Download 第四章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
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  4I
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