| 研究生: |
慈復明 Tzu, Fu-Ming |
|---|---|
| 論文名稱: |
液晶平面顯示器非均勻性薄膜的光學特性 Optical Characteristics of Non-uniform Films in Thin Film Transistor-Liquid Crystal Displays |
| 指導教授: |
周榮華
Chou, Jung-Hua |
| 學位類別: |
博士 Doctor |
| 系所名稱: |
工學院 - 工程科學系 Department of Engineering Science |
| 論文出版年: | 2011 |
| 畢業學年度: | 99 |
| 語文別: | 英文 |
| 論文頁數: | 115 |
| 中文關鍵詞: | 光學檢查 、厚度 、最小感知差 、光學密度 、色度 、色差 、色域 |
| 外文關鍵詞: | Optical inspection, thickness, just noticeable difference, optical density, chromaticity, color difference, color gamut |
| 相關次數: | 點閱:173 下載:5 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本論文提出對於彩色濾光片三原色的非均勻性薄膜非接觸性的光學檢測方法。使用光譜儀,光電倍增管與線性相機掃描圖形,利用最小可視差現象作量化。結果顯示,沿著非均勻膜的厚度,色度與光學密度的變化;膜厚與光學密度呈現凹陷特性,色度卻呈現凸起現象。在藍色膜的量測方面,膜厚變化為正斜率的線性關係,色度與光學密度變化為負斜率的線性關係。
此外,三原色的藍色,紅色與綠色所形成的三角形色域空間結果分析,厚膜有比較多的色域空間,薄膜則是較少的色域空間。色度中橫向座標與紅色變化有關,為CIE x 的函數;綠色與藍色變化與縱向有關,為CIE y的函數。相較於國家電視標準委員會所制定的100%色域空間,厚膜的色域面積為93%,薄膜的色域面積為28%。
誤差分析採用三個標準差於99.7%的信心區間,符合目前平面顯示器的要求。提供的方法可以非常準確的量化彩色濾光片的式樣,甚至比最小的人眼可視差還要低。
An innovative non-contact optical inspection method is developed to quantify a set of red, green and blue layers of a non-uniform thin-film through a CCD-based line-scan, a spectrometer, and a photomultiplier tube to link the digital imaging. Using the features of thickness, chromaticity and optical density profile across the non-uniformity, the results indicate the tendency of thickness and optical density to have concave profiles, whereas the chromaticity distribution is convex. Moreover, a linear relation with a positive slope is demonstrated for thickness, but a negative slope exists between the chromaticity and optical density for blue film.
Moreover, a triangle of color gamut in CIE 1931 for R, G, and B can express the convergence of chromatic tendency. The thick film, the more color gamut; the thin film, the less color gamut in CIE color space, expresses a proportional relation for thickness and transmittance. Moreover, the experiment improves that red color is the function of CIE x, and greenness and blueness are the function of CIE y. Thick film is shown a 93% of color space and thin film is exhibited a 28% of color gamut based on NTSC of 100% color gamut.
All of the measurements with uncertainties of 99.7% confidence interval satisfy the requirements of the flat panel display. The proposed method can accurately quantify the pattern of R, G, and B of color filter in TFT-LCDs; even the perceptibility is lower than the just noticeable difference (JND).
[1] D. M. Tsai and S. T. Chuang, "1D-based defect detection in patterned TFT-LCD panels using characteristic fractal dimension and correlations," Machine Vision and Applications, vol. 20, pp. 423-434, Oct. 2009.
[2] J. Yatulis , R. Butler , M. Higgins , C. LaPlante , S. J. Chae , C. G. Jhun and W. Y. Kim, "A large-area electronics processing platform using laser technology for the customization of liquid crystal displays," Electronic Materials Letters, vol. 5, pp. 195-200, Dec. 2009.
[3] V. B. Kreng and H. T. Wang, "The interaction of the market competition between LCD TV and PDP TV," Computers & Industrial Engineering, vol. 57, pp. 1210-1217, Nov. 2009.
[4] V. B. Kreng and H. T. Wang, "A technology replacement model with variable market potential - An empirical study of CRT and LCD TV," Technological Forecasting and Social Change, vol. 76, pp. 942-951, Sep. 2009.
[5] D. E. Mentley, "State of flat-panel display technology and future trends," Proceedings of the IEEE, vol. 90, pp. 453-459, Apr. 2002.
[6] J. T. Lin , F. K. Wang , S. L. Lo , W. T. Hsu and Y. T. Wang, "Analysis of the supply and demand in the TFT-LCD market," Technological Forecasting and Social Change, vol. 73, pp. 422-435, May. 2006.
[7] A. de Vaan, "Competing display technologies for the best image performance," Journal of the Society for Information Display, vol. 15, pp. 657-666, 2007.
[8] T. Miyamoto , S. Nagano and N. Igarashi, "Technical developments for widescreen LCDs, and products employed these technologies," NEC Technical Journal, vol. 2, pp. 62-66, Sep. 2007.
[9] A. L. Fischer, "LCD panel market readjusts," Photonics Spectra, vol. 41, pp. 64-68, Sep. 2007.
[10] F. Okumura, "Development of poly-Si TFT in NEC," NEC Research & Development, vol. 40, pp. 424-428, Oct. 1999.
[11] M. Olifierczuk and J. Zielinski, "Determination of LCD electro-optical parameters using mathematical model to obtain optimized device operating under high external illumination," Molecular Crystals and Liquid Crystals, vol. 488, pp. 100-109, 2008.
[12] Y. Ishii, "The world of liquid-crystal display TVs - Past, present, and future," Journal of display technology, vol. 3, pp. 351-360, Dec. 2007.
[13] P. Oikonomakos , J. Fournier and S. Moore, "Implementing cryptography on TFT technology for secure display applications," in Samrt Card Research and Advanced Application, Proceedings. vol. 3928, ed: Springer-Verlag Berlin, 2006, pp. 32-47.
[14] S. S. Kim , B. H. Berkeley , J. H. Park and T. Kim, "New era for TFT-LCD size and viewing-angle performance," Journal of the Society for Information Display, vol. 14, pp. 127-134, Feb. 2006.
[15] F. M. Tseng , Y. J. Chiu and J. S. Chen, "Measuring business performance in the high-tech manufacturing industry: A case study of Taiwan's large-sized TFT-LCD panel companies," Omega-International Journal of Management Science, vol. 37, pp. 686-697, Jun. 2009.
[16] http://en.wikipedia.org/wiki/TFT_LCD, 20100617.
[17] "Hitachi's super-TFT to challenge CRT technology," Microelectronics Journal, vol. 27, pp. 13-14, Sep. 1996.
[18] Y. Koike and K. Okamoto, "Super high quality MVA-TFT liquid crystal displays," Fujitsu Scientific & Technical Journal, vol. 35, pp. 221-228, 1999.
[19] P. S. Shih , W. H. Wang , H. L. Pan and K. H. Yang, "A new pixel design and a novel driving scheme for multi-domain vertically aligned LCDs," Journal of the Society for Information Display, vol. 15, pp. 145-150, Feb. 2007.
[20] C. Cai , A. Lien , P. S. Andry , P. Chaudhari , R. A. John , E. A. Galligan , J. A. Lacey , H. Ifill , W. S. Graham and R. D. Allen, "Dry vertical alignment method for multi-domain homeotropic thin-film-transistor liquid crystal displays," Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers, vol. 40, pp. 913-917, Dec. 2001.
[21] A. Lien , C. Cai , R. A. John , J. E. Galligan and J. Wilson, "16.3 ' QSXGA high resolution wide viewing angle TFT-LCDs based on ridge and fringe-field structures," Displays, vol. 22, pp. 9-14, Apr. 2001.
[22] S. J. Kim , S. Y. Lee , J. S. Park , J. H. Ko , I. S. Lee , Y. T. Hong , H. S. Soh and W. Y. Kim, "Technology trends for improving contrast ratio in IPS mode," Molecular Crystals and Liquid Crystals, vol. 443, pp. 43-47, 2005.
[23] N. Aoki , S. Komura , T. Furuhashi , M. Adachi , O. Itou , T. Miyazawa and M. Ohkura, "Advanced IPS technology for mobile applications," Journal of the Society for Information Display, vol. 15, pp. 23-29, Jan. 2007.
[24] R. Lu , Q. Hong , Z. B. Ge and S. T. Wu, "Color shift reduction of a multi-domain IPS-LCD using RGB-LED backlight," Optics Express, vol. 14, pp. 6243-6252, Jun. 2006.
[25] J. J. Lyu , J. Sohn , H. Y. Kim and S. H. Lee, "Recent trends on patterned vertical alignment (PVA) and fringe-field switching (FFS) liquid crystal displays for liquid crystal television applications," Journal of display technology, vol. 3, pp. 404-412, Dec. 2007.
[26] "IPS-Pro (Evolving IPS technology)," http://www.ips-alpha.co.jp/en/technology/ips.html, 2010, March.
[27] "Quarterly LED & CCFL backlight report," Display Research, 2009.
[28] K. C. Lee , S. H. Moon , B. Berkeley and S. S. Kim, "LED-backlight feedback control system with integrated amorphous-silicon color sensor on an LCD panel," Journal of the Society for Information Display, vol. 14, pp. 161-168, Feb. 2006.
[29] K. Kakinuma, "Technology of wide color gamut backlight with light-emitting diode for liquid crystal display television," Japanese Journal of Applied Physics Part 1-Regular Papers Brief Communications & Review Papers, vol. 45, pp. 4330-4334, May. 2006.
[30] R. B. Lu , S. Gauza and S. T. Wu, "LED-lit LCD TVs," Molecular Crystals and Liquid Crystals, vol. 488, pp. 246-259, 2008.
[31] R. Lu , X. Nei and S. T. Wu, "Color performance of an MVA-LCD using an LED backlight," Journal of the SID, vol. 16/11, pp. 1139-45, 2008.
[32] C. Sugitani and K. Takahashi, "LED performance and LED B/L technology required for LED displays in manufacturing industry," NEC Technical Journal, vol. 2, pp. 79-82, Sep. 2007.
[33] C. C. Sun , I. Moreno , S. H. Chung , W. T. Chien , C. T. Hsieh and T. H. Yang, "Brightness management in a direct LED backlight for LCD TVs," Journal of the Society for Information Display, vol. 16, pp. 519-526, Apr. 2008.
[34] C. Y. Wu , T. F. Wu , J. R. Tsai , Y. M. Chen and C. C. Chen, "Multistring LED backlight driving system for LCD panels with color sequential display and area control," IEEE Transactions on Industrial Electronics, vol. 55, pp. 3791-3800, Oct. 2008.
[35] R. J. Xie , N. Hirosaki and T. Takeda, "Wide color gamut backlight for liquid crystal displays using three-band phosphor-converted white light-emitting diodes," Applied Physics Express, vol. 2, Feb. 2009.
[36] G. Harbers , S. J. Bierhuizen and M. R. Krames, "Performance of high power light emitting diodes in display illumination applications," Journal of display technology, vol. 3, pp. 98-109, 2007.
[37] H. Chen , J. Sung , T. Ha and Y. Park, "Locally pixel-compensated backlight dimming on LED-backlit LCD TV," Journal of the Society for Information Display, vol. 15, pp. 981-988, Dec. 2007.
[38] G. Y. Jeong, "High-performance high-efficiency LED-backlight driving system for LCD panels," Journal of the Society for Information Display, vol. 17, pp. 723-734, Sep. 2009.
[39] J. L. Park and S. Lim, "LCD backlights, light sources, and flat fluorescent lamps," Journal of the Society for Information Display, vol. 15, pp. 1109-1114, Dec. 2007.
[40] Y. K. Lo , K. H. Wu , K. J. Pai and H. J. Chiu, "Design and implementation of RGB LED drivers for LCD backlight modules," IEEE Transactions on Industrial Electronics, vol. 56, pp. 4862-4871, Dec. 2009.
[41] J. C. Liou and F. G. Tseng, "120 Hz low cross-talk stereoscopic display with intelligent LED backlight enabled by multi-dimensional controlling IC," Displays, vol. 30, pp. 148-154, Dec. 2009.
[42] W. Lee , K. Patel and M. Pedram, "White-LED backlight control for motion-blur reduction and power minimization in large LCD TVs," Journal of the Society for Information Display, vol. 17, pp. 37-45, Jan. 2009.
[43] H. Kato and C. Sugitani, "Wide gamut display using LED backlight - Technical developments and actual products," NEC Technical Journal, vol. 1, pp. 75-79, Jul. 2006.
[44] H. J. Chiu , Y. K. Lo , J. T. Chen , S. J. Cheng , C. Y. Lin and S. C. Mou, "A high-Efficiency dimmable LED driver for low-power lighting applications," IEEE Transactions on Industrial Electronics, vol. 57, pp. 735-743, Feb. 2010.
[45] H. J. Chiu and S. J. Cheng, "LED backlight driving system for large-scale LCD panels," IEEE Transactions on Industrial Electronics, vol. 54, pp. 2751-2760, Oct. 2007.
[46] M. Anandan, "Progress of LED backlights for LCDs," Journal of the Society for Information Display, vol. 16, pp. 287-310, Feb. 2008.
[47] R. W. Sabnis, "Color filter technology for liquid crystal displays," Displays, vol. 20, pp. 119-129, Nov. 1999.
[48] T. C. Yen and P. L. Tso, "Fine line-width black matrix of a color filter by an advanced polishing method," Journal of Micromechanics and Microengineering, vol. 14, pp. 867-875, Jul. 2004.
[49] J. E. Hardis, "Improving color measurement of displays," Proceeding of SPIE, Optical Engineer, vol. 2658, 1996.
[50] S. H. Kim , J. D. Park and K. D. Lee, "Fabrication of a nano-wire grid polarizer for brightness enhancement in liquid crystal display," Nanotechnology, vol. 17, pp. 4436-4438, Sep. 2006.
[51] T. L. Chiu and J. H. Lee, "Color gamut variation of LED-lit LCD at different module temperatures," Optics Communications, vol. 283, pp. 373-378, Feb. 2010.
[52] H. F. Chen , T. H. Ha , J. H. Sung , H. R. Kim and B. H. Han, "Evaluation of LCD local-dimming-backlight system," Journal of the Society for Information Display, vol. 18, pp. 57-65, Jan. 2010.
[53] K. Nakashima, "Hybrid inspection system for LCD color filter panels," IEEE Instrument and Measurement Technology Conference, vol. 2, pp. 689-692, 1994.
[54] "Flat panel display measurement standard," Video Electronic Standards Association (VESA), vol. 2, 2005.
[55] "New Standard: Definition of measurement index (SEMU) for luminance Mura in FPD Image quality inspection," pp. 1-6, 2002.
[56] C. J. Lu and D. M. Tsai, "Defect inspection of patterned thin film transistor-liquid crystal display panels using a fast sub-image-based singular value decomposition," International Journal of Production Research, vol. 42, pp. 4331-4351, 2004.
[57] B. C. Jiang , C. C. Wang and H. C. Liu, "Liquid crystal display surface uniformity defect inspection using analysis of variance and exponentially weighted moving average techniques," International Journal of Production Research, vol. 43, pp. 67-80, 2005.
[58] J. Y. Lee and S. I. Yoo, "Automatic detection of region-mura defect in TFT-LCD," IEICE Transactions on Information and Systems, vol. E87D, pp. 2371-2378, Oct. 2004.
[59] F. M. Tzu and J. H. Chou, "Slit-Mura detection through non-contact optical measurements of in-line spectrometer for TFT-LCDs," IEICE Transactions on Electronics, vol. E92C, pp. 364-369, Mar. 2009.
[60] M. Melgosa , R. Huertas and R. S. Berns, "Relative significance of the terms in the CIEDE2000 and CIE94 color-difference formulas," J. Opt. Soc. Am A, vol. 21, pp. 2269-2175, 2004.
[61] N. K. Park and S. I. Yoo, "Evaluation of TFT-LCD defects based on human visual perception," Displays, vol. 30, pp. 1-16, 2009.
[62] H. Murai , K. Ekawa , J. Takashima , H. Naito and N. Nakatsuka, "Mura-detection method by using a slit-beam ellipsometer," Journal of the Society for Information Display, vol. 15, pp. 281-286, 2007.
[63] M. Mahy , L. V. Eycken and A. Oosterlinck, "Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV," Color research and application, vol. 19, pp. 105-121, 1994.
[64] A. J. Werner, "Luminous transmittance, and chromaticity of colored filter glass in CIE 1964 uniform color space," Applied Optics, vol. 7, pp. 849-856, 1968.
[65] J. Hwang , D. H. Lee , S. Park , Y. W. Kim and S. N. Park, "Measurement uncertainty evaluation for emission color and luminance of displays," Applied Optics, vol. 48, pp. 99-105, 2009.
[66] C. J. Sansonetti , M. L. Salit and J. Reader, "Wavelengths of spectral lines in mercury pencil lamps," Applied Optics, vol. 35, pp. 74-77, Jan. 1996.
[67] J. Reader , C. J. Sansonetti and J. M. Bridges, "Irradiances of spectral lines in mercury pencil lamps," Applied Optics, vol. 35, pp. 78-83, Jan. 1996.
[68] CIE, "Industrial colour-difference evaluation," CIE Technical Report, vol. 116, 1995.
[69] CIE, "Improvement to industrial colour-difference evaluation," CIE Technical Report, vol. 142, 2001.
[70] H. Gross, "Handbook of optical systems," Wiley-VCH, p. pp.365~366, 2005.
[71] R. Cohen , D. Exerowa , T. Kolarov , T. Yamanaka and T. Tano, "Foam films stabilized with lysophosphatidylcholine: A comparison of microinterferometric and Fourier transform infrared spectroscopy thickness measurements," Langmuir, vol. 13, pp. 3172-3176, Jun. 1997.
[72] E. G. Steward, "Fourier optics an introduction," Ellis Horwood PHYSICS Series, pp. 62-82, 1983.
[73] Otuska, "Operational manual for measurement thickness," Otuska Inc., 2006.
[74] M. H. Godinho , L. V. Melo and P. Brogueira, "Atomic force microscopy evidence of patterning urethane/urea copolymers," Materials Science & Engineering C-Biomimetic and Supramolecular Systems, vol. 23, pp. 919-922, Dec. 2003.
[75] A. Lasagni and F. Mucklich, "Study of the multilayer metallic films topography modified by laser interference irradiation," Applied Surface Science, vol. 240, pp. 214-221, Feb. 2005.
[76] G. Sharma and H. J. Trussell, "Digital color imaging," IEEE Transactions on Image Processing, vol. 6, pp. 901-932, Jul. 1997.
[77] G. Spekowius, "Characterization of color CRT display systems for monochrome applications," Journal of Digital Imaging, vol. 12, pp. 102-113, Aug. 1999.
[78] G. W. Chang and Y. C. Chen, "Colorimetric modeling for vision systems," Journal of Electronic Imaging, vol. 9, pp. 432-444, Oct. 2000.
[79] B. Bastani , B. Cressman and B. Funt, "Calibrated color mapping between LCD and CRT displays: A case study," Color research and application, vol. 30, pp. 438-447, Dec. 2005.
[80] S. Y. Choi , M. R. Luo , M. R. Pointer and P. A. Rhodes, "Investigation of large display color image appearance I: Important factors affecting perceived quality," Journal of Imaging Science and Technology, vol. 52, 2008.
[81] R. C. Carter and L. D. Silverstein, "Size matters: Improved color-difference estimation for small visual targets," Journal of the Society for Information Display, vol. 18, pp. 17-28, Jan. 2010.
[82] "Standard test method for measurement of small color differences between CERAMIC wall or floor tile," ASTM, pp. 609-690, 2000.
[83] M. R. Luo and C. B. Rigg, "The development of the CIE 2000 color-difference formula: CIEDE2000," Color research and application, vol. 26, pp. 340-350, 2000.
[84] A. Rizzi , D. Gadia and D. Marini, "Analysis of tristimulus interdifference and contextual color correction," Journal of Electronic Imaging, vol. 15, 2006.
[85] D. L. MacAdam, "The theory of the maximum visual efficiency of colored materials," J Opt.Soc.Am., vol. 25, pp. 249-252, 1935.
[86] D. L. MacAdam, "Specification of small chromaticity differences," J Opt.Soc.Am., vol. 33, pp. 18-26, 1943.
[87] D. L. MacAdam, "Visual Sensitivities to Color Differences in Daylight," J Opt.Soc.Am., vol. 32, pp. 247-273, 1943.
[88] D. L. MacAdam, "Loci of constant hue and brightness determined with various surrounding colors," J Opt.Soc.Am., vol. 40, pp. 589-595, 1950.
[89] http://en.wikipedia.org/wiki/MacAdam_ellipse, 2010/9/30.
[90] D. L. MacAdam, "Color measurement," Springer Series in Optical Science, vol. 27, p. 131, 1985.
[91] D. Strocka, "Color difference formulas and visual acceptability," Applied Optics, vol. 10, pp. 1308-1313, 1971.
[92] J. Y. Hardeberg, "Acquisition and research of color imag: Colorimetric and multispectral approach," A dissertation submitted in partial fulfillment of the degree of Doctor, Paris, France, pp. 29-31, 1999.
[93] H. C. Chen and S. J. Wang, "The use of visible color difference in the quantitative evaluation of color image segmentation," IEEE Transactions on advanced packaging, vol. 3, pp. 593-596 2004.
[94] F. M. Tzu and J. H. Chou, "Perceptual detection in color difference for fragmental panel of LCD," Microsystems, Packaging, Assembly Conference Taiwan, 2006 International, IEEE, pp. 197-200, 2006.
[95] G. Sharma , W. Wu and E. N. Dalal, "The CIEDE2000 color-difference formula: Implementation notes, supplementary, test data, and mathematical observations," Color research and application, vol. 30, pp. 21-30, 2005.
[96] J. Scarminio , A. Urbano and B. Gardes, "The Beer-Lambert law for electrochromic tungsten oxide thin films," Materials Chemistry and Physics, vol. 61, pp. 143-146, Oct. 1999.
[97] V. P. Dick and V. A. Loiko, "Model for coherent transmittance calculation for polymer dispersed liquid crystal films," Liquid Crystals, vol. 28, pp. 1193-1198, Aug. 2001.
[98] L. Wind and W. W. Szymanski, "Quantification of scattering corrections to the Beer-Lambert law for transmittance measurements in turbid media," Measurement Science & Technology, vol. 13, pp. 951-951, Jun. 2002.
[99] F. M. Tzu and J. H. Chou, "Optical density measurement of thin-film transistor liquid crystal display by a monochrome light-emitting diode," Applied Optics, vol. 48, pp. 3165-3169, Jun. 2009.
[100] H. Kyushima , H. Shimoi , A. Atsumi , M. Ito , K. Oba and Y. Yoshizawa, "The development of falt panel PMT," IEEE Nuclear Science Symposium Conference Record, vol. 1, 2000.
[101] U. Akgun , A. S. Ayan , G. Aydin , F. Duru , J. Olson and Y. Onel, "Afterpulse timing and rate investigation of three different Hamamatsu photomultiplier tubes," Journal of Instrumentation, vol. 3, Jan. 2008.
[102] http://www.becker-hickl.de/pdf/ampmt.pdf, 2010/9/30.
[103] Y. H. Tsneg and D. M. Tsai, "Defect detection of uneven brightness in low-contrast images using basis image representation," Pattern Recognition, vol. 43, pp. 1129-1141, Mar. 2010.
[104] H. I. Son, "Automatic inspection method for macro defects in TFT-LCD color filter fabrication process," IEICE Electronics Express, vol. 6, pp. 516-521, Apr. 2009.
[105] H. Il Son, "Automatic inspection method for macro defects in TFT-LCD color filter fabrication process," IEICE Electronics Express, vol. 6, pp. 516-521, Apr. 2009.
[106] O. Axner , F. M. Schmidt , A. Foltynowicz , J. Gustafsson , N. Omenetto and J. D. Winefordner, "Absorption spectrometry by narrowband light in optically saturated and optically pumped collision and Doppler broadened gaseous media under arbitrary optical thickness conditions," Applied Spectroscopy, vol. 60, pp. 1217-1240, Nov. 2006.
[107] Y. J. Xu and Q. L. Da, "Standard and mean deviation methods for linguistic group decision making and their applications," Expert Systems with Applications, vol. 37, pp. 5905-5912, Aug. 2010.
[108] S. R. Tripathi , M. Aoki , K. Mochizuki , I. Hosako , T. Asahi and N. Hiromoto, "Practical method to estimate the standard deviation in absorption coefficients measured with THz time-domain spectroscopy," Optics Communications, vol. 283, pp. 2488-2491, Jun. 2010.
[109] T. S. Liu, "Probability density function of small separation between two inertial particles in homogenous isotropic turbulence," Physics of Fluids, vol. 22, Apr. 2010.
[110] L. T. Santos , F. A. Dorini and M. C. C. Cunha, "The probability density function to the random linear transport equation," Applied Mathematics and Computation, vol. 216, pp. 1524-1530, May. 2010.
[111] http://en.wikipedia.org/wiki/Probability_Density_Function, 2010/9/30.
[112] D. J. Rumsey, "Teaching bits: "Random thoughts on teaching"," Journal of Statistics Education, vol. 18, pp. 1-4, 2010.
[113] C. Lee , A. Zeleke and H. Wachte, "Where do students get lost: The concept of variation," ICOTS6, pp. 1-4, 2002.
[114] F. C. Lin , Y. P. Huang , C. M. Wei and H. P. D. Shieh, "Color filter-Less LCDs in achieving high contrast and low power consumption by stencil field-sequential-color method," Journal of display technology, vol. 6, pp. 98-106, Mar. 2010.
[115] http://jp.hamamatsu.com/products/sensor-etd/pd002/pd395/index_en.html.
[116] http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg, 2010/9/30.