Portifólio dos trabalhos realizados na disciplina Formação Continuada em Tecnologia Educacionais na Web do Curso de Qualificação em Tutoria ofertado pelo CECIERJ em 2016.
Portifólio dos trabalhos realizados na disciplina Formação Continuada em Tecnologia Educacionais na Web do Curso de Qualificação em Tutoria ofertado pelo CECIERJ em 2016.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
This article is all about what AI trends will emerge in the field of creative operations in 2024. All the marketers and brand builders should be aware of these trends for their further use and save themselves some time!
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
8. 清华大学综合论文训练
第 3 页 共 77 页
Abstract:
In the dissertation the defocusing in volume holograms has been discussed in detail.
The math expressions of spectral distribution after defocusing are deduced from basic
Fresnel diffraction and the Fourier transform property of lens. It is proved that the
spectrum after defocusing and the spectrum of Fractional Fourier transform can also be
described as Fourier spectrum under some restrictions and the physical significance of
the result is given by deduction of applied optics. With the mathematic model, the
numerical outcome of the spectral distribution after defocusing is given.
Furthermore, the mathematic model from spectra plane to image plane is put
forward. With the help of the model, the numerical results of different defocusing
values, apertures and fill factors have been discussed. The interpixel cross talk and the
intensity of received light are analyzed and key parameters of the system are optimized.
After the optimizations, the performance of the system is satisfied.
Finally, the flow chart for calculating the optimal parameters of systems of decided
SLM and CCD is given. It is the basis of further experiment.
Key word: defocusing, fractional fourier transform, interpixel cross talk, volume
storage
20. 清华大学综合论文训练
第 15 页 共 77 页
情况,直接可以将我们得到的结果叠加即可。
121
2
1
1
22 )]2(
2
exp[)( dxxxx
f
f
f
ikmTx
rectCxU
x
x
(13)
设 xmTx x 1 ,由此可得:
dxxmT
f
f
x
f
ik
x
f
fikx
rectmTxTm
f
f
f
ik
CxU x
x
xx ])(exp[)
2
exp()]2(
2
exp[)( 2
2
22
22
22
(14)
考虑到如果能够忽略其中的二次项因子,那么我们的讨论将大大简化。考虑
到 x 的最大值为
2
x
,代入一组典型值: 10f , 100f , 6
10532
,
3
1026
x ,所以有: 00100.01097987.9
2
42
2
x
f
fk
即 ix
f
fik
001.0000000.1]
2
exp[ 2
2
。也就是说,这一项实际上其模接近 1,幅
角接近 0,在离焦不大的情况下可以忽略(这很大程度上是因为 x 是小量,x 的平
方就成为二阶小量)。
上面通过数量级的分析直观的给出了结果,进一步对这个问题进行讨论,我
们建立如下评价函数:
dxxmT
f
f
x
f
ik
x
f
fikx
rect
dxxmT
f
f
x
f
ik
x
f
fikx
rect
x
x
x
x
x
])(exp[]
2
exp[
])(exp[]1)
2
exp([
)(
2
2
2
2
2
2
2
(15)
如果能够满足在我们关心的 2x 的取值范围内,有上述评价函数的模在百分之
五以内,我们就认为已经达到了很好的工程近似。
m 是自变量之一,代表研究的像素在 SLM 上的具体位置,假设我们使用的 SLM
在 x 方向的像素数目为 1024 个,则它取值在 0 到 1023 之间。 2x 是衍射屏上一点
的坐标。观察式 9 和 10,我们发现 m 与 2x 的绝对值大小是没有意义的。真正起作
21. 清华大学综合论文训练
第 16 页 共 77 页
用的是他们的差值。为此,我们定义新的变量 xmTx 2 作为自变量,假设
Tx=26*1e-3,考虑到对称性,将坐标原点建立在 SLM 的中心处,对于有 x 方向有
1024 个像素的 SLM,m=512,所以 mTx=13.2;又我们实际感兴趣的谱面范围最多
是在-6 到 6 之间(对应的孔径为 12),那么 其取值范围在-11.3 到 11.3 之间。
考虑到绝对焦距的大小在离焦的评价中也是没有实际意义的,因此我们令
f
f
作为新的离焦量评价,考虑到实际的应用,取值正负 0.4 以内;
dxx
f
ik
x
f
ikx
rect
dxx
f
ik
x
f
ikx
rect
x
x
)exp()
2
exp(
)exp(]1)
2
exp([
),(
2
2
(16)
我们定义 dxx
f
ik
x
f
ikx
recty
x
)exp()
2
exp(),( 2
1
(17)
dxx
f
ikx
recty
x
)exp()(2
(18)
则有
),(
)(),(
),(
1
21
y
yy
(19)
考虑到很难解析的找到在 2x 的取值范围内上述评价函数的最大值,我们考虑
对上式求数值解。
仍然代入一组典型值: 100f , 6
10532
, 3
1026
x 。
]10,10[ , ]4.0,4.0[
先取 05.0 得到图像如下:
24. 清华大学综合论文训练
第 19 页 共 77 页
机的处理范围,也就是说这些点上虽然值超过了我们前面假定的工程误差范围 5%,
但是,这是一种假象。
回到 9 式,我们忽略其中的二次项因子,得到:
dxxmT
f
f
x
f
ikx
rectmTxTm
f
f
f
ik
CxU x
x
xx ])(exp[)]2(
2
exp[)( 22
22
22
(20)
仍然采用 xmTx 2 作为新的自变量,我们有:
f
ffSincfmTiTm
f
ik
C
f
SincmTTm
f
ik
C
dxx
f
ix
rectmTTm
f
ik
CU
xxx
xxx
x
xx
)()2exp()
2
exp(
)()]2(
2
exp[
)
2
exp()()]2(
2
exp[)(
22
22
22
2
(21)
当离焦量为 0 时,也就是 0 ,上式就退化为一个像素平移后的傅立叶变换
的情况:
f
x
ffSincfmTiCU xx
2
2 )(]2exp[)( (22)
由此可见,在少量离焦的情况下,得到得仍然是一个像素的傅立叶变换频谱,
只是其零级的位置移动了,谱面本身没有扩展。值得注意的一点是,仍然可以用
Fourier 分析的理论来解决我们的问题。也就是说,在我们讨论的范围内,Fourier
分析仍然适用,包括卷积定理和关于滤波器设计的一些结论。
25. 清华大学综合论文训练
第 20 页 共 77 页
第三章. 谱面光场分布的理论理解与数学建模
我们下面的讨论建立在对接收屏是 SLM 的傅立叶变换的基础上,这个基础经
过上面的大量讨论,是符合实际情况的。对于单个的像素而言,从衍射的角度看,
只要 Sinc 函数的主瓣通过了,我们就知道了其结构的大部分。根据线性系统的叠
加特性,我们只需要保留每个像素的主瓣就可以了。也就是说,在承认这个全息
存储系统的线性情况下,如果我们能够保证单个像素存在时的正确读出,我们就
可以实现这些像素线性叠加后形成的图的读出。
从一般的角度来理解 SLM 的每个像素通过光学系统后的光场分布,我们有以
下的结果:
光场分布=单个 pixel 的衍射+pixels 间的干涉 (23)
对于图 2 所示 SLM,我们已经讨论了单个像素一个方向衍射的情况,结果如
式 11(对应分数傅立叶变换的情况)和式 21(对应一般的离焦情况)所示,我们
将其扩展到整个 SLM。
1. 一般离焦情况下的谱面分布:
M
m
N
n
yxyxyxmn fSincfSincfnTfmTiTnTm
f
ik
aCffu
1 1
2222
)()()](2exp[)](
2
exp[),(
f
nTy
f
f
mTx
f
yx
22
, (24)
当离焦量为 0 时,得到如下熟知的结论:
f
y
f
f
x
f
fnTfmTjafSincfSincCffu
M
m
N
n
yxmnyx
2
2
1 1
0 )](2exp[)()(),(
(25)
以上两式是从傅立叶变换角度求解谱面分布问题的数学模型。对于非离焦情
况下的 Fourier 变换,我们知道,其本身具有平移的不变性。对于每一个 SLM 的
像素而言,其衍射的谱面分布呈 Sinc 函数,在屏移动后,其主瓣的位置是不变的。
26. 清华大学综合论文训练
第 21 页 共 77 页
变化的,只是分布的一个相位因子,因此我们得以从 25 式中提出公因子 Sinc。
对 25 进一步分析,我们可以看到:当 f 、 f 为 0 时,Sinc 函数得到最大值 1,
对于衍射的主极大中心。而对于后面的相位因子之和,此时也是最大值。也就是
说由于干涉的 0 级与衍射的 0 级相重合,所以主极大很大,这就直接导致光场分
布使得的能量非常的集中,这种情况严重的影响了材料的动态特性 M#。
一个值得注意的校验结果是:如果我们在 SLM 上加白图的话,那么由前面
SLM 本身的结构,我们此时的 SLM 构成空间光栅。光栅的透光处为 x 、 y ,周
期为 xT 、 yT 。根据光栅理论,我们有:
2
sin
2
sin
2
sin
2
sin
sinsin
y
y
x
x
NM
Cu
(26)
其中
f
xx 2
,
f
yy 2
,
f
xTx
x
22
,
f
yTy
y
2
2
。
上述公式可以作为校验一个方法。另外,我们常用的黑白棋盘格实际上也可
以通过上面的光栅理论做出解释。如果存储的不是白图而是棋盘格,那么此时,
我们有:
2
sin
2
sin
2
sin
2
sin
sinsin
y
y
x
x
NM
Cu
(27)
其中
f
xx 2
,
f
yy 2
,
f
xTx
x
24
,
f
yTy
y
2
4
也就是说,无论我们存储的是一个什么周期的图像,起单缝衍射的因子是不
变的,这是由最小的像素结构决定的。改变的是缝间的干涉因子。当存储棋盘格
时,其光栅空间周期为原来的 2 倍。
如果从几何光学与物理光学结合分析,我们可以得到如下图:
27. 清华大学综合论文训练
第 22 页 共 77 页
图 9 记录标准傅立叶变换图
由于同样级次的衍射光的衍射角是相同的,而平行光将在焦面上会聚为一点,
因此谱面上将不可避免的出现能量集中。为了改善这种情况,一个很显然的想法
是离焦记录。由上面的公式 21 可以看出,在离焦的情况下,像素的衍射不再保持
平移的空间不变性,此时衍射的主极大与干涉的主极大不再重合,很显然,此时
谱面中心的能量强度将显著下降,具体的情况我们将在下面讨论。
2. 满足分数傅立叶变换的离焦:
其理论的推导可以有两种方式。一种是根据分数傅立叶变换的傅立叶算法得
来,一种是直接从分数傅立叶变换的角度出发,应用平移公式得到。
对于第一种情况,我们有:
M
m
N
n
yx
yxyxmn
fSincfSinc
fnTmTffTnTm
f
ik
a
Cffu
1 1
22222222
2
)()(
]}cos)cos1()(2)cos21(cos)[(
sin2
exp{
),(
22
22
c o s,
s i n
c o s,
s i n
yfnT
f
f
xfmT
f
f
y
x
(28)
对于第二种情况,我们有:
M
m
yxx
N
n
y
y
x
xmn nTfmTfG
nT
finT
mT
fimTaffu
1 1
),()]
2
cos
(sin)
2
cos
(sinexp[),(
28. 清华大学综合论文训练
第 23 页 共 77 页
11
11
22
1
22
111
sin
)(2
tan
)(
exp],[ dydx
f
fyfxi
f
fyfxiy
rect
x
rectCffG
yx
sin
]
2
tan2exp[
sin
)2exp(
fi
fki
fi
kdi
C
, p
2
(29)
上述两个公式是讨论分数傅立叶变换离焦的基础。可以通过它们进行数值模
拟等计算,给出有价值的结果。关于这些公式的应用,我们将在下面给出。
36. 清华大学综合论文训练
第 31 页 共 77 页
所以离焦量为: cosff
由上图计算可得:
f
D
f
d
22
tan
,所以 f
D
d
f
对比两式,可以得到:
D
d
cos
对于记录平面在焦面之后的情况,类似的我们可以得到:
f
D
d
f ,
D
d
cos
如果确定保留衍射 Sinc 的主瓣,我们有
2
sin
2
x
x
f
d ,
2
sin
2
y
y
f
d 。
由此可见,分数傅立叶变换的阶数直接由系统的结构确定了,而阶数直接决
定了离焦量。
注意在上述两种情况下,透镜的间隔均为 f2 。用几何光学容易验证在任一情
形下,输出面与输入平面共轭,且放大率为-1(倒像)。这里正好实现了几何光学
与分数傅立叶变换(或者说 Fresnel 衍射积分)的回归。尽管用几何光学我们无法
得到波前的很多信息,但是根据成像的理论,我们却能够很容易的得到一些重要
的结论。
对于光场分布的进一步讨论需要在公式 28、29 的指导下进行,可以直接对多
像素的光场的分布进行数值模拟计算。这种模拟的方法与上一节基本一致,请读
者模仿上节的程序,自己完成。我们这里从序列的分数傅立叶变换角度,对这个
问题进行数值模拟,讨论限定在一维的情况。
数值模拟条件:设记录焦面的孔径为 3mm,SLM 的长度为 30mm,对于记录
平面在焦面前的情况, 1.0cos ,对应的 1.4706 弧度,相应的 p=0.9362 为傅
立叶变换的阶数。设每个像素的尺寸是 10um,空间周期为 20um,共有 32 个像素
排列。每个像素点内采样 100 点,为了防止串扰,在将非周期的空间排列周期化
时,在十倍于 SLM 的尺寸区域内函数取 0 值。此时对应的谱面分布为:
41. 清华大学综合论文训练
第 36 页 共 77 页
第七章 关于谱面的压缩所引起的读出时像素间串扰的
讨论和系统参数选取:
1. 从谱面到像面的数学建模
正如上面讨论的,谱面的压缩实际上是通过加入矩形窗截取了谱面的部分得
到的。滤波后得到的谱面通过后组光学系统(再进行一次傅立叶变换)在 CCD 上
读出图像。由此可见,可以通过 Sinc 与矩形框相乘得到图示的频谱,在 CCD 上读
出时是二者的傅立叶变换的卷积,即矩形框和 Sinc 的卷积。按照 Rect 函数(代表
孔径光阑)位置不变,讨论 SLM 上的某个像素的谱面经截取的分布,那么整个系
统的数学模型是:
以 x 方向为例,由公式 21,我们可以得到 SLM 上第 m 个像素通过第一组透
镜后,得到的谱面为 )(2 U ,这时通过孔径光阑(或者说视场光阑)截取后,得到
'
Re)( 2
2
x
ctU ,如果是保留衍射的主极大,那么其中的
x
f
12
'
,其中 为光波
长,
1f 为第一组透镜焦距。通过第二组透镜后,考虑到此时接收的平面在第二组
的后焦面上,所以在 CCD 上得到的是记录平面的非严格傅立叶变换(公式 2),参
看图 14,我们得到
1
003
1
22
2
3
2
0
1
2
1
2
1
222
11
22
2
3
2
0
1
2
1
2
1
222
1
2
3
2
033
)exp()
2
exp(
2
Re)()2exp()exp()
2
exp()
2
exp(
2
Re)()2exp()exp()
2
exp()(
f
mT
fffG
f
Tmi
x
f
ik
C
f
x
ct
f
mTx
Sinc
f
x
mTiCFTm
f
i
f
Tmi
x
f
ik
C
f
x
ct
f
mTx
Sinc
f
mTx
mTiTm
f
i
CFx
f
ik
CfU
x
x
x
x
x
xxx
x
x
x
x
x
xxx
(30)
42. 清华大学综合论文训练
第 37 页 共 77 页
2
3
3
1
3
1
3
31
1
2
1
2
3
2
*]Re)2[exp(
2
Re)(][
f
x
f
f
f
Sinc
f
f
ctmTfiC
f
x
ct
f
mTx
CSincFfG
x
x
x
x
x
xx
x
x
xx
(31)
上式中*表示卷积。
将上式代入,并将自变量换为 x3,有:
]
2
*Re)
2
)[exp(
2
exp()exp()( 33
2
32
3
21
22
233
x
x
x
xxx mTx
Sinc
mTx
ct
f
xmTi
x
f
ik
f
Tmi
CxU
(32)
1
2
f
f
,表示横向放大倍数。
上式是我们解决分析离焦记录后,读出时 CCD 上像面分布的依据,也是我们
下面分析像素间串扰的依据。其具体应用我们在下面展开。
对于分数傅立叶变换的情况,我们仍然有两种可以选择的讨论方式:如果从
分数傅立叶变换的傅立叶算法出发,根据式 11,类似于上面的推导,我们将得到
与上面类似的结论,具体推导请读者自己完成,此处限于篇幅,略。显然,这种
方法实际上与分数傅立叶变换的关系不大。如果我们直接从分数傅立叶变换的角
度来看待这个问题,可以得到如下结论(讨论仍然限定在一维):
根据公式 29,我们实际上可以得到对于第 m 个像素,在谱面上将得到:
)()]
2
cos
(sinexp[)( xx
x
x mTfG
mT
fimTfu
1
1
22
11
sin
)(2
tan
)(
exp][ dx
f
fxi
f
fxix
rectCfG
x
(33)
这时通过孔径光阑(或者说视场光阑)截取后,得到
'
Re)( 2
x
ctfu ,如果是
43. 清华大学综合论文训练
第 38 页 共 77 页
保留衍射的主极大,那么其中的
2
sin
2
'
x
f
,其中 为光波长, f 为第一组透
镜焦距。通过第二组透镜后,相当于对谱面进行了分数傅立叶变换,参看图 20,
我们得到
2
2
33
sin
2
Re)()]
2
cos
(sinexp[)(
x
xx
x
xx
f
x
ctmTfG
mT
fimTFfU
(34)
上式是从分数傅立叶变换角度来讨论问题的出发点。由于对于分数傅立叶变
换而言,它不存在对应的卷积定理,而且很多问题利用分数傅立叶变换的性质讨
论起来仍然很繁琐。因此,我们考虑采用傅立叶变换的性质讨论当阶次接近 1
(0.9-1.1)时的分数傅立叶变换的性质,方法与前述一般离焦分析是相同的。
2. 关于减小像素间串扰的数学建模:
根据我们前面的讨论,我们知道对于单个像素而言,在阶数接近 1 时分数傅
变的谱面分布与傅立叶变换的谱面分布在幅度上是类似的,我讨论将两种情况化
为一种讨论。
由式 32 给出了 U3 的表达式,首先需要明确的一点,是对于 Rect 与 Sinc 函数
卷积前的相因子的处理问题。由于 U3 处是放置 CCD 的地方,因此记录的是光强
度,也就是说,前面的两个相因子在强度的记录中是不起作用的,忽略之,我们
有:
2
*]Re)
2
[exp()( 33
2
3
333
x
x
x
xx mTx
Sinc
mTx
ct
f
xmTi
CxU
(35)
考虑到
MT
d
2
(见图 11 及分析),暂代
x
x
f
dd
12
,我们有
xx MT
f
1
,
所以:
44. 清华大学综合论文训练
第 39 页 共 77 页
2
*]Re)2[exp()( 333
333
x
x
x
x
x
mTx
Sinc
mTx
ct
x
M
m
iCxU
(36)
对上式换元,令
x
u
mTx
x
3
,也就是说相当于我们将讨论的平面等价到物
面,得到:
2
*]Re)2[exp(
2
*]Re)2)[exp(2exp()(
4
2
33
x
u
x
u
x
u
x
u
x
u
x
u
x
x
u
x
Sinc
x
ct
x
M
m
iC
x
Sinc
x
ct
x
M
m
i
M
Tm
iCxU
(37)
对相邻像素的影响为:
x
x
x
x
x
x
x
x
T
T
xx
T
T dxdt
tx
Sinc
t
M
m
idxxUI
2
2
2
2
2
2
2
2
31
2
)2exp()( (38)
对于相邻第二个像素的影响为:
x
x
x
x
x
x
x
x
T
T
xx
T
T dxdt
tx
Sinc
t
M
m
idxxUI
2
3
2
3
2
2
2
2
3
2
3
2
32
2
)2exp()( (39)
下面我们重点讨论对相邻像素影响。显然,绝对的 I1、I2 的大小是没有意义的。
我们应该考虑它们与产生串扰的对应场点的能量比值。对于产生串扰的源点而言,
其对于的 CCD 像素上的光强积分为:
2
2
2
2
2
2
2
2
30
2
)2exp()(
x
x
x
x
x
x
dxdt
tx
Sinc
t
M
m
idxxUI
xx
(40)
重新定义如下评价函数来表示:
45. 清华大学综合论文训练
第 40 页 共 77 页
0
1
1
I
I
E (41)
0
2
2
I
I
E (42)
仿真的 SLM 结构如图 2, 3
10*16
x , 3
10*23
y , 3
10*26
yx TT
假设从中心到边缘有 20 个像素,CCD 上的读出对应如下 20 幅图:
图 24 从中心到边缘像素读出时像面幅度分布
如果将上面的图画在同一个坐标系中,我们得到:
75. 清华大学综合论文训练
第 70 页 共 77 页
E1 的曲线,我们就可以定出此时的离焦量必须小于边缘离焦的一半。也就是说,
为了更好的均化谱面,此时我们的离焦量应该是边缘离焦的一半。
在确定了离焦量之后,我们应该进一步对谱面进行数值模拟,观察谱面的均
化情况是否合乎我们的要求。如果此时谱面仍然没有很好的均化,我们必须重新
改变 值,即将 值取大些,比如 0.8,再次重复上述过程,直到从中心到边缘像
素的能量、串扰和谱面能量分布均达到我们预期的要求。上述过程用流程图表示
如下:
Input the fill
factors of SLM
and CCD
Calculate I0,E1
under different
k
Input the max
value of Center
E0
Find the minimal
k
Find the maximal
defocusing value
Input the
marginal E0 and
Vignetting
Calculate the
spectrum
distributing
OK?
K=K+delta
No
Yes
Start Out put results
图 43 求解一般情况下的系统参数流程图
6. 边缘像素渐晕问题的解决
我们讨论的渐晕的前提是在系统的入射光为均匀平面波。当入射光为高斯光