C6 Frequency Analysis of Optical Imaging Systems
C6 Frequency Analysis of Optical Imaging Systems
Ideal image
The geometrical-optics prediction of the image for a perfect imaging system
Convolution form of PSF
Image can be written as a convolution
Reduced coordinates
In order to achieve space invariance in the imaging operation, it is necessary to remove the effects of magnification and image inversion
where
Conclusion of the above analysis
Thus in this general case, for a diffraction-limited system we can regard the image as being a convolution of the image predicted by geometrical optics with an impulse response that is the Fraunhofer diffraction pattern of the exit pupil
the finite entrance pupil or the finite exit pupil
Abbe theory
Only a certain portion of the diffracted components generated by a complicated object are intercepted by this finite pupil
光学传感器
Optical Sensors1意义Optical methods are among the oldest and best-established techniques for sensing biochemical analytes.“快速发展”this chapter will focus on how to exploit the interaction of an analyte with optical radiation in order to obtain essential biochemical information.2Instrumentation2.1Optical Elementa light source——to generate a light beam with specific characteristics;direct this light to some modulating agent;a photodetector——processing the optical signal3光纤意义2009年诺贝尔物理学奖——英国华裔科学家高锟以及美国科学家威拉德·博伊尔和乔治·史密斯。
高锟在“有关光在纤维中的传输以用于光学通信方面”取得了突破性成就，他将获得今年物理学奖一半的奖金。
博伊尔和史密斯发明了半导体成像器件——电荷耦合器件（CCD）图像传感器，分享当年物理学奖另一半奖金。
1966年，高锟发表了一篇题为《光频率介质纤维表面波导》的论文，开创性地提出光导纤维在通信上应用的基本原理，描述了长程及高信息量光通信所需绝缘性纤维的结构和材料特性。
简单地说，只要解决好玻璃纯度和成分等问题，就能够利用玻璃制作光学纤维，从而高效传输信息。
1966年被全世界公认为光纤通信的发明年，论文的首席作者华裔高馄博士也就被全世界公认为光纤通信的发明家，由于他取得的成果，被称为“光纤之父”。
Wide-field Fourier transform spectral imaging
a r X i v :0802.3773v 1 [p h y s i c s .o p t i c s ] 26 F eb 2008Wide-field Fourier transform spectral imagingMichael Atlan and Michel GrossLaboratoire Kastler Brossel,´Ecole Normale Sup´e rieure,Universit´e Pierre et Marie-Curie -Paris 6,Centre National de la Recherche Scientifique,UMR 8552;24rue Lhomond,75005Paris,France(Dated:February 27,2008)We report experimental results of parallel measurement of spectral components of the light.The temporal fluctuations of an optical field mixed with a separate reference are recorded with a high throughput complementary metal oxide semi-conductor camera (1Megapixel at 2kHz framerate).A numerical Fourier transform of the time-domain recording enables wide-field coherent spectral imaging.Qualitative comparisons with frequency-domain wide-field laser Doppler imaging are pro-vided.Many coherent spectral detection schemes using a sin-gle detector (or balanced detection)to detect tempo-ral fluctuation spectra in an optical mixing configura-tion rely on Fourier Transform spectroscopy (FTS)for signal measurement [1,2].They provide a high spec-tral resolution and shot-noise sensitivity.They allow to shift away the 1/f noise of laser intensity fluctuations since the measurement is done with GHz-bandwidth de-tectors.Most imaging configurations require a spatial scanning of the beam,but two approaches to parallel co-herent spectral imaging with a solid-state array detector were presented recently :full-field laser Doppler imag-ing (LDI)[3,4,5]and frequency-domain wide-field LDI (FDLDI)[6,7,8].In the former approach,the tempo-ral fluctuations of an optical object field impinging on a complementary metal oxide semi-conductor (CMOS)camera are recorded.Spectral imaging is done by cal-culating the intensity-fluctuation spectrum by a Fourier transform (FT).One major weakness of this approach lies in its inapplicability in low-light conditions.The lat-ter approach uses a spatiotemporal heterodyne detection,which consists in recording an optical mix of the object field with an angularly tilted and frequency-shifted lo-cal oscillator (LO).It enables to measure spectral maps with a high sensitivity but requires to acquire the spectral components sequentially by sweeping the LO frequency.We present an alternative approach,designed to combine the advantages of both methods.It uses the properties of digital off-axis holography and FTS to enable exploring of the temporal frequency spectrum of the object field.Basically,the parallel spectral imaging instrument pre-sented here uses a CMOS camera to record the intensity fluctuations of an object field mixed with a separate ref-erence (LO);the field spectral components are calculated by FTS.The experimental setup is based on an optical interfer-ometer sketched in Fig.1.A CW,80mW,λ=658nm diode (Mitsubishi ML120G21)provides the main laser beam (field E L ,angular frequency ωL ).A small part of this beam is split by a prism to form a reference (LO)beam,while the remaining part is expanded and illu-minates an object in reflection with an averageincidenceFIG.1:Setup.LD :single mode laser diode.M :mirror.BE :beam expander.BS :beam splitter.E :object field.E LO :local oscillator field.angle α≈45◦.The object is made of a USAF 1951target set in front of a 4mm-thick transparent tank,filled with a non dilute intralipid (TM)10%emulsion.To benefit from heterodyne gain,the field scattered by the object,E ,is mixed with the LO field E LO (|E LO |2/|E |2∼103),and is detected by a CMOS camera (LaVision HighSpeedStar 4,10bit,1024×1024pixels at ωS /(2π)=2.0kHz frame rate,pixel area d pix 2with d pix =17.5µm,set at a dis-tance d =50cm from the object.A 10mm focal length lens is placed in the reference arm in order to create an off-axis (θ≈1◦tilt angle)virtual point source in the object plane.This configuration constitutes a lensless Fourier holographic setup [9].In the detector plane,the LO and object fields are:E LO (t )=E LO e iωL t +c.c.E (x,y,t )=E (x,y,t )e iωL t +c.c.(1)where c .c .is the complex conjugate term.The LO beam is a spherical wave propagating along z ,and thus the LO field envelope E LO does not depend on x,y,t .The object field envelope E ,which contains information on the ob-ject shape,and which may exhibit speckle,depends on position x,y .It also depends on time t because of dy-namic scattering.The intensity I recorded by the camera can be expressed as a function of the complex fields :I (x,y,t )=+E(x,y,t)E∗LO+E∗(x,y,t)E LO whereFIG.4:Spectrum of thefield dynamically backscattered by a non dilute suspension of intralipid10%obtained by averaging the objectfield intensity over50×50pixels.FTS(solid gray curve)and FDLDI(points)spectra.Horizontal axis is the frequencyω/(2π)in kHz,vertical axis is signal in linear arbitrary units.2048frequency pointsωare linearly spaced between theNyquist frequencies±1.0kHz.The measurement time of the1024×1024×2048data cube is≃1s,and the FT3D calculation time on a personal computer is about 1hour nowadays.Fig.3(a)to3(d)show the images of the objectfield intensity| E|2in the target plane for the fre-quency componentsω/(2π)=0(a),187.5(b),500.0(c)and937.5Hz(d)(128×256pixels crops of the total holo-gram,displayed in logarithmic scale).Forω=0(a),the LO beam noise is dominant and the target is not visible. Forω=0,the USAF target is visible but the bright-ness and SNR of the image will decrease with frequency ((b)to(d)).Fig.3(e)shows the image obtained by aver-aging over all frequencies.We have compared these re-sults with wide-field FDLDI images[6,7]obtained with a charge-coupled device(CCD)camera(PCO Pixelfly: 1280×1024pixels,framerate:8Hz)with four-phase de-modulation over32images per spectral point,in the same experiment.Fig.3shows the128×256pixels FDLDI im-ages at0(f),187.5(g),500.0(h)and937.5Hz(i),while image(j)corresponds to the average over all frequen-cies.The USAF target is seen on all the images.For ω=0,the target appears as a contrast-reversed image [6].Since the pixel size of the CCD camera(6.7×6.7µm) is smaller than its CMOS counterpart(17.5µm×17.5µm), the extension of FDLDI image is larger(the acceptance angle of the receiver is proportional to the inverse of the pixel size).The white dashed rectangle of Fig.3j corre-sponds to the CMOS-imagerfield of view.Although the number of recorded spectral points was kept low for the FDLDI measurement compared to the FTS scheme(64 vs.2048),the total measurement time was much greater (256seconds vs.1second).This difference is due to the throughput discrepancy between the CCD(1.3Mpixel@ 8Hz)and the CMOS(1.0Mpixel@2kHz)receivers. We have computed the frequency spectrum of the light diffused by the intralipid emulsion with FTS.This spec-trum is obtained by averaging the objectfield intensity over a50×50pixels region of the reconstructed image. The lineshape is plotted on Fig.4as a solid gray curve. We have compared its shape with the one obtained with the FDLDI technique(Fig.4points).The agreement is good except in the tails of the spectrum.The FTS fre-quency response is imperfectlyflat,because of the CCD finite exposure time(1/ωS)that yields signal low pass filtering[15,16].Moreover,because the signal temporal evolution is sampled at2kHz,temporal sampling aliases and spectrum overlap are expected around the Nyquist frequencies±1kHz.In this Letter,we have shown that the spatiotemporal heterodyne detection recently introduced[6,7,8]can be adapted to a wide-field Fourier transform spectral imag-ing scheme with a high throughput array detector.By using an off-axis optical mixing configuration,the object-LOfields cross terms are shifted away from center of the detector reciprocal plane(k-space),contrarily to the ob-ject and LO self-beating contributions,which remain un-shifted.It is then possible to reject the local oscillator and the objectfield self-beating contributions accounting for noise.The heterodyne gain provided by optical am-plification of the objectfield by the LOfield is essential for a high frame rate camera measurement in low-light conditions,since the objectfield intensity decreases with the camera exposure time.The ability tofilter-offthe LO beam noise,yields an optimal sensitivity of1photo-electron of noise per pixel.This limit has been reached with4-phase detection[17],which consists of a discrete Fourier transform on4data points to calculate a sin-gle frequency component of the objectfield.Here,the expected noise limit is the same for each frequency com-ponent of the objectfield obtained by discrete Fourier transform.This method mightfind applications in dy-namic light scattering analysis of colloidal suspensions and microfluidic systems.[1]E.Pike,Review of Physics in Technology1,180(1970).[2]D.Chung,K.Lee,and E.Mazur,Applied physics.B,Lasers and optics64,1(1997).[3]A.Serov,W.Steenbergen,and F.de Mul,Optics Letters27,300(2002).[4]A.Serov and sser,Opt.Express13,6416(2005).[5]A.Serov,B.Steinacher,and sser,Opt.Ex.13,3681(2005).[6]M.Atlan,M.Gross,T.Vitalis,A.Rancillac,B.C.For-get,and A.K.Dunn,Optics Letters31(2006).[7]M.Atlan and M.Gross,Review of Scientific Instruments77,1161031(2006).[8]M.Atlan and M.Gross,Journal of the Optical Societyof America A24,2701(2007).[9]G.W.Stroke,Applied Physics Letters6,201(1965).[10]U.Schnars and W.Juptner,Appl.Opt.33,179(1994).[11]C.Wagner,S.Seebacher,W.Osten,and W.Juptner,Applied Optics38,4812(1999).[12]U.Schnars and W.P.O.Juptner,Meas.Sci.Technol.13,R85(2002).[13]T.M.Kreis,Optical Engineering41,771(2002).[14]E.Cuche,P.Marquet,and C.Depeursinge,Applied Op-tics39,4070(2000).[15]P.Picart,J.Leval,D.Mounier,and S.Gougeon,Opt.Lett.28,1900(2003).[16]M.Atlan,M.Gross,and E.Absil,Optics Letters32,1456(2007).[17]M.Gross and M.Atlan,Optics Letters32,909(2007).。
光学仪器检测呼吸中的生物标志物
现代医学仪器与应用 2008 年第 20 卷第 1 期 M odeical Equipment and Application Feb. 2008. V故障及其排除方法了解得更清晰，为 以后的学习、工作打下坚实的实践基础。有利于学
策J]. 医 育 索 2006, 5(10): 927-928. [ 学教 探 ，
本研究应用的是简易型虚拟仿真技术， 该技术构 建的系统模型结构简单、 操作方便， 非常适合医学检 验实验教学， 也易于推广到其他检验教学仪器的模型 构建， 有较好的应用前景。
参考文献 fll 谢国明， 郑军. 医学检验仪器学实验教学面临的问题及对
孙丰荣， 刘泽， 李艳玲， 基于模型的CT 三维医学图像 等.
非常短的、 间隔一致的光脉冲， 每一脉冲仅有数飞米 的长度， 激光产生非常窄而又相等的间隙， 形成很宽 的光谱， 就像日 常用的梳子一样。 在实验中， 学生志愿者对光学腔呼气， 气体就在 腔中 被光脉冲 梳滤， 通过检测哪一种颜色的 光被吸收 和吸收的数量， 研究人员就能检查到特殊的分子和它 们的浓度。例如， 参加实验的人如果是吸烟者， 其呼
出的一氧化碳就是不吸烟者的 5 倍。这种光学梳可以
m onoxide), 氢过氧化物 (hydroperoxide) 、 亚硝酸盐 (nitrite) , 硝酸盐 (nitrate) 、 戊烷 (pentane) ,. 乙烷
(ethane) 这些重要的哮喘生物标志物，就能够更明 确地对哮喘进行诊断。 目前应用于呼吸成分的痕量检查的方法仪器体
孙连荣， 姜元章， 任玲. 虚拟现实技术及其在高校教学中的
生主动地、 理解性地学习，能有效地提高教学效率
和教学质量。
应用[J]. 石油教育， [ 2003, (5): 41- 44.
chapter 1(1)
ym +1 = Aym + Bθ m
θ m +1 = Cym + Dθ m
From these equation, we have
ym +1 − Aym B y − Aym +1 θ m +1 = m + 2 B
θm =
And then:
ym + 2 = 2bym +1 − F 2 ym
linear differential equations
ym A θ = C m
Fundamentals of Photonics
B y0 D θ 0
2011-4-27
m
ym +1 = Aym + Bθ m
θ m +1 = Cym + Dθ m
8
CHAPTER 1---- Optical Resonator
An optical resonator, the optical counterpart of an electronic resonant circuit, confines and stores light at certain resonance frequencies. It may be viewed as an optical transmission system incorporating feedback; light circulates or is repeatedly reflected within the system, without escaping.
ym = y0 F m sin(mφ + φ0 ) = ymax F m sin(mφ + φ0 )
化学专业英语-Instrumental Analysis
Wavelength selectors
For most spectroscopic analysis, radiation that consists of a limited, narrow, continuous group of wavelengths called a band is required. A narrow bandwidth enhances the sensitivity of the absorbance measurements, may provide selectivity to both emission and absorption method, and is frequently a requirement from the standpoint of obtaining a linear relationship between the optical signal and concentration. Ideally, the output from a wavelength selector would be radiation of single wavelength or frequency. No real wavelength selector even approaches this ideal. Two types of wavelength selector are encountered, filter and monochromator.
General properties of electromagnetic radiation
Many of the properties of electromagnetic radiation are conveniently described by means of a classical sinusoidal wave model, which embodies such parameters as wavelength, frequency, velocity, and amplitude. In contrast to other wave phenomena, such as sound, electromagnetic radiation requires no supporting medium for its transmission and thus passes readily through a vacuum. The wave model fails to account for phenomena associated with the absorption and emission of radiant energy. To understand these processes, it is necessary
Report-SE
Classical model
Microscopic roughness Interfaces Native oxide
Material + Ambient Mixture of neighboring materials Oxide + Voids Material (crystalline) + Amorphous material + Voids
• Inhomogeneity of OPSL layer • Proportion of materials • Total OPSL layer thickness • Refractive index evolution
Indium Tin Oxide (ITO) on glass Graded layer model with incohereness and index
Optical model
Parameter values
Lorentz oscillator
Ultra thin SiO2 layer on Si Film thickness and index
Optical model
Ultra Thin SiO2 Film
•Uniaxial anisotropy model •Optical axis normal to surface
Polymer Waveguide
Displays - OLED
Optical model
•EIL : Electron Injection Layer •ETL : Electron Transition Layer •EML : Emission Material Layer •HTL : Hole Transition Layer •HIL : Hole Injection Layer
光谱分析的课件
注意：考虑损耗时加入系数
ν m +1
频率
e −2α L
ㄱ
Free spectral range: 自由频谱宽度
12
① 相位谐振条件：一个来回光的相位变化为2π的整数倍
3.2.3 Interferometer-based optical spectrum analysis
迈克尔逊干涉仪 仪器结构原理——光路示意图
2009/09/14 Test and Measurement for Optical Devices and Systems
outline
3.1 Introduction 3.2 types of optical spectrum analyzers 3.3 anatomy of a diffraction-grating-based OSA 3.4 operation and key specifications of diffractiongrating-based OSA
反射系数
反射率： E R= r E0
2
=
δ 4 R1 R2 sin 2 2
(1 − R1 )(1 − R2 ) + 4
δ R1 R2 sin 2 2
基于相位光栅的超分辨率成像方法
Two classical techniques are widely used to image phase objects: phase contrast methods [1–3] and interferometry [16]. With modern development of electronic devices such as detectors, for instance CCD sensors, digital holography has become in a practical powerful tool for analysis and quantification of phase samples [4– 10]. In particular, a highly attractive interferometric configuration, named as common-path interferometry (CPI), provides significantly increased environmental stability and decreased system complexity in comparison with other interferometric architectures. CPI setup can be viewed as a classical Mach–Zehnder configuration with the particularity that both imaging and reference
光学常数的测量方法
数据分析－图谱处理 Constructing an IR Chemical Image
artificial pattern
Specific absorption band selected
数据分析－图谱处理
>C=O -CH stretching -OH
数据分析－图谱处理
>C=O -CH stretching -OH
Ce 薄膜
为获得完整的光学常数谱，需要进行 KK变换。一般说来，KK 变换原则上需要已知全波段上的吸收光谱和反射光谱数据，并 在光谱测量范围两端，尤其是远红外波段和远紫外端对已有光 谱测量数据作合理外推，同时可以用求和规则来检测和论证这 种外推以及KK变换结果的合理性。
椭圆偏振光谱
第二类方法： 椭圆偏振光谱法：通过反射光束或透射光束振幅衰减和相位改 变的同时测量，它可以经由光谱测量，而不必借助KK变换直 接求得被测样品的光学常数。
数据分析－图谱处理
傅里叶退卷积光谱：可以将严重重叠的谱带分开，增强红外光 谱的分辨能力。实测光谱是干涉图函数和切趾函数分别进行傅 里叶变换的卷积， 退卷积光谱就是将卷积得到的实测光谱退卷积，即将实测光 谱重新变成干涉图，然后选择一个合适的切趾函数与干涉图 相乘，再重新进行傅里叶变换就完成退卷积计算。
椭圆偏振光谱
其中： 对于均匀材料：
实际测量时，固定偏振片在0-90o间的 某些角度上，旋转分析器，可得到调 制的强度比。
椭偏光谱
椭圆偏振光谱
同步辐射椭偏光谱：掠角入射，高亮度的光源将 大大提高信号的强度
ANKA infrared beamline
特殊样品环境－变温
研究材料温度下的相变
小结
测量方式选择：根据样品情况选择
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When incoherent, the impulse responses in the image plane vary in uncorrelated herent imaging system is linear in intensity
Time-varying phasor
6.1.1 A Generalized Model
All imaging elements may be lumped into a single "black box" The significant properties of the system can be completely described by specifying only the terminal properties of the aggregate The "terminals" of this black box consist of the planes containing the entrance and exit pupils
where represents the mean or center frequency of the optical wave, then the complex function U(P, t) may be regarded as the time-varying phasor representation of u(P, t)
For a polychromatic wave u(P, t), we suppress all positive frequency components of its Fourier spectrum, and double its negative-frequency components
where
Conclusion of the above analysis
Thus in this general case, for a diffraction-limited system we can regard the image as being a convolution of the image predicted by geometrical optics with an impulse response that is the Fraunhofer diffraction pattern of the exit pupil
Amplitude point-spread function
The light amplitude about the ideal image point is simply the Fraunhofer diffraction pattern of the exit pupil
where the pupil function P is unity inside and zero outside the projected aperture
Reduced coordinates
In order to achieve space invariance in the imaging operation, it is necessary to remove the effects of magnification and image inversion
Ideal image
The geometrical-optics prediction of the image for a perfect imaging system
Convolution form of PSF
Image can be written as a convolution
We shall refer either to the exit pupil or simply to the "pupil" of the system
Diffraction-limited
An imaging system is said to be diffraction-limited if a diverging spherical wave is converted by the imaging system into a new perfectly spherical wave If the system has any aberrations, it is not diffraction-limited
Representation of illumination
In the case of monochromatic illumination it was convenient to represent the complex amplitude of the field by a complex phasor that was a function of space coordinates When the illumination is polychromatic but narrowband, it is represented by a time-varying phasor that depends on both time and space coordinates
6.1 GENERALIZED TREATMENT OF IMAGING SYSTEMS
We shall first broaden our discussion beyond a single thin positive lens, finding results applicable to more general systems of lenses And then remove the restriction to monochromatic light, obtaining results for "quasi-monochromatic" light
Regarding diffraction effects as resulting from the exit pupil
The image amplitude is represented by a superposition integral
In the absence of aberrations, the response h arises from a spherical wave (of limited extent) converging from the exit pupil towards the ideal image point (u = M, v = M).
6.1.3 Polychromatic Illumination
For the illumination generated by real optical sources, including lasers, is never perfectly monochromatic The statistical nature of the time variations of illumination amplitude and phase can influence the behavior of an imaging system in profound ways
When coherent, the impulse responses in the image plane must be added on a complex amplitude basis
A coherent imaging system is linear in complex amplitude
the finite entrance pupil or the finite exit pupil
Abbe theory
Only a certain portion of the diffracted components generated by a complicated object are intercepted by this finite pupil
Two types of illumination
spatially coherent
while any two object points may have different relative phases, their absolute phases are varying with time in a perfectly correlated way the phasor amplitudes at all points on the object are varying in totally uncorrelated fashions
6.1.2 Effects of Diffraction on the Image
Diffraction effects play a role only during passage of light from the object to the entrance pupil, or alternatively and equivalently, from the exit pupil to the image The image resolution is limited by
laser zirconium arc lamps
Incoherent light is obtained from diffuse or extended sources
gas discharges the sun