3D Holography

This is a project that I have spent at least three months. I learnt a lot from it, and is digging deeper.

Big thanks to my seniors Zhongyuan Guo and Zhaoyu Gong for their guidance. Thanks to my teacher Xing Chen for his careful instructions.

Course

I finally made a Matlab application and we can get a stereo view of an object after encoding it and put on an SLM. I have put the code on Github here.

Some thoughts about holography are put here.

Below is a brief course article:

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Competition

We competed in Zhejiang Physics Innovation Competition. Below are the research article and speech powerpoint.

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光电材料笔记

记录一些在光学材料与元件制造课程中的整理和总结。

光学玻璃

无规网络学说
- 网络形成体
- 网络中间体
- 网络外体
命名与化学成分
- 折射率
- 阿贝数
- 相对部分色散

物理光学笔记

记录一下自己在学习物理光学过程中的思考和总结。

光的电磁理论基础

光波的傅立叶分析

实际光波是一个波列。波的单色性和波列长度有关。

有效空间频率范围 $\Delta k=\pi/L$

有效波长范围 $\Delta \lambda=\lambda^2/2L$

时间频率范围 $\Delta \nu=\Delta \left(c/\lambda\right)=c/2L$

随机过程复习总结

随机过程课程的复习总结笔记。

1. Markov 过程

状态转移矩阵

$p_{ij}^n=P(X_{t_0+n}=j\mid X_{t_0}=i)$

CK方程： $\vec\mu^{(n)}=\vec\mu^{0}P^n$

常返和暂留

常返：状态 $i$ 出发有限次可回

常见考点：求出所有互达等价类，各状态的周期和常返性，计算所有正常返态的平均回转时，计算极限概率

是否常返：

有限马尔可夫链可以利用闭互达等价类直接判断：如果状态空间 $I$ 有限，则状态 $i$ 常返当且仅当 $i$ 的互达等价类是闭的，且这时 $i$ 一定是正常返
利用互达等价类减少计算：若状态 $i$ 和 $j$ 互达，则 $d(i)=d(j)$ （周期相等），$i$ 常返/正常返当且仅当 $j$ 常返/正常返
通过计算来判断：计算 $f_{ii}=\sum\limits_{n}f_{ii}^{(n)}$, $f_{ii}=1$ 常返，$f_{ii}<1$ 暂留。其中 $f_{ij}^{(n)}$ 是 $i$ 出发在第 $n$ 步首次击中 $j$ 的概率。对于非封闭的互达等价类，通过计算 $f_{ii}$ 说明暂留性。
是否正常返：计算平均回转时 $\mu_i=\sum\limits_n nf_{ii}^{(n)}$, 看是否有限, 若无限则为零常返

极限概率：

利用平稳分布
若状态 $j$ 为暂留或零常返，则对所有 $i$, $\lim_\limits{n\to\infty} p_{ij}^{(n)}=0$

平稳分布

初始分布与一步分布相同：$\pi P=\pi$。

比如：$\pi_1=\frac 1 2 \pi_1+\frac 1 3\pi_2$ , 是指从初始状态 $\pi_1$ 一步后到 $\pi_1$ 再从 $\pi_1$ 以 $\frac 1 2$ 概率回到 $\pi_1$，一步后到 $\pi_2$ 再从 $\pi_2$ 以 $\frac 1 3$ 概率回到 $\pi_1$。

对互达等价类（不可约状态集）的计算：

闭的 $\implies$ 正常返 $\implies$ 平稳分布存在且唯一， $\pi_i=\frac 1 {\mu_i}$
若为非周期正常返，则任何状态 $i,j,\lim_\limits{n\to\infty}p_{ij}^{(n)}=\pi_j$

吸收概率和平均吸收时间

用递推的思想。

设 $h_i=P(T_a<\infty\mid X_0=i)$ 表示从状态 $i$ 出发在有限时间内能访问状态 $a$ 的概率，其中 $T_a$ 为首次访问状态 $a$ 的时间，有 $h_i=\sum_\limits{j}p_{ij}h_j$.

设 $a_i=E(T_a\mid X_0=i)$ 表示从 $i$ 出发首次访问 $a$ 的平均步数，有 $a_i=1+\sum_\limits{j}p_{ij}a_j$.

2. 独立增量过程

泊松过程

定义

独立增量过程
$N(0)=0$
$N(t)-N(s)\sim \pi(\lambda(t-s))$
$\displaystyle P(N(t)-N(s)=k)=\frac{[\lambda (t-s)]^ke^{-\lambda(t-s)}}{k!}$

数字特征

均值 $\mu_N(t)=E(N(t))=\lambda t$
方差 $D_N(t)=\lambda t$
自协方差函数 $C_N(s,t)=\lambda \min{s,t}$
自相关函数 $R_N(s,t)=E(N(s)N(t))=\lambda \min{s,t}+\lambda^2 st$

推广

合成、分解后依旧是泊松过程
非齐次：$\lambda=\lambda(t)$
${N(t)}$ 为强度 $\lambda$ 的泊松过程 $\iff$ 时间间隔 $T_1,T_2,\cdots$ 相互独立，且服从均值为 $1/\lambda$ 的指数分布

布朗运动

特殊的正态过程

定义

独立增量过程
$X(0)=0$
$X(t)-X(s)\sim N(0,\sigma^2(t-s))$

数字特征

对标准布朗运动 $B(t)={X(t)/\sigma}$

$\mu_B(t)=0$
$D_B(t)=t$
$C_B(s,t)=\min{s,t}$
$R_B(s,t)=\min{s,t}$

推广

${B(t);t\geq 0}$ 是标准布朗运动，则：

${B(t+\tau)-B(\tau)}$ 也是
${\displaystyle \frac 1 c B(c^2t)}$ 也是
$\widetilde B(t)=t\displaystyle B(\frac 1 t) $ 也是（定义 $0$ 处为 $0$）

布朗桥过程：

${B(t);0\leq t\leq 1\mid B(1)=0}$
$\mu=0$
$\sigma^2=t(1-t)$
对 $0\leq s\leq t\leq 1, \operatorname{Cov}(B(s),B(t)\mid B(1)=0)=s(1-t)$

首中时间相关

$P(\max\limits_{0\leq s\leq t}B(s)\geq y)=P(T_y\leq t)=2P(B(t)\geq y)$

3. 平稳过程

宽平稳过程

均值为常数
自相关函数只和时间差有关

各态历经性

记 $\langle X(t)\rangle=\displaystyle\lim_\limits{T\to \infty} \frac{1}{2T}\int_{-T}^{T}X(t)dt$

均值各态历经性： $\langle X(t)\rangle=\mu_X$
自相关函数各态历经性：$\langle X(t)X(t+\tau)\rangle=E[X(t)X(t+\tau)]=R_X(\tau)$
（宽）各态历经过程：均值函数和自相关函数都有各态历经性

重要推论：

若 $\lim\limits_{\tau\to\infty} R_X(\tau) $ 存在，则 ${X(t)}$ 对均值具有各态历经性当且仅当 $\lim_\limits{\tau\to \infty} R_X(\tau)=\mu_X^2$

频率域表述

平均功率 $= R_X(0)=\displaystyle \frac 1 {2\pi}\int_{-\infty}^{\infty} S_X(\omega) \operatorname{d} \omega$
维纳-辛钦公式：$S_X(\omega)$ 和 $R_X(t)$ 互为傅立叶变换对

常用变换：$\displaystyle e^{-a|\tau|}\leftrightarrow \frac{2a}{a^2+\omega^w}$

TP-LINK电子设计竞赛校赛总结

日记

2020.8.24–25 和国学长还有王晓雯一起参加电赛校赛，刚刚结束了电子设计小学期，趁热打铁一波。光电还有一组，是谢昊、雷学姐和沈学姐，大家一起，真的很开心。

Stringless Piano

2020-08-22

Projects / Electronics

这是电子系统设计课程的项目。

C代码及部分说明我放到了GitHub （时间太紧张了，来不及整理）

关于PCB设计原理的思考直接写到了报告中：

C++ Notes

C++学习笔记，主要是华为海思的动作识别项目中用到C++，边用边学边用边记笔记。

代码风格

Holography Notes

2020-08-06

Notes / Optics

This is a note for my work in holography field.

全息

什么是全息？

一种信息的记录方式罢了。

1971年拿了诺奖。

Laser Holography

I started doing semi-conductor holography with my roommates and Jiahao Jiang who has graduated now in our Sophomore year.

Here is the link to that project.

I have to say that I forget most of the details, but configuring my own fixer and developer (显影液和定影液) and building the optic path and finally seeing the results is a procedure that has no technical content but somehow a sense of accomplishment.

全息的路艰难而漫长，但是充满有趣与理想。我想，还是不写蹩脚的英文了，用中文回顾一下我的所思所想。

Image-Matching Road

2020-08-06

Notes / Deep Learning

This is a note for image-matching things in the deep learning field.

Started this in 2020’s summer and it is a part of an SRTP project regarding an AR app with Haojie He and Lingming Zhang.

SuperPoint & SuperGlue

Overview

SuperPoint is a great feature extractor.

SuperGlue is a good image-matching network based on features extracted from images.

It is a really nice project by Magic Leap.

I did a little simplification and put the code here.

Experience and thoughts

For SuperPoint, I think it is a mature network and can be used as a helpful feature extracting tool. (And there are some wonderful tricks in the code! )

For SuperGlue, I didn’t quite get the key to it, such as the Attention Network and the Encoding Method.

In addition, it is quite hard to transfer models from SuperGlue. I have already transferred SuperPoint into Libtorch code, which can be used in C++. It is also easy to transfer to ONNX or other frameworks. However, I suffered greatly in transferring SuperGlue into libtorch code or ONNX. Hence the SuperGlue can work fine on Python but has some difficulty ( for me ) to be deployed.

So I think, later on, I will find a more simple ( hopefully, also more powerful ) matching network so that it can be easily deployed. Or maybe I can create my own networks and do some training.

FSO communication system

2020-07-30

Projects / Optics

This is the project I have done in 2020 UIUC’s OPTIC summer program.

Thank you all , my teammates!

Group Number : 3
Group Leader : Longqian Huang
Group members : Liang Sun, Yuxuan Liu, Junchi Feng, Yuhao Ma, Jinquan Shi, Zhuo Cheng, Yiru Pan, Dongao Cui, Muxi Zhao

By the way, I think I did a great job in the presentation. The recording of our presentation is here. The powerpoint (Keynote) can be accessed here.

Or you can get I quick view of the presentation below: (without the video)

Next is our output article :)

Free Space Optical Communication System

1. What is FSO Communication System

We read the review and searched the Wikipedia to get a overview of FSO Communication System.

FSO Communication is an idea of wireless communication using light based on the theory of light propagation in free space.

Devices using technology of FSO communication make up a system. It is a outdoor system of wireless optical communication system (WOCS) and has some branches. Below is a classification tree of WOCS [1] :

From that we know that we have choices of terrestrial links and space links. We considered both and think that terrestrial links is practical but space links is as well interesting and maybe a future-hot point.

Below is a diagram of FSO communication link [1] (which maybe what we will construct in the next few days):

2. System Design

2.1 Type of the system

We will construct Ground-to-Satellite Link as the type of the FSO communication system. Below is a concept figure of the system.

2.2 Wavelength to use

The main consideration is attenuation after propagating long distance. From [2] we know to make attenuation less, infrared band is a good choice. Then we have two choices:

850 nm
1550 nm

We digged further and found that 1550 nm lasers are considered “eye safe” at much higher power levels than traditionally used 850nm lasers.

So our choice for wavelength is 1550 nm. And the benefits are as follows [1] :

reduce background noise and Rayleigh scattering
high transmitter power
Eye-save wavelength ( the maximum permissible exposure for eye is much higher at 1550 nm wavelength )

2.3 Laser Type

2.3.1 LED or CW

To be clear:

A light-emitting diode (LED) is a semiconductor light source that emits light when current flows through it.
A continuous wave (CW) laser is a laser that emits a continuous laser beam with a controlled heat output, as beam duration and intensity.

For ground-to-satellite links, we don’t think a light of LED can surrive after passing the atmosphere. So we definitely choose CW laser.

2.3.2 Comparasion

We have four choices and they all have own advantages and disadvantages:

Gas laser

Carbon dioxide laser are stable and less sensitive to atomospheric effects
Large volume and unreliability

Solid-state laser

Stable and narrow spectral linewidth
Very high peak power

Semiconductor laser

Compact in size, light weight, easy to operate
Quite low output power hence require additional amplifier for long distance communication
Diodes require great care

Fiber laser [4]

The laser light is both generated and delivered by an inherently flexible medium, which allows easier delivery to the focusing location and target.
Fiber lasers can have active regions several kilometers long, and so can provide very high optical gain.
Fiber lasers are compact compared to solid-state or gas lasers of comparable power ( because the fiber can be bent and coiled)
The additional power and better beam quality provide cleaner cut edges and faster cutting speeds

2.3.3 Choice of laser device type

It seems that fiber laser is great in comparison with others. We first considered solid state laser but fiber laser seems to be better and it has many applications in telecommunications. So we choose fiber laser as our type of laser device.

2.4 Modulator

We have two consideration of the modulator, to be clear:

Electro-optic modulator [6]

An electro-optic modulator (EOM) is an optical device in which a signal-controlled element exhibiting an electro-optic effect is used to modulate a beam of light.
Acoustic-optic modulator [5]

An acousto-optic modulator (AOM), uses the acousto-optic effect to and shift the frequency of light using sound waves.

We found little applications in telecommunications about acoustic-optic modulator and it seems electro-optic modulator has a more mature technology. We found that $LiNbO_3$ has nice performance in the application of long distance communication and there are a lot of type we could choose as provided in [7]. So we choose electro-optic modulator for our ground-to-satellite FOS communication system goal.

To be more specific, we will use $LiNbO_3$ Mach-Zehnder Modulator for its good performance.

3. Simulation

3.1 Demo: FSO communication system

We considered the composition of the system and drew a structure graph as below:

We put our emphasis on the Transmitter part and the following sections are our simulation work.

3.1.1 Layout

Below is the layout of our communication system. We used OptiSystem software to do the simulation.

The transmitter part is in the left and we will dig into it later.

In the middle is the FSO Channel. Since Ground-to-Satellite system has at least 90 km (see regions of atmosphere diagram below) , we set the range of the FSO channel 100 km. On the left and right of the FSO channel are two opticla amplifiers, from simulation result we can found their role in the system.

On the right is the Receiver part. It consists of PIN Photodiode (which transfer optic wave into electric signal), Law Pass Bessel Filter (which is used to filter out noise) and Data Recovery Module (which do the demodulation and get the recovered signal).

We use BER Analyter to analyse the bit error rate of the system.

3.1.2 Simulation result

Above is our simulation result from which we can found that loss is huge. The reason is FSO channel is too long.

Because of the time and technology limitation, we didn’t get a good simulation result. Below is something we considered:

how to overcome the problem of very big loss
how to choose the laser power
how to choose photodetector
- photodiode
- optical power detector
- optical phase detector
how to choose filters
- low pass
  - Gaussian filter
  - Bessel filter
  - etc.
- height pass
- band pass
how to set parameters of optical amplifier
- gain
- noise figure

3.2 Optical transmitter

From COSMOL, we get the some insight of the modulator. But it is not that clear.

We use OptiSystem to construct our optical transmitter and further more, we digged a little deeper and build a demo of the whole FSO communication system.

Below are the layout of our system.

From the figure we can see the structure of the transmitter clearly.

We use simple Bit Sequence Generator to generate electric signal and use NRZ Pulse Generator to generate electric pulse.
We use Fiber Laser as our laser device. As there isn’t Fiber Laser device in the software, we put a CW Laser and add a description. CW Laser can generate 1550 nm optical wave.
We use $LiNbO_3$ Mach-Zehnder Modulator in our transmitter. The reasons have been stated in section 2.
Put the optic signal and electric pulse into the MZ Modulator, we can get the modulated optical signal.

Above are the details of our transmitter, we then use Optical Power Meter and Optical Spectrum Analyzer to do the simulation.

Results are as follows :

We can see from the figure that the transmitter has $2.485$ dBm los and the output power is $56.432\times 10^{-3} W$. We need optical amplifiers to make it larger.

3.3 Electro-optic Modulation Process

In order to give a more specific model, we use COMSOL to simulate the Electro-optic modulation process. Below are what we have done.

We choose the wave optics module.

Then we perform the 2D geometrical modeling since the system is symmetric.

We can find that the structure has core and cladding:

Next we set the boundary conditions so that the COSMOL can do the calculation. We set the applied voltage boundary of the light or rather the boundary of the wave:

Before calculation, we set some configurations:

(To be clear: “步骤 $k$ ” <—> “ Step $k$ ” , “求解器配置” <—> “Solver Configuration” and “作业配置” <—> “ Work Configuration” )

Finally, we get the simulation result. In the figure it is the distribution of the electric field in the waveguide. We also get the loss, transmittance and reflectance of the system.

(The first line of the figure “表面：电场模” <—> “Surface: Electric field mode” )

However, we cannot get the change of the phase. It seems that the software has some limitation. And we didn’t consider the electric signals. These are something that can be improved.