1
第五节 典型的双光束干涉系统及其应用一、典型干涉系统
1、斐索 ( Fizeau ) 干涉仪：等厚干涉型的干涉仪
L3
G
L2
P
Q
L1
激光平面干涉仪
1）激光平面干涉仪的组成和工作原理
2
a
e?
2）主要用途
测定平板表面的平面度和局部误差
测量平行平板的平行度和小角度光楔的楔角
测量透镜的曲率半径
3
测量平行平板的平行度和小角度光楔的楔角
L3
G
L2
Q
L1
激光平面干涉仪
e?
a
4
D
h
R1 R
2
P
Q
2
8
11
8
2
21
2




Nh
k
D
RR
D
h
测量透镜的曲率半径牛顿环
5
球面干涉仪
L
L
L
L
P Q
6
小结：
基本特点：（ 1）属于等厚干涉
（ 2）干涉光束，一个来自标准反射面，
一个来自被测面。
重点掌握：（ 1）光程差与厚度的关系。
（ 2）厚度变化与条纹弯曲方向的关系。
（ 3）干涉面间距变化与条纹移动的关系。
条纹分析：
22
n
H
e
e注意应用比例关系：
7
2、迈克尔逊干涉仪
（ The Michelson interferometer）
Extended
source
Beam
splitter
Reflective coating
Mirror
Compensating
plate
1）干涉仪结构
分光板和补偿板
平面反射镜
干涉原理
2）干涉条纹的性质
等厚干涉
等倾干涉
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）定域面位置不同（
）光程差变化量：（
注意：
2
21 S
S特点,M1 和 M2 垂直时是等倾干涉，否则为等厚干涉。
掌握：
（ 1）系统结构，
（ 2） M1或 M2垂直于光线移动时对条纹的影响
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3、泰曼干涉仪（ Twyman interferometer）
特点：在迈克尔逊干涉仪的一个光路中加入了被测光学器件
Contour lines
Fringes of equal
thickness
10
4、马赫－曾德干涉仪
（ Mach-Zehnder interferometer）
测量光一次通过被测域
It is preferred to measuring
large transparent objects.
2）干涉仪结构
1）应用场合和测量的基本原理
3）条纹性质分析
11
频率偏移器
A B P
二、其他干涉技术
1、数字波面干涉术目的：产生移动的干涉条纹，用光电器件探测条纹的变化。
基本原理：利用光学拍频中干涉条纹强度随时间变化的性质。
外差干涉原理
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tiE
tyxiyxEtyxE
rr
)(e x p
,e x p,,,
0






则合成的光波：
。，参考光波为设：干涉光波频率为
tyxEyxEEyxEtyxI rrr,c o s,2,,,0220
光强分布：
-4 -2 0 2 4
0,0
0,2
0,4
0,6
0,8
1,0
t
I(x,y,t)
条纹是随时间变化的量。
13
T
tyx
r
2),(
tyxEyxEEyxEtyxI rrr,c o s,2,,,0220
光强分布：
A B
t
I
T?t
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2、傅里叶变换光谱仪原理：利用光源的相干长度对条纹可见度的影响，
测量光源的光谱分布 。
相干长度：光谱宽度为的光源能够产生干涉的最大光程差

dkikkII
dkikikkIdkkI
dkkkIdkkI
dkkkII
)ex p ()()0(
2
1
)]ex p ()[ ex p ()(2)(2
)c o s ()(2)(2
c o s1)(2)(
0
00
00
0











设,I0(k)为随波数而变化的谱密度函数，整个光谱分布在（ -?,+?）之间,?为两光路的光程差。则：
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）（
）（傅里叶变换对：
2 )ex p ()(
2
1
)(
1 )ex p ()()(
0
0




dikWkI
dkikkIW
在麦克尔逊干涉仪中，通过移动 M2，改变?获得
W(?),再通过反傅里叶变换计算出 I0(k)。
W(?)
I(?)
dkikkIIIW )e x p ()()0(21- )()( 0
设
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Homework (11-5)
1,Using red cadmium light,?=643.8nm,
Michelson in his original experiment
could still see interference fringes
after he had moved one of the mirrors
25cm away from the coincidence
position,How many fringes did he
count?
P244 9&16
下一节
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Armand H,L,Fizeau
Armand H,L,Fizeau (1819-1896),
French physicist,was born of a
wealthy French family that enabled
him to be financially independent,
Instead of shunning work,however,
he devoted his life to diligent scientific
experiment,His most important
achievement was the measurement of
the speed of light in 1849.
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Albert Abraham Michelson
Albert Abraham Michelson (1852-1931)
was born in Strelno,Prussia,He moved to the
United States with his parents when he was 2,
He graduated from,and taught at,the U,S,
Naval Academy and later worked at the Case
School of Applied Science,Clark University
and the University of Chicago,In 1907 he was
awarded the Nobel prize in physics,the first
American scientist to be so honored,
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Michelson is best known for his precise
determination of the velocity of light,
for inventing the interferometer that
bears his name,He also made
noteworthy contributions to
astronomy,spectroscopy and
geophysics,was proficient in tennis
and other sports,played the violin,
and liked to paint landscapes.
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Frank Twyman
He is a manager,at Adam Hilger Ltd.,
astronomical and optical instrument
makers in London,
The Twyman interferometer is
particularly useful for the testing of
optical components such as lenses,
prisms and mirrors.