CN102628799A - Method and system of time-domain optical coherence tomography without depth scan - Google Patents
Method and system of time-domain optical coherence tomography without depth scan Download PDFInfo
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Abstract
Description
技术领域 technical field
本发明涉及光学相干层析成像(Optical Coherence Tomography,简称OCT),尤其涉及一种无需深度扫描的时域光学相干层析成像(Time-domain OpticalCoherence Tomography,简称TD-OCT)方法与系统。The present invention relates to optical coherence tomography (Optical Coherence Tomography, OCT for short), in particular to a method and system for Time-domain Optical Coherence Tomography (TD-OCT for short) without depth scanning.
背景技术 Background technique
光学相干层析成像(OCT)是近年来发展起来的一种光学层析成像技术,它能够对高散射介质如生物组织内部几个毫米深度范围内的微小结构进行高分辨率非侵入成像,在生物组织活体成像和医疗成像诊断等领域具有广泛的应用前景。Optical coherence tomography (OCT) is an optical tomography technology developed in recent years. It can perform high-resolution non-invasive imaging of microstructures within a few millimeters in highly scattering media such as biological tissues. It has broad application prospects in the fields of living tissue imaging and medical imaging diagnosis.
最早的OCT系统是时域光学相干层析成像系统(TD-OCT)(参见在先技术[1],D.Huang,E.A.Swanson,C.P.Lin,J.S.Schuman,W.G.St inson,W.Chang,M.R.Hee,T.Flotte,K.Gregory,C.A.Puliafito and J.G.Fujimoto,“Optical coherencetomography”,Science,Vol.254,pp.1178-1181,1991)。它通过光学参考臂的轴向深度扫描并记录相对应不同深度处的干涉信号强度得到样品的一维层析图(A-line)。TD-OCT的探测速度比较低,如果探测过程中被测样品有运动,就会容易产生运动模糊。如果强制提高TD-OCT的轴向深度扫描速度以增加探测速度会导致系统灵敏度的下降。The earliest OCT system was Time-Domain Optical Coherence Tomography (TD-OCT) (see prior art [1], D. Huang, E.A. Swanson, C.P. Lin, J.S. Schuman, W.G. Stinson, W. Chang, M.R. Hee , T. Flotte, K. Gregory, C.A. Puliafito and J.G. Fujimoto, "Optical coherencetomography", Science, Vol.254, pp.1178-1181, 1991). It scans the axial depth of the optical reference arm and records the interference signal intensity at different depths to obtain a one-dimensional tomogram (A-line) of the sample. The detection speed of TD-OCT is relatively low. If the measured sample moves during the detection process, motion blur will easily occur. If the axial depth scanning speed of TD-OCT is forced to increase to increase the detection speed, the system sensitivity will decrease.
频域光学相干层析成像系统(Fourier-domain Optical Coherence Tomography,简称FD-OCT)是一种新型OCT系统(参见在先技术[2],N.Nassif,B.Cense,B.H.Park,S.H.Yun,T.C.Chen,B.E.Bouma,G.J.Tearney and J.F.de Boer,“In vivo humanretinal imaging by ultrahigh-speed spectral domain optical coherencetomography”,Optics Letter,Vol.29,pp.480-482,2004),它通过探测干涉谱并对其作逆傅里叶变换得到样品的一维层析图(A-line),相对于早先的时域光学相干层析成像系统(TD-OCT)具有无需深度方向扫描、成像速度快和探测灵敏度高的优势,能更好地满足生物组织活体成像以及医疗成像诊断的实时性要求。但是,FD-OCT获得的层析图中包含着若干寄生像,限制了FD-OCT的应用。这些寄生像分别是:直流背景,自相干噪声和复共轭镜像。其中,直流背景和自相干噪声的存在降低了FD-OCT的信噪比,影响了成像质量;而复共轭镜像的存在,使FD-OCT无法区分正负光程差(探测光路相对参考光路的光程差),测量时待测样品只能置于零光程差位置的一侧,导致有效探测深度范围减少一半。另外,FD-OCT的信噪比随着光程差的增加也会急剧下降。Frequency domain optical coherence tomography (Fourier-domain Optical Coherence Tomography, referred to as FD-OCT) is a new type of OCT system (see prior art [2], N.Nassif, B.Cense, B.H.Park, S.H.Yun, T.C.Chen, B.E.Bouma, G.J.Tearney and J.F.de Boer, "In vivo humanretinal imaging by ultrahigh-speed spectral domain optical coherencetomography", Optics Letter, Vol.29, pp.480-482, 2004), it detects the interference spectrum and The one-dimensional tomogram (A-line) of the sample is obtained by inverse Fourier transform. Compared with the earlier time-domain optical coherence tomography system (TD-OCT), it has the advantages of no need for depth direction scanning, fast imaging speed and detection The advantage of high sensitivity can better meet the real-time requirements of biological tissue imaging and medical imaging diagnosis. However, the tomogram obtained by FD-OCT contains several parasitic images, which limits the application of FD-OCT. These spurious images are: DC background, autocoherent noise and complex conjugate image. Among them, the existence of DC background and self-coherent noise reduces the signal-to-noise ratio of FD-OCT and affects the imaging quality; and the existence of complex conjugate mirrors makes it impossible for FD-OCT to distinguish between positive and negative optical path differences (the detection optical path is relative to the reference optical path The optical path difference), the sample to be tested can only be placed on the side of the zero optical path difference position during measurement, resulting in a reduction of the effective detection depth range by half. In addition, the signal-to-noise ratio of FD-OCT will drop sharply as the optical path difference increases.
并行FD-OCT与传统基于单点照明的FD-OCT的主要区别在于,它通过采用线状光照明待测样品实现FD-OCT二维层析图(B-scan)的并行探测。(参见在先技术[3],Branislay Grajciar,Michael Pircher,Adolf F.Fercher and RainerA.Leitgeb,“Parallel Fourier domain optical coherence tomography for in vivomeasurement of the human eye”,Optics Express,Vol.13,pp.1131-1137,2005)。该方法一般通过在光路中添加柱面凸镜实现对待测样品的线状光照明,并利用二维光电探测阵列并行记录频域干涉条纹,重建得到一幅待测样品的二维层析图(B-scan)。并行FD-OCT由于避免了对待测样品的横向机械式扫描,成像速度更快,对运动模糊不敏感。但是,和传统的FD-OCT一样,并行FD-OCT仍然存在复共轭镜像寄生像等问题。The main difference between parallel FD-OCT and traditional FD-OCT based on single-point illumination is that it realizes the parallel detection of FD-OCT two-dimensional tomogram (B-scan) by using linear light to illuminate the sample to be tested. (See prior art [3], Branislay Grajciar, Michael Pircher, Adolf F.Fercher and RainerA.Leitgeb, "Parallel Fourier domain optical coherence tomography for in vivomeasurement of the human eye", Optics Express, Vol.13, pp.1131 -1137, 2005). This method generally realizes the linear light illumination of the sample to be tested by adding a cylindrical convex mirror in the optical path, and uses a two-dimensional photodetection array to record frequency-domain interference fringes in parallel, and reconstructs a two-dimensional tomogram of the sample to be tested ( B-scan). Parallel FD-OCT has faster imaging speed and is less sensitive to motion blur because it avoids the transverse mechanical scanning of the sample to be tested. However, like traditional FD-OCT, parallel FD-OCT still has problems such as complex conjugate mirror parasitic images.
发明内容 Contents of the invention
本发明的目的是为了克服上述在先技术的不足,提供一种无需深度扫描的时域光学相干层析成像的方法与系统。本发明只需一次曝光即可实现一维光学相干层析成像,具有结构简单、成像速度快、无寄生像、对运动模糊不敏感的特点。The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, and provide a time-domain optical coherence tomography method and system without depth scanning. The invention can realize one-dimensional optical coherence tomography imaging with only one exposure, and has the characteristics of simple structure, fast imaging speed, no parasitic image and insensitivity to motion blur.
本发明的技术解决方案如下:Technical solution of the present invention is as follows:
一种无需深度扫描的时域光学相干层析成像的方法,该方法是在时域光学相干层析成像方法的基础上,用柱面凸镜代替干涉参考臂的聚焦透镜形成线状参考光,并通过倾斜参考臂的参考平面反射镜在参考光线状长度方向上引入连续的光程差,用一维光电探测器阵列代替点光电探测器,获得待测样品同一个探测点连续不同深度处的干涉信号,通过去直流背景之后,对该干涉信号沿参考光线状长度方向作希尔伯特变换即可得到待测样品的层析图。A time-domain optical coherence tomography method without depth scanning, the method is based on the time-domain optical coherence tomography method, using a cylindrical convex mirror to replace the focusing lens of the interference reference arm to form a linear reference light, And by tilting the reference plane reflector of the reference arm, continuous optical path difference is introduced in the direction of the reference ray-like length, and the point photodetector is replaced by a one-dimensional photodetector array to obtain the same detection point of the sample to be tested at different depths. After the interference signal is removed from the DC background, the tomogram of the sample to be tested can be obtained by performing Hilbert transformation on the interference signal along the length direction of the reference light.
本发明无需深度扫描的时域光学相干层析成像的方法的具体步骤如下:The specific steps of the method for time-domain optical coherence tomography without depth scanning in the present invention are as follows:
①在时域光学相干层析成像方法的基础上,用柱面凸镜代替干涉参考臂的聚焦透镜形成线状参考光;①On the basis of the time-domain optical coherence tomography method, a cylindrical convex mirror is used to replace the focusing lens of the interference reference arm to form a linear reference light;
②使参考臂的参考平面反射镜在由线状参考光长度方向和参考光照明方向组成的平面内倾斜,在线状参考光线状长度方向上引入连续的光程差;参考光入射到倾斜平面反射镜上的入射角为θ,其中θ取值范围为-60°≤θ≤60°;② Make the reference plane reflector of the reference arm tilt in the plane composed of the length direction of the linear reference light and the illumination direction of the reference light, and introduce a continuous optical path difference in the length direction of the linear reference light; the reference light is incident on the inclined plane and reflected The incident angle on the mirror is θ, where the value range of θ is -60°≤θ≤60°;
③用一维光电探测器阵列代替点光电探测器,获得待测样品同一个探测点连续不同深度处的干涉信号;系统工作后,所述的一维光电探测器阵列记录的干涉信号如式(1)所示:③ Replace the point photodetectors with a one-dimensional photodetector array to obtain the interference signals at the same detection point of the sample to be tested at different depths; after the system works, the interference signals recorded by the one-dimensional photodetector array are as follows: 1) as shown:
其中:m是所述一维光电探测器阵列的探测单元序号,I(m)是所述一维光电探测器阵列第m个探测单元探测到的干涉信号强度;Isig、Iref、Iin分别是参考光信号强度、样品光信号强度和入射光信号强度;z是待测样品的相对纵向深度位置,p代表所述一维光电探测器阵列的单个探测单元宽度,σ代表被测样品到所述一维光电探测器阵列的成像放大率,z0是一个常数;R(z)是待测样品相对纵向深度位置z处的反射率或背向散射率;γ(m)是低相干光源的空间相干度函数,c是光速,是一个相位常数,*表示卷积运算;Wherein: m is the detection unit sequence number of the one-dimensional photodetector array, and I(m) is the interference signal intensity detected by the mth detection unit of the one-dimensional photodetector array; I sig , I ref , I in are the reference light signal intensity, the sample light signal intensity and the incident light signal intensity respectively; z is the relative longitudinal depth position of the sample to be measured, p represents the width of a single detection unit of the one-dimensional photodetector array, σ represents the imaging magnification of the measured sample to the one-dimensional photodetector array, z 0 is a constant; R(z) is the relative Reflectance or backscattering rate at longitudinal depth position z; γ(m) is the spatial coherence function of low-coherence light sources, c is the speed of light, Is a phase constant, * means convolution operation;
④对所述的干涉信号进行平均处理,得到直流背景如式(2)所示:④ The interference signal is averaged to obtain a DC background as shown in formula (2):
其中:M是所述一维光电探测器阵列的探测单元总数;将式(1)减去式(2),得到初步去除直流背景的干涉信号,如式(3)所示:Wherein: M is the detection unit total number of described one-dimensional photodetector array; Subtract formula (2) from formula (1), obtain the interference signal that removes the DC background initially, as shown in formula (3):
Inodc(m)=I(m)-Idc; (3)I nodc (m)=I(m) -Idc ; (3)
⑤对步骤④所得的式(3)作以m为变量的傅里叶变换得到式(4):5. the formula (3) of step 4. gained is done the Fourier transform with m as variable and obtains formula (4):
其中:fm代表对应m的傅里叶变换频谱,代表以m为变量的傅里叶变换;将式(4)信号先乘上一个区间大小为2π的矩形窗函数
E′nodc(fm)=Enodc(fm)·W(fm); (5)E' nodc (f m ) = E nodc (f m )·W(f m ); (5)
再将式(5)信号作以fm为变量的逆傅里叶变换得到完全去除直流背景的干涉信号,如式(6)所示:Then, the signal of formula (5) is subjected to inverse Fourier transform with f m as a variable to obtain the interference signal that completely removes the DC background, as shown in formula (6):
其中代表以fm为变量的逆傅里叶变换;in Represents the inverse Fourier transform with f m as a variable;
⑥对步骤⑤所得的去背景干涉信号(6)作以m为变量的希尔伯特变换得到式(7):6. To the background interference signal (6) obtained in step 5., do Hilbert transform with m as a variable to obtain formula (7):
其中代表以m为变量的希尔伯特变换;将信号式(6)和式(7)合成得到式(8),in Represents the Hilbert transform with m as a variable; the signal formula (6) and formula (7) are synthesized to obtain formula (8),
⑦将步骤⑥所得信号式(8)的自变量m转换为自变量z,即得到待测样品的一维层析图,如式(9)所示:⑦ Convert the independent variable m of the signal formula (8) obtained in step ⑥ into the independent variable z, that is, obtain the one-dimensional chromatogram of the sample to be tested, as shown in the formula (9):
I0(z)=4IrefIinR(z)*|γ(z)|。 (9)I 0 (z)=4I ref I in R(z)*|γ(z)|. (9)
⑧通过精密平移台对待测样品沿与照明光光轴方向垂直的平面作二维扫描,重复以上步骤②~⑦得到待测样品的三维层析图。⑧ Scan the sample to be tested in two dimensions along the plane perpendicular to the optical axis of the illumination light through the precision translation stage, and repeat the above steps ② to ⑦ to obtain the three-dimensional tomogram of the sample to be tested.
一种实现上述方法的无需深度扫描的时域光学相干层析成像系统,包括低相干光源,在低相干光源的照明方向上顺序放置准直扩束器和迈克尔逊干涉仪,该迈克尔逊干涉仪的分光器将入射光分为透射光束和反射光束,其特点在于:在所述的透射光束方向依次设置柱面透镜和倾斜摆放的平面反射镜构成参考臂光路,在所述的反射光束方向依次设置第一聚焦透镜和待测样品构成探测臂光路,所述的待测样品放置在一个精密移动平台上;在所述的迈克尔逊干涉仪输出端顺序放置第二聚焦透镜和一维光电探测器阵列;该一维光电探测器阵列通过图像数据采集卡和计算机连接;所述的柱面透镜将入射平行光会聚为线状光,产生一个线状参考光;所述的平面反射镜倾斜摆放,在参考光线状长度方向上引入连续的光程差;所述的柱面透镜的焦距和所述的第一聚焦透镜的焦距相同;所述的待测样品和平面反射镜分别与所述的一维光电探测器阵列构成物像共轭关系;所述的一维光电探测器阵列的探测单元阵列方向和所述的参考臂光路中的线状照明光长度方向在同一个平面内。A time-domain optical coherence tomography system without depth scanning for realizing the above method, including a low-coherence light source, a collimating beam expander and a Michelson interferometer are sequentially placed in the illumination direction of the low-coherence light source, and the Michelson interferometer The beam splitter divides the incident light into a transmitted beam and a reflected beam. Its characteristics are: in the direction of the transmitted beam, a cylindrical lens and a plane mirror placed obliquely are arranged in sequence to form a reference arm optical path, and in the direction of the reflected beam The first focusing lens and the sample to be tested are arranged in sequence to form the optical path of the detection arm, and the sample to be tested is placed on a precision mobile platform; the second focusing lens and the one-dimensional photodetector are sequentially placed at the output end of the Michelson interferometer device array; the one-dimensional photodetector array is connected to the computer through the image data acquisition card; the cylindrical lens converges the incident parallel light into a linear light to generate a linear reference light; the tilted pendulum of the plane reflector put, introduce continuous optical path difference in the reference ray-like length direction; the focal length of the cylindrical lens is the same as the focal length of the first focusing lens; The one-dimensional photodetector array constitutes a conjugate relationship of the object image; the direction of the detection unit array of the one-dimensional photodetector array and the length direction of the linear illumination light in the light path of the reference arm are in the same plane.
所述的低相干光源为宽带光源,其光谱典型半高全宽为几十纳米到几百纳米,如发光二极管或超辐射发光二极管或飞秒激光器或超连续谱光源等。The low-coherence light source is a broadband light source with a typical full width at half maximum of its spectrum ranging from tens of nanometers to hundreds of nanometers, such as light-emitting diodes or superluminescent light-emitting diodes or femtosecond lasers or supercontinuum light sources.
所述的准直扩束器由物镜和若干透镜组成。The collimating beam expander is composed of an objective lens and several lenses.
所述的一维光电探测器阵列是线阵CCD或线阵CMOS或线阵InGaAs或其它具有光电信号转换功能的一维探测器阵列。The one-dimensional photodetector array is a linear CCD or linear CMOS or linear InGaAs or other one-dimensional detector array with photoelectric signal conversion function.
所述的精密移动平台可以沿三个互相垂直方向做微米级精度的平移。The precision mobile platform can perform translation with micron-level precision along three mutually perpendicular directions.
该系统的工作情况如下:The system works as follows:
低相干光源发出的光经准直器扩束后,在迈克尔逊干涉仪中待分成两束,一束光经过参考臂,在柱面凸镜的会聚作用平面内聚焦,产生一个线状照明光,入射到倾斜的平面反射镜上,另一束光经探测臂入射到待测样品内,从平面反射镜回来的反射光和从待测样品内不同深度处反射或背向散射回来的样品光分别沿参考臂和探测臂返回,在迈克尔逊干涉仪中会合发生干涉,干涉信号经过聚焦透镜聚焦后由一维光电探测器阵列记录,经图像数据采集卡数模转换后送入计算机进行数据处理,得到待测样品沿照明光光轴方向的一个一维层析图。通过精密平移台对待测样品沿与照明光光轴方向垂直的平面作二维扫描,得到待测样品的三维层析图。The light emitted by the low-coherence light source is expanded by the collimator and split into two beams in the Michelson interferometer. One beam of light passes through the reference arm and is focused in the converging plane of the cylindrical convex mirror to produce a linear illumination light. , incident on the inclined plane mirror, another beam of light is incident on the sample to be tested through the detection arm, the reflected light from the plane mirror and the sample light reflected or backscattered from different depths in the sample to be tested Return along the reference arm and the detection arm respectively, and meet in the Michelson interferometer for interference. The interference signal is recorded by the one-dimensional photodetector array after being focused by the focusing lens, and sent to the computer for data processing after digital-to-analog conversion by the image data acquisition card. , to obtain a one-dimensional tomogram of the sample to be tested along the optical axis of the illumination light. The sample to be tested is scanned two-dimensionally along a plane perpendicular to the optical axis of the illumination light through a precision translation stage to obtain a three-dimensional tomogram of the sample to be tested.
与现有技术相比,本发明的有益效果是:Compared with prior art, the beneficial effect of the present invention is:
本发明无需深度扫描的时域光学相干层析成像的方法的特点是利用线状参考光和倾斜放置的平面参考反射镜在线状参考光长度方向上引入连续的光程差,使用空间滤波和希尔伯特变换分析方法一次性获得待测样品的一维层析信息,在不牺牲系统信噪比的情况下,提高成像速度,实现无需深度扫描的时域光学相干层析成像。The feature of the method of time-domain optical coherence tomography without depth scanning in the present invention is to introduce a continuous optical path difference in the length direction of the linear reference light by using a linear reference light and an obliquely placed plane reference mirror, using spatial filtering and Hill The Burt transform analysis method obtains the one-dimensional tomographic information of the sample to be tested at one time, improves the imaging speed without sacrificing the signal-to-noise ratio of the system, and realizes time-domain optical coherence tomography without deep scanning.
与在先技术1相比,本发明无需轴向深度扫描,成像速度快,对运动模糊不敏感,对干涉仪和样品的稳定性要求不高。Compared with the prior art 1, the present invention does not require axial depth scanning, has fast imaging speed, is insensitive to motion blur, and has low requirements on the stability of the interferometer and the sample.
与在先技术2和3相比,本发明系统结构简单,没有寄生像问题的困扰,图像信噪比不随光程差的增加而下降。Compared with the
附图说明 Description of drawings
图1为本发明无需深度扫描的时域光学相干层析成像系统的光路和结构示意图。FIG. 1 is a schematic diagram of the optical path and structure of the time-domain optical coherence tomography system without depth scanning according to the present invention.
具体实施方式 Detailed ways
下面结合实施例和附图对本发明作进一步说明,但不应以此限制本发明的保护范围。The present invention will be further described below in conjunction with the embodiments and accompanying drawings, but the protection scope of the present invention should not be limited thereby.
请参阅图1。图1为本发明无需深度扫描的时域光学相干层析成像系统的光路和结构示意图。由图1可见,本发明无需深度扫描的时域光学相干层析成像系统包括低相干光源1,在该低相干光源1的照明方向上顺序放置准直扩束器2、迈克尔逊干涉仪3,该迈克尔逊干涉仪3的分光棱镜31将入射光分为探测臂光路34和参考臂光路32,参考臂光路32的末端为一个柱面凸镜36和倾斜摆放的平面反射镜33,探测臂光路34的末端为一个聚焦透镜37和待测样品35,待测样品35放置在一个精密移动平台(图中未示)上;迈克尔逊干涉仪3输出端顺序放置聚焦透镜4和线阵CCD探测器5;线阵CCD探测器5通过图像数据采集卡6和计算机7连接。该系统的特点是所述参考臂光路32末端的柱面凸镜36将入射平行光会聚为线状光,产生一个线状参考光;所述参考臂光路32末端的倾斜平面反射镜33在参考光线状长度方向上引入连续的光程差。See Figure 1. FIG. 1 is a schematic diagram of the optical path and structure of the time-domain optical coherence tomography system without depth scanning according to the present invention. It can be seen from Fig. 1 that the time-domain optical coherence tomography system without depth scanning of the present invention includes a low-coherence light source 1, and a collimating beam expander 2 and a
所述的迈克尔逊干涉仪3中在平面反射镜33前的柱面凸镜36和待测样品35前的聚焦透镜37的焦距相同;所述的待测样品35和平面反射镜33分别与线阵CCD探测器5在系统光路上是物像共轭关系;所述的线阵CCD探测器5的探测单元阵列方向和所述的参考臂光路32中的线状照明光长度方向在同一个平面内。The focal length of the cylindrical
低相干光源1发出的宽光谱光经准直器2扩束后,在迈克尔逊干涉仪3中被分光棱镜31分成两束,一束透射光在参考臂光路32中经柱面凸镜36产生一个线状照明光,再被倾斜的平面反射镜33反射逆向返回;另一束反射光经探测臂光路34入射到放置在精密平移台(图中未示)上的待测样品35内,从平面反射镜33反射回来的光和从待测样品35内不同深度处反射或背向散射回来的光分别沿参考臂光路32和探测臂光路34返回,在迈克尔逊干涉仪3中汇合发生干涉,再经聚焦透镜4聚焦,成像在线阵CCD探测器5上,转换成电信号后,经图像数据采集卡6数模转换后送入计算机7进行数据处理,得到待测样品35沿照明光光轴方向的一个一维层析图。The wide-spectrum light emitted by the low-coherence light source 1 is expanded by the collimator 2, and then split into two beams by the
所述的参考臂光路32中的参考平面反射镜33在由线状参考光长度方向和参考光照明方向组成的平面内倾斜,参考光入射到倾斜平面反射镜33上的入射角为θ。The
所述的线阵CCD探测器5记录到所述的待测样品35同一个探测点连续不同深度处的干涉信号为:The interference signals recorded by the linear array CCD detector 5 at the same detection point of the sample to be tested 35 at different depths are:
其中:m是所述的线阵CCD探测器5的探测单元序号,I(m)是线阵CCD探测器5第m个探测单元探测到的干涉信号强度;Isig、Iref、Iin分别是参考光信号强度、样品光信号强度和入射光信号强度;z是待测样品35的相对纵向深度位置,p代表线阵CCD探测器5的单个探测单元宽度,σ=F2/F1代表一维成像系统的横向放大率,F1代表聚焦透镜37和柱面凸镜36的焦距,F2代表聚焦透镜4的焦距,z0是一个常数;R(z)是待测样品35相对纵向深度位置z处的反射率或背向散射率;γ(m)是所述低相干光源1的空间相干度函数,c是光速,是一个相位常数,*表示卷积运算。Wherein: m is the detection unit serial number of described linear array CCD detector 5, and I (m) is the interference signal intensity that the mth detection unit of linear array CCD detector 5 detects; I sig , I ref , I in respectively is the reference optical signal intensity, the sample optical signal intensity and the incident optical signal intensity; z is the relative longitudinal depth position of the sample to be measured 35, p represents the width of a single detection unit of the line array CCD detector 5, σ=F 2 /F 1 represents the lateral magnification of the one-dimensional imaging system, F 1 represents the focal length of the focusing
首先,对干涉信号式(10)进行平均处理,得到直流背景如式(11)所示:First, the interference signal formula (10) is averaged, and the DC background is obtained as shown in formula (11):
其中:M是线阵CCD探测器5的探测单元总数;将式(10)减去式(11),得到初步去除直流背景的干涉信号,如式(12)所示:Wherein: M is the total number of detection units of the linear array CCD detector 5; Subtract formula (11) from formula (10) to obtain the interference signal that initially removes the DC background, as shown in formula (12):
Inodc(m)=I(m)-Idc; (12)I nodc (m)=I(m) -Idc ; (12)
接着对信号式(12)作以m为变量的傅里叶变换得到式(13):Then do the Fourier transform of the signal formula (12) with m as a variable to obtain the formula (13):
其中:fm代表对应m的傅里叶变换频谱,代表以m为变量的傅里叶变换;将信号式(13)先乘上一个区间大小为2π的矩形窗函数
E′nodc(fm)=Enodc(fm)·W(fm); (14)E' nodc (f m ) = E nodc (f m )·W(f m ); (14)
再将信号式(14)作以fm为变量的逆傅里叶变换得到完全去除直流背景的干涉信号,如式(15)所示:Then take the signal formula (14) as the inverse Fourier transform with f m as the variable to obtain the interference signal that completely removes the DC background, as shown in formula (15):
其中代表以fm为变量的逆傅里叶变换。in Represents the inverse Fourier transform with f m as the variable.
对去除背景信息的干涉信号(15)作以m为变量的希尔伯特变换得到式(16):Hilbert transform the interference signal (15) with m as the variable to get the formula (16):
其中代表以m为变量的希尔伯特变换;将信号式(15)和式(16)合成得到式(17),in Represents the Hilbert transform with m as a variable; the signal formula (15) and formula (16) are synthesized to obtain formula (17),
I0(m)=|IHilbert(m)|2+|I′nodc(m)|2=4IrefIinR(z)*|γ(m)|; (17)I 0 (m)=|I Hilbert (m)| 2 +|I′ nodc (m)| 2 =4I ref I in R(z)*|γ(m)|; (17)
最后,将信号式(18)的自变量m转换为自变量z,即得到待测样品35的一维层析图,如式(18)所示:Finally, the independent variable m of the signal formula (18) is converted into the independent variable z, that is, the one-dimensional chromatogram of the
I0(z)=4IrefIinR(z)*|γ(z)|。 (18)I 0 (z)=4I ref I in R(z)*|γ(z)|. (18)
通过精密平移台(图中未示)对待测样品35沿与照明光光轴方向垂直的平面作二维扫描,重复以上过程得到待测样品35的三维层析图。The
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