Chap. 2 Principles of optical instruments 光学仪器的基本原理.

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 物镜的聚光本领

2.8 Aberrations 象差概述

一、 construction of human eye 人眼的结构

（ looked as optical instrument)

Pupil 瞳孔— control the luminous flux entering the human eye.

Some norms ：

Crystalline humor—the convex lens with adjustable focal length.Retina—accept the image.

In the view of geometric optics,

晶状体

视网膜

Human eyePreface

二、 reduced eye

F'

n=1

n'=4/3

f '=22.8mm

三、 adjustment function of human eye

Normal eye正常眼

Far point∞

Near point （ changes with the age ）Distance of distinct vision 25 cm

{远点

近点

明视距离

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 .

Myopic eyeNearsighted eye

Hyperopic eyeFarsighted eye

Abnormal eye

Myopic eye 近视眼 — the far point is finite, correcting through the concave lensHyperopic eye 远视眼— the near point goes further, correcting through the convex lens

Astigmatic eye 散光眼— curvature of cornea is inhomogeneous

Focal power ： '

1f

Unit ： diopter=1/m

度数 =100× 屈光度

光焦度屈光度 = 1/ 米

Degree=100 ×diopter

角膜曲率不均匀

一、 The concept of magnifying power

2.1 Magnifying power of aided visual instruments Magnifying glass

1. Sensing of human eye to the size of object

u

Visual angle u is subtended by the object at the human eye

2. Magnifying power

-l

u'

P

Q

P'

Q'

-l'

Q

P

物体对人眼张开的视角 u

眼睛对物体大小的感觉

uu

uu

ll

M'''

tantan

uu

uu

ll

M'''

tantan

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.

u{Far object ： the visual angle is subtended by the object at the human eye. (telescope)

Near object: the visual angle is subtended by the object , which is put at the distance of distinct vision (microscope)

二、 amplifying lens / magnifying glass 放大镜

•

25 cm

F

u

u'

Magnifying power of lens

''

''tan

f

y

f

y

p

yu

25tan

yu

'

' 25tantan

fuu

M

yy'

y

-p'

∴ 3×

*2.2 Huygens eyepiece and Ramsden eyepiece

一、 function of eyepieces

An eyepiece consists of two or more thin lenses

Eye lens 接目镜（视镜）

Field lens 向场镜（场镜）{

二、 two kinds of eyepieces1. Huygens eyepiece 惠更斯目镜

H' H•F

L1 L2

Large magnifying power,Broad field of view,Correct the aberration.

Functions:

objective

'2

'

1

'

2

'

1 21

2,,3 ffadafaf

combine ： af23' Remove the chromatic aberration

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

消色差

adafaf32

,, '2

'1

combine ： af43'

Properties:（ 1 ） Ramsden eyepiece can be directly used as

magnifying glass. （ 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.

直接可当放大镜使用

2.3 Magnifying power of microscope

Simplify into a lens

Microscope

The objective —a set of lenses, short f1'

The eyepiece—a set of lenses ， f2

{

Optical interval △ = F1'F2

△ ～ l （ length of a tube 筒长）small f1' , f2

F1'

F2

• •

objective

eyepiece

•-u'

-y1'

y

,25

tany

u

'

2

'1

2

'1'tan

fy

fy

u

'2

'1'tanfy

u

Magnifying power of microscope ：

目物Mfyy

yfy

M '2

'1

'2

'1 25

25

'

1'

1

'1

'1

fff

yy 物

∴

''2

'1

2525fff

M

'

2'

1' fff

'

25f

M

2.4 magnifying power of telescope

telescope

ObjectiveLarge f1'

eyepiece{ {

{

reflector—reflecting telescope

lens—refracting telescope

convex—Kepler’s telescope

concave—Galileo’s telescope

一、 Kepler’s telescope/ Keplerian telescope

The object at infinity

objectiveeyepiece

•F1' F2u

-u'

= 0 '2

1

2

1'tanf

y

f

yu

'1

1'

1

1tanfy

fy

u -y1

远物，小视角开普勒望远镜

伽利略望远镜

Magnifying power ：

'2

'1

'1

'1

'2

'1

'

tantan

ff

fyfy

uu

M

∴ '2

'1

ff

M

Finite object objectiveeyepiece

F1' F2•

'2

'1

'1

'1

'2

'1

'

tan

tan

f

p

py

fy

u

uM


∴ '

2

'1

f

pM

M<0 ， inverted image

u-u'

二、 Galileo’s telescope/ Galilean telescope

M>0, erect virtual image'

2

'1

ff

M

三、 reflecting telescope （ astronomical telescope ）Newton’s telescope 牛顿式反射望远镜

Gregory’s telescope 格雷戈里式望远镜

Cassegrain’s telescope 卡斯格伦式望远镜

Schmidt telescope

Hubble space telescope 哈勃太空望远镜

0,0 '2

'1 ff

eyepiece

F2•F1'u u'


objective

Now,

施密特望远镜

四、 Extender instrument of laser 激光扩束器

Convergence point can produce ionizationUpside-down Galilean telescope 倒装的伽利略望远镜

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

’ ， f

2’ 。

supplement

2.5 (Optical) Stop/diaphragm and pupil 光阑光瞳

一、 The concept of stop/diaphragmStop——the plate with loophole of optical system

Function ：1. Limit the aperture angle

2. Limit the rays of paraxial

3. Control the luminous flux

4. prevent stray light

Classifying ( function)

☆Effective diaphragm/stop —limit the aperture angle of object on the axis

Field diaphragm/stop —limit the paraxial image formation 限制轴外成象

{

透光孔

以作用分类：

有效光阑

视场光阑

限制轴上物点孔径角

二、 Effective stop(aperture stop) and pupilEffective stop——limit the entrance beam most of all stops

For the point of axis

• •P Q

P—“1”effective stopQ—“2”effective stop

1 2

（ 1 ） varies with different specific object points;

Properties ：

在所有各光阑中，限制入射光束最起作用的那个光阑。

有效光阑 ( 孔径光阑 )

• •P P'

A

BB'

A'A’B’is the effective stop of point P

Entrance pupil 入射光瞳—— limit entrance rays, the image of effective stop by former system

Exit pupil 出射光瞳—— limit exit rays, the image of effective stop by latter system

{Either real object or image

（ 2 ） limitation of image ray can be looked as the limitation of object ray.

限制入射光线，有效光阑被它前面的光学系统成的象

限制出射光线，有效光阑被它后面的光学系统成的象

*2.6 Outline of photometry-transmission of light energy

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。

Radiation flux density e(λ)— 单位波长范围间隔内的辐射通量。

,dd

e

0

de

二、 Visibility function

555v

（ 1 ） varies with different persons（ 2 ） varies with background brightness

（ if the background is dark, it moves to the short wave.)

properties ：

光能量传递——辐射度学可见光范围——光度学

555nm

（ unit ：W ）

v()1.0

谱辐射通量密度

视见函数standard luminosity curve

标准亮度曲线

三、 Luminous flux ΦLuminous flux—it is only that part of the total radiation flux, which is visible and can affect the eye. devKdvKd mm

Km最大光视效能

Km= 683 lm/W luminous flux of homochromatic light ：

devd 683luminous flux of polychromatic light ：

00

683 devd

Luminous efficiency: P

unit ： lumen （ lm

光通量

发光效率

光源耗电功率

四、 Intensity of illumination 发光强度

Intensity of illumination—luminous flux per unit solid angle

dd

I unit ： cd (candle)

If the intensity of illumination of a source in all directions, then

IId 4

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）

SI 中，七个基本单位之一

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

五、 Incidence and exitance

Illuminance E—the flux per unit area incident onto a real or imaginary surface.

dSd

E

Point light source

2

2 coscosR

IdS

RdSIdSId

E

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

dSd

M unit ： lux, lm/m2

α

dS

R

勒克斯

勒克斯

单位面积上接收的光通量

照度和出射度

六、 Illuminating power 亮度

Illuminating power L—the luminous flux per unit solid angle per unit projected area.

S

dS

dΩθ

ddS

dL

cos

unit ： cd/m2

cosdSdI

L By the definition of intensity of illumination, we have 　　

Expansive light source dI cosθ

L is independent of θ Lambert’s cosine law

Diffuse reflection Lambertian reflectorLambert source

辐射面上单位投影面积，在单位立体角内辐射的光通量。

由发光强度定义， L 可写为：

扩展光源

朗伯光源朗伯定律

七、 Principle of three primary colors 三原色原理

The light of nature can be mostly obtained by the combining of different proportional luminous flux of three colors.

R (=700 nm)

G ( =546.1 nm)

B (=435.8 nm){

shot 拍摄：分光系统分解 R

GB

光电转换 ER

EG

EB

Transmit or storepictures

DisplayER

EG

EB

加到彩色显象管Red picturesGreen picturesBlue pictures

Color pictures

光通量按不同比例混合可得到自然界大多数颜色的光

Photoelectric conversion

discompose

Colorful kinescope

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

2

2..0

' 1

ANRLE

L0——illuminating power of object in the vacuum

——transverse magnification

RN.A.——numerical aperture

unR AN sin.. n ——the refractive index of object

u ——aperture angle

u

象面照度

孔径角

Illuminance of image surface

二、 Light gathering power of telescope, relative aperture


2

''

fd

E

d ——objective aperture of telescope

d/f '——relative aperture

Reflecting telescope 1/3.33Refracting telescope 1/18.9

三、 Light gathering power of camera

2

''

fd

E {Far object

Near object

2

'0'

4

fdL

E

2

'0'

16

fdL

E

望远镜的聚光本领相对孔径

d/f '


F number ( 光圈数）— the reciprocal value of relative aperture,

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

1 1.4 2 2.8 4 5.6 8 11 16

Relative aperture

d/f '1/1 1/1.4 1/2 1/2.8 1/4 1/5.6 1/8 1/11 1/16


2561

1281

641

321

161

81

41

21

1

F 数 that is, f '/d

*2.8 Aberrations 象差

Monochromatic aberrations

Point of axis（ broad beam ）

Spherical aberration

Point of paraxial

Near point（ broad beam ）

coma

Far point（ sharp beam ）

Cu

rvature of field

astigmatism

distortion

Pin

cush

ion

distortion

Barrel

distortion

Classification of aberrations

Chromatic aberrations

The refractive index of the material of a lens is different for different wavelengths.由于透镜对不同波

长光会聚能力不同引起的

Chromatic aberration ：Constringence （ V 数）

CF

D

nnn

V 1

nD——yellow refractive index

nF——blue refractive index

nC——red refractive index

Remove chromatic aberration

1. Combination of two different materials

2. Two lenses are made of the same material

'2'1'

2'

1'

2'

1' 2

1,

111ffd

ffd

fff

0'

ddf

Satisfy,

then ，

色差

消色差

倒色散系数，阿贝数

Chap. 2

Chap. 2 Principles of optical instruments 光学仪器的基本原理.

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Transcript of Chap. 2 Principles of optical instruments 光学仪器的基本原理.