拉曼光谱背景扣除算法及其应用研究
|
摘要
拉曼光谱是一种散射光谱,是光通过介质时入射光与分子相互作用而引起的频率发生变化的散射,是一种利用分子振动-转动信息的光谱分析法。它作为一种新兴发展起来的的分析手段可提供快速、简便、可重复,无需对样品进行前处理的检测,通过光纤探头或石英器皿就可直接测量,从而对物质进行无损伤、快速的定性定量分析。但测定过程中,样品含有杂质或荧光吸收物质时会产生荧光干扰,且当激发光子提供了足够的能量以致产生荧光时,拉曼信号将变模糊甚至被掩盖。因此通过寻求避免荧光干扰的方法来改进其应用成了拉曼光谱学家们一直致力的问题。部分物质在测量时虽然有荧光干扰,但荧光辐射不足以全部湮灭拉曼信号时,仍可采集下拉曼光谱,此时光谱有一定的荧光背景,影响数据的进一步分析。
本论文主要运用化学计量学的方法对拉曼背景扣除算法进行了研究,通过查找和阅读大量中外文献,对拉曼光谱原理、特点,拉曼光谱仪与拉曼光谱技术发展历程等内容做了概述。
本文通过引入了惩罚最小二乘(Penalized Least Squares)和小波系数收缩(Wavelet Shrinkage)等平滑算法来滤除拉曼光谱中的高频噪声,与本文介绍的几种预处理方法相比具有一定的优势。同时也介绍了建立聚类,判别分析与回归分析模型的化学计量学方法。
本文为扣除影响分析结果的荧光背景,我们提出了基于连续小波变换和惩罚最小二乘的算法baseline Wavelet,通过真实样本分析结果表明：所提出的背景扣除算法能在不丢失有效信息的前提下有效地将背景扣除。通过比较在滤除噪声和扣除背景前后建立聚类模型与判别分析模型,如PCA、Random Forest等模型,扣除背景后分离度和分类结果均有改善。另外分析了baseline Wavelet背景扣除算法中参数的设定对拟合背景平滑度的影响。
本文通过提出自适应迭代重加权惩罚最小二乘airPLS算法对大量的样本进行背景扣除来建立回归模型。它利用稀疏矩阵技术,该方法能够快速有效扣除光谱中荧光背景。通过实例分析airPLS算法在定量方面的应用。通过比较几种背景扣除算法后建立的回归分析模型,说明airPLS算法在几种方法中不仅具有好的效果且在在运算时间上也有很好的优势,适合大批量的样本集。
Raman spectroscopy is kind of scattering spectrum, which is caused by the light through the media and molecular interaction of the frequency changed by the scattering, using the information of vibrational rotational in a spectrometric method. It developed as a new analytical tools which provide fast, simple, repeatable, and samples need not pre-treatment, can measured directly by the fiber optic probe or through the quartz vessel. So it provides rapid and non destructive qualitative quantitative analysis. During the measurement procedure, as samples containing impurities or fluorescent material will bring the fluorescence interference and the excitation photon provides sufficient energy so that produce the fluorescence, the Raman signals will all be blurred or swamped by fluorescence.
Although Raman spectra of some materials have fluorescent interference, but the fluorescence radiation is not sufficient to swamp the Raman signal, which can still be collected with Raman instruments. The Raman spectra have a certain background, which will affect further analysis of spectra using chemometrics method. Raman background correction algorithms are studied in this thesis, the brief introduction about domestic and foreign researching status in the Raman spectra, the purpose and significance of this thesis, and the main contents and methods are presented. By finding and reading a lot of literature, the theory and characteristics of Raman spectroscopy, instrument and development of Raman techniques were outlined.
Penalized Least Squares and Wavelet Shrinkage are introduced in this paper to filter out high frequency noise in the Raman spectra. They have advantages when comparison with other soothing methods. Also we described the chemometric methods such as clustering, discriminant analysis and regression analysis model.
Again, based on continuous wavelet transform and penalized least squares algorithms, the baselineWavelet is proposed and applied for baseline correction. The results show that background correction without missing important information. By comparion of models of cluster and discriminant analysis, such as PCA, Random Forest, before and after filtering noise and background correction, the separability and classification results are respectively improved. The influence of the lambda parameter from baselineWavelet on the smoothness of the fitted baseline has been clearly explained and clarified.
We proposed the adaptive iterative re-weighted penalized least squares algorithm, which uses sparse matrix techniques to correct the baseline quickly and effectively. Since large number of samples is required for establishing the regression model. Example of quantitative analysis of airPLS algorithm is applied. By comparison of the built regression models which the spectra was pretreated with several baseline correction methods, the airpls baseline correction method has been demonstrated that it can fit the better baseline, have the smaller RMSECV values and require less computation time. The airpls method is very suitable for correcting the baseline of large amount calibration spectra when built the regression models with chemometrics algorithms.
本论文主要运用化学计量学的方法对拉曼背景扣除算法进行了研究,通过查找和阅读大量中外文献,对拉曼光谱原理、特点,拉曼光谱仪与拉曼光谱技术发展历程等内容做了概述。
本文通过引入了惩罚最小二乘(Penalized Least Squares)和小波系数收缩(Wavelet Shrinkage)等平滑算法来滤除拉曼光谱中的高频噪声,与本文介绍的几种预处理方法相比具有一定的优势。同时也介绍了建立聚类,判别分析与回归分析模型的化学计量学方法。
本文为扣除影响分析结果的荧光背景,我们提出了基于连续小波变换和惩罚最小二乘的算法baseline Wavelet,通过真实样本分析结果表明：所提出的背景扣除算法能在不丢失有效信息的前提下有效地将背景扣除。通过比较在滤除噪声和扣除背景前后建立聚类模型与判别分析模型,如PCA、Random Forest等模型,扣除背景后分离度和分类结果均有改善。另外分析了baseline Wavelet背景扣除算法中参数的设定对拟合背景平滑度的影响。
本文通过提出自适应迭代重加权惩罚最小二乘airPLS算法对大量的样本进行背景扣除来建立回归模型。它利用稀疏矩阵技术,该方法能够快速有效扣除光谱中荧光背景。通过实例分析airPLS算法在定量方面的应用。通过比较几种背景扣除算法后建立的回归分析模型,说明airPLS算法在几种方法中不仅具有好的效果且在在运算时间上也有很好的优势,适合大批量的样本集。
Raman spectroscopy is kind of scattering spectrum, which is caused by the light through the media and molecular interaction of the frequency changed by the scattering, using the information of vibrational rotational in a spectrometric method. It developed as a new analytical tools which provide fast, simple, repeatable, and samples need not pre-treatment, can measured directly by the fiber optic probe or through the quartz vessel. So it provides rapid and non destructive qualitative quantitative analysis. During the measurement procedure, as samples containing impurities or fluorescent material will bring the fluorescence interference and the excitation photon provides sufficient energy so that produce the fluorescence, the Raman signals will all be blurred or swamped by fluorescence.
Although Raman spectra of some materials have fluorescent interference, but the fluorescence radiation is not sufficient to swamp the Raman signal, which can still be collected with Raman instruments. The Raman spectra have a certain background, which will affect further analysis of spectra using chemometrics method. Raman background correction algorithms are studied in this thesis, the brief introduction about domestic and foreign researching status in the Raman spectra, the purpose and significance of this thesis, and the main contents and methods are presented. By finding and reading a lot of literature, the theory and characteristics of Raman spectroscopy, instrument and development of Raman techniques were outlined.
Penalized Least Squares and Wavelet Shrinkage are introduced in this paper to filter out high frequency noise in the Raman spectra. They have advantages when comparison with other soothing methods. Also we described the chemometric methods such as clustering, discriminant analysis and regression analysis model.
Again, based on continuous wavelet transform and penalized least squares algorithms, the baselineWavelet is proposed and applied for baseline correction. The results show that background correction without missing important information. By comparion of models of cluster and discriminant analysis, such as PCA, Random Forest, before and after filtering noise and background correction, the separability and classification results are respectively improved. The influence of the lambda parameter from baselineWavelet on the smoothness of the fitted baseline has been clearly explained and clarified.
We proposed the adaptive iterative re-weighted penalized least squares algorithm, which uses sparse matrix techniques to correct the baseline quickly and effectively. Since large number of samples is required for establishing the regression model. Example of quantitative analysis of airPLS algorithm is applied. By comparison of the built regression models which the spectra was pretreated with several baseline correction methods, the airpls baseline correction method has been demonstrated that it can fit the better baseline, have the smaller RMSECV values and require less computation time. The airpls method is very suitable for correcting the baseline of large amount calibration spectra when built the regression models with chemometrics algorithms.
引文
[1]Raman C V, Krishnan K S. A new type of secondary radiation. Nature,1928, 121(3048):501～502.
[2]Landsberg G, Mandelstam L. Eine neue Erscheinung bei der Lichtzerstreuung in Krystallen. Naturwissenschaften,1928,16:557～558.
[3]常建华,董绮功.波谱原理及解析[M].北京：科学出版社,2001.
[4]邓开发.激光技术与应用[M].长沙：国防科技大学出版社,2002.
[5]Pelletier M J. Analytical applications of Raman spectroscopy[M]. Wiley-Blackwell,1999.
[6]Vankeirsbilck T, Vercauteren A, Baeyens W, et al. Applications of Raman spectroscopy in pharmaceutical analysis. TrAC trends in analytical chemistry, 2002,21(12):869-877.
[7]de Veij M, Deneckere A, Vandenabeele P, et al. Detection of counterfeit Viagra (R) with Raman spectroscopy. Journal of Pharmaceutical and Biomedical Analysis,2008,46(2):303～309.
[8]Mazurek S, Szostak R. Quantification of atorvastatin calcium in tablets by FT-Raman spectroscopy. Journal of Pharmaceutical and Biomedical Analysis, 2009,49(1):168～172.
[9]Mazurek S, Szostak R. Quantitative determination of captopril and prednisolone in tablets by FT-Raman spectroscopy. Journal of Pharmaceutical and Biomedical Analysis,2006,40(5):1225～1230.
[10]谭红琳,李智东.乙醇,甲醇,食用酒用工业酒精的拉曼光谱测定.云南工业大学学报,1999,15(2)：1～3.
[11]周殿凤.拉曼光谱在中药注射剂鉴定中的应用初探.光学仪器,2008,30(6)：42～44.
[12]吴小琼,郑建珍,刘文涵,等.激光拉曼光谱内标法测定葡萄糖液浓度.光谱学与光谱分析,2007,27(7)：1344～1346.
[13]马寒露,董英,张孝芳,等.拉曼光谱法快速检测掺入梨汁的浓缩苹果汁.分析测试学报,2009,28(5)：535～538.
[14]袁洪福,陆婉珍.现代光谱分析中常用的化学计量学方法.现代科学仪器,1998,5：6～9.
[15]Wold S, Esbensen K, Geladi P. Principal component analysis. Chemometrics and intelligent laboratory systems,1987,2(1-3):37～52.
[16]Eisen M B, Spellman P T, Brown P O, et al. Cluster analysis and display of genome-wide expression patterns. Proceedings of the National Academy of Sciences of the United States of America,1998,95(25):14863.
[17]Geladi P, Kowalski B R. Partial least-squares regression:a tutorial. Analytica ChimicaActa,1986,185:1～17.
[18]Liu R X, Kuang J, Gong Q, et al. Principal component regression analysis with. Computer methods and programs in biomedicine,2003,71(2):141～147.
[19]Andrews D F. A robust method for multiple linear regression. Technometrics, 1974,16(4):523～531.
[20]Liang Y Z, Leung A K M, Chau F T. A roughness penalty approach and its application to noisy hyphenated chromatographic two-way data. Journal of Chemometrics,1999,13(5):511～524.
[21]Boelens H F M, Dijkstra R J, Eilers P H C, et al. New background correction method for liquid chromatography with diode array detection, infrared spectroscopic detection and raman spectroscopic detection. Journal of Chromatography A,2004,1057(1-2):21～30.
[22]Mazet V, Carteret C, Brie D, et al. Background removal from spectra by designing and minimising a non-quadratic cost function. Chemometrics and Intelligent Laboratory Systems,2005,76(2):121～133.
[23]Shao X G, Cai W S, Pan Z X. Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis. Chemometrics and Intelligent Laboratory Systems,1999,45(1-2):249～256.
[24]Ruckstuhl A F, Jacobson M P, Field R W, et al. Baseline subtraction using robust local regression estimation. Journal of Quantitative Spectroscopy and Radiative Transfer,2001,68(2):179～193.
[25]Ferraro J R, Nakamoto K, Brown C W. Introductory raman spectroscopy[M]. Academic Pr:2003.
[26]刘照军,赵存华,韩礼刚,等.现代高分辨拉曼光谱仪的配置及应用研究.光谱学与光谱分析,2010,2(2)：567～570.
[27]Campion A, Kambhampati P. Surface-enhanced Raman scattering. Chemical Society Reviews,1998,27(4):241～250.
[28]Bishop C M, SpringerLink. Pattern recognition and machine learning[M]. Springer New York:2006.
[29]中国科学院大连化学物理研究所分子光谱组.改用激光器做光源的拉曼光谱仪.分析化学,1975(03)：230～233.
[30]张敏,张建锋,李林强,等.激光拉曼探针在流体包裹体研究中的应用.世界核地质科学,2007,24(04)：238～244.
[31]Bowden M, Gardiner D J, Rice G, et al. Line scanned micro Raman spectroscopy using a cooled CCD imaging detector. Journal of Raman Spectroscopy,1990,21(1):37～41.
[32]Angel S M, Myrick M L. Near-infrared surface-enhanced Raman spectroscopy using a diode laser. Analytical Chemistry,1989,61(15):1648～1652.
[33]贾鹏,张行愚,王青圃,等.激光二极管抽运的自拉曼Nd:YVO_4激光器.中国激光,2006,33(10)：1309～1313.
[34]Wang Y, McCreery R L. Evaluation of a diode laser/charge coupled device spectrometer for near-infrared Raman spectroscopy. Analytical Chemistry, 1989,61(23):2647～2651.
[35]Colthup N B, Daly L H, Wiberley S E. Introduction to infrared and Raman spectroscopy[M]. Academic press New York:1990.
[36]朱贵云,杨景和.激光光谱分析法[M].北京：科学出版社,1989.
[37]程光煦.拉曼布里渊散射：原理及应用[M].北京：科学出版社,2001.
[38]周宇超.拉曼光谱仪.中国医学装备,2004,1(04)：58～59.
[39]尤静林,黄世萍,童朝阳,等.高温拉曼光谱仪.光学仪器,1999,21(01)：21～26.
[40]刘可滇.便携式拉曼光谱仪的设计.分析仪器,2009(04)：22～25.
[41]孙家远.拉曼光谱测量系统中的光学结构设计：[硕士学位论文].长春：长春理工大学,2009.
[42]Miller F A, Harney B M. Variable temperature sample holder for Raman spectroscopy. Applied spectroscopy,1970,24(2):291～292.
[43]Hansen P B, Eskildsen L, Stentz J, et al. Rayleigh scattering limitations in distributed Raman pre-amplifiers. Photonics Technology Letters, IEEE,1998, 10(1):159～161.
[44]胡永明,陈哲,孟洲,等.全保偏光纤迈克尔逊干涉仪.中国激光,1997,24(10)：891～894.
[45]Baraga J J, Feld M S, Rava R P. Rapid near-infrared Raman spectroscopy of human tissue with a spectrograph and CCD detector. Applied spectroscopy, 1992,46(2):187～190.
[46]Wollman S T, Bohn P W. Evaluation of polynomial fitting functions for use with CCD arrays in Raman spectroscopy. Applied spectroscopy,1993,47(1): 125～126.
[47]Hirschfeld T, Chase B. FT-Raman spectroscopy:development and justification. Applied spectroscopy,1986,40(2):133～137.
[48]Taylor L S, Zografi G. The quantitative analysis of crystallinity using FT-Raman spectroscopy. Pharmaceutical research,1998,15(5):755～761.
[49]Andrade P O, Bitar R A, Yassoyama K, et al. Study of normal colorectal tissue by FT-Raman spectroscopy. Analytical and Bioanalytical Chemistry,2007, 387(5):1643～1648.
[50]Robert B. Resonance Raman spectroscopy. Photosynthesis research,2009, 101(2):147～155.
[51]Spiro T G. Resonance Raman spectroscopy. New structure probe for biological chromophores. Accounts of Chemical Research,1974,7(10):339～344.
[52]Kneipp K, Wang Y, Kneipp H, et al. Single molecule detection using surface-enhanced Raman scattering (SERS). Physical Review Letters,1997, 78(9):1667～1670.
[53]Ozaki Y, Cho R, Ikegaya K, et al. Potential of near-infrared Fourier transform Raman spectroscopy in food analysis. Appl. Spectrosc,1992,46(10): 1503～1507.
[54]Mizuno A, Kitajima H, Kawauchi K, et al. Near infrared Fourier transform Raman spectroscopic study of human brain tissues and tumours. Journal of Raman Spectroscopy,1994,25(1):25～29.
[55]Nie S, Marzilli P A, Marzilli L G, et al. Near-infrared Fourier transform Raman spectroscopy of photolabile organocobalt B12 and model compounds.3. Vibrational assessment of factors affecting the cobalt-carbon bond in models. Journal of the American Chemical Society,1990,112(16):6084～6091.
[56]Pappas D, Smith B W, Winefordner J D. Raman spectroscopy in bioanalysis. Talanta,2000,51(1):131～144.
[57]郑楚生,郑凯文.拉曼光谱在宝玉石鉴定中的应用.光散射学报,2000,12(1)：15～21.
[58]李睿,周金池,卢存福.拉曼光谱在生物学领域的应用.生物技术通报,2009(12)：62～64.
[59]褚明福,邹乐西,仲敬荣.拉曼和红外光谱在核材料研究中的应用.稀有 金属,2005,29(01)：106～111.
[60]陈健,肖凯军,林福兰.拉曼光谱在食品分析中的应用.食品科学,2007,28(12)：554～558.
[61]Baena J R, Lendl B. Raman spectroscopy in chemical bioanalysis. Current Opinion in Chemical Biology,2004,8(5):534～539.
[62]Griffiths J. Raman spectroscopy for medical diagnosis. Anal Chem,2007, 79(11):3975～3978.
[63]李现常,张石定,崔亚量.拉曼光谱在考古学中的应用及进展.科技信息,2009,29～30.
[64]Bersani D, Lottici P P. Applications of Raman spectroscopy to gemology. Analytical and Bioanalytical Chemistry,397(7):2631～2646.
[65]Hanlon E B, Manoharan R, Koo T W, et al. Prospects for in vivo Raman spectroscopy. Physics in Medicine and Biology,2000,45(2):1～59.
[66]祖恩东,孙一丹,张鹏翔.天然、合成红宝石的拉曼光谱分析.光谱学与光谱分析,2010,30(8)：2164～2166.
[67]冯敏,王玉芳,郝建民,等.拉曼光谱方法研究SiC晶体的晶型.光散射学报,2003,15(3)：158～161.
[68]李占龙,周密,左剑,等.红外光谱和拉曼光谱法分析玉米种子的成分.分析化学,2007,35(11)：1636-1638.
[69]梁逸曾,吴海龙,俞汝勤.化学计量学.现代科学仪器,1998,(5)：3～6.
[70]Savitzky A, Golay M J E. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry,1964,36(8):1627～1639.
[71]Madden H H. Comments on the Savitzky-Golay convolution method for least-squares-fit smoothing and differentiation of digital data. Analytical Chemistry,1978,50(9):1383～1386.
[72]Steinier J, Termonia Y, Deltour J. Smoothing and differentiation of data by simplified least square procedure. Analytical Chemistry,1972,44(11): 1906～1909.
[73]Gorry P A. General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method. Analytical Chemistry,1990,62(6): 570～573.
[74]Cooley J W, Tukey J W. An algorithm for the machine calculation of complex Fourier series. Math. Comput,1965,19(90):297～201.
[75]Eilers P H C. A Perfect Smoother. Analytical Chemistry,2003,75(14): 3631-3636.
[76]Whittaker E T. On a New Method of Graduation. Proceedings of the Edinburgh Mathematical Society,1922,41(1):63～75.
[77]Green P J, Silverman B W. Nonparametric regression and generalized linear models:a roughness penalty approach[M]. Chapman & Hall/CRC:1994.
[78]Eilers P H C, Boelens H F M. baseline correction with asymmetric least squares smoothing.2005, http://www.science.uva.nl/-hboelens/publications/draftpub/Eilers_2005.pdf.
[79]Daubechies I. Ten lectures on wavelets[M]. Society for Industrial Mathematics, 1992.
[80]Alsberg B K, Woodward A M, Winson M K, et al. Wavelet denoising of infrared spectra. Analyst,1997,122(7):645～652.
[81]Ehrentreich F, Sumchen L. Spike removal and denoising of Raman spectra by wavelet transform methods. Analytical Chemistry,2001,73(17):4364～4373.
[82]Tan H W, Brown S D. Wavelet analysis applied to removing non constant, varying spectroscopic background in multivariate calibration. Journal of Chemometrics,2002,16(5):228～240.
[83]Alsberg B K, Woodward A M, Kell D B. An introduction to wavelet transforms for chemometricians:A time-frequency approach. Chemometrics and intelligent laboratory systems,1997,37(2):215～239.
[84]Donoho D L. De-noising by soft-thresholding. Information Theory, IEEE Transactions on,1995,41(3):613～627.
[85]Mallat S G. A wavelet tour of signal processing[M]. Academic Pr:1999.
[86]Starck J L, Candes E J, Donoho D L. The curvelet transform for image denoising. Image Processing, IEEE Transactions on,2002,11(6):670～684.
[87]O'Grady A, Dennis A C, Denvir D, et al. Quantitative Raman spectroscopy of highly fluorescent samples using pseudosecond derivatives and multivariate analysis. Analytical Chemistry,2001,73(9):2058～2065.
[88]Hu Y, Jiang T, Shen A, et al. A background elimination method based on wavelet transform for Raman spectra. Chemometrics and intelligent laboratory systems,2007,85(1):94～101.
[89]Carlos Cobas J, Bernstein M A, Mart-Pastor M, et al. A new general-purpose fully automatic baseline-correction procedure for 1D and 2D NMR data. Journal of Magnetic Resonance,2006,183(1):145～151.
[90]Lindgren F, Geladi P, Wold S. The kernel algorithm for PLS. Journal of Chemometrics,1993,7(1):45～59.
[91]Dayal B S, MacGregor J F. Improved PLS algorithms. Journal of Chemometrics,1997,11(1):73-85.
[92]Martin A. A comparison of nine PLS1 algorithms. Journal of Chemometrics, 2009,23(10):518～529.
[93]Barker M, Rayens W. Partial least squares for discrimination. Journal of Chemometrics,2003,17(3):166～173.
[94]Breiman L, Friedman J, Olshen R, et al. Classification and Regression Trees[M]. Wadsworth and Brooks:Monterey, CA,1984.
[95]Breiman L. Random Forests. Machine Learning,2001,45(1):5～32.
[96]Breiman L. Bagging predictors. Machine Learning,1996,24(2):123～140.
[97]Vapnik V N. The nature of statistical learning theory[M]. Springer Verlag: 2000.
[98]Li H, Liang Y, Xu Q. Support vector machines and its applications in chemistry. Chemometrics and Intelligent Laboratory Systems,2009,95(2):188～198.
[99]Boser B E, Guyon I M, Vapnik V N. A training algorithm for optimal margin classifiers. Proceedings of the fifth annual workshop on Computational learning theory,1992,144～152.
[100]Schokopf B, Smola A J, Williamson R C, et al. MIT Press,2000,12: 1207～1245.
[101]Martens H, Naes T. Multivariate calibration[M]. John Wiley & Sons Inc,1992.
[102]Manne R. Analysis of two partial-least-squares algorithms for multivariate calibration. Chemometrics and Intelligent Laboratory Systems,1987,2(1～3): 187～197.
[103]Zhang Z M, Chen S, Liang Y Z, et al. An intelligent background correction algorithm for highly fluorescent samples in Raman spectroscopy. Journal of Raman Spectroscopy,2010,41(6):659～669.
[104]Zhang Z M, Chen S, Liang Y Z. Baseline correction using adaptive iteratively reweighted penalized least squares. Analyst,2010,135(5):1138～1146.
[2]Landsberg G, Mandelstam L. Eine neue Erscheinung bei der Lichtzerstreuung in Krystallen. Naturwissenschaften,1928,16:557～558.
[3]常建华,董绮功.波谱原理及解析[M].北京：科学出版社,2001.
[4]邓开发.激光技术与应用[M].长沙：国防科技大学出版社,2002.
[5]Pelletier M J. Analytical applications of Raman spectroscopy[M]. Wiley-Blackwell,1999.
[6]Vankeirsbilck T, Vercauteren A, Baeyens W, et al. Applications of Raman spectroscopy in pharmaceutical analysis. TrAC trends in analytical chemistry, 2002,21(12):869-877.
[7]de Veij M, Deneckere A, Vandenabeele P, et al. Detection of counterfeit Viagra (R) with Raman spectroscopy. Journal of Pharmaceutical and Biomedical Analysis,2008,46(2):303～309.
[8]Mazurek S, Szostak R. Quantification of atorvastatin calcium in tablets by FT-Raman spectroscopy. Journal of Pharmaceutical and Biomedical Analysis, 2009,49(1):168～172.
[9]Mazurek S, Szostak R. Quantitative determination of captopril and prednisolone in tablets by FT-Raman spectroscopy. Journal of Pharmaceutical and Biomedical Analysis,2006,40(5):1225～1230.
[10]谭红琳,李智东.乙醇,甲醇,食用酒用工业酒精的拉曼光谱测定.云南工业大学学报,1999,15(2)：1～3.
[11]周殿凤.拉曼光谱在中药注射剂鉴定中的应用初探.光学仪器,2008,30(6)：42～44.
[12]吴小琼,郑建珍,刘文涵,等.激光拉曼光谱内标法测定葡萄糖液浓度.光谱学与光谱分析,2007,27(7)：1344～1346.
[13]马寒露,董英,张孝芳,等.拉曼光谱法快速检测掺入梨汁的浓缩苹果汁.分析测试学报,2009,28(5)：535～538.
[14]袁洪福,陆婉珍.现代光谱分析中常用的化学计量学方法.现代科学仪器,1998,5：6～9.
[15]Wold S, Esbensen K, Geladi P. Principal component analysis. Chemometrics and intelligent laboratory systems,1987,2(1-3):37～52.
[16]Eisen M B, Spellman P T, Brown P O, et al. Cluster analysis and display of genome-wide expression patterns. Proceedings of the National Academy of Sciences of the United States of America,1998,95(25):14863.
[17]Geladi P, Kowalski B R. Partial least-squares regression:a tutorial. Analytica ChimicaActa,1986,185:1～17.
[18]Liu R X, Kuang J, Gong Q, et al. Principal component regression analysis with. Computer methods and programs in biomedicine,2003,71(2):141～147.
[19]Andrews D F. A robust method for multiple linear regression. Technometrics, 1974,16(4):523～531.
[20]Liang Y Z, Leung A K M, Chau F T. A roughness penalty approach and its application to noisy hyphenated chromatographic two-way data. Journal of Chemometrics,1999,13(5):511～524.
[21]Boelens H F M, Dijkstra R J, Eilers P H C, et al. New background correction method for liquid chromatography with diode array detection, infrared spectroscopic detection and raman spectroscopic detection. Journal of Chromatography A,2004,1057(1-2):21～30.
[22]Mazet V, Carteret C, Brie D, et al. Background removal from spectra by designing and minimising a non-quadratic cost function. Chemometrics and Intelligent Laboratory Systems,2005,76(2):121～133.
[23]Shao X G, Cai W S, Pan Z X. Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis. Chemometrics and Intelligent Laboratory Systems,1999,45(1-2):249～256.
[24]Ruckstuhl A F, Jacobson M P, Field R W, et al. Baseline subtraction using robust local regression estimation. Journal of Quantitative Spectroscopy and Radiative Transfer,2001,68(2):179～193.
[25]Ferraro J R, Nakamoto K, Brown C W. Introductory raman spectroscopy[M]. Academic Pr:2003.
[26]刘照军,赵存华,韩礼刚,等.现代高分辨拉曼光谱仪的配置及应用研究.光谱学与光谱分析,2010,2(2)：567～570.
[27]Campion A, Kambhampati P. Surface-enhanced Raman scattering. Chemical Society Reviews,1998,27(4):241～250.
[28]Bishop C M, SpringerLink. Pattern recognition and machine learning[M]. Springer New York:2006.
[29]中国科学院大连化学物理研究所分子光谱组.改用激光器做光源的拉曼光谱仪.分析化学,1975(03)：230～233.
[30]张敏,张建锋,李林强,等.激光拉曼探针在流体包裹体研究中的应用.世界核地质科学,2007,24(04)：238～244.
[31]Bowden M, Gardiner D J, Rice G, et al. Line scanned micro Raman spectroscopy using a cooled CCD imaging detector. Journal of Raman Spectroscopy,1990,21(1):37～41.
[32]Angel S M, Myrick M L. Near-infrared surface-enhanced Raman spectroscopy using a diode laser. Analytical Chemistry,1989,61(15):1648～1652.
[33]贾鹏,张行愚,王青圃,等.激光二极管抽运的自拉曼Nd:YVO_4激光器.中国激光,2006,33(10)：1309～1313.
[34]Wang Y, McCreery R L. Evaluation of a diode laser/charge coupled device spectrometer for near-infrared Raman spectroscopy. Analytical Chemistry, 1989,61(23):2647～2651.
[35]Colthup N B, Daly L H, Wiberley S E. Introduction to infrared and Raman spectroscopy[M]. Academic press New York:1990.
[36]朱贵云,杨景和.激光光谱分析法[M].北京：科学出版社,1989.
[37]程光煦.拉曼布里渊散射：原理及应用[M].北京：科学出版社,2001.
[38]周宇超.拉曼光谱仪.中国医学装备,2004,1(04)：58～59.
[39]尤静林,黄世萍,童朝阳,等.高温拉曼光谱仪.光学仪器,1999,21(01)：21～26.
[40]刘可滇.便携式拉曼光谱仪的设计.分析仪器,2009(04)：22～25.
[41]孙家远.拉曼光谱测量系统中的光学结构设计：[硕士学位论文].长春：长春理工大学,2009.
[42]Miller F A, Harney B M. Variable temperature sample holder for Raman spectroscopy. Applied spectroscopy,1970,24(2):291～292.
[43]Hansen P B, Eskildsen L, Stentz J, et al. Rayleigh scattering limitations in distributed Raman pre-amplifiers. Photonics Technology Letters, IEEE,1998, 10(1):159～161.
[44]胡永明,陈哲,孟洲,等.全保偏光纤迈克尔逊干涉仪.中国激光,1997,24(10)：891～894.
[45]Baraga J J, Feld M S, Rava R P. Rapid near-infrared Raman spectroscopy of human tissue with a spectrograph and CCD detector. Applied spectroscopy, 1992,46(2):187～190.
[46]Wollman S T, Bohn P W. Evaluation of polynomial fitting functions for use with CCD arrays in Raman spectroscopy. Applied spectroscopy,1993,47(1): 125～126.
[47]Hirschfeld T, Chase B. FT-Raman spectroscopy:development and justification. Applied spectroscopy,1986,40(2):133～137.
[48]Taylor L S, Zografi G. The quantitative analysis of crystallinity using FT-Raman spectroscopy. Pharmaceutical research,1998,15(5):755～761.
[49]Andrade P O, Bitar R A, Yassoyama K, et al. Study of normal colorectal tissue by FT-Raman spectroscopy. Analytical and Bioanalytical Chemistry,2007, 387(5):1643～1648.
[50]Robert B. Resonance Raman spectroscopy. Photosynthesis research,2009, 101(2):147～155.
[51]Spiro T G. Resonance Raman spectroscopy. New structure probe for biological chromophores. Accounts of Chemical Research,1974,7(10):339～344.
[52]Kneipp K, Wang Y, Kneipp H, et al. Single molecule detection using surface-enhanced Raman scattering (SERS). Physical Review Letters,1997, 78(9):1667～1670.
[53]Ozaki Y, Cho R, Ikegaya K, et al. Potential of near-infrared Fourier transform Raman spectroscopy in food analysis. Appl. Spectrosc,1992,46(10): 1503～1507.
[54]Mizuno A, Kitajima H, Kawauchi K, et al. Near infrared Fourier transform Raman spectroscopic study of human brain tissues and tumours. Journal of Raman Spectroscopy,1994,25(1):25～29.
[55]Nie S, Marzilli P A, Marzilli L G, et al. Near-infrared Fourier transform Raman spectroscopy of photolabile organocobalt B12 and model compounds.3. Vibrational assessment of factors affecting the cobalt-carbon bond in models. Journal of the American Chemical Society,1990,112(16):6084～6091.
[56]Pappas D, Smith B W, Winefordner J D. Raman spectroscopy in bioanalysis. Talanta,2000,51(1):131～144.
[57]郑楚生,郑凯文.拉曼光谱在宝玉石鉴定中的应用.光散射学报,2000,12(1)：15～21.
[58]李睿,周金池,卢存福.拉曼光谱在生物学领域的应用.生物技术通报,2009(12)：62～64.
[59]褚明福,邹乐西,仲敬荣.拉曼和红外光谱在核材料研究中的应用.稀有 金属,2005,29(01)：106～111.
[60]陈健,肖凯军,林福兰.拉曼光谱在食品分析中的应用.食品科学,2007,28(12)：554～558.
[61]Baena J R, Lendl B. Raman spectroscopy in chemical bioanalysis. Current Opinion in Chemical Biology,2004,8(5):534～539.
[62]Griffiths J. Raman spectroscopy for medical diagnosis. Anal Chem,2007, 79(11):3975～3978.
[63]李现常,张石定,崔亚量.拉曼光谱在考古学中的应用及进展.科技信息,2009,29～30.
[64]Bersani D, Lottici P P. Applications of Raman spectroscopy to gemology. Analytical and Bioanalytical Chemistry,397(7):2631～2646.
[65]Hanlon E B, Manoharan R, Koo T W, et al. Prospects for in vivo Raman spectroscopy. Physics in Medicine and Biology,2000,45(2):1～59.
[66]祖恩东,孙一丹,张鹏翔.天然、合成红宝石的拉曼光谱分析.光谱学与光谱分析,2010,30(8)：2164～2166.
[67]冯敏,王玉芳,郝建民,等.拉曼光谱方法研究SiC晶体的晶型.光散射学报,2003,15(3)：158～161.
[68]李占龙,周密,左剑,等.红外光谱和拉曼光谱法分析玉米种子的成分.分析化学,2007,35(11)：1636-1638.
[69]梁逸曾,吴海龙,俞汝勤.化学计量学.现代科学仪器,1998,(5)：3～6.
[70]Savitzky A, Golay M J E. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry,1964,36(8):1627～1639.
[71]Madden H H. Comments on the Savitzky-Golay convolution method for least-squares-fit smoothing and differentiation of digital data. Analytical Chemistry,1978,50(9):1383～1386.
[72]Steinier J, Termonia Y, Deltour J. Smoothing and differentiation of data by simplified least square procedure. Analytical Chemistry,1972,44(11): 1906～1909.
[73]Gorry P A. General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method. Analytical Chemistry,1990,62(6): 570～573.
[74]Cooley J W, Tukey J W. An algorithm for the machine calculation of complex Fourier series. Math. Comput,1965,19(90):297～201.
[75]Eilers P H C. A Perfect Smoother. Analytical Chemistry,2003,75(14): 3631-3636.
[76]Whittaker E T. On a New Method of Graduation. Proceedings of the Edinburgh Mathematical Society,1922,41(1):63～75.
[77]Green P J, Silverman B W. Nonparametric regression and generalized linear models:a roughness penalty approach[M]. Chapman & Hall/CRC:1994.
[78]Eilers P H C, Boelens H F M. baseline correction with asymmetric least squares smoothing.2005, http://www.science.uva.nl/-hboelens/publications/draftpub/Eilers_2005.pdf.
[79]Daubechies I. Ten lectures on wavelets[M]. Society for Industrial Mathematics, 1992.
[80]Alsberg B K, Woodward A M, Winson M K, et al. Wavelet denoising of infrared spectra. Analyst,1997,122(7):645～652.
[81]Ehrentreich F, Sumchen L. Spike removal and denoising of Raman spectra by wavelet transform methods. Analytical Chemistry,2001,73(17):4364～4373.
[82]Tan H W, Brown S D. Wavelet analysis applied to removing non constant, varying spectroscopic background in multivariate calibration. Journal of Chemometrics,2002,16(5):228～240.
[83]Alsberg B K, Woodward A M, Kell D B. An introduction to wavelet transforms for chemometricians:A time-frequency approach. Chemometrics and intelligent laboratory systems,1997,37(2):215～239.
[84]Donoho D L. De-noising by soft-thresholding. Information Theory, IEEE Transactions on,1995,41(3):613～627.
[85]Mallat S G. A wavelet tour of signal processing[M]. Academic Pr:1999.
[86]Starck J L, Candes E J, Donoho D L. The curvelet transform for image denoising. Image Processing, IEEE Transactions on,2002,11(6):670～684.
[87]O'Grady A, Dennis A C, Denvir D, et al. Quantitative Raman spectroscopy of highly fluorescent samples using pseudosecond derivatives and multivariate analysis. Analytical Chemistry,2001,73(9):2058～2065.
[88]Hu Y, Jiang T, Shen A, et al. A background elimination method based on wavelet transform for Raman spectra. Chemometrics and intelligent laboratory systems,2007,85(1):94～101.
[89]Carlos Cobas J, Bernstein M A, Mart-Pastor M, et al. A new general-purpose fully automatic baseline-correction procedure for 1D and 2D NMR data. Journal of Magnetic Resonance,2006,183(1):145～151.
[90]Lindgren F, Geladi P, Wold S. The kernel algorithm for PLS. Journal of Chemometrics,1993,7(1):45～59.
[91]Dayal B S, MacGregor J F. Improved PLS algorithms. Journal of Chemometrics,1997,11(1):73-85.
[92]Martin A. A comparison of nine PLS1 algorithms. Journal of Chemometrics, 2009,23(10):518～529.
[93]Barker M, Rayens W. Partial least squares for discrimination. Journal of Chemometrics,2003,17(3):166～173.
[94]Breiman L, Friedman J, Olshen R, et al. Classification and Regression Trees[M]. Wadsworth and Brooks:Monterey, CA,1984.
[95]Breiman L. Random Forests. Machine Learning,2001,45(1):5～32.
[96]Breiman L. Bagging predictors. Machine Learning,1996,24(2):123～140.
[97]Vapnik V N. The nature of statistical learning theory[M]. Springer Verlag: 2000.
[98]Li H, Liang Y, Xu Q. Support vector machines and its applications in chemistry. Chemometrics and Intelligent Laboratory Systems,2009,95(2):188～198.
[99]Boser B E, Guyon I M, Vapnik V N. A training algorithm for optimal margin classifiers. Proceedings of the fifth annual workshop on Computational learning theory,1992,144～152.
[100]Schokopf B, Smola A J, Williamson R C, et al. MIT Press,2000,12: 1207～1245.
[101]Martens H, Naes T. Multivariate calibration[M]. John Wiley & Sons Inc,1992.
[102]Manne R. Analysis of two partial-least-squares algorithms for multivariate calibration. Chemometrics and Intelligent Laboratory Systems,1987,2(1～3): 187～197.
[103]Zhang Z M, Chen S, Liang Y Z, et al. An intelligent background correction algorithm for highly fluorescent samples in Raman spectroscopy. Journal of Raman Spectroscopy,2010,41(6):659～669.
[104]Zhang Z M, Chen S, Liang Y Z. Baseline correction using adaptive iteratively reweighted penalized least squares. Analyst,2010,135(5):1138～1146.