02共轴球面组近轴成像解析.pptx

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,#,P,物理与光电信息学院,School of Physics and OptoElectronics Technology,FUJIAN NORMAL UNIVERSITY,Fuzhou,Fujian 350007,China,1,Imaging,Real and virtual objects,real and virtual images,Object space and Image space,物与像的共轭性,物像之间的等光程性,实像,:若出射的同心光束是会聚的,我们称像点,Q,为实像,虚像,:若出射的同心光束是发散的,我们称像点,Q,为虚像,1.Real and virtual objects,real and virtual images,同心光束,(concentric beam),：,各光束本身或其延长线交于同一点的光束。在各向同性媒质中对应球面波。,Q:,真实的发光点一定起到实物的作用吗？,实物,:,在某个光具组中，若入射的是发散的同心光束，则其发散中心,Q,为实物。,虚物,:,如果入射的是个会聚的同心光束，则相应的会聚中心,Q,为虚物。,光具组,(optical system),：,由若干反射面或折射面组成的光学系统,发光点,Q,射出的同心光束经镜面反射后成为发散光束,据反射定律,:,反射线的延长线严格的交于镜面后同一点,Q(,虚像,),真实发光点,Q,经,L,1,成像与,Q,1,(,实像),当透镜,L,2,插在,Q,1,之前时,对,L,2,来说入射的光束是会聚,会聚点,Q,1,就是,L,2,的虚物,L,2,将入射的光束进一步会聚到,Q,2,L,2,使,Q,1,成实像于,Q,2,。,实物不一定成实像，虚物不一定成虚像,理想光具组,一个能使任何同心光束保持同心性的光具组,理想光具组将空间每个物点,Q,和相应的像点,Q,组成一一对应关系.,(2)物方(物空间)由所有物点组成的空间,像方(像空间)由所有像点组成的空间,2.,物方与像方 物与像的共轭性,(3)如何区分某个点是物点还是像点,判断方法：看它是与入射光束还是与出射光束相联系。,Q,是入射光束的交点，故在物方是物点。,Q,是出射光束的交点，故在像方是像点。,(4)共轭点：物方和像方的点不仅一一对应，而且根据光的可逆性原理，如果将发光点移到原来像点的位置,Q,上，并使光线沿反方向射入光具组，它的像将成在原来物点的位置,Q,上，这样一对相互对应的点,Q,和,Q,称共轭点。,(5)判断：物方媒质,n,像方媒质,n,物点所在空间媒质折射率为,n ,入射实际光线所在空间。,像点所在空间媒质折射率为,n,出射实际光线所在空间。,3.,物像之间的等光程性,（,1,）,由费马原理可导出一个重要结论：,物点,Q,和像点,Q,之间各光线的光程都相等。,由费马原理：物像间的光程都应取极值或恒定值，这些连续分布的实际光线的光程都取极大值或极小值是不可能的，唯一可能性是取恒定值，即它们的光程都相等,（,2,）虚光程,为了把物像之间的等光程原理推广到虚物或虚像情形，引入“虚光程”的概念,。,（,3,）等光程面,P39-40,反射等光程面：椭球面，抛物面，双曲面，平面,折射等光程面：折射球面的齐明点（,aplanatic points,）,2,共轴球面组近轴成像,(paraxial approximation),Why is imaging necessary:Huygens principle-Spherical&parallel ray bundles,points at infinity,Refraction at spherical surfaces(paraxial approximation),逐面成像,1.Why are focusing instruments necessary?,Ray bundles:spherical waves and plane waves,Point sources and point images,Huygens principle and why we can see around us,Ideal imaging system:,each point in the object is mapped onto a single point in the image,Each poin,t in an object scatters the incident illumination into,a spherical wave,according to the Huygenss principle.,A few microns away from the object surface,the rays emanating from all object points become,entangled,delocalizing object details.,To relocalize object details,a method must be found,to reassign(“focus”)all the rays that emanated from a single point object into another point in space,(the“image.”),The latter function is the topic of the discipline of,Optical Imaging.,(e.g.satellite dish),Parabloid mirror:perfect focusing,Lens:main instrument for imageformation,The curved surface makes the rays bend proportionally to their distance,from the“,optical axis,”,according to Snells law.Therefore,the divergent,wavefront becomes convergent at the right-hand(output)side.,Real imaging systems introduce blur.,Aspherical Surfaces:ideal optical elements,P151 P189,Ideal lens,Why optical systems do,not,focus perfectly,Diffraction,Aberrations,However,in the,paraxial approximation,to,Geometrical Optics,that we are about to embark upon,optical systems,do focus perfectly,To deal with,aberrations,we need,non-paraxial,Geometrical Optics(,higher order approximations,),To deal with,diffraction,we need,Wave Optics,defocus imperfect focus,2.Refraction at single spherical surface,For each ray,must calculate,：,point of intersection with sphere,Angle between ray and normal to surface,Apply Snells law to find direction of propagation of refracted ray,Paraxial approximation,：,In paraxial optics,the approximations(1st order Taylor)are used:,sin,tan,cos,1,(1+,),0.5,1+0.5,:the angle between a ray and the optical axis(,0,and it is the same with(2.23)in p43,n,n,1,n,2,n,3,P,2,P,Q,A,1,Q,1,A,2,Q,2,A,3,Q,3,1,2,3,P,1,P,3,S,1,S,1,S,2,S,2,S,3,S,3,对光具组,1,有,(,n,n,1,s,1,s,1,r,1,),，计算起点为,A,1,对光具组,2,有,(,n,1,n,2,s,2,s,2,r,2,),，计算起点为,A,2,对光具组,3,有,(,n,2,n,3,s,3,s,3,r,3,),，计算起点为,A,3,3.,逐面成像,3 The Thin Lens,Thin lens equation,焦面及成像作图,Multi-element systems,On-axis object Q is imaging at Q,1,through refracion interface,1,firstly,then Q,1,is the virtual object as to interface,2,and its image is Q,2,.,Two refraction imaging equations are given,1.Thin Lens Equations,Sign Convention for Spherical Refraction,Light from the left,S f +left of vertex,(real object),S,f,+right of vertex,(,real image),R +if C is right of vertex,y,y,+above optical axis,Or see page 43(Chinese),At first interface,At second interface,if =,d,then .,d,:thickness of the lens is very small,在薄透镜中,A,1,和,A,2,，,几乎重合为一点，该点叫透镜的光心记为,O,薄透镜的物距,S,和像距 都是从光心,O,开始算的。,so,，,as to thin lense,，,we get,1,f,两式相加消去得,据焦距定义 或,s=,We get:,and,将单个球面焦距公式代入得,如果物象方折射率 ，则有,此式给出了薄透镜焦距与 的关系，称为,磨镜者公式,(,lensmakers equation),。,将焦距公式代入 式中，则有,This is the thin lens equation,if ,then,Gaussian Lens Formula,会聚透镜：具有实焦点,(,f,和,f,0),的透镜叫正透镜。,反之为负透镜或发散透镜,注意：透镜放在不同的环境中起到的作用可能是不一样的。,例如若把空气中的凸透镜放在折射率大于透镜材料的液体中，则该透镜就起到凹透镜的作用。,不能仅凭透镜的形状来断定它是正透镜还是负透镜,Light entering from the left,，,(),if is on the left of vertex,，,then s0 （real object,）,(),is on the right of vertex,，,then 0,（,real image,）,Using the distance measured from the focal points,(),when the object is on the left of,，,x,0,()when the image is on the right of,，,0,F,F,Combining with the Gaussian Equation,we get,Newtonian Form of the Thin Lens Equation,Transverse magnification of the thin lens,：,so,or,if,，,that is,，,the lens is in air,(),transverse magnification,如题图所示，折射率为,1.5,，中心厚度为,7.5cm,的透镜，左右表面的曲率半径分别为,20cm,和,30cm,，左表面左方,40cm,处的轴上放置高为,0.5cm,的小物求在傍轴条件下，最后成像的位置、高度及像的倒正、虚实和缩放,?,解：，对于左表面，,n,=1,，,s,1,=40cm,（实物），,n,=1.5,，,r,1,=-20cm,，可求得,s,1,=-30cm,，放大率为,V,1=-,ns,1,/,n,s,1=0.5,，成的是正立缩小的虚像。,对于右表面，仍然遵从 ，此时,n,=1.5,，,s,2,=(30+7.5)cm,（实物），,n,=1,，,r,2,=-30cm,，,s,2,=-300cm/7,，放大率为,V,2,=-,ns,2,/,n,s,2=12/7,。相对中间的虚像而言，成的是正立放大的虚像。,总的来看，放大率为,V,=,V,1,V,2,=6/7,，所成的像的高度为,3cm/7,。所以所成的是正立缩小的虚像。注意虚像和实像的概念。,2.,焦面及成像作图,入射光线从左右入射,物方焦面（第一焦面，前焦面）,像方焦面（第二焦面，后焦面）,通过物方焦点,F,与光轴垂直的平面叫物方焦面。,焦面的共轭平面,:,因焦点与轴上无穷远点共轭,焦面的共轭也在无穷远处,焦面上轴外点的共轭在轴外无穷远,倾斜的平行光束的方向可由 或 与光心,O,的连线来确定，这连线叫副光轴。相应的对称轴称主光轴,。,（1）,通过光心,O,的光线，经透镜后方向不变。,（2）通过物方焦点,F,的光线，经透镜后平行于光轴。,（3）平行于光轴的光线经透镜后的出射光线一定通过像方焦点,The two rays passing through the two focal points and the chief ray can be ray-traced directly,Imaging condition:ray-tracing,real&virtual images,image:real&inverted,image:virtual&erect,image:virtual&erect,image:virtual&erect,All real images formed by a single thin lens will be inverted.,A positive transverse magnification means an erect image,while a negative value means the image is inverted.,Page 167(English),3.,透镜组成像,(,Multi-element systems,),利用逐次成像物象距公式或逐次成像作图法即可求透镜组最后成像的性质，性质包括,（像的位置，缩放，倒正虚实等）,凸透镜,L,1,和凹透镜,L,2,的焦距分别为20.0,CM,和40.0,CM，L,2,在,L,1,之右40.0,CM，,傍轴小物放在,L,1,之左30.0,CM，,求它的像。,例题1,解：,（1）作图法,第一次成像用特殊光作图，第二次以后成像利用焦面性质，这样可保证入射的两光线与出射光线共轭，光线在透射组中是连续的。,（2）高斯公式逐面成像法,第一次对,L,1,成像,s,1,=30.0cm f,1,=20.0cm,计算起点为,O,1,=60.0cm （,实象）,（放大）,第2次对,L,2,成像,s,2,=-20.0cm f,2,=-40.0cm,计算起点为,O,2,cm （,实象）,（放大）,（放大的，倒立的）,最后成像在,O,2,右侧距离40.0,cm,处，成放大的倒立的实象。,（3）用牛顿公式,第1次对,L,1,成像,x,1,=10.0cm，f,1,=20.0cm,=40.0cm （,实象）,（倒立，放大）,第2次对,L,2,成像,x,2,=20.0cm，f,2,=-40.0cm,，=80cm（,实象）,（倒立，放大）,最后成像在,F,右侧，距离80.0,cm,处，成倒立放大的实象,由上面可以看出用三种方法得到的结果相同。,例题2,凸透镜,L,1,和,L,2,及其焦点的位置示图6-9中，将傍轴小物,PQ,放在,L,1,的第一焦面上，用作图法求它的像。,4,理想光具组理论,The Thick lens,Focal Lengths&Principal Planes,PSs and FLs for thin lenses,The significance of principal planes,1.The thick lens,Rays bend in“two steps”,Equivalent to a thin lens placed“somewhere”within the thick element.,The location of this“equivalent thin lens”is the,Principal Plane,of the thick element,The,very,thick lens,Funny things happening:,rays diverge upon exiting from the element,i.e.,too much positive power leading to a negative element!,2.Focal Lengths&Principal Planes,EFL:Effective Focal Length(or simply“focal length”),FFL:Front Focal Length,BFL:Back Focal Length,FP:Focal Point/Plane,PS:Principal Surface/Plane,A ray traversing the lens through its optical center emerges parallel to the incident direction.Extending both the incoming and outgoing rays until they cross the optical axis locates what are called the nodal points.,节点的物理意义：通过它们的任意共轭光线方向不变,When the lens is surrounded on both sides by the same medium,generally air,the nodal and principal points will be coincident.,The six points,two focal,two principle,two nodal,consitute the cardinal points of the system.,3.PSs and FLs for thin lenses,The principal planes coincide with the(collocated)glass surfaces,The rays bend precisely at the thin lens plane,(=collocated glass surfaces&PP),4.The significance of principal planes,Examples on Page 271:,The principal planes can lie completely outside the lens systems.,Though differently configured,each lens in either group of Fig5.3 has the same power.,The thick lens(See page 272),The equation of the thick lens immersed in air with Gaussian form is same to the equation of thin lens,that is,where,The object and image distances are measured from the PLs,f,effective focal length,The location of principle points,(Fig5.4 on page 272),Transverse magnification,Example one,(page 273),Positive when the planes lie to the right of their respective vertices,The thick lens system,(See page 273),A compound thick lens consisting of two thick lens,or page 59 Fig2-26 in Chinese,The same procedures can be extended to three or more lenses,