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1、第第2讲几何光学和眼几何光学和眼睛睛第1页，共53页，编辑于2022年，星期一Magnification Power透镜的透镜的放大倍率放大倍率Often,positive lenses are rated with a single magnification,such as 4x.In principle,any positive lens can be used at an infinite number of possible magnifications.However,when a viewer adjusts the object distance so that the ima
2、ge appears to be essentially at infinity(which is a comfortable viewing distance for most individuals(明视距离明视距离),the magnification is given by the relationship:Object under observationThus,a 25-mm focal-length positive lens would be a 10 x magnifier！那么，那么，50 x的镜头的焦距是多少？（提问）的镜头的焦距是多少？（提问）Magnification
3、=250 mm/f 第2页，共53页，编辑于2022年，星期一Virtual Images 虚像虚像When the object is less than one focal length away from a lens,no image occurs,but a virtual image is said to occur if you look back through the lens.Objectf 0Virtual imagefdof第3页，共53页，编辑于2022年，星期一fIt depends on how much of the lens is used,that is,t
4、he aperture 孔径光阑.Only one plane(平面）is imaged(i.e.,is in focus)at a time.But wed like objects near this plane to at least be almost in focus.The range of distances in acceptable focus is called the depth of field.Out-of-focus planeFocal planeObjectImageSize of blur in out-of-focus planeApertureThe sm
5、aller the aperture,the more the depth of field 通过孔径越小，焦深就越大.Depth of Field 焦深焦深孔径(光阑)第4页，共53页，编辑于2022年，星期一The pinhole camera 针孔照相机针孔照相机You can make an entire room into a camera this way by cutting a small hole in a wall and looking at the opposite wall.This is called the camera obscura.ObjectImagePi
6、nholeIf all light rays are directed through a pinhole,it forms an image with an infinite depth of field.The first person to mention this idea was Aristotle.The concept of the focal length is inappropriate for a pinhole lens.The magnification is still di/do.意大利Torino都灵大教堂耶稣裹尸布造假事件思考：针孔照相机的优点是什么？什么情况下
7、会用针孔照相机？我们常用的照相机为什么不用针孔照相机？（提问）第5页，共53页，编辑于2022年，星期一都灵的主教堂都灵的主教堂圣乔瓦尼大教堂圣乔瓦尼大教堂（Duono di San Giovsnni,Piazza San Giovanni）第6页，共53页，编辑于2022年，星期一如何发现裹尸布是造假的？如何发现裹尸布是造假的？第7页，共53页，编辑于2022年，星期一The F-number,“f/#”,of a lens is the ratio of its focal length and its diameter.f/#=f/dffd1fd2f/#=1f/#=2Large f-nu
8、mber lenses collect more light but are harder to engineer.F-number光圈光圈F值值f完整的照相机光圈是：f1，f1.4，f2，f2.8，f4，f5.6，f8，f11，f16，f22，f32，f44，f64第8页，共53页，编辑于2022年，星期一Another measure of a lens size is the numerical aperture.Its the product of the medium refractive index and the marginal ray angle.NA =n sin(a)Hi
9、gh-numerical-aperture lenses are bigger.faNumerical Aperture 数值孔径数值孔径Why this definition?Because the magnification can be shown to be the ratio of the NA on the two sides of the lens.第9页，共53页，编辑于2022年，星期一F/#and NA光圈光圈F值与数值孔径之间的关系值与数值孔径之间的关系In many cases,the best coupling you can get occurs when you
10、match the f/#between optical systems.Realistic f/#s:lens 2fibers 1.5数值孔径匹配的重要性。例题：把数值孔径2.0的光学系统耦合到数值孔径为1.5的光学系统中，光通量耦合效率是多少？第10页，共53页，编辑于2022年，星期一And this arrangementmaps position to angle:Lenses can also map angle to position.From the object to the image,we have:1)A distance f2)A lens of focal leng
11、th f3)A distance f出射角和入射光源位置有关没有放大率，位置只和入射角有关第11页，共53页，编辑于2022年，星期一Prism 棱镜棱镜顶角棱镜的全内反射棱镜的全内反射可作指纹读取器可作指纹读取器偏向角Deviation angleApex angle第12页，共53页，编辑于2022年，星期一FTIR and fingerprintingSee TIR from a fingerprint valley and FTIR from a ridge.第13页，共53页，编辑于2022年，星期一Prism pair for dispersion compensation棱镜对可
12、以用来补偿色散棱镜对可以用来补偿色散The minimum deviation angle when Brewster incidenceThe apex angle at Brewster incidence第14页，共53页，编辑于2022年，星期一Dispersion of plane glass and prism第15页，共53页，编辑于2022年，星期一Telescopes望远镜望远镜A telescope should image an object,but,because the object will have a very small solid angle,it shou
13、ld also increase its solid angle significantly,so it looks bigger.So wed like D to be large and use two lenses to square the effect.where M=-di/doSo use di do for both lenses.Note that this is easy for the first lens,as the object is really far away!M1M2Image plane#1Image plane#2Keplerian telescope第
14、16页，共53页，编辑于2022年，星期一Telescope Terminology 望远镜术语望远镜术语第17页，共53页，编辑于2022年，星期一Telescopes(contd)The Galilean Telescope:one negative and one positive lensesThe merit?f1 0The analysis of this telescope is a homework problem!第18页，共53页，编辑于2022年，星期一The Cassegrain Telescope卡塞格林望远镜卡塞格林望远镜Telescopes must collec
15、t as much light as possible from the generally very dim objects many light-years away.Its easier to create large mirrors than large lenses(only the surface needs to be very precise).ObjectIt may seem like the image will have a hole in it,but only if its out of focus.If a 45-mirror reflects the beam
16、to the side before the smaller mirror,its called a Newtonian telescope.牛顿望远镜第19页，共53页，编辑于2022年，星期一No discussion of telescopes would be complete without a few pretty pictures.NGC 6543-Cats Eye Nebula 星云-one of the most complex planetary nebulae ever seenGalaxy Messier 81Uranus 天王星 is surrounded by it
17、s four major rings and by 10 of its 17 known satellites 第20页，共53页，编辑于2022年，星期一Microscopes显显微镜微镜Image plane#2Microscopes work on the same principle as telescopes,except that the object is really close and we wish to magnify it.When two lenses are used,its called a compound microscope.Standard distanc
18、es are s=250 mm for the eyepiece and s=160 mm for the objective,where s is the image distance beyond one focal length.In terms of s,the magnification of each lens is given by:The magnification of the microscope is the M1M2Image plane#1Eye-pieceObjectivef1f2第21页，共53页，编辑于2022年，星期一If an optical system
19、lacks cylindrical symmetry,we must analyze its x-and y-directions separately:Cylindrical lenses 柱透镜柱透镜A spherical lens focuses in both transverse directions.A cylindrical lens focuses in only one transverse direction.When using cylindrical lenses,we must perform two separate ray-matrix analyses,one
20、for each transverse direction.第22页，共53页，编辑于2022年，星期一Large-angle reflection off a curved mirror also destroys cylindrical symmetry 反射镜的入射角过大会导致柱面不对称反射镜的入射角过大会导致柱面不对称Optic axis before reflectionOptic axis after reflectionThe optic axis makes a large angle with the mirror normal,and rays make an angle
21、with respect to it.Rays that deviate from the optic axis in the plane of incidence are called“tangential子午面.”Rays that deviate from the optic axis to the plane of incidence are called“sagittal弧矢面.“(We need a 3D display to show one of these.)tangential ray第23页，共53页，编辑于2022年，星期一Ray Matrix for Off-Axis
22、 Reflection from a Curved Mirror 反射镜离轴反射矩阵反射镜离轴反射矩阵If the beam is incident at a large angle,q,on a mirror with radius of curvature,R:where Re=R cosq for tangential rays 子午and Re=R/cosq for sagittal rays 弧矢ROptic axistangential ray 子午q第24页，共53页，编辑于2022年，星期一Aberrations 像差像差Aberrations are distortions
23、that occur in images,usually due to imperfections in lenses,some unavoidable,some avoidable.They include:Chromatic aberration 色差Spherical aberration 球差Astigmatism 像散Coma 慧差Curvature of field 场弯曲Pincushion and Barrel distortion 畸变Aberrations cant be modeled with ray matrices.Designers beat them by ma
24、king lenses with multiple elements,that is,several lenses in a row.Some zoom lenses can have as many as a dozen or so lenses.栅（枕）形畸变桶形畸变第25页，共53页，编辑于2022年，星期一Chromatic Aberration 色差色差Because the lens material has a different refractive index for each wavelength,the lens will have a different focal l
25、ength for each wavelength.Recall the lens-makers formula:Here,the refractive index is larger for blue than red,so the focal length is less for blue than red.第26页，共53页，编辑于2022年，星期一Chromatic aberration can also be minimized using additional lenses色差可以用附加透镜消除色差可以用附加透镜消除In an Achromat,the second lens ca
26、ncels the dispersion of the first.Achromats use two different materials,and one has a negative focal length.第27页，共53页，编辑于2022年，星期一Spherical Aberration in Mirrors 反射反射镜球差镜球差For all rays to converge to a point a distance f away from a curved mirror requires a paraboloidal surface.抛物面镜可消除反射球差 But this
27、only works for rays with qin=0.但是仅仅对平行光成立Spherical surfaceParaboloidal surface第28页，共53页，编辑于2022年，星期一Spherical Aberration in Lenses透镜球差透镜球差So we use spherical surfaces,which work better for a wider range of input angles.Nevertheless,off-axis rays see a different focal length.Lenses have spherical abe
28、rration,too.第29页，共53页，编辑于2022年，星期一Minimizing spherical aberration in a focusPlano-convex lenses(with their flat surface facing the focus)are best for minimizing spherical aberration when focusing.One-to-one imaging works best with a symmetrical lens(q=).R1=Front surface radius of curvatureR2=Back su
29、rface radius of curvature轴向球差横向球差注意：同样的平凸透镜，入射方向不同，像差也不同入射方向LALA最小球差最小球差第30页，共53页，编辑于2022年，星期一Spherical aberration can be minimized using additional lenses两个镜子可以消两个镜子可以消除球差除球差The additional lenses cancel the spherical aberration of the first.第31页，共53页，编辑于2022年，星期一Astigmatism 像散像散When the system lack
30、s cylindrical symmetry,we say it has astigmatism.A simple cylindrical lens or off-axis curved-mirror reflection will cause this problem.qCure astigmatism with another cylindrical lens or off-axis curved mirror.布儒斯特角切割的介质也可补偿像散弧矢面焦点子午面焦点第32页，共53页，编辑于2022年，星期一布儒斯特角切割的介质也可补偿像散M1M2M3M4P1P2pumpTi:sTi:sap
31、phire oscillator setup第33页，共53页，编辑于2022年，星期一Coma 慧差慧差Coma causes rays from an off-axis point of light in the object plane to create a trailing comet-like blur directed away from the optic axis.A lens with considerable coma may produce a sharp image in the center of the field,but become increasingly
32、blurred toward the edges.For a single lens,coma can be partially corrected by bending the lens.第34页，共53页，编辑于2022年，星期一Curvature of field 像场弯曲像场弯曲Curvature of field causes a planar object to project a curved(non-planar)image.Rays at a large angle see then lens as having an effectively smaller diameter
33、 and an effectively smaller focal length,forming the image of the off axis points closer to the lens.第35页，共53页，编辑于2022年，星期一Pincushion and Barrel DistortionThese distortions are fixed by an“orthoscopic doublet”or a“Zeiss orthometer.”第36页，共53页，编辑于2022年，星期一Photography lenses 照相机透镜组照相机透镜组Double GaussPet
34、zvalPhotography lenses are complex!Especially zoom lenses.These are older designs.Modern lenses can have 10 elements!第37页，共53页，编辑于2022年，星期一Geometrical Optics terms 厚透镜厚透镜第38页，共53页，编辑于2022年，星期一Commercial softwares for optical designs 可免费下载实验室有http:/ of the Eye人人眼解剖学眼解剖学Eye slides courtesy of Prasad K
35、rishna,Optics I student 2003.Incoming light第40页，共53页，编辑于2022年，星期一The cornea,iris,and lens 角膜、瞳孔和晶状体角膜、瞳孔和晶状体The cornea is a thin membrane that has an index of refraction of around 1.38.It protects the eye and refracts light(more than the lens does!)as it enters the eye.Some light leaks through the c
36、ornea,especially when its blue.The iris controls the size of the pupil,an opening that allows light to enter through.The lens is jelly-like lens with an index of refraction of about 1.44.This lens bends so that the vision process can be fine tuned.When you squint,you are bending this lens and changi
37、ng its properties so that your vision is clearer.The ciliary muscles bend and adjust the lens.第41页，共53页，编辑于2022年，星期一Near-sightedness(myopia)近视近视In nearsightedness,a person can see nearby objects well,but has difficulty seeing distant objects.Objects focus before the retina.This is usually caused by
38、an eye that is too long or a lens system that has too much power to focus.Myopia is corrected with a negative-focal-length lens.This lens causes the light to diverge slightly before it enters the eye.Near-sightedness轴性近视和调节性近视视力表的数值不等于近视度数。例如，1.0=200度第42页，共53页，编辑于2022年，星期一Far-sightedness(hyperopia)远
39、视远视Far-sightedness(hyperopia)occurs when the focal point is beyond the retina.Such a person can see distant objects well,but has difficulty seeing nearby objects.This is caused by an eye that is too short,or a lens system that has too little focusing power.Hyperopia is corrected with a positive-foca
40、l-length lens.The lens slightly converges the light before it enters the eye.Far-sightednessAs we age,our lens hardens,so were less able to adjust and more likely to experience far-sightedness.Hence“bifocals.”第43页，共53页，编辑于2022年，星期一Astigmatism is a common problem in the eye.眼像散眼像散第44页，共53页，编辑于2022年，星
41、期一Retina vs digital camera第45页，共53页，编辑于2022年，星期一Spatial response of retina:lateral connections第46页，共53页，编辑于2022年，星期一Temporal response:after images第47页，共53页，编辑于2022年，星期一激光视力矫正术激光视力矫正术 屈光不正是人类共同的、最常见和最普遍的眼病。资料表明，世界平均近视发生率为22%，远视患者数目和近视相近。我国近视发生率为31%，是近视眼患病率最高的国家之一。现代屈光手术是以70年代出现的放射状角膜切开术（RK）为开端，它是屈光手术
42、发展史上的一个光辉里程碑，八十年代初期，IBM的科学家探讨使用准分子激光蚀刻半导体芯片，1983年美国的Trokel医生证实准分子激光可以用于角膜切削和塑形，从而引发了眼科屈光手术的革命。LASIK技术上世纪90年代初传入中国。10年来，各家医疗机构技术、设备跟随着国际视光学技术发展的脚步不断升级。1995年美国FDA批准PRK的中、低度近视的临床应用，1999年通过LASIK(用于高度近视、远视及散光的临床治疗)。1999年底美国已经有100万例LASIK。我国于1992年引进准分于激光开展PRK，随后开展LASIK。估计目前我国已有700800台各类型号的准分子激光治疗仪。准分子激光手术在
43、全球其他国家已开展了近16年，而且已经很普及了，国内也开展8年多了，是目前国际眼科屈光领域最热门的学科，也是公认的目前最先进的矫正成人近视、远视、散光的治疗方法，其安全性、精确性、效果的长久性等都获得了美国FDA认证。目前准分子激光矫正屈光不正手术以LASIK为主。第48页，共53页，编辑于2022年，星期一角膜屈光度矫正手術（物理刀）LASIK用紫外激光（准分子激光器）在角膜表面做烧蚀（ablation）角膜表面曲率变化使焦点恢复到视网膜上(2 of failure，而且有眩光)。第49页，共53页，编辑于2022年，星期一Schematic representation of incisi
44、on created by a scanned photo disrupting laser pulse train.Though any pattern can be realized,high speed scanning of a moderately strongly focused beam is best achieved with a scanning geometry that is cylindrically symmetric.The spot-to-spot spacing and individual photo disruption feature size dete
45、rmine the smoothness and quality of the incisional plane.角膜屈光度矫正手术（飞秒激光刀）FS-LASIK第50页，共53页，编辑于2022年，星期一Intraoperative and postoperative photographs of femtosecond laser flap creation:(a)surgical view of planar resection after corneal applanation,demonstrating beginning of layer of microcavitations 1
46、60 m below the corneal surface;(b)continued scanning produces a plane at the desired flap diameter;(c)successive arc cuts are stacked as the scanning objective lens is moved away from the cornea to create the hinged side-cut flap architecture;(d)and(e)elevated corneal flap demonstrating well-defined
47、 side cuts and excellent tissue bed quality;(f)typical postoperative appearance at 1 week.第51页，共53页，编辑于2022年，星期一6.Your friend Alice uses corrective eyeglasses of power-10D.a)When Alice is not using her eyeglasses,is her retina located in front of or behind her eyes focal plane?b)When you look at Ali
48、ces eye behind her eyeglasses,how much smaller or bigger does the pupil of her eye appear compared to its actual size(suppose the distance between her pupil and her eyeglasses is 2cm)?c)If Alice wants to look at the moon through a Keplerian astronomical telescope,without her eyeglasses on,how does she have to adjust the eyepiece in order to see a clear image?7.Derive the matrix formula for thick lensHomework 091015 第52页，共53页，编辑于2022年，星期一Calculation of deviation angleWe want to write as第53页，共53页，编辑于2022年，星期一