One example is given of a fast speed wide angle telescope design that uses freeform aspherics to give great performance gains compared to conventional aspherics
A modification of the Double-Gauss design with two diffractive surfaces is described with very enhanced performance. The key is an interaction between the aberrations of the two diffractive surfaces and the aberrations of a curved substrate lens.
A survey of some unusual telescope designs. One has a 20 meter diameter f/1.0 spherical primary mirror while others are suitable for amateur astronomers to make.
One example is given of a fast speed wide angle telescope design that uses freeform aspherics to give great performance gains compared to conventional aspherics
A modification of the Double-Gauss design with two diffractive surfaces is described with very enhanced performance. The key is an interaction between the aberrations of the two diffractive surfaces and the aberrations of a curved substrate lens.
A survey of some unusual telescope designs. One has a 20 meter diameter f/1.0 spherical primary mirror while others are suitable for amateur astronomers to make.
Modified freeform offner, august 11, 2021Dave Shafer
An Offner 1.0X relay system can be given a greatly increased field size with good aberration correction by adding to the design two 45 degree flat fold mirrors that are given some freeform aspheric deformation.
Innovation in optical design - a short historyDave Shafer
A short history of innovation in optical design, with literally "thinking outside the box" - seeing new optical ways to use a particular spatial region, like a box.
Freeform aspheric version of the 1.0 x offner relay, june 08, 2019Dave Shafer
A better version of my other Slideshare posting on this topic, with fancier graphics - due to my co-author Luc Gilles. Notice, in particular, the 5 reflection design at the end of the slides. It would be much more useful than the 3 reflection design, due to a wide separation of object and image.
Schmidt's three lens corrector for a spherical mirrorDave Shafer
Schmidt's aspheric plate in a Schmidt telescope design can be replaced by a group of three spherical lenses, as Schmidt himself showed, but he died before he could publish anything on this. Here I show many alternate versions to Schmidt's design.
Multiple solutions in very simple optical designsDave Shafer
Several optical design examples show how multiple solutions can exist even in very simple systems. Time spent in looking for them is often more useful then simply optimizing the first solution that you find, which may not be the best of the alternates..
Extreme pixels per volume optical designDave Shafer
The surprising benefits are shown of superimposing a diffractive surface on top of an aspheric surface to get very high performance designs with a very narrow spectral bandwidth. The combination on the same surface allows independent control of a ray's direction and phase..
Dennis gabor's catadioptric design and some new variationsDave Shafer
A variety of optical designs are developed and discussed, inspired by Gabor's very simple and largely unknown design. Some are extremely high NA (0.999!!!) with a wide field of view and diffraction-limited correction.
A survey of some interesting Gregorian telescope designs includes some with all spherical surfaces as well as some with a 20 meter spherical f/1.0 primary mirror and sub-aperture corrector mirrors.
Lens designs with extreme image quality featuresDave Shafer
A variety of lens designs is described which have some image quality feature which is extreme - like an extremely wide spectral bandwidth or extremely high resolution.
Modified freeform offner, august 11, 2021Dave Shafer
An Offner 1.0X relay system can be given a greatly increased field size with good aberration correction by adding to the design two 45 degree flat fold mirrors that are given some freeform aspheric deformation.
Innovation in optical design - a short historyDave Shafer
A short history of innovation in optical design, with literally "thinking outside the box" - seeing new optical ways to use a particular spatial region, like a box.
Freeform aspheric version of the 1.0 x offner relay, june 08, 2019Dave Shafer
A better version of my other Slideshare posting on this topic, with fancier graphics - due to my co-author Luc Gilles. Notice, in particular, the 5 reflection design at the end of the slides. It would be much more useful than the 3 reflection design, due to a wide separation of object and image.
Schmidt's three lens corrector for a spherical mirrorDave Shafer
Schmidt's aspheric plate in a Schmidt telescope design can be replaced by a group of three spherical lenses, as Schmidt himself showed, but he died before he could publish anything on this. Here I show many alternate versions to Schmidt's design.
Multiple solutions in very simple optical designsDave Shafer
Several optical design examples show how multiple solutions can exist even in very simple systems. Time spent in looking for them is often more useful then simply optimizing the first solution that you find, which may not be the best of the alternates..
Extreme pixels per volume optical designDave Shafer
The surprising benefits are shown of superimposing a diffractive surface on top of an aspheric surface to get very high performance designs with a very narrow spectral bandwidth. The combination on the same surface allows independent control of a ray's direction and phase..
Dennis gabor's catadioptric design and some new variationsDave Shafer
A variety of optical designs are developed and discussed, inspired by Gabor's very simple and largely unknown design. Some are extremely high NA (0.999!!!) with a wide field of view and diffraction-limited correction.
A survey of some interesting Gregorian telescope designs includes some with all spherical surfaces as well as some with a 20 meter spherical f/1.0 primary mirror and sub-aperture corrector mirrors.
Lens designs with extreme image quality featuresDave Shafer
A variety of lens designs is described which have some image quality feature which is extreme - like an extremely wide spectral bandwidth or extremely high resolution.
A high performance design is described that uses freeform aspherics to give an unobscured reflective telescope with a 22 degree field of view at f/2.0 on a flat image with no vignetting. The entrance pupil is out in front of the system, one focal length in front, and that is very difficult to achieve.
The optimum lens design form is found where the number of lenses keeps increasing in different design versions but severe space constraints limit the design configurations.
In this term paper most of the types of lens aberrations have been discussed and also have discussed about the use of this knowledge. The aberrations covered in this presentation are:-
Monochromatic Aberrations--Spherical Aberration, Coma, Field Curvature, Distortion, Astigmatism. Chromatic Aberrations - Longitudinal Chromatic Aberrations and Transverse Chromatic Aberrations.
Aberration in optics refers to a defect in a lens such that light is not focused to a point, but is spread out over some region of space, and hence an image formed by a lens with aberration is blurred or distorted.
A freeform aspheric version of the classic Dyson design gives much improved aberration correction and makes for designs that are fast speed and have a large field size, especially large rectangular strip fields
A wide angle fast speed unobscured freeform aspheric mirror design for the IR is shown to be enormous in size compared to an all refractive 3 element lens of germanium with conventional aspherics and better performance.
New optical system corrected for all third order aberrations for all conjugat...Dave Shafer
An afocal unit magnification optical system is described which is corrected for 3rd order spherical aberration, coma, astigmatism, Petzval and distortion for all conjugate distances
The biblical Exodus - what really happened?Dave Shafer
An attempt to explain by natural causes most of the events of the biblical Exodus as If they had actually happened. Whether or not they did happen is not relevant to this presentation.
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...Neo4j
Leonard Jayamohan, Partner & Generative AI Lead, Deloitte
This keynote will reveal how Deloitte leverages Neo4j’s graph power for groundbreaking digital twin solutions, achieving a staggering 100x performance boost. Discover the essential role knowledge graphs play in successful generative AI implementations. Plus, get an exclusive look at an innovative Neo4j + Generative AI solution Deloitte is developing in-house.
UiPath Test Automation using UiPath Test Suite series, part 6DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Sudheer Mechineni, Head of Application Frameworks, Standard Chartered Bank
Discover how Standard Chartered Bank harnessed the power of Neo4j to transform complex data access challenges into a dynamic, scalable graph database solution. This keynote will cover their journey from initial adoption to deploying a fully automated, enterprise-grade causal cluster, highlighting key strategies for modelling organisational changes and ensuring robust disaster recovery. Learn how these innovations have not only enhanced Standard Chartered Bank’s data infrastructure but also positioned them as pioneers in the banking sector’s adoption of graph technology.
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
zkStudyClub - Reef: Fast Succinct Non-Interactive Zero-Knowledge Regex ProofsAlex Pruden
This paper presents Reef, a system for generating publicly verifiable succinct non-interactive zero-knowledge proofs that a committed document matches or does not match a regular expression. We describe applications such as proving the strength of passwords, the provenance of email despite redactions, the validity of oblivious DNS queries, and the existence of mutations in DNA. Reef supports the Perl Compatible Regular Expression syntax, including wildcards, alternation, ranges, capture groups, Kleene star, negations, and lookarounds. Reef introduces a new type of automata, Skipping Alternating Finite Automata (SAFA), that skips irrelevant parts of a document when producing proofs without undermining soundness, and instantiates SAFA with a lookup argument. Our experimental evaluation confirms that Reef can generate proofs for documents with 32M characters; the proofs are small and cheap to verify (under a second).
Paper: https://eprint.iacr.org/2023/1886
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
GridMate - End to end testing is a critical piece to ensure quality and avoid...ThomasParaiso2
End to end testing is a critical piece to ensure quality and avoid regressions. In this session, we share our journey building an E2E testing pipeline for GridMate components (LWC and Aura) using Cypress, JSForce, FakerJS…
Maruthi Prithivirajan, Head of ASEAN & IN Solution Architecture, Neo4j
Get an inside look at the latest Neo4j innovations that enable relationship-driven intelligence at scale. Learn more about the newest cloud integrations and product enhancements that make Neo4j an essential choice for developers building apps with interconnected data and generative AI.
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
Mental Health: Maintaining balance and not feeling pressured by user demands.
Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentations
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
3. Sagittal rays are collimated
between the two reflections,
while tangential rays form an
intermediate image. No
astigmatism for narrow ring field.
Single
spherical
mirror, 2
reflections
4. tangential
No astigmatism
sagittal
Higher order astigmatism is
opposite sign to lower order
Design has Petzval and astigmatism from two reflections on
concave mirror, but higher-order astigmatism allows for one
good astigmatism-free field point. Sagittal field is always exactly
flat for object at center of curvature of a spherical mirror.
5. Non-reversing mirror. Concave in horizontal
direction, convex in vertical direction
Mirror sends rays across the front of mirror and gives two reflections off
of the same concave surface. Only one reflection in vertical direction
The convex vertical curvature is to keep the image from being very tall and skinny in the vertical direction.
A cylinder mirror with two reflections is non-reversing but would give a tall and skinny image
6. My door handle – is
concave in one
direction and convex
in other. Towards
the base it becomes
convex in both
directions. Print
reflection is nonreversed in middle
of handle but then
becomes reversed
near the base.
7. Three reflections, no
astigmatism for very narrow
ring field. Petzval keeps
adding with more reflections,
but sagittal field is always flat.
2 intermediate images for tangential
rays, but only one for sagittal rays
Sagittal rays
focus here
8. Four reflections, no astigmatism
for very narrow ring field.
This is a “whispering gallery”
phenomenon. N reflections are
possible with a single surface.
As go towards top of
sphere, get more reflections
9. Field Point A
Two other four-reflection no-astigmatism
solutions. Even very simple systems can have
more than one solution to a given condition
(here it is no astigmatism). For “n” reflections
there are n-1 separate field heights with no
astigmatism.
If this spherical mirror is replaced by a glass
sphere, then TIR keeps the “Whispering Gallery”
rays going around and around forever with little
attenuation.
Field Point B
Field point B
Astigmatism
curves
Field point A
10. Even very simple systems can have more
than one solution to a particular problem.
Here there are multiple field heights where
N reflections gives no astigmatism, yet it is
just a single spherical mirror. Always look
for alternate solutions in any situation.
11. Single reflective surface NA=1.0 aplanat
Focal length = radius
of mirror, due to
negative diffractive
power or effect of
Fresnel surface.
No spherical aberration
or coma of any order
Spherical
mirror with
diffractive
surface, or
reflective
Fresnel lens.
Simple diffractive
power – no diffractive
or reflective asphericity
12. 1) A thin (zero thickness) system can be corrected for 3rd
order spherical aberration for all conjugates if it satisfies
certain conditions
2) These conditions require certain values of Petzval
and pupil aberration, and a system thickness of zero.
3) This is very counter-intuitive!
4) A single surface can meet these conditions, and
that is very surprising!
13. An aspheric Mangin mirror can meet the required Petzval
condition by the right combination of lens power and mirror power.
But it is not zero thickness
14. No aspheric is required if separate lens from mirror and then bend the lens.
But still is not zero thickness
15. Diffractive
mirror
Diffractive mirror has zero thickness, can be given required Petzval.
This is corrected for 3rd-order spherical aberration for all conjugates.
Negative diffractive power, positive mirror power
Petzval of diffractive power is always zero
16. Possible use of this idea
2X to 10X
zoom beam
expander
Reflective
diffractive
element works
over a range of
conjugates
17. Pre-correction
mirror
Post - correction
mirror
If need both images to exact
same scale, then use sandwich
beam splitter and pre-correction
Beamsplitter in
converging light
puts in several
different types of
aberrations, in
conventional view,
but if shift axis it is
only a small offcenter piece of axial
pupil and spherical
aberration. Can
then be corrected
with a weak power
spherical mirror.
19. Offner concentric 2 mirror relay versions
Three reflections. Working distance
= concave radius/2
Five reflections. Working distance =
2/3 concave radius
Notice the 10X
scale difference
20. Two spherical mirrors, 5 reflections, plus fold mirrors = thin
package in this plane, narrow width out of plane. Correction for
spherical aberration, coma, astigmatism, Petzval and distortion.
21. 5X, anastigmat
Curved image
Concentric spheres
5X, no 3rd, 5th
spherical aberration
More obscuration
Bad coma
Not concentric
If magnification is used as a
variable then there is this
3.73X solution where the 3rd,
5th, and 7th order spherical
aberration = 0. Bad coma
Obscuration = 60% diameter.
Not concentric
23. Stray light problem
Blue shows
outer rays of
light cone.
4 reflection stray
light path
Rays hit
area
unused
by main
ray path
Main image
Small
unused
area of
mirror
around
hole
Red shows
inner rays of
obscuration
Small unused area around
hole in concave mirror allows
for a four reflection light
path to get through the
system. This can be stopped
by sizing the hole to be
larger.
24. The 4 reflection stray light path, an
unexpected phenomenon, is not just a
problem. It is also an opportunity to
explore new designs that are based on this
phenomenon.
Let us see what can be done with
multiple reflections between two spherical
mirrors.
25. Concentric spheres anastigmats
Obscuration = 45% diameter,
Concave mirror area (ignore hole) =
22X effective area of obscured pupil.
Obscuration = 70% diameter
Concave mirror area (ignore hole) =
22 X effective area of obscured pupil
For a given effective area of the obscured pupil, you need the
same amount of large mirror area (ignoring the hole) in both
designs. But the 2 reflection design requires a 30% larger
diameter concave mirror than the 4 reflection design. Both
designs are anastigmats.
26. If we drop the concentric arrangement,
what can be done to correct for Petzval as
well as the other aberrations, to get a flat
image anastigmat? There are only two
surfaces and both are spheres. Is it
possible? I’m glad you asked.
27. Flat Image Anastigmat - 3.3X Relay
Magnification is an important variable
and 3.3X is needed for this solution
2 spheres, 4 reflections,
corrected for 3rd-order
spherical aberration, coma,
astigmatism and Petzval.
Mirrors have same radius
28. Move field off-axis until system
becomes unobscured. Then the 4
reflections are on 4 separate mirrors.
Then we can independently vary 4 radii
instead of just 2. But keep them spheres.
Result is unobscured flat image
anastigmat. Next slide shows infinite
conjugate example but finite conjugate
examples work well too.
29. 4 spherical
mirrors – all
nearly the
same radius
Finite
conjugate
versions
are also
possible
Flat image anastigmatic telescope. Best used for ring field or strip field.
30. What else can be done with mirrors the
same radius?
We started with concentric mirrors and 2
reflections, then added reflections, then
dropped concentricity.
Now let us back up a little and start over
again with just two spherical mirrors and
only two reflections. The mirrors are not
concentric and have the same radius.
32. Pupil position for no astigmatism
Two symmetrical systems make coma cancel, give a 1.0X magnification aplanat
Each half has a stop position which eliminates
astigmatism, since each half has coma. But
pupil can’t be in both places at the same time.
33. Astigmatism-correcting pupil positions are imaged onto each other by
positive power field lens.
System is then corrected for spherical aberration, coma,
and astigmatism, but there is Petzval from field lens.
34. Thick meniscus field lens pair has positive power but no Petzval or axial or lateral color
Result is corrected for all 5 Seidel aberrations, plus axial and
lateral color. This shows how a simple building block of two
spherical mirrors was turned into something quite useful.
35. Equal radii (R) spherical mirror pair
2 reflection separation = .866 R, 4 reflections = .588 R, 6 reflections = .434 R
There is always a mirror separation where after any number of
even reflections the object and image are at the mirror vertex
locations. Then 3rd –order spherical aberration is always
corrected. Why is that? A big mystery! Only true for equal
radii on mirrors. Use as a long path cell for gas absorption?
36. Two spheres, equal and
opposite radii R, and
separated by R/2 . This
6 reflection system is --1.0X, afocal, and is
corrected for 3rd order
spherical aberration,
coma, astigmatism,
Petzval, and distortion
for all conjugates
Two spheres, six reflections
Different mirror separation
from previous slide examples
37. Alternate solution – same
mirrors but different spacing,
of .866 R instead of R/2
This is +1.0X afocal and
every point is imaged back
onto itself after 6 reflections,
with no 3rd –order
aberrations.
Two spheres, six reflections
The lesson here is that even
very simple systems can have
more than one solution region.
38. Is there any use for
this system, which
images the whole 3D
space between the
mirrors back onto
itself with good
image quality?
6 reflections gives +1.0X
39. These designs so far are almost all
with just spherical surfaces.
What can be done with simple
aspheric designs?
40. Two conics (oblate
spheroids) with same
radius and object and
image at mirror centers
gives correction for
spherical aberration,
coma, astigmatism, and
Petzval.
3.7X relay
With 2 spheres it is corrected only
for spherical aberration and Petzval
41. Schwarzschild two aspheric mirror design for collimated light
With just two mirrors the first order layout is an important design variable
Unobscured version
Schwarzschild flat image anastigmat with two oblate spheroids
Concave mirror must be 2.4X larger than convex mirror for collimated input
42. 2 aspheric
diffractive
mirrors
Or two aspheric
Fresnel mirrors
Corrected for spherical aberration, coma, astigmatism, and Petzval
Diffractive surface adds variables to mirror surface
43. Two conic mirrors, three
reflections.
Corrected for spherical
aberration, coma, and
astigmatism, but only for
this geometry configuration.
Alternate solution –
Another example of
multiple solutions in
a simple system
45. Image derotator for system with an intermediate image
Intermediate image
Grazing intersection angle
can give huge size, and
limits possible f# of system
46. Fast f# solution – split wavefront
Derotator for system
with intermediate image
47. 5X, anastigmat
5X, no 3rd, 5th
spherical aberration
More obscuration
Bad coma
With just two spheres you cannot correct 3rd and 5th
order spherical aberration and also 3rd order coma – you
need more variables. If you stay with spheres then you
need another mirror. One unusual solution has a third
mirror that is almost flat and is three mirrors but four
reflections. It is sort of a folded version of the design on
the upper left here and it is shown next.
48. The nearly flat 3rd
mirror allows the
design to be corrected
for 3rd and 5th order
spherical aberration
and 3rd order coma and
astigmatism.
3 spherical mirrors, 4 reflections
50. Diffraction-limited at .6328 for 15 mm
output beam, in 3X expanded direction
Astigmatism between tilted spherical mirrors can give
intentional anamorphic effects.
51. Offner patent design. Anastigmat that can also be corrected for Petzval
Unobscured system requires three off-axis conics
52. Unobscured ring-field design corrected for spherical
aberration, coma, astigmatism and Petzval with a centered
aspheric. Very good higher-order aberration. First and last
mirrors are imaged onto each other by middle mirror.
53. Folded version of design
Best higher-order aberrations when both first and last
mirrors are centered parabolas.
54. A conic mirror with a pupil at either
focii has no astigmatism of any order
2 or 3 conic mirrors can have their focii coincide
Conic axes don’t have to be colinear
No astigmatism
No astigmatism
pupil
pupil
Co-linear ellipses
Crossed axis ellipses
56. Offner concentric design, 2 spheres with 3 reflections, used with collimated input
1.0X afocal pupil relay design
Pupils are at center of curvature.
Corrected for coma and astigmatism and
Petzval but not for spherical aberration
pupil
pupil
Afocal 3 spheres design, with magnification
2.0X afocal pupil relay design
Field mirror images pupils to be at centers
of curvature of both mirrors. For 2.0X or
any other afocal magnification this also
corrects for Petzval
pupil
pupil
58. Combined systems
This will show how two very simple
systems can be combined to give a new
design with very attractive characteristics
59. Same system used backwards
Concentric spheres
Real image anastigmat
Virtual image anastigmat
Any concentric system of spherical surfaces has exactly the
same aberrations, to all orders, when used backwards.
Very strange, but true!
60. Unobscured virtual image anastigmat
Offner 1.0X relay, also concentric
Combined
systems. Virtual
image is relayed
to a real image.
By dropping concentricity, can
correct Petzval and distortion too.
61. This telescope/spectrometer from the previous slide, with 5
spherical mirrors, was sent to Saturn on the Cassini spacecraft
and another one will arrive at the asteroid Vesta in July 2011.
This design was one of my first patents, back in 1975.
62. This is a lot of
material to remember,
but this is all available
as a Powerpoint file
that you can have.