a Z piezoelectric device (Physik Instrumente, P-721.20). 7.

(17) The specification of the piezoelectric device controller and the piezoelectric device in our setup are shown below,. Table.1. The specification of the digital PZT controller for Physik Instrumente, E-710.4CL .. Table.2. The specification of the piezoelectric device for Physik Instrumente, P-731.8C and Physik Instrumente, P-721.20.. 8.

(18) (6) Photodiode The circuit diagram of the reversed-biased PIN photo diode (Thorlabs, DET210) is shown in fig.4.. Fig.4. Circuit Block Diagram. (7) Low-noise current preamplifier In our setup, the low-noise current preamplifier (Stanford Research, SR570) was used. The amplifier can amplify small signals from current source. The instrument is battery-powered operation for optimum noise performance. Two first-order RC filters can provide lowpass, highpass, and bandpass filtering functions. An RS-232 interface allows remote controlling.. 9.

(19) (8) Digital - analog convertor In our setup, the National Instruments, DAQ Card TM-6024E was used. The convertor have 16 analog inputs, 2 analog output, sampling rate is 200 kS/s, 12-bit resolution and Multifunction I/O.. (9) Programmable controller interface The program was created by Borland C++ builder. The controller interface is shown in Fig.5. By the controller interface, user can set the scanning position, the scanning area, and the pixel of the image.. Fig.5. The programmable controller interface. 10.

(20) 2.2 Measurement principle Conventional confocal microscopy [8] use light beam focus on a sample through the objective, and obtain the signal. Light from outside of the focus is filtered out by a spatial filter (e.g. pinhole). However, differential confocal microscope(DCM) uses the sharp slope of the axial response curve of the confocal and measure the surface profile of a sample. Depend on this slope; the surface variation of a sample will change the signal. The sensitivity of this effect can be utilized to image surface structures with nanometer scale depth resolution. The experimental setup is similar to a typical confocal microscope, but the sample is placed slightly near or away from the focal point. The simulated response curve is shown in Fig. 6 [9]. The full width at half maximum (FWHM) of the response curve d. is：. where λ is the wavelength, sinα is numerical aperture [9,10]. In our experiment, if NA of objective is 0.8, wavelength λ is 632.8nm, then theoretical d is 0.697μm.. 11.

(21) Fig.6. Axial response curve of the confocal microscope.. The detailed measuring process is as follows: 1. We obtained the axial response curve of a sample by scanning the PZT in Z direction [Fig.7-1.].. Fig.7-1. To obtain the axial response curve by scanning the PZT in Z direction.. 12.

(22) 2. Sample was placed slightly near or away from the focal point. Then we obtained a 2D image by scanning the PZT along the X and Y direction [Fig.7-2.].. Fig.7-2. To obtain a 2D image by scanning the PZT along the X and Y direction.. 3. From recorded 2D dataset, we found the maximum and minimum intensity [Fig.7-3.]. (e.g. In this case, the maximum is 1.352539；the minimum is -2.302246.). Fig.7-3. To found the max. and min. intensity from recorded 2D dataset. 13.

(23) 4. To choose the suitable dynamic range from the axial response curve according to the maximum and minimum value [Fig.7-4.]. (e.g. In this case, the variation of intensity is about 3.654785 which is obtained from 1.352539-(-2.302246).). Fig.7-4. To choose the suitable dynamic range from the axial response curve according to the maximum and minimum value.. 5. To calculate the slope of the chosen linear area [Fig.7-5.]. (Note：The correction of PZT is also necessary that will be discussed in Chapter 3). In this case, the variation of voltage is about 3.67431, and the dynamic range is 720nm. If considering the correction of PZT, the dynamic range is revised to 617.829192 nm. Thus, the slope is about 5.947129154.. Fig.7-5. To calculate the slope of the chosen linear area. 14.

(24) 6. Let the minimum of the two dimension matrix shift to zero [Fig.7-6.].. Fig.7-6. Let the minimum of the two dimension matrix shift to zero.. 7. Then, we can obtain the variable information of sample height after all the element of the data divided by the slope [Fig.7-7.].. Fig.7-7. To obtain the variable information of sample height after all the element of the data divided by the slope. 15.

(25) 8. Finally, the structural information and surface image were shown [Fig.7-8.].. Fig.7-8. The structural information and surface image were shown.. 16.

(26) 2.3 Maximum likelihood estimation (MLE) algorithm In this study, maximum likelihood estimation (MLE) was used to improve the lateral resolution of our DCM images [11]. MLE is a mathematic method generally used for producing estimates of the noisy image by some form of random noise. The randomness is due to the statistical nature of the quantum emissions. Because the random noise properties of confocal and DCM can be best described by a Poisson point process [12], the log-likelihood function represents the measured noisy data were actually collected. To utilize the expectation-maximization (EM) algorithm for calculating the maximum likelihood estimation for the noisy data, the EM-MLE solution is [13],. f(x) is object function, h is the point spread function, m(y) is the recorded image, x is the vector in the object space, y is the vector in the image space. The method of image reconstruction is based on finding a solution, f(x), according to the iterative algorithm. In principle, the algorithm is solved for its maximum. In blind deconvolution, assuming convergence of the iteration, the maximal resolution of f( ) and h( ) become the reconstructed image and the reconstructed PSF. 17.

(27) On the other hand, with the non-blind deconvolution, h( ) is assumed to be known from prior measurement, and the denoised algorithm is solved only for f( ). Finally, the iteration will stop when the change between two resolutions is sufficiently small.. 18.

(28) Chapter 3 System calibration. 3.1 The correction of the piezoelectric device There are two control modes in our digital PZT controller. For the purpose of correcting the deviation between the command of position control and voltage control in z direction, we measured the axial response curve several times by the command of position control and voltage control respectively (as shown in Fig.8 (a) and (b)). Then, we chose the same dynamic range (0.4μm) from these linear area to compare their variation of intensity. These data were averaged and shown in Fig.8(c). In this figure, we can see that the averaged variable range of intensity by position control is larger than voltage control. According to this result, we calculated the correction factor between position command and voltage command was,. On the other hand, for the purpose of correcting the deviation between the command of position control and voltage control in x and y directions, we scan a test target whose interval between linear pair is 10μm (the total length is 1mm). Fig.9 and Fig. 10 show the test target image observed from optical microscope (4X, 50X, and 100X objectives).. 19.

(29) Fig.8. The axial response curve for the command of position control and voltage control. (a) The axial response curve for the command of position control. (b) The axial response curve for the command of voltage control. (c) The variation of intensity for same dynamic range (0.4μm) between position control and voltage control.. Fig.9. The test target image observed from optical microscope (4X objective).. 20.

(30) Fig.10. The test target image from optical microscope(50X, 100X objective).. Then, we scanned this test target by the DCM. The scanning pixel was 64 x 64, scanning area was 64μm x 64μm. The image is shown in fig.11 (a).. Fig.11. The image of test target obtained from the DCM. (a) DCM image. (b) we selected three parts of intervals from Fig.11(a) and averaged these data.. 21.

(31) Although we set the scanning area to 64μm x 64μm, the image was actually only 50μm x 50μm ( the interval between linear pair is 10μm ) in the Fig.11(a). So, we selected three parts of intervals and averaged these data (i.e. in Fig.11(b)). On this basis, we calculated the correct factor as. .. 22.

(32) 3.2 Axial resolution Fig. 12 shows the axial response curve of a mirror in our DCM setup. The full width at half maximum (FWHM) of main peak is about 0.8μm by using a NA 0.8 objective that is deviated from the theoretical value, 0.697μm, may caused by the aberration effect [14, 15](as showed in the inset of Fig.12).. Fig.12. Measured axial response curve of a mirror.. In order to obtain surface profile from axial response curve, we estimate the axial resolution from the slope of the linear dynamic range. Depend on this slope, the surface variation of sample will cause the change of signal. In the linear area, the variation of light intensity(ΔI) and the height of sample (Δh) have the relational formula：Δh = ΔI / r. Therefore, the slope (r) could be obtained by dividing the variable signal (ΔI) by the distance of movement (Δh). According to the slope, we can know the variable 23.

(33) information of sample height. The axial resolution is defined by the uncertainty (ΔE), which is the noise mainly from the fluctuation of the light source, mechanical vibration of the optical system and so on. In perfect situation, the variation of the signal is a straight line during the linear area. Even if the fluctuation of noise comes into existence, we also can use a straight line to fit the measured signal. Consequently, the depth resolution is defined as the uncertainty of the sample height, is equal to Δ E/r. Then, the axial resolution is better if the value of ΔE/r is lower. In order to estimate the value of ΔE/r, the signal during the linear area was normalized. The maximum value is 1, and the minimum value is 0. The relation between the slope r and the dynamic range D is,. The axial resolution is represented as ΔEn․D. The ΔEn is the value of average noise which after intensity normalization. In Fig.13, the measured data points were fitted by a straight line of slope r after the signal normalization. In addition, the uncertainty ΔE is 0.841% and the dynamic range is 0.5μm. So, the axial resolution in our setup is about 4.2nm, and the dynamic range is 500nm for an objective with NA=0.8.. 24.

(34) Fig.13. Linear signal of our differential confocal microscope with objective 100x NA=0.8, the uncertainty ΔE = 0.841%, dynamic range=500nm, so the depth resolution =4.2nm.. 25.

(35) 3.3 Lateral resolution To demonstrate the lateral resolution in our developed DCM system, we scan the edge of a cover glass fin X direction and Y direction individually. After the intensity is normalized that we can obtain the data shown in Fig. 14(a) and 14(b). According to the method [16], the transverse resolution is decided from the distance between the intensity is 0.2 and 0.8. We observed that the lateral resolution is different from X and Y direction. The resolution in X direction is about 0.677μm while that in Y direction is only 0.422μm.. Fig.14. Scanning the edge of a cover glass to measure the lateral resolution. (a) the resolution in X-axis is about 0.677μm, (b) the resolution in Y-axis is about 0.422μm.. 26.

(36) Based on this finding, we try to alter the scanning program to change the scanning velocity of PZT, i.e. it will stay longer time for each pixel in X direction. Thus, we increased the stay time for 0.01, 0.02, 0.03, 0.05 second for each pixel in X direction. In Fig.15, the sample is a test target (Edmund, T39-857), and the image of the edge of the pattern was improved distinctly from blurred to clear.. Fig.15. By altering the scanning program, the image was improved from blurred to clear. (a) Stay 0.01 second for each pixel in X direction (b) Stay 0.02 second for each pixel in X direction. (c) Stay 0.03 second for each pixel in X direction. (d) Stay 0.05 second for each pixel in X direction.. 27.

(37) 3.4 Signal-to-noise ratio We measured the signal-to-noise ratio (SNR) fin our setup by a dynamic signal analyzer (Stanford Research System, SR780). The spectrum of the confocal reflectional signal is shown in Fig.16, and the mainly noise was seen at 60 Hz. Hence, the SNR is about 75.7dB.. Fig.16. The spectrum of the confocal reflectional signal obtained from a dynamic signal analyzer.. 28.

(38) Chapter 4 Results. 4.1 Microlens First, We measured the surface profile of microlens and compared with the images observed from a common optical microscope in Fig.17(a) and a scanning electron microscope in Fig.17(b). As a matter of fact, the diameter of these mirolens is 1μm.. Fig.17. The image of microlens. (a) The image observed in optical microscope. (b) The image acquired from the scanning electron microscope(SEM).. Fig.18 shows our DCM image where pixel number is 256 x 256 and scanning area is 25.6μm x 25.6μm. The height of microlens is represented in the top and right inset of Fig. 18. The measured result of microlens is about 150nm height and 1μm diameter that is identical with the SEM measurement.. 29.

(39) Fig.18. The DCM image of microlens.. 4.2 Polymer Membrane The surface image of a polymer membrane obtained from a optical microscope is shown in Fig.19.. Fig.19. The surface image of a polymer membrane from the optical microscope.. 30.

(40) Fig.20 shows the results of our DCM measurement. The roughness of a polymer membrane can be seen apparently. Because this polymer membrane is a kind of material to compose the artificial vascular graft, investigate the roughness of membrane surface is important. If the situation for capability of coagulation and anti-coagulation between this material and blood is unbalanced, it will bring about thrombus.. Fig.20. The DCM image of a polymer membrane.. 4.3 1-D Phase Grating we diagnosed the surface features of holographic optical elements and compared with those images from atomic force microscope (AFM). Fig.21(a) shows an AFM image of a phase grating with 5μm x 5μm image size. Fig.21(b) shows the 1-D profile along the line of Fig.21(a), the average height of the grating is about 475nm, and the average period is about 1.03μm. 31.

(41) The surface image obtained by our DCM system is shown in Fig.21(c), the pixels is 128 x 128 and scanning area is 5.12μm x 5.12μm. Fig.21(d) shows the 1-D profile along the line of Fig.21(c), the average height of the grating is about 500nm, and the average period is about 1.1μm.. Fig.21. The AFM and DCM image of the 1-D phase grating. (a) AFM image of the grating. (b) 1-D profile along the line of Fig.21(a). (c) DCM image of the grating. (d) 1-D profile along the line of Fig.21(c).. Fig.22(a) shows an AFM image of a phase grating with 5μm x 5μm image size. Fig.22(b) shows the 1-D profile along the line of Fig.22(a), the average height of the grating is about 140 nm, and the average period is about 1.05μm. Then, the. 32.

(42) obtained DCM image is shown in Fig.22(c) where pixel number is 128 x 75 and scanning area is 7.17μm x 4.2μm. The 1D profile along the line of Fig.22(c) is shown in Fig.22(d), the average height in this grating is about 150nm and the average period of the grating is about 1.1μm. Although the grating fabricated was not uniform, and the scanning area was different from AFM and DCM, the results can be comparable.. Fig.22. The AFM and DCM image of 1-D phase grating. (a) AFM image of the grating. (b) 1-D profile along the line of Fig.22(a). (c) DCM image of the grating. (d) 1-D profile along the line of Fig.22(c).. 33.

(43) 4.4 2-D Photonic crystal Finally, we measured the surface features of holographic optical elements, 2-D photonic crystal, and compared with those images from scanning electron microscope (SEM) and atomic force microscope (AFM). Fig.23 shows a SEM image of a 2-D photonic crystal with 8.7μm x 12.8μm image size. It can be seen that the period of the 2-D photonic crystal is about 1.1μm.. Fig.23. The SEM image of a 2-D photonic crystal. The scale bar is 5μm.. On the other hand, Fig.24(a) shows an AFM image of the 2-D photonic crystal with 5μm x 5μm image size. It displays not only the surface profile of the grating, but also the information about depth. Fig.24(b) shows the 1-D profile along the line of Fig.24(a). we can see the maximum and minimum depth are labeled about 301.82nm and 25.32nm individually, the measured depth is approximately 276.5nm.. 34.

(44) Fig.24. The AFM image of 2-D photonic crystal. (a) shows an AFM image of the 2-D photonic crystal with 5μm x 5μm image size. (b) shows the 1-D profile along the line of Fig.23(a).. Then, the obtained DCM image is shown in Fig.25(a) where pixel number is 128 x 128 and scanning area is 10.2μm x 10.2μm. Fig.25(b) shows the 1-D profile along the line of Fig.25(a). In Fig.25(b), the average depth about 300nm is measured and the average period is around 1.05μm. Although the 2-D photonic crystal fabricated was not uniform, and the scanning area was different in SEM, AFM and DCM, the results can be comparable.. Fig.25. The DCM image of the 2-D photonic crystal. (a) DCM image. (b) shows the 1-D profile along the line of Fig.25(a). 35.

(45) 4.5 lateral resolution improvement Finally, we used the Maximum likelihood estimation (MLE) algorithm to improve our DCM image performance. These deblurred image are shown as below,. 1. Microlens. Fig.26. The MLE image of microlens. (a) The measured lateral PSF in our setup. (b) The DCM image of microlens. (c) After MLE algorithm, the image of microlens was deblurred and more sharpness.. 36.

(46) 2. Polymer Membrane. Fig.27. The MLE image of polymer membrane. (a) The measured lateral PSF in our setup. (b) The DCM image of polymer membrane. (c) After MLE algorithm, the image of polymer membrane was deblurred and more sharpness.. 3. 1-D Grating. Fig.28. The MLE image of 1-D grating. (a) The measured lateral PSF in our setup. (b) The DCM image of grating. (c) After MLE algorithm, the image of grating was deblurred and more sharpness.. 37.

(47) 4. 2-D Photonic crystal. Fig.29. The MLE image of 2-D photonic crystal. (a) The measured lateral PSF in our setup. (b) The DCM image of 2D photonic crystal. (c) After MLE algorithm, the image of the grating was deblurred and more sharpness.. From the above results, lateral PSF was obtained by scanning the edge of cover glass, the images which iterated after MLE algorithm are more distinct than raw images.. 38.

(48) Chapter 5 Discussion and conclusion. In this thesis, we have developed a DCM system and improve its resolution by using MLE algorithm. Using the nanometer depth sensitivity of DCM, we have measured the surface profile of several devices, including microlens, polymer membrane, one-dimensional phase grating and two-dimensional photonic crystal successfully. The advantages of DCM technique includes, (1) When the height variation in a sample is extreme small, the edge effect will be strengthened on the axial height by the DCM technique. (2) Grating and photonic crystal will not be broken after the measurement by DCM. (4) User can change objectives with different NA according to the property of the sample, to correspond with all kinds of dynamic range and resolution we needed. Moreover, if combing transmission detection configuration in out existing refection mode DCM setup. The technique can obtain not only the surface profile of the microlens, but also the focal length and spot size. These information will be helpful for microlens fabrication which can applied in photonics, optoelectronics, biology, medicine, and material science [20, 21, 22]. However, because the MLE algorithm based on the system measured may not describes the transfer characteristics of the imaging system under all conditions [23,. 39.

(49) 24], an accurate PSF should be measured under conditions that exactly replicate the conditions under which the image was acquired. This approach is impractical as each sample has its own optical characteristics that are not easy to replicate provided that they can be measured to a reasonable accuracy.. 40.

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