南开大学光学工程内部课件Oct 28th
Need Q ~ 105 or greater Led to super mirrors
polished to Angstroms ion beam machining polished to ~ 100 nanometers limited by grit size
Laser gyro developed for aircraft
tCCW = 8R 2c R
Travel time cw
tCW = 8R 2c - R
Time difference
Dt 4 A c2
Number of fringes
DN = 4 A cl
Fringe shift ~ 4 % for 2 rev/sec
Laser gyro
Interferometers
Interferometer
What is interferometer?
Interferometer is the optical setup which split incident light into two beams and then recombines them to create an interference fringe.
N=2L/ l =2L/ l
Phase change (in terms of wavelengths):
DN=Nm - N=2Ln/l- 2L/l= 2L/l (n-1)
The Michelson-Morley Experiment
1881
White light fringes
Adjust the mirrors to make the two path has the same path length, one can see white light fringes.
MZI in integrated optics
Optical modulators at tens to hundreds Gb/s
Sagnac interferometer
Another version of Sagnac interferometer
Laser gyro
Light travel time ccw
TTM interferometric Objective
Gravity Wave Detection
Einstein predicted that accelerated massive objects produce time-dependent gravitational fields, gravity waves, that propagate as “warpages” of spacetime at the speed of light. Very tiny: dL/L of ~10-21 for inspiraling binary neutron stars. How to detect the tiny effect???
Interference Fringes
Fringes of equal inclination
Equal inclination + Equal thickness
Fringes of Michelson Interferometer
Application Sample
Measuring the Refraction Index
Let E (r , t ) present a light beam.
The light goes through an interferometer and is splitted
into two beams which travel different pathes. On the screen, the intensity of the interference fringe is given by:
Application Sample
L = thickness. n = index of refraction Number of wavelengths in the block (2 times):
Nm=2L/ln=2Ln/ l
Number of wavelengths in same distance without block:
Visibility
I max - I min Fringe Amplitude V= = I max I min Average Intensity
M1
BS (0<V<1)
d
M2 M1’
Screen
d increases from 0 to infinity. How does V change with d? Keep constant or …?
Conventional mirrors
Fizeau interferometer
Twyman-Green interferometer
Mirau interferometer
Interferometric Testing
Typical Measurement Results – Flatness/Shape – Critical Dimensions – Roughness – Depths and Volumes – Film thickness – Dynamic Response • Typical Parts Measured – Optics (flats, spheres, torics, aspheres, prisms, windows) – Semiconductor Products (wafers, MEMS) – Data Storage (hard disk read heads, disks, suspensions) – MEMS (pressure sensors, accelerometers, micro-mirrors) – Cutting and Grinding Implements – Precision Machine Parts – Coatings (AR, anti-corrosion coatings)
The LIGO project
The LIGO folks think big…
The longer the interferometer arms, the better the sensitivity.
So put one in space, of course.
Mach-Zehnder interferometer
∆φ = 2π /λ
= 2d
d
When one of the two mirrors is moved by ½ l, the optical path length is change by l and the fringe pattern is moved by one fringe.
Interference Fringes
M1
d
BS
M2 M1’
Screen
When M2//M1’, Fringes of Equal inclination appar
Interference Fringes
Equal inclination interference
Inner rings have higher order and larger angular width. So in the border, fringes are denser.
Interferogram Examples
Astronomical interferometry
B
variable delay (B.S) Delay line
Astronomical interferometry
Coherence
Visibility of interference fringes
Gravity Wave Detection
LIGO: Laser Interferometric Gravitational wave Observatory -World’s largest interferometers: 4-km -2 in Hanford, WA; 1 in Livingston, LO; …… - >400 scientists -Projected sensitivity ~3 x 10-23 DL ~ 10-19 m (10-9 Ang.)
Closed loop Laser can oscillate both directions High reflectivity mirrors
Improve fringe resolution Earth rotation = 1 rev/day at poles 25 ppm of fringe
Interference Fringes
M1
d
BS
M2 M1’
Screen
When M2 is not parallel to M1’, there are two possibilities. If d~0, fringe of equal thickness appears. If d>>0, Fringes of equal inclination and thickness can be observed.
The Michelson Interferometer
In a Michelson interferometer, an incident beam is splitted by a half-reflector (beam splitter) so that one beam strikes a fixed mirror and the other a movable mirror. The reflected beams are collimated by the half-reflector. Therefore an interference pattern results.
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a
n1
i1
a1
D B
n2
A
i2
n1 C
a2
d
由折射定律和几何关系可得出：
n1siin 1n2siin 2
AD AB siin1
AC C Bd/coi2s AB2dtain2
1、非相干叠加 独立光源的两束光或同一光源的不同部位所发出 的光的位相差“瞬息万变”
1
0
cosdt0
II1I2
叠加后光强等与两光束单独照射时的光强之和，
无干涉现象
2、相干叠加 满足相干条件的两束光叠加后
II1I22I1I2co s
位相差恒定，有干涉现象
若 I1 I2
§1.1.5 相干与不相干叠加
矢量合成方法
x1A 1cots (1)0
x 2 A 2 co t s 2) ( 0
A
AA 12A2 22A 1A2co2s0 (1)0
A2
y2
y2
y
0arcA A 1 1tc sa io1 1 n n s0 0 A A 2 2c sio2 n 2s 0 0O
3、光强 光波是电磁波。 光波中参与与物质相互作用（感光作用、生理
作用）的是 A 矢量，称为光矢量。 A 矢量的振动称为光振动。
光强：在光学中，通常把平均能流密度称为光强， 用 I 表示。
I A2
机械波的独立性和叠加性
发生干涉的条件： 1、频率相同 2、观察时间内波动不中断 3、相遇出振动方向几乎在同一直线上 干涉现行的特性：
2d
k0,1,2…
干涉加强
干涉减弱
明纹位置
暗纹位置
两相邻明（或暗）条纹间的距离称为条纹间距。
南开大学光学工程内部课件Sep 7th
Brief history of optics (cont’ed)
平面镜 (《经下》19/—/42· —) 经：景迎日。说在转。 影子可以由反射(迎)太阳(的光线)形 成。理由在于翻转
经说：景，日之光反烛人，则景在日与人之间。
如果太阳之间
Brief history of optics (cont’ed)
母国光 战元龄著 《光学》 人民教育出版社
参考书目
ftp://202.113.227.137 Username: optics Password: optics-nk
/opt/index/
/course/optics/
《淮南万毕术》，公元前120左右，淮南王刘安及 其门客的著作。记录了用冰制作透镜的方法： “削冰令圆，举以向日，以艾承其影，则火生。” 还记录了潜望镜的雏形：“取大镜高悬，置水盆 于其下，则见四邻矣。”
Brief history of optics (cont’ed)
谭峭《化书》，约公元940年(南 唐)。书中有一段十分有趣的记 录：小人常有四镜。一名圭，一 名珠，一名砥，一名盂。圭视者 大，珠视者小，砥视者正，盂视 者倒。观彼之器，查我之型，由 是无大小，无短长，无妍丑，无 美恶。描述的很有可能是四种透 镜的成像性质。圭是双凹发散透 镜，珠是双凸透镜，砥是平凹透 镜，盂是平凸透镜。
一个受到光照射的人，看起来就好像他在发射出（光线）一样。人的下 部成为（像的）上部，而人的上部成为（像的）下部。人的脚（好像发 出）光在下方被遮蔽（即照到了针孔的下方），（但另一些光线）在上 方成像。人的头（好像发出）光在上方被遮蔽（即照到了针孔的上方）， （但另一些光线）在下方成像。在（离开光源、反射体或像）较远或较 近的某个位置上，有一个距激光的点（端）（即针孔），结果像就只被 允许通过聚集之处（库）的光线所形成
南开大学光学工程内部课件Oct 19th
E1 (r , t ) E01 exp i(k1 r t 1 ) E2 (r , t ) E02 exp i(k2 r t 2 ).
Two plane waves meet at P
Superposition of two beams
The transmitted light is incident onto a screen containing two narrow slits
Young’s Double Slit Experiment
The symmetric narrow slits, S1 and S2 act as the two light sources The waves from the two slits come from the same source S0 and therefore are always in phase.
m
= 0, ±1, ±2, …
Interference Equations
Y:measured vertically from the zeroth order maximum Assumptions
L >>d,
d >>λ
y =LtanθLsinθ
I I1 I 2 2 I1I 2 cos(kd sin ) I1 I 2 2 I1I 2 cos(kdy / L)
Other Coherent Sources
Currently, it is much more common to use a laser as a coherent source The laser produces an intense, coherent,
南开大学光学工程内部课件Nov-16th
If the primary wave was simply to propagate
from S to P, it is
E
0
e i[t k ( r0 )]
r0
The two equations must be exactly the same. So we introduce a /2 phase difference between the primary wave and the secondary wave to make the two equations so.
dS d 2 ( sin )
Fresnel Dif2 2( r0 )cos
So
dS 2 rdr. Constant!!! r0
We have
El
(1)l 1
2Kl A r0
equation (a) becomes
E E1 Em
2
2
Fresnel Diffraction
From equation (b) we have
E
E1
E2 2
E m 1 2
Em
Since K() goes from 1 to 0 over a great many zones, we can neglect any variation between adjacent zones, i.e. │E1│= │E2│, │Em-1│= │Em│. So
Em 2
)
Em 2
(a)
or
E
E1
E2 2
(
E2 2
E3
E4 2
南开大学光学工程内部课件Lecture 2
—— Range Instrumentation prism, right.
BM 60 90 right
Ray Tracing
Reflection from Flat Surface
—— Range Instrumentation prism, left, roof.
BM 100 90 left roof
CR 180 roof
Ray Tracing
Reflection from Flat Surface
—— Rhomb prism. It has two reflective faces 斜方棱镜，又名菱形棱镜
BC 0 (Rhomb)
Ray Tracing
Reflection from Flat Surface
Reflection from Flat Surface
—— Isosceles prism, three reflective faces, roof
CR 45 roof (Schmidt)
Ray Tracing
Reflection from Flat Surface
—— Isosceles prism, three reflective faces, roof
Reflection Prism
—— Isosceles prism (Classification code: R), single reflective face. 等腰棱镜(代号:D), 一次反射型
The Dove Prism (AR45)
Ray Tracing
Reflection from Flat Surface
• In fact, if the UV and IR are included, most any substance will sow some absorption. So anomalous dispersion exist somewhere throughout the spectrum
BM 60 90 right
Ray Tracing
Reflection from Flat Surface
—— Range Instrumentation prism, left, roof.
BM 100 90 left roof
CR 180 roof
Ray Tracing
Reflection from Flat Surface
—— Rhomb prism. It has two reflective faces 斜方棱镜，又名菱形棱镜
BC 0 (Rhomb)
Ray Tracing
Reflection from Flat Surface
Reflection from Flat Surface
—— Isosceles prism, three reflective faces, roof
CR 45 roof (Schmidt)
Ray Tracing
Reflection from Flat Surface
—— Isosceles prism, three reflective faces, roof
Reflection Prism
—— Isosceles prism (Classification code: R), single reflective face. 等腰棱镜(代号:D), 一次反射型
The Dove Prism (AR45)
Ray Tracing
Reflection from Flat Surface
• In fact, if the UV and IR are included, most any substance will sow some absorption. So anomalous dispersion exist somewhere throughout the spectrum
大学光学L绪论PPT学习教案
解: 水相对于空气的折射率为 n (n 4 / 3)
根据折射定律，有
O
y' y
Q'
x
i2
i1 M
空 气
水
n1 sin i1 sin i2
Q
y x tan i1
y' x tan i2
y' y tan i1 y sin i1 cos i2 y 1 n2 sin2 i1
tan i2 sin i2 cos i1
第18页/共47页
5）光强定义为一个平均值的原因
响应时间：能够被感知或被记录所需的最短时间 人眼的响应时间：t 0.1s
109 s 最好的仪器的响应时间大约：
T 1015 s
光波的振动周期：t T
人眼和接收器只能感知光波的平均能流密度 有实际意义的是光波的平均能流
第19页/共47页
三、光 谱
n1；n2
第30页/共47页
n1 sin i1 n2 sin i2
斯涅尔定律（W.Snell ）
介质折射率不仅与介 质种类有关，而且与光 的波长有关。在同一种 介质中，长波折射率小 ，短波的折射率大。
第31页/共47页
[例题1] 在水中深度为y 处有一发光点Q，作QO垂直于水面，求射
出水面折射线的延长线与QO交点Q '的深度 y 与' 入射角 i1 的关系
1）单色光：仅有单一波长的光叫单色光，否则 是非单色光。
2）谱密度： dI ~ d i() dI
d
3）光谱：谱密度随波长变化的分布曲线
I 0 dI 0 i()d
4）连续光谱：光谱随波长的变化分布连续叫做
连续光谱
第20页/共47页
《光学基本知识讲座》课件
光学在军事中的应用
总结词
光学技术在军事侦察和武器系统中的应用
详细描述
光学技术在军事领域的应用包括红外侦察、 激光雷达、瞄准和测距等。这些技术提高了 军事侦察和武器系统的精度和效率，对现代
战争的胜负具有关键作用。
04
光学发展历程
光学发展史简介
古代光学
古代文明对光的研究和利用，如反射、折射等简单光 学现象的发现和应用。
全息摄影技术
总结词
全息摄影原理及应用
详细描述
全息摄影技术利用光的干涉和衍射原理，记 录并重现三维物体的光波信息。全息照片具 有立体感和视角任选的特性，广泛应用于产 品展示、艺术创作和安全识别等领域。
光学在医学中的应用
总结词
光学在医学诊断和治疗中的应用
详细描述
光学技术在医学领域具有广泛的应用 ，如光学显微镜用于细胞观察，激光 用于手术切割和眼科治疗，以及光学 成像技术用于无创检测和诊断。
文艺复兴时期
科学方法的兴起，对光的本质和传播方式的研究逐渐 深入。
19世纪
光学理论体系逐渐完善，如波动光学和几何光学的发 展。
光学重大发明和发现
01
02
03
牛顿的棱镜实验
揭示了白光是由不同颜色 的光组成，奠定了光谱学 的基础。
干涉现象的发现
为波动光学的建立提供了 重要依据。
激光的发明
开创了光学的新领域，对 科技、工业、医疗等领域 产生了深远影响。
实验材料
光源、衍射板、屏幕等 。
Hale Waihona Puke 实验步骤将光源对准衍射板中心 ，调整光源与衍射板距 离；观察衍射现象并记
录。
注意事项
注意保护眼睛，避免直 接照射光源；调整仪器
南开大学光学工程内部课件Sep_16th
Refraction at curved surface
Similar, the second or image focus is the axial point Fi where the image is formed when S0= . And the second or image focal length fi as equal to Si in the special case, we have
Why are focusing instruments necessary?
Refraction at curved surface
Imaging In order to image S at location P, the time it takes for each and every portion of a wavefront leaving S to converge at point P must be identical. So:
which followed with
n1 n2 1 n2 S i n1 S0 ( ) SM 2 MS ' R MS ' SM
Refraction at curved surface
Discussion Sign convention for spherical refraction surfaces and thin lenses
Refraction at curved surface
Fermat’s Principle maintains that the optical path length (OPLSS’) will be stationary （实际上，物与像之间根据费马原 理具有等光程性）, i.e.:
南开大学光学工程内部课件Sep 28th
The objective lens has a short focal length, ƒo<1 cm The ocular lens (eyepiece) has a focal length, ƒe, of several cm L>> ƒo and ƒe
Compound Microscope
The image seen by the eye, I2, is virtual, inverted and very much enlarged
The magnification of the microscope is the product of the magnifications of the objective and the ocular lens
Normal
vision has a far point of infinity
Farsightedness
Also called hyperopia The image focuses behind the retina Can usually see far away objects clearly, but not nearby objects
m o
angle with lens angle without lens
Simple Magnifier
The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye
Presbyopia and Astigmatism
Diopters
Compound Microscope
The image seen by the eye, I2, is virtual, inverted and very much enlarged
The magnification of the microscope is the product of the magnifications of the objective and the ocular lens
Normal
vision has a far point of infinity
Farsightedness
Also called hyperopia The image focuses behind the retina Can usually see far away objects clearly, but not nearby objects
m o
angle with lens angle without lens
Simple Magnifier
The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye
Presbyopia and Astigmatism
Diopters
光学和光子学概述PPT讲稿
• 分波面干涉、分振幅干涉和分振动面干涉。
现在您浏览的位置是第九页，共三十八页。
四、光的衍射
• 1. 基本概念
• ① 衍射定义 • 光绕过障碍物偏离直线传播而进入几何阴影，
并在屏幕上出现光强分布不均匀的现象。
• ② 衍射条件
障碍物的线度和光的波长可以比拟
• ③ 衍射的分类
a. 菲涅耳衍射：近场、求和、点光源。 b. 夫琅和费衍射：远场、积分、平行光。
表2 霾、云和降水天气的物理参数
天气类型
霾M 霾L 霾H 雨M 雨L 冰雹H 积云C.1 云C.2 云C.3 云C.4
N (cm-3) 100 cm-3 100 cm-3 100 cm-3 100 cm-3 1000 m-3 10 m-3 100 cm-3 100 cm-3 100 cm-3 100 cm-3
m 0.827 N A3 / 4
(9)
式中，m为瑞利散射系数（cm-l）；N为单位体积中的分 子数（cm-1）；A为分子的散射截面（cm2）；为光波长 （cm）。
现在您浏览的位置是第二十页，共三十八页。
由于分子散射波长的四次方成反比。波
长越长，散射越弱；波长越短，散射越强烈。
故可见光比红外光散射强烈，蓝光又比红光
现在您浏览的位置是第八页，共三十八页。
三、光的干涉
• 1. 基本概念 • ①光的电磁理论 • 光是某一波段的电磁波， 其速度就是电磁
波的传播速度；可见光在电磁波谱中只占很小 的一部分，波长在 390 ~ 760 nm 的狭窄范围 以内。
• ②相干条件
• 频率相同、振动方向相同、相位差恒定。
• ③干涉的分类
O2
4.7
9.6
从表1不难看出，对某些特定的波长，大气呈现出极为强烈的吸
现在您浏览的位置是第九页，共三十八页。
四、光的衍射
• 1. 基本概念
• ① 衍射定义 • 光绕过障碍物偏离直线传播而进入几何阴影，
并在屏幕上出现光强分布不均匀的现象。
• ② 衍射条件
障碍物的线度和光的波长可以比拟
• ③ 衍射的分类
a. 菲涅耳衍射：近场、求和、点光源。 b. 夫琅和费衍射：远场、积分、平行光。
表2 霾、云和降水天气的物理参数
天气类型
霾M 霾L 霾H 雨M 雨L 冰雹H 积云C.1 云C.2 云C.3 云C.4
N (cm-3) 100 cm-3 100 cm-3 100 cm-3 100 cm-3 1000 m-3 10 m-3 100 cm-3 100 cm-3 100 cm-3 100 cm-3
m 0.827 N A3 / 4
(9)
式中，m为瑞利散射系数（cm-l）；N为单位体积中的分 子数（cm-1）；A为分子的散射截面（cm2）；为光波长 （cm）。
现在您浏览的位置是第二十页，共三十八页。
由于分子散射波长的四次方成反比。波
长越长，散射越弱；波长越短，散射越强烈。
故可见光比红外光散射强烈，蓝光又比红光
现在您浏览的位置是第八页，共三十八页。
三、光的干涉
• 1. 基本概念 • ①光的电磁理论 • 光是某一波段的电磁波， 其速度就是电磁
波的传播速度；可见光在电磁波谱中只占很小 的一部分，波长在 390 ~ 760 nm 的狭窄范围 以内。
• ②相干条件
• 频率相同、振动方向相同、相位差恒定。
• ③干涉的分类
O2
4.7
9.6
从表1不难看出，对某些特定的波长，大气呈现出极为强烈的吸