《应用光学》PPT课件.ppt

In sec.4.3 we have mentioned that in order to keep the angle of two mirrors unchanged,the two mirrors are usually made on a common glass.4.4 prism(棱镜棱镜)and its unfolding(展开展开)nThese kinds of optical elements are called prisms.The prism in fig.4.9 is called Penta prism(五角棱镜五角棱镜)nFig.4.10 shows the appearance of a right-angle prism.It is a triangle cylinder(三角柱体三角柱体).nThe plane or section which is perpendicular to each prism is called main section(主截面主截面).nThe rays lie in the main section will lie still in the same section after passing through the prism.Fig.4.10 Basic definitionBACOptical axis:ABCLength of ABC:AB+BCGeometrical length of axisIncident faceIncident face：AC AC Emerging faceEmerging face：BCBCWorking faceWorking face：AC,BC,ABAC,BC,ABRidgeRidge楞：楞：the intersection line the intersection line of working faceof working faceMain section(Main section(主截面主截面,光轴截面光轴截面)：ABC faceABC faceBACOptical axis：the middle line of working face Principal section：2Complex PrismEquivalent action of prismFFPF Incident faceIncident faceEmerging faceEmerging faceFFIncident faceIncident faceEmerging faceEmerging faceConclusionEquivalent action of a prism in optical system corresponds with a parellel glass board（平行平板）（平行平板）unfolding of prismnThis method,unfolding the prism,canceling the reflection and replacing prisms refractions by glass blocks refraction,is called prism unfolding.n把棱镜的光轴截面沿着它的把棱镜的光轴截面沿着它的反射面展开反射面展开，取消棱镜的反射，以平行玻璃板的折射代取消棱镜的反射，以平行玻璃板的折射代替棱镜折射的方法称为替棱镜折射的方法称为“棱镜的展开棱镜的展开”。The prism must be demanded to meet two requirements:nAfter unfolding the prism,the two faces of the glass block must be parallel to each other.(棱镜展开后玻璃板的两个表面棱镜展开后玻璃板的两个表面必须平行必须平行)nWhen the prism locates in converging rays,the axis must be perpendicular to both incident and emergent faces.(如果棱镜位于会如果棱镜位于会聚光束中，则光轴必须和棱镜的入射及出射表面聚光束中，则光轴必须和棱镜的入射及出射表面相相垂直垂直）Methods of unfolding:按入射光线的顺序，以反射面为镜面，求按入射光线的顺序，以反射面为镜面，求其对称像，并依次画出反射棱镜的展开图其对称像，并依次画出反射棱镜的展开图。简单说：逐个作出棱镜经反射面所成的像简单说：逐个作出棱镜经反射面所成的像ABCOSSCExample 1CABBASSSExample 2Some tipical prisms 4.4.1 Right-angle prismACBAO1O2O3The right-angle prism can deviate the axis through any angle90-/290-/2deviated the axis through Fig.4.2 Isosceles prism4.4.2 Penta prism(五角棱镜五角棱镜)ABCDEL:the length of the axis光轴长度光轴长度D:The maximum aperture 通光口径通光口径904.5 roof surfaces and roof prisms(屋脊面和屋脊棱镜屋脊面和屋脊棱镜)Right-angle prismRoof prism两个互相垂直两个互相垂直的反射面称为的反射面称为屋脊面屋脊面nIn order to get an image similar to the object,two surfaces at 90whose intersection lies in the hypotenuse(斜边斜边)can be used to replace one of the reflecting surfaces.nThese special surfaces are called roof surfaces(屋脊面屋脊面).nA prism containing roof surfaces is called roof prism(屋脊棱镜屋脊棱镜).What is the role of the roof prism?nThe addition of the roof to the prism is to introduce an extra inversion to the image or change the total reflecting number from odd to even,keep the original axis and image orientation in the main section unchanged.In this way we can add a reflection and get an image similar to the object.n在不改变光轴方向和主截面内成像方向的条件下，在不改变光轴方向和主截面内成像方向的条件下，使像倒置使像倒置一次一次，或使系统总的反射次数由，或使系统总的反射次数由奇数变奇数变成偶数成偶数，从而达到物像相似的要求，从而达到物像相似的要求Fig.4.18 Principle of roof surfacex xy yz zx x y y z z x xy yz zPlanar donation method of room prism屋脊棱镜的平面表示方法屋脊棱镜的平面表示方法4.6 imaging property of parallel glass block and prism size calculationnWe mentioned in the previous section that by using a prism to replace mirrors corresponds to add a parallel glass block.Fig.4.21 Parallel glass blockThat means a parallel glass block only makes the image plane shift a certain distance,having no influence on the imaging property.The equivalent air thickness:(4.2)n光线移动的距离随入射光线移动的距离随入射角的不同而不同角的不同而不同 n同样也随平板的厚度不同样也随平板的厚度不同而变化同而变化n上式表明上式表明:L L因不同的因不同的I I1 1值不同而不同值不同而不同.n即从具有不同入射角的各条光线经平行平面板折即从具有不同入射角的各条光线经平行平面板折射后，具有不同的轴向位移量，射后，具有不同的轴向位移量，n这就说明，同心光束经平行平面板后变为非同心这就说明，同心光束经平行平面板后变为非同心光束，成像是不完善的。光束，成像是不完善的。n也可以看出平行平面板的厚度也可以看出平行平面板的厚度d d 愈大，成像不完愈大，成像不完善程度也愈大。善程度也愈大。4-7 determination of image orientations for mirrors and prismsyzxxzy（a）4.7.1 mirror and prism system with single main sectionnmirror and prism system with single main section means that all of the main sections of the mirrors and prisms coincide with one another.nIf there is no roof surface in the system the orientation of z which is normal to the main section will be parallel to all of the reflecting surfaces.nAccording to the mirror imaging properties,the object and the image are symmetrical to the mirror,so the orientation of z in image space will be as the same as that of z in the object space no matter how many reflections have happened.nHowever,if there is a roof surface in the system,according to the roof surface property,the orientations z and z will be reversed.nIn this way we can easily determine the orientation of z in a mirror and prism system with the single main section.nFirst of all,suppose there is no roof surfaces in the system and means z will be the same orientation as z.non this condition,if the total number of the reflectors is even,the image will be similar to the object,y and y have the same orientation if the orientation of axis x coincides with x,as shown in fig.4.25(a).nOn the contrary,if the orientation of axis x is reversed to x,y will be opposite to y,as shown in fig.4.25(b).nSimilarly,if the total number of the reflectors is odd,the image will be a mirror image,y and y have the opposite orientation of axis x coincides with x,as shown in fig.4.26(a).nOn the contrary,if the orientation of the axis x is reversed to x,y will have the same orientation as y,as shown in fig.4.26(b).nThus,for a mirror and prism system with single main section we can get the following rules,as shown in table 4.2.Table 4.2 orientation rules for yThe emergent axis and incident(x,x)Number of reflectorsy and yCoincideEvenThe same orientationCoincideOddReverseReverseEvenReverseReverseOddThe same orientation总结判断单一主截面的平面镜棱镜系总结判断单一主截面的平面镜棱镜系统中，主截面内成像的方向规则如下：统中，主截面内成像的方向规则如下：1.1.光轴同向：光轴同向：光轴反射次数为偶数，光轴反射次数为偶数，y y和和yy同向；同向；光轴反射次数为奇数时，光轴反射次数为奇数时，y y和和yy反向。反向。2.2.光轴反向：光轴反向：光轴反射次数为偶数，光轴反射次数为偶数，y y和和yy反向；反向；光轴反射次数为奇时，光轴反射次数为奇时，y y和和yy同向；同向；注意：注意：n1 1、上面提到的光轴，同向和反向是广义的，、上面提到的光轴，同向和反向是广义的，同向不仅仅指入射光轴和出射光轴平行，同向不仅仅指入射光轴和出射光轴平行，凡是光轴偏转角小于凡是光轴偏转角小于9090均认为是同向的，均认为是同向的，大于大于9090认为是反向的；认为是反向的；n2 2、当系统中有屋脊棱镜时，不影响主截面、当系统中有屋脊棱镜时，不影响主截面内像方向，光轴看成是在棱上反射，计算内像方向，光轴看成是在棱上反射，计算光轴反射时只计算一次，计算总反射次数光轴反射时只计算一次，计算总反射次数时，屋脊面计算两次时，屋脊面计算两次.nIf there is a roof surface in the system,according to its imaging property,it does not affect the orientations which lie in the man section,thus,on this condition the above rules can also be used.nFor the roof surface the axis can be taken as if it is reflected at the roof line and the reflector number should be counted as on time.However,for the total number of reflectors,the roof surface should be counted twice.方法方法1.x,x与光轴与光轴同向同向。2.没有没有或或偶数偶数屋脊面时，屋脊面时，z与与z同向同向；奇数奇数屋屋脊面时，脊面时，z与与z反向反向。3.当当x与与x同向同向时，时，偶次反射偶次反射y与与y同向同向，奇次奇次反射反射y与与y反向；反向；x与与x反向反向时，时，偶次反射偶次反射y与与y反向反向，奇次反射奇次反射y与与y同向。同向。Example A:FIG.4.27(a)、（、（b）yzxyzxyzxyzx8,Similar iamge7,mirror iamge4.7.2 Mirror and prism system with two 4.7.2 Mirror and prism system with two main sections perpendicular to each thermain sections perpendicular to each ther123o1o2o3o4yxzyzx132Similar image123o1o2o3o4yxzyzx132o1o2o3o4For prism 1 and 3:The axis rotates 180,so x and x is reversed，The mumber of reflector is 2,y and y is reversed.For prism 2：The orientation of x is opposite to x and the mumber of reflector is 2，so z is opposite to zPrism can change the orientation of object and image in main section棱镜只能改变主截面内的物像方向棱镜只能改变主截面内的物像方向Some examples:y yz zx xx xz zy yRight-handRight-handLeft-handLeft-handy yz zx xx xy yz zRight-handRight-handRight-handRight-handx xy yz zx xz zy y45Right-handRight-handLeft-handLeft-handyzxyzxyzxyzx