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Chap. 2 Principles of optical instruments
光学仪器的基本原理
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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 物镜的聚光本领 2.8 Aberrations 象差概述
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Human eye 一、construction of human eye 人眼的结构 Preface
(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 focal length. 晶状体 Retina—accept the image. 视网膜
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{ 二、reduced eye 三、adjustment function of human 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 eye of a spherical surface . n=1 n'=4/3 F' f '=22.8mm 三、adjustment function of human eye { Far point∞ 远点 Normal eye 正常眼 Near point(changes with the age) 近点 Distance of distinct vision 25 cm 明视距离
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Myopic eye Nearsighted eye Hyperopic eye Farsighted eye
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Myopic eye 近视眼 — the far point is finite,
Abnormal eye Myopic eye 近视眼 — the far point is finite, correcting through the concave lens Hyperopic eye远视眼— the near point goes further, correcting through the convex lens Astigmatic eye 散光眼—curvature of cornea is inhomogeneous 角膜曲率不均匀 Unit :diopter=1/m Focal power: 屈光度= 1/米 光焦度 Degree=100 ×diopter 度数=100×屈光度
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2.1 Magnifying power of aided visual instruments
Magnifying glass 一、The concept of magnifying power
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-l -l' 1. Sensing of human eye to the size of object u
Q 眼睛对物体大小的感觉 u -l P Visual angle u is subtended by the object at the human eye 物体对人眼张开的视角u 2. Magnifying power Q' Q u' -l' P P'
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{ l:the image length on the retina without aided instrument.
l': the image length on the retina with aided instrument. u':the visual angle with aided instrument. { Far object:the visual angle is subtended by the object at the human eye (telescope) u Near object: the visual angle is subtended by the object , which is put at the distance of distinct vision (microscope)
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二、amplifying lens / magnifying glass 放大镜
u' • F -p' y u 25 cm Magnifying power of lens ∴ 3×
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*2.2 Huygens eyepiece and Ramsden eyepiece
一、function of eyepieces Large magnifying power, Broad field of view, Correct the aberration. Functions: { Eye lens 接目镜(视镜) An eyepiece consists of two or more thin lenses Field lens 向场镜(场镜) 二、two kinds of eyepieces 1. Huygens eyepiece 惠更斯目镜 L1 L2 • objective H' F H
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• combine: Remove the chromatic aberration properties:
消色差 properties: (1) achromatism 消色差性 (2)Huygens eyepiece can only be placed after the objective, and magnify the image which is in the distance of distinct vision. 只能接在物镜后,使成象在明视距离,起放大作用 (3)large field of view 2. Ramsden eyepiece 冉斯登目镜 • H' H F
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(1) Ramsden eyepiece can be directly used as magnifying glass.
combine: 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 eyepiece can be directly used as magnifying glass, While Huygens eyepiece can only observe the image. (3)The system is relatively long.
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2.3 Magnifying power of microscope
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{ Microscope The objective —a set of lenses, short f1'
The eyepiece—a set of lenses,f2 { Simplify into a lens F1' F2 • objective eyepiece -u' -y1' y Optical interval △ = F1'F2 △ ~ l(length of a tube 筒长) small f1' , f2
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Magnifying power of microscope:
∴
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2.4 magnifying power of telescope
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{ { { 一、Kepler’s telescope/ Keplerian telescope = 0 u • -y1 -u'
reflector—reflecting telescope Objective Large f1' { lens—refracting telescope 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 = 0 objective eyepiece F1' F2 u • -y1 -u'
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∴ • ∴ Magnifying power: M<0,inverted image Finite object
objective eyepiece F1' F2 • u -u' Magnifying power: ∴
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二、Galileo’s telescope/ Galilean telescope
eyepiece F2 • F1' u u' objective Magnifying power: M>0, erect virtual image 三、reflecting telescope(astronomical telescope) Now, Newton’s telescope 牛顿式反射望远镜 Schmidt telescope 施密特望远镜 Gregory’s telescope 格雷戈里式望远镜 Hubble space telescope 哈勃太空望远镜 Cassegrain’s telescope 卡斯格伦式望远镜
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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’ 。
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2.5 (Optical) Stop/diaphragm and pupil 光阑 光瞳
一、The concept of stop/diaphragm Stop——the plate with loophole of optical system 透光孔 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 aperture angle of object on the axis { Classifying ( function) 有效光阑 限制轴上物点孔径角 Field diaphragm/stop —limit the paraxial image formation 限制轴外成象 以作用分类: 视场光阑
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二、Effective stop(aperture stop) and pupil
有效光阑(孔径光阑) 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—“1”effective stop • • Q P Q—“2”effective stop 1 2 Properties: (1)varies with different specific object points;
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{ A' A A’B’is the effective stop of point P • • P 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
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*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 v() 二、Visibility function standard luminosity curve 1.0 视见函数 标准亮度曲线 properties: (1)varies with different persons 555nm (2)varies with background brightness (if the background is dark, it moves to the short wave.)
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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. unit:lumen (lm Km 最大光视效能 Km= 683 lm/W luminous flux of homochromatic light: luminous flux of polychromatic light: Luminous efficiency: 光源耗电功率 发光效率
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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 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 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)
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五、Incidence and exitance
照度和出射度 Illuminance E—the flux per unit area incident onto a real or imaginary surface. unit:lux, lm/m2 单位面积上接收的光通量 勒克斯 α Point light source R dS Surface light source Exitance M—the flux emitted per unit area of a source of radiation 单位面积上辐射出来的光通量 unit:lux, lm/m2 勒克斯
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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。 S dΩ θ dS unit:cd/m2 By the definition of intensity of illumination, we have 由发光强度定义,L可写为: Expansive light source dI cosθ 扩展光源 Lambert’s cosine law L is independent of θ Lambert source 朗伯定律 Diffuse reflection Lambertian reflector 朗伯光源
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{ 七、Principle of three primary colors 三原色原理 R (=700 nm)
G ( =546.1 nm) B (=435.8 nm) { The light of nature can be mostly obtained by the combining of different proportional luminous flux of three colors. 光通量按不同比例混合可得到自然界大多数颜色的光 shot拍摄: 分光系统分解 R G B 光电转换 ER EG EB Transmit or store pictures Display 加到彩色显象管 Red pictures Green pictures Blue pictures Color pictures Photoelectric conversion discompose Colorful kinescope
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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 象面照度 L0——illuminating power of object in the vacuum ——transverse magnification u RN.A.——numerical aperture n ——the refractive index of object u ——aperture angle 孔径角
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{ 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 ——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 { Far object Illuminance of image surface Near object
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F number (光圈数)—the reciprocal value of relative aperture,
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 f '/d Relative aperture d/f ' 1/1 1/ /2 1/ /4 1/5.6 1/8 1/11 1/16 Illuminance of image surface
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*2.8 Aberrations 象差 Classification of aberrations
Monochromatic aberrations Chromatic aberrations Point of axis (broad beam) Point of paraxial Near point ( broad beam ) Far point (sharp beam) The refractive index of the material of a lens is different for different wavelengths. distortion Spherical aberration coma astigmatism 由于透镜对不同波长光会聚能力不同引起的 Curvature of field Barrel distortion Pincushion distortion
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Chromatic aberration:
色差 Constringence(V数) 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, then, Chap. 2
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