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Chap. 2 Principles of optical instruments 光学仪器的基本原理 2.1 Magnifying power of aided visual instruments Magnifying glass 助视仪器的放大本领 放大镜 *2.2 Huygens eyepiece and Ramsden eyepiece 惠更斯目镜和冉斯登目镜 2.3 Magnifying power of microscope 显微镜的放大本领 2.4 Magnifying power of telescope 望远镜的放大本领 2.5 (Optical) Stop/diaphragm and pupil 光阑 光瞳 *2.6 Outline of photometry-transmission of light energy 光度学概述 2.7 Light gathering power of objective Preface Human eye 一、construction of human eye 人眼的结构 (looked as optical instrument) In the view of geometric optics, Some norms: Pupil 瞳孔—control the luminous flux entering the human eye. Crystalline humor—the convex lens with adjustable foc 晶状体 length. Retina—accept the image. 视网膜 二、reduced eye From the point of geometric optics, human eye can be looked as coaxial lenses with different mediums. So it can be simplified as a reduced a spherical surface . n=1eye of n'=4/3 F' f '=22.8mm 三、adjustment function of human eye 远点 Far point∞ { Normal eye 正常眼 近点 Near point(changes with the age) Distance of distinct vision 明视距离 25 cm Myopic eye Nearsighted eye Hyperopic eye Farsighted eye Abnormal eye Myopic eye — the far point is finite, correcting through Hyperopic eye远视眼— the near point goes further, correcting throug Astigmatic eye 散光眼—curvature of cornea is inhomogen 近视眼 角膜曲率不均匀 1 Focal power: ' f Unit :diopter=1/m 光焦度 Degree=100 ×diopter 屈光度= 1/米 度数=100×屈光度 .1 Magnifying power of aided visual instrument Magnifying glass 一、The concept of magnifying power 1. Sensing of human eye to the size of object 眼睛对物体大小的感觉 Q u -l P Visual angle u is subtended by the object at the human 物体对人眼张开的视角u 2. Magnifying power Q' Q u' P' P l ' tan u ' u ' M l tan u u -l' l ' tan u ' u ' M l tan u u l:the image length on the retina without aided instru l': the image length on the retina with aided instrume u':the visual angle with aided instrument. Far object:the visual angle is subtended by the o at the human eye. u Near object: the visual angle is subtended by the o which is put at the distance of { 二、amplifying lens / magnifying glass y' y • u' F -p' y u 25 cm Magnifying power of lens y' y y ' tan u ' ' p f f y tan u 25 tan u ' 25 M ' ∴ tan u f 3× 放大镜 *2.2 Huygens eyepiece and Ramsden eyepiece 一、function of eyepieces Functions: Large magnifying power, Broad field of view, Correct the aberration. An eyepiece consists ofEye lens two or more thin lenses Field lens { 二、two kinds of eyepieces 1. Huygens eyepiece 惠更斯目镜 L1 objective L2 • H' F H 接目镜(视镜) 向场镜(场镜) f1' 3a, f 2' a, d 2a 1 ' f1 f 2' 2 3 Remove the chromatic aberration combine:f ' a 2 消色差 properties: (1) achromatism 消色差性 (2)Huygens eyepiece can only be placed after the obje and magnify the image which is in the dista distinct vision. 只能接在物镜后,使成象在明视距离 (3)large field of view 2. Ramsden eyepiece 冉斯登目镜 • F H' H combine: 2 f1' a, f 2' a, d a 3 3 ' f a 4 Properties: (1) Ramsden eyepiece can be directly used as magnifying glass.直接可当放大镜使用 (2)Comparing with Huygens eyepiece, Ramsden eyepie can be directly used as magnifying glass, While Huygens eyepiece can only observe th (3)The system is relatively long. 2.3 Magnifying power of microscope Microscop e The objective —a set of lenses, short f1' Simplify into The eyepiece—a set of lenses,f2 a lens { objective y • F2 • • F1 ' y1 ' u' eyepiece Optical interval △ = F1'F2 △ ~ l(length of a tube 筒长) small f1' , f2 y tan u , 25 ' ' y y 1 tan u ' '1 f2 f2 ' y tan u ' 1' f2 Magnifying power of microscope: y1' f 2' y1' 25 M 物 M目 ' y 25 y f 2 y1' f1' 物 ' ' y f1 f1 ∴ 25 M ' f 25 25 M ' ' ' f1 f 2 f ' f1' f 2' f 2.4 magnifying power of telescope reflector—reflecting telescope { { Objective lens—refracting telescope Large f ' 1 telescope convex—Kepler’s telescope eyepiece 远物,小视角 开普勒望远镜 concave—Galileo’s telescope { 伽利略望远镜 一、Kepler’s telescope/ Keplerian telescope The object at infinity objective u =0 y1 tan u f2 ' eyepiece F1' F2 -y1• u' y1 y1 tan u ' ' f1 f1 y1 f 2' Magnifying power: ' tan u y1' f 2' f1' M ' ' ' tan u y1 f1 f2 ∴ Finite object f1' M ' f2 M<0,inverted image objective u eyepiece F1' F2 • -u' Magnifying power: ' ' 1 ' 2 ' 1 ' 2 tan u y f p M ' ' tan u y1 p1 f ∴ p1' M ' f2 二、Galileo’s telescope/ Galilean telescope eyepiece objective u u' F1' F2 f1' 0, f 2' 0 • Magnifying power: f1' M ' f2 M>0, erect virtual image 三、reflecting telescope(astronomical telescope Now, Newton’s telescope 牛顿式反射望远镜 Schmidt telescope Gregory’s telescope 格雷戈里式望远镜 Cassegrain’s telescope 施密特望远镜 Hubble space telescope 卡斯格伦式望远镜 哈勃太空 四、Extender instrument of laser 激光扩束器 Convergence point can produce ionization Upside-down Galilean telescope 倒装的伽利略望远镜 supplement 设开普勒望远镜和伽利略望远镜的物镜和目镜之间的距离 均为10cm,视角放大率均为3倍,分别求它们的 f1’,f2’ 。 2.5 (Optical) Stop/diaphragm and pupil 光阑 光瞳 一、The concept of stop/diaphragm Stop——the plate with loophole of optical透光孔 system Function: 1. Limit the aperture angle 2. Limit the rays of paraxial 3. Control the luminous flux 4. prevent stray light ☆Effective diaphragm/stop —limit the apertur Classifying 有效光阑 限制轴上物点孔径角 ( function) Field diaphragm/stop —limit the paraxial ima 以作用分类: for 视场光阑 { 有效光阑(孔径光阑) 二、Effective stop(aperture stop) and pupil Effective stop——limit the entrance beam most of all stops 在所有各光阑中,限制入射光束最起作用的那个光阑。 For the point of axis • P Properties: P—“1”effective stop • Q Q—“2”effective stop 1 2 (1)varies with different specific object points; A' A A’B’is the • • effective stop P P' of point P B B' (2)limitation of image ray can be looked as the limitation of object ray. Entrance pupil入射光瞳——limit entrance rays, the image of effective stop by former system { 限制入射光线,有效光阑被它前面的光学系统成的象 Exit pupil 出射光瞳——limit exit rays, the image of effective stop by latter system 限制出射光线,有效光阑被它后面的光学系统成的象 Either real object or image *2.6 Outline of photometry-transmission of light energy 光能量传递——辐射度学 可见光范围——光度学 一、Radiant flux 辐射通量 Radiant flux ε —单位时间内,某一面积发射出来的全部辐射能量。 (unit:W) Radiation flux density e(λ)—单位波长范围间隔内的辐射通量。 谱辐射通量密度 d e , d e d 0 二、Visibility function 555 v properties: 视见函数 v() standard luminosity curve 1.0 (1)varies with different persons (2)varies with background brightness (if the background is dark, it moves to the short wave.) 标准亮度曲线 555nm 三、Luminous flux Φ 光通量 Luminous flux—it is only that part of the total radiation flux, which is visible and can affect the eye. d K mv d K mv e d Km unit:lumen (lm 最大光视效能 Km= 683 lm/W luminous flux of homochromatic light: d 683v e d luminous flux of polychromatic light: d 683 v e d 0 Luminous efficiency: 发光效率 0 P 光源耗电功率 四、Intensity of illumination 发光强度 Intensity of illumination—luminous flux per unit solid angle 表征光源在一定方向范围内发出的 d I d 光通量的空间分布的物理量 unit:cd (candle) SI中,七个基本单位之一 If the intensity of illumination of a source in all directions, then Id 4I 坎德拉是一光源在给定方向上的发光强度, 该光源发出频率为5.40×1014 Hz的单色辐射, 而且在此方向上的辐射强度为1/683 W/sr。 (sr为球面度) 五、Incidence and exitance 照度和出射度 Illuminance E—the flux per unit area incident onto d E dS a real or imaginary surface. unit:lux, lm/m2 单位面积上接收的光通量 勒克斯 Point light source Id I cos dS R 2 I cos E dS dS R2 Surface light source R α dS Exitance M—the flux emitted per unit area of a source d M dS of radiation. 单位面积上辐射出来的光通量 unit:lux, lm/m2 勒克斯 六、Illuminating power 亮度 Illuminating power L—the luminous flux per unit solid angle per unit projected area. 辐射面上单位投影面积,在单位立体角内辐射的光通量。 d L dS cos d unit:cd/m2 S dΩ θ dS By the definition of intensity of illumination, we have dI L dS cos Expansive light source dI cosθ 扩展光源 Lambert source 朗伯光源 由发光强度定义,L可写为: L is independent of θ Lambert’s cosine law Diffuse reflection Lambertian reflector 朗伯定律 七、Principle of three primary colors 三原色原理 { R (=700 nm) The light of nature can be mostly obtained by the combining of different proportional luminous flux of three colors. G ( =546.1 nm) B (=435.8 nm) shot拍摄: 分光系统分解 pictures discompose E Display R EG EB 光通量按不同比例混合可得到自然界大多数颜色的光 R G B 加到彩色显象管 Colorful kinescope 光电转换 Photoelectric conversion Red pictures Green pictures Blue pictures ER EG EB Transmit or store Color pictures 2.7 Light gathering power of objective 物镜的聚光本领 Light gathering power of objective is the physical quantity of the ability to gather the luminous flux. 一、 light gathering power of microscope, numerical aperture Illuminance of image surface E L0 RN . A. ' 2 象面照度 1 2 L0——illuminating power of object in the vacuum ——transverse magnification RN.A.——numerical aperture RN . A. n sin u u n ——the refractive index of object u ——aperture angle 孔径角 二、 Light gathering power of telescope, relative aperture 望远镜的聚光本领 相对孔径 Illuminance of image surface d E ' f 2 ' d ——objective aperture of telescope d/f '——relative aperture Reflecting telescope 1/3.33 d/f Refracting telescope 1/18.9 三、 Light gathering power of camera ' Illuminance of image surface d E ' f ' 2 Far object E L0 d 2 ' 4 f 2 L0 d ' Near object E ' 16 f { ' F number (光圈数)—the reciprocal value of relative aperture, F数 that is, f '/d Generally,F 1:K presents the relative aperture of objective. 如国产海鸥DF型照相机 F 1:2 F number 1 f '/d Relative aperture 1.4 2 2.8 4 5.6 8 11 16 1/1 1/1.4 1/2 1/2.8 1/4 1/5.6 1/8 1/11 1/16 d/f ' Illuminance of image surface 1 1 2 1 4 1 8 1 16 1 32 1 64 1 128 1 256 *2.8 Aberrations 象差 Classification of aberrations Monochromatic aberrations Point of axis (broad beam) Point of paraxial Near point ( broad beam ) distortion The refractive index of the material of a lens is different for different wavelengths. Barrel distortion Pincushion distortion astigmatism coma Far point (sharp beam) Curvature of field Spherical aberration Chromatic aberrations 由于透镜对不同波 长光会聚能力不同 引起的 Chromatic aberration: 色差 Constringence(V数)V nD 1 nF nC 倒色散系数,阿贝数 nD——yellow refractive index nF——blue refractive index nC——red refractive index Remove chromatic aberration 消色差 1. Combination of two different materials 2. Two lenses are made of the same material Satisfy, 1 1 1 d 1 ' ' , d f f 1 2 ' ' ' ' ' f f1 f 2 f1 f 2 2 ' df then, 0 d Chap. 2