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

2. 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

3. 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

4. { 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

5. Myopic eye
Nearsighted eye
Hyperopic eye
Farsighted eye

6. 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

8. 2.1 Magnifying power of aided visual instruments
Magnifying glass
一、The concept of magnifying power

9. -l -l' 1. Sensing of human eye to the size of object uQ
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'

10. { 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)

11. 二、amplifying lens / magnifying glass 放大镜u' • F
-p' y u
25 cm
Magnifying power of lens ∴ 3×

12. *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

13. • 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

14. （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.

15. 2.3 Magnifying power of microscope

16. { 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

17. Magnifying power of microscope：∴

18. 2.4 magnifying power of telescope

19. { { { 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'

20. ∴ • ∴ Magnifying power： M<0，inverted image Finite object
objective
eyepiece
F1' F2 • u
-u'
Magnifying power： ∴

21. 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

22. 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’ 。

23. 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

24. 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;

25. { 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

26. *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.)

27. 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

28. 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）

29. 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

30. 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

31. { 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

32. 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

33. { 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

34. 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

35. *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

36. 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