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ТОП 10 -> Заведения в Туймазах -> Рестораны -> Кафе «Отдых» ОктябрьскийКафе «Отдых» Октябрьский в рубрике Рестораны и Заведения в Туймазах
ТОП-10 | Рестораны | Кафе «Отдых» Октябрьский
Кафе «Отдых» Октябрьский
РБ, г.Октябрьский, ул.Ленина, д.12
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Детский зал: без выходных время 10.00-23.00 без перерыва
Пивной бар: без выходных время 11.00-01.00 без перерыва
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An instance of the data type node_list is a doubly linked list of nodes. It is implemented more efficiently than the general list type list < node > (Linear Lists). However, it can only be used with the restriction that every node is contained in at most one node_list. Also many operations supported by list < node > (for instance size) are not supported by node_list.
node_list L introduces a variable L of type node_list and initializes it with the empty list.
void L.append(node v) appends v to list L.
void L.push(node v) adds v at the front of L.
void L.insert(node v, node w) inserts v after w into L.
node L.pop() deletes the first node from L and returns it.
node L.pop_back() deletes the last node from L and returns it.
void L.del(node v) deletes v from L.
bool L.member(node v) returns true if v L and false otherwise.
bool L(node v) returns true if v L and false otherwise.
node L.head() returns the first node in L (nil if L is empty).
node L.tail() returns the last node in L (nil if L is empty).
node L.succ(node v) returns the successor of v in L.
node L.pred(node v) returns the predecessor of v in L.
node L.cyclic_succ(node v) returns the cyclic successor of v in L.
node L.cyclic_pred(node v) returns the cyclic predecessor of v in L.
bool L.empty() returns true if L is empty and false otherwise.


Transalpi di Bontempi Mario & C. s.n.c.
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This page began as a way to show off the pictures we (Deborah Peters and Stephen Bloch) had taken of various reconstructed medieval pavilions we've lived in and/or built. But I anticipate it becoming also an impetus to discussion of various designs for medieval tents, how to build them, how to live in them, etc. Accordingly I've put in a Taxonomy of Tent Designs discussing different structures and construction methods, a collection of medieval pictures of tents useful as iconographic evidence, a custom tent measurement calculator, and links to as many other relevant Web sites as I could find. If you find bugs in the calculator, if you know of other sites I should link to, or if you can contribute good pictures or descriptions of reconstructed tents, please e-mail me.
Note: we are not in the business of building and selling pavilions. We do not have a catalogue, we do not have a price list, we do not have a mail-order policy, etc. I'll be happy to provide suggestions and moral support from my experience and that of other tentmakers I know, should you be inspired to build your own, but I will not build your tent.
Many of the pictures on these pages are shown in "thumbnail" format, linked to larger versions of the same picture. So if a particular picture piques your curiosity and you want to see more details, try clicking on it.
We originally developed our interest in this area through our participation in the Society for Creative Anachronism, a medieval hobbyist organization whose tens of thousands of members cover a vast spectrum of historical accuracy and interests. At the "high-accuracy" end of this spectrum are people doing academically credible, museum-quality research and reconstruction. Other members are more interested in sword-fighting (as a sport, not a research area), flirting, and drinking homebrew (not unworthy aims in themselves -- I've tried a little of all three). More recently, we've been participating in La Belle Compagnie, a Hundred Years War living-history group. Anyway, this Web site aspires to the "high-accuracy" end: I'm interested in how tents were actually built and used in the Middle Ages, and how to reconstruct them today.
Many of the photographs on this site, and much of the testing experience of the tents discussed here, are from the Pennsic War. This largest event of the SCA year is held in western Pennsylvania in early to mid-August, and attracts approximately 10,000 participants (from both the SCA and other medievalist groups), some of whom stay for as long as two weeks. At this event, and at numerous smaller and briefer events, most participants sleep in tents or pavilions of some sort, varying from blue plastic tarps to high-tech backpacking tents to careful reconstructions of actual medieval tents.
We held a panel discussion of tentmaking techniques at Pennsic 1997, with a one-hour field trip to examine the participants' own efforts. Interest was high, and the level of expertise of the participants varied from Myfanwy, who'd built one pavilion, to us, with two, to Mistress Barbary, at several hundred, to the people from Medieval Miscellanea and Tentmasters, who had built and sold thousands. I was somewhat surprised that so few people showed up wanting to show off their own efforts on the field trip.
A similar class has been held at Pennsic each year since. Each year the number of participants, and the number of pavilions to visit, has grown, and the field trip has stretched to three hours (for the die-hards who last that long).
Note to participants in past classes: I saw a number of you taking photographs, both full-view and detail, of the tents we visited. If anyone would like to contribute photographs to this Web site, I'd be very grateful; please contact me at sbloch@adelphi.edu.
Deborah and I have for a number of years been part of the Enchanted Ground camp at Pennsic. Enchanted Ground, founded by Duke Cariadoc of the Bow, is based on the conceit that, due to some sort of enchantment, this patch of ground is no longer a part of the twentieth century but rather of the Middle Ages. Inside it there is no discussion of things that didn't exist in the Middle Ages, and we avoid obviously modern camp gear: cooking equipment, bedding, clothing, and (most relevantly to this page) housing such as tents.
We didn't build this one, we borrowed it from the (now-defunct) Gwyntarian Musicians' Guild. Although its shape resembles those of various medieval tents, its internal structure has no resemblance to any that I know of: it had a single center pole, with about a dozen ropes going up the pole, through pulleys or loops at the top, and down at an angle to the circular welded steel hoop that held the shape of the shoulder. This hoop was stabilized by a number of cross-braces (also welded steel, with lots of wing-nuts), the assembly and disassembly of which took hours of frustrating work and caused injuries ranging from mild burns (from steel sitting in direct August sun for hours) to bruises to badly pinched fingers. The main advantage of this structure is that no guy-lines extend beyond the footprint of the tent.
At some point Deborah decided to build her own pavilion based on the many pictures of pavilions in King Rene d'Anjou's Book of Love, aka Le Cueur d'Amours Espris. We completed this pavilion as a joint project in 1994, aided by the Calon Scrolls special issue on pavilions. (The Calon Scrolls is the arts-and-sciences newsletter of the Kingdom of Calontir, which has something of a reputation for pavilioning.) More pictures (both of our pavilion and of those in King Rene's book) and construction details are on another page.
When Deborah started building the first tent, she was single. By the time it was finished, she and I had met and were considering marriage. We quickly found the tent too small for both of us, a week's food, clothing, music, and musical instruments. So we built a larger tent in 1996, based on the pictures of oval pavilions in King Rene's book. More pictures, and discussion of construction details, are on another page.
Oh, by the way, none of these tents, to my knowledge, has ever collapsed or flown away in a Pennsic storm.
As I've paid more attention to pavilion design, I started trying to organize the many different designs to keep them straight in my own mind. The result is my Taxonomy of Pavilion Designs; additions and corrections will be cheerfully accepted! Look here for discussion of construction techniques.
listed by source. If you have other such pictures, please contact me!
These links include not only tents and pavilions, but yurts, sheds, taverns, etc.
Disclaimer: I haven't assessed the quality of research going into all these pages; I expect the reader to do that for him/herself.
Tanya Guptill (ska Mira Silverlock), another SCA member who builds pavilions, has developed a page on Medieval Pavilion Resources, including lots of on-line sources relevant to pavilion making, including a significant amount on Mongolian yurts/gers.
She also hosts the Sacred Spaces Archive (Sacred Spaces is the newsletter of the Known World Architectural Guild, and this site includes a number of articles on tents, houses, and furniture).
Karen Larsdatter's period illustrations of people setting up and taking down tents, and period illustrations of market merchant booths.
See also her blog posts on sixteenth-century tents and fifteenth-century tents. Lots of good links!
Mark S. Harris's collection of Rialto articles on dwellings, with subcategories for tents, yurts, castles, cities, thatched huts, carpentry, etc.
Pavilion Information from House Greydragon. This is apparently an SCA household that has built several pavilions on Daffyd's hub-and-spoke design (with some modifications which they say help the spokes stay in place). They also have a number of photos of a surviving 16th-century (???) pavilion in a museum in Basel, Switzerland.
Max and Mickel's Easy No-Bake Pavilion, a different approach to building a circular tent. They point out that the design is equally usable with external guy lines, vertical side poles, or the hub-and-spoke construction. The page includes a lot of detail on the practicalities of construction and set-up, e.g. what kinds of seams, shopping list with prices, etc.
Panther Pavilions, a commercial maker of medievalish pavilions.
Past Tents, another commercial maker (in the U.K.). Best known for their hub-and-spoke tents.
Four Seasons Tentmasters, another commercial maker.
Dragonwing Pavilions, another commercial maker; this site includes a number of interesting articles about tent construction (and one about London Bridge!).
Alexander the Lost's Griffin's Den tavern, set up on site at Pennsic.
Devin O Raudh's wooden shed.
Donna Hrynkiw's collection of illustrations of medieval tents (also flags and banners).
Will McLean's blog posts about medieval tent construction, including lots of medieval illustrations, quotations and translations from tailors' manuals and account books about tents, and photos of his own reconstructed round tent (c1400 AD).
I intend this section to eventually become a decent bibliography for tent reconstruction. But for now, I'll just put in a few entries; recommendations for others will be cheerfully accepted!
Torvald Faegre, Tents: the Architecture of the Nomads.
This book discusses a variety of tents built by nomadic cultures around the world: Bedouin and Berber tents in one chapter, Turkish black tents in another, Mongolian yurts in another, North American tipis in another, sub-Saharan felt huts in another, etc. Each chapter includes, if I remember correctly, photos, measurements, drawings of distinctive construction details, discussion of materials and why this particular tent design developed in this particular culture.
The Calon Scrolls special issue on pavilions, "Pavilions: History and Construction" by Baroness Barbary Elspeth Ham and Countess Susannah Griffon, volume IV number 6. The Calon Scrolls is a regional newsletter of the Kingdom of Calontir, the SCA regional chapter covering Missouri, Kansas, etc.
Nomad Tent Types in the Middle East, by Peter Alford Andrews. He's an academic whose particular research interest is Middle Eastern tents; I've exchanged some email with him, and at his request I've Webbed this announcement of his new book.
An article by David Kuijt (ska Master Dafydd ap Gwystl) on his spoked pavilion design.
These are the pages I know of that contain links to this one; if you're interested in this page, you may well be interested in other stuff on these pages. If I'm missing any, please E-mail me.
Kostymelinker, somebody's page of links relevant to historical costume. I can't tell you much more than that, as I don't read much Norwegian.
The Barony of Dragonship Haven in Connecticut.
The Dwellings Page of the Anachronists' Encyclopaedia, maintained by the Shire of Uma (somewhere in Sweden).
The Renendex, a collection of information about King René d'Anjou.
H. Landon Falls, an SCA member at the University of Virginia.
The Rowany Festival's Period Camp Page. The Rowany Festival is a major annual SCA event put on by the Barony of Rowany in Lochac (Australia), and it has its own version of Enchanted Ground.


Brooklyn Public Library is seeking a Pre-HSE instructor to teach intermediate level adult basic education classes. Instructor will teach reading, writing and math to adults using curriculum developed by BPL and including CCSS.
Requirements: BA/BS required. MA in education a plus; Proven effectiveness with struggling learners; Strong organizational skills required; 6 hours/week +1 hours for prep and administrative work. Classes are evening & Saturday. Salary: $38 per hour.
The ESOL Teacher is a part-time position to assist speakers of other languages in improving their English skills. Lessons should have a focus on communication, but also include practice in all skills areas – speaking, listening, reading, and writing. For more information about Mercy Center, please visit http://www.mercycenterbronx.org.
Teach a beginner level ESOL class according the schedule of class days and times.
Prepare and make copies of instructional materials.
Collaborate with Adult Education Program Manager and Curriculum Manager to ensure lesson plans follow the outlined curriculum.
Take daily attendance and maintain minimum student attendance as outlined by funding agencies.
Maintain communication with Adult Education Administrative staff about stuent progress, class details, etc.
Bachelor's Degree and TEFL certification.
At minimum two years' experience teaching ESL to adult populations.
Experience working with adults and immigrants.
Excellent communication, organizational, and written skills.
Ability to problem solve and multi-task in a fast-paced environment.
Literacy Partners (www.literacypartners.org) is seeking an Outreach and Recruitment Coordinator to recruit adult learners for testing, assessment, and enrollment in High School Equivalency (HSE) classes on Staten Island. Working collaboratively with Head Start, UPK, and other early childhood education programs, we serve low-income and immigrant parents of young children who are building their English language, literacy and numeracy skills.
This search will remain open until the position has been filled. Interviews and observations will begin in the immediate future.
Literacy Partners is an Equal Opportunity Employer.
Riis Settlement seeks an experienced, creative, hard-working and dynamic ESOL instructor to work 9 hours per week in the evenings (Tuesday, Wednesday, Thursday, 6:00 p.m.-9:00 p.m.). Successful candidates will have experience creating student-centered learning environments, using a communicative approach, and incorporating civic engagement, job readiness and technology in the classroom. The ESOL Instructor will work within the Immigrant Services Program to provide limited English proficient adults with contextualized instruction that gives students the civic and English language skills to effectively participate in the English-speaking environment in which they live. The instructor fosters a classroom environment that offers participants the resources, opportunities and support needed to help them grow and achieve self-sufficiency.
Provide contextualized, content-based English language instruction at beginning, intermediate and/or advanced levels. Provide authentic language tasks, interactive activities, and opportunities to practice speaking and writing for fluency.
Design and implement engaging lesson plans that incorporate best practices in TESOL and adult education and assist students in meeting the curriculum standards for appropriate NRS level through a variety of instructional methods adapted to diverse learning styles.
Incorporate civic engagement into ESOL classroom instruction.
Design and administer student assessment tools that gauge student learning and monitor achievement of performance outcomes.
Create a welcoming environment that fosters community and learning among program participants.
Submit bi-weekly unit plans that address material to be covered in class.
Assist with registration and pre- and post-testing as needed (training will be provided if not certified to administer BEST Plus).
Attend staff development activities and monthly program meetings.
Assist with reporting requirements as needed, including student goal-setting and outcome assessment.
Thorough, detailed knowledge and understanding of English grammar with the ability to clearly explain all verbs, tenses and parts of speech.
Ability to interact with diverse ethnic populations and empathize with people unfamiliar with local culture.
Ability to work both independently and collaboratively with team.
Advanced computer literacy and proficiency in Microsoft XP.
Ethical and professional conduct that facilitates the building of a respectful, trusting and collaborative relationship with program staff and students.
Send resume and 3 references to Johan Lopez, Program Coordinator, at jlopez@riissettlement.org. Please type "Your Name – ESOL Instructor" in the subject line. Applications will be reviewed on a rolling basis and qualified candidates will be contacted by phone to schedule an interview.
Provide classroom instruction, completely in English, to speakers of other languages to assist in improving their English language skills - speaking, reading, writing, listening. Prepare lesson plans based on course book topics and maintain records of work done in class as well as student attendance. Must be proficient in English and have good working knowledge of grammar and language usage. Good interpersonal skills and ability to explain things effectively is desirable. Must comply with record keeping and attend monthly professional development and administrative meetings.
Ridgewood Bushwick Senior Citizen Council (RBSCC), INC. is seeking a part- time Spanish HSE Instructor. Days and times available include: T, Wed & TH: 5:45 PM - 9:00 PM. Salary: $ 44.11 per hour.
Please email resume and cover letters to srios@rbscc.org or fax to 718-381-9680, Attn: Sharon Rios.


text:
Q: Wrap ionic chips within ion-item Ionic 4 I have a requirement where in i need to wrap ionic chips within ion-item of ion-list.
Below is the code for it.
<ion-content>
    <ion-list>
        <ion-item *ngIf="showLayout" class="wrapname">
            <ion-chip color="danger" item-content>
                <ion-label >Secondary Label</ion-label>
                <ion-icon name="close"></ion-icon>
            </ion-chip>
            <ion-chip color="danger" item-content>
                <ion-label >Secondary Label</ion-label>
                <ion-icon name="close"></ion-icon>
            </ion-chip>
            <ion-chip color="danger" item-content>
                <ion-label >Secondary Label</ion-label>
                <ion-icon name="close"></ion-icon>
            </ion-chip>
        </ion-item>
    </ion-list>
</ion-content>

Below is the scss code for it.
.wrapname{
    word-wrap: break-word;
    white-space: pre-wrap;
    width:100%;
}

I have used word-wrap,but still its not working.
Am i going wrong somewhere??

A: In Ionic 4 to get <ion-chip> items to wrap inside of <ion-item>, you need to put them inside of a <ion-label text-wrap class="ion-text-wrap">. So in your example, you'd do the following:
<ion-content>
    <ion-list>
        <ion-item *ngIf="showLayout">
            <ion-label text-wrap class="ion-text-wrap">
                <ion-chip color="danger">
                    <ion-label>Secondary Label</ion-label>
                    <ion-icon name="close"></ion-icon>
                </ion-chip>
                <ion-chip color="danger">
                    <ion-label>Secondary Label</ion-label>
                    <ion-icon name="close"></ion-icon>
                </ion-chip>
                <ion-chip color="danger">
                    <ion-label>Secondary Label</ion-label>
                    <ion-icon name="close"></ion-icon>
                </ion-chip>
            </ion-label>
        </ion-item>
    </ion-list>
</ion-content>

I ran into this same problem and wrapping the ion-chip inside ion-label resolved the issue for me.

A: You can simply achieve this with the help of *ngFor
Check below code :
.ts:
 items = ["Test","Test1","Test12","Test123", "Test1234", "Test12345", "Test123456", "Test1234567", "Test123456", "Test12345", "Test1234", "Test123", "Test12", "Test1", "Test"];

.html:
<ion-content padding>
    <ion-chip *ngFor="let item of items;" color="danger" item-content style="margin-left: 10px;">
        <ion-label > {{ item }}</ion-label>
        <ion-icon name="close"></ion-icon>
    </ion-chip>
</ion-content>

Will create a list of chips as below :

StackBiz Demo: https://stackblitz.com/edit/ionic-vscljq
Hope this will helps.

redpajama_set_name: RedPajamaStackExchange


The only reason x-com might win is because boombl4 and worldedit are getting ready for wesg.
you meant WIndigo threw ?
or mb x-com playuing only online???cause they use cheats???
they played many times on polish lans.
Why always when i bet on winstrike they playing like that??
Winstrike never been a good team, xkom came in as favorites.
only one favorite in the ecs cup won their first map.
No, these are typical QBF for which comeback is not a problem.
winstrike deserve to get fucked, only wins if they are underdogs.


The physicians and staff at the Surgery Center of Decatur want your experience to be as pleasant as possible. If you have any questions or concerns about your procedure, please do not hesitate to contact us. We also welcome comments and suggestions about your experience; we are constantly striving to make sure that we exceed the expectation of you, our patient.
Hours of Operation: Monday-Friday, 6:00 a.m. – 5:00 p.m.


Editor's note: Stop doing and start thinking a little bit more, says Giada Di Stefano, Professor of Strategy at HEC Paris. Some research and insights into the impact of reflection on productivity.
In the working paper "Learning by Thinking: How #reflection Aids Performance", Giada Di Stefano, Professor of Strategy at HEC Paris, shows that reflecting on what you've done enables you to do it better next time.


Appliance-maker Electrolux is facing another complaint filed by Muslim employees at the company's St. Cloud plant.
Last year, a machine operator who worked at the plant alleged that Electrolux ignored employees' requests to pray and break fast at sunset during the holy month of Ramadan. That led to the company adjusting its meal schedule to accommodate the Muslim workers.
But shortly before the holiday began this year, workers learned that their 30-minute meal breaks would be reduced to 20 minutes.
Machine operator Ahmed Said said 20 minutes is not enough time to eat and pray after sunset during the holy month of Ramadan.
"I hope they will correct this problem so we will have an environment where people can work together, because no matter if you are Christian, Muslim, Hindu, Buddhist, or atheist, in Electrolux, we are one team. And when you are one team, your productivity is good," Said noted.
Taneeza Islam, civil rights director for the Minnesota chapter for the Council on American-Islamic Relations, said workers have not been able to fulfill their religious obligations this month.
"And now that Ramadan is almost done, it's unfortunate these employees haven't been able to eat and pray this entire month. But we're hoping this will not happen again in coming years," Islam said.
An Electrolux spokesman said in an email to MPR News the current schedule was preferred by the majority of employees, and allows the Muslim workers to eat and pray away from the production line.


text:
Home Time Zones Time Change Dates Malaysia Kuala Lumpur
Time Change 2021 in Kuala Lumpur, Malaysia
Last change: 1936
DST end
Jan 1, 1936, 12:00 midnight
Time Zones:
Daylight Saving Time (DST) Not Observed in Year 2021
Kuala Lumpur observed Malaysia Time (MYT) all year.
DST was not in use in 2021.
The previous DST change in Kuala Lumpur was on January 1, 1936.
Try selecting a different year below.
Which countries & states use DST and which do not?
Other years: 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024
Daylight Saving Time Info
About Daylight Saving Time
DST in year 2023
Upcoming time changes
History of Daylight Saving Time
Daylight Saving Time spelling
Daylight Saving Time History in Kuala Lumpur
Kuala Lumpur last observed Daylight Saving Time in 1936.
Kuala Lumpur has observed DST for 4 years between 1933 and 1936.
See Worldwide DST Statistics

redpajama_set_name: RedPajamaCommonCrawl


Took some reference of Louise Brooks with me to Drink and Draw last night. After drawing her with a skull in her hand for absolutely no reason (I blame the alcohol I was drinking), it occurred to me that I have an opportunity to do something fun. So I thought it would be funny to do a poster for a long lost Fritz Lang movie that of course never happened.
That's is superb. Great, as ever.
Love it. What inspired the fold-marks? Because it's kinda brilliant.
Just wanted it to have an old poster feel.
Amazing. I want that poster too!
Loved it so much I did one myself! Already doing it as you posted Dave and yours is much more creative, damn you!
I almost love this more than my daughter.
So many great things combined in this piece! damn you!


Australian orders are dispatched with Australia Post via Standard eParcel or Express Post.
International orders are generally shipped using Australia Post by Registered Post International Parcel. This is a non trackable service.
Express Courier International is our trackable service and it is faster.
Express Courier International is a reliable, cost-effective, international courier service.
It offers reliable door-to-door delivery of documents and goods to over 200 countries and territories within 2 to 4 business days between metropolitan areas of major cities.
Unfortunately the situation is beyond our control and lies at the feet of the postal service. We cannot guarantee the postal service, so once it is in their hands it is beyond our control.
Opting for a trackable delivery method is your best insurance to minimise risk.
Some orders are returned to Frameskin as unclaimed. This means that the postal service have tried to deliver the package to your address and no-one has been there to receive and sign for it. It is standard practice for postal companies to leave a notice (or two) that a delivery attempt has been made, and that the recipient may need to attend the post office to collect their item. The package will remain with the postal service for a period of time (which varies between countries), after which they are deemed unclaimed and returned to sender.
We DO NOT send orders to parcel lockers.


Our new lighter poker camera is suitable for those who like to smoke while gambling to use. In a situation where other poker players are smoking as well, the lighter would become an ideal carrier of poker camera. With a poker camera fixed inside, the lighter can not only be used to light your cigarette, but also can be used to scan marked cards. The scanning distance of the camera is 20-40cm. After lighting your cigarette, you can put the lighter where is good for the camera to scan the marked cards that have been shuffled already.


If you need to undertake auto repairs for your Citroen 11 1.9 then it is always a good idea to possess a Workshop Manual to keep just for personal reference just in case you need to know methods to take off a particular component including Door and match it again in the correct manner.
Citroen 11 1.9 Workshop Manuals can offer you targeted diagnostic guidelines for the car therefore if something is not working it can help you determine what the problem is and easy methods to repair it. You can then decide if this can be achieved by yourself or if the job is too big you could make a booking for your 11 1.9 in to a decent garage.


text:
\section{Mid-infrared adaptive optics in the ELT era}\label{sec:intro}

The next generation of ground-based optical/IR telescopes, the Extremely Large Telescopes (ELTs) will require substantial seeing correction to get the full scientific gain from the large aperture sizes. Scaling today's adaptive optics (AO) technologies to the sizes required for ELTs poses significant challenges: AO systems will be fully integrated into the telescope's operation, either by including a large adaptive mirror in the telescope's main optical path\cite{gilmozzi07}, or by requiring instruments to have built-in AO systems\cite{crampton07}. To provide better sky coverage and correction over a wider field than today's systems, laser guide stars (LGS) will become routinely used alongside natural guide stars, either in single or multiple configurations, thus making possible more advanced AO observing modes such as multi-object AO (MOAO), multi-conjugate AO (MCAO) and laser tomographic AO (LTAO). Both technologically and operationally, this poses some very complex demands.

At mid-IR wavelengths ($\lambda >$ 3 $\mu$m) AO will for the first time be required to observe at or close to the diffraction limit on ground-based telescopes. As the Kolmogorov turbulence power spectrum drops off steeply with increasing wavelength, diffraction limited performance in the mid-IR should be significantly less challenging than at optical wavelengths. Indeed, on today's 8-m-class telescopes, AO becomes obsolete longwards of 17 $\mu$m as observations are intrinsically limited by diffraction rather than seeing. On the scales of an ELT, however, an improvement in resolution of almost an order of magnitude is available in the N-band by correcting for atmospheric seeing.

Despite the AO requirements for mid-IR observations being less strenuous than at visible and near-infrared (NIR) wavelengths, applying AO corrections to mid-IR observations brings its own very specific problems.

\begin{description}
\item[Using NIR-optimised AO systems.] Where ELTs use large adaptive mirrors in the optical path of the telescope, such as in the European ELT (E-ELT), the system will be tailored to NIR observations; this can give rise to chromatic errors when applied in the mid-IR.
\item[Thermal background subtraction.] Subtraction of the thermal background is a crucial part of observing mid-IR radiation from the ground. Traditional chopping methods may not be possible on ELT-sized telescopes because of the large mirror sizes, so alternative methods must be identified or developed\cite{brandl_metis08}. The combination of AO correction and fast field switching observations for background will require careful planning and calibration.
\item[Atmospheric turbulence in the IR.] Infrared radiation is sensitive to the presence of water vapour in the atmosphere, which causes partial or complete opacity of the atmosphere in certain parts of the IR spectrum. In addition, the presence of water vapour is expected to cause increased differential refraction and atmospheric turbulence. These issues are discussed in more detail in the following sections.
\end{description}

This paper discusses a number of problems with carrying out AO-assisted mid-IR observations on an ELT that arise from the dispersion of the refractive index of air, and the sensitivity of IR radiation to the presence of water vapour in the atmosphere. Of particular interest are those effects expected to occur when AO wavefront sensing is performed at a different wavelength than the science observations, as is the likely situation for a mid-IR ELT instrument. A detailed understanding of this chromaticity is essential for assessing the wavefront sensing and dispersion correction needs for a mid-IR ELT instrument designed for (near-) diffraction-limited operation.

Section~\ref{sec:dispersion} introduces the concept of refractivity and how it evolves from visible to mid-IR wavelengths. We describe the formulation we use for calculations of refractivity and atmospheric input parameters. Section~\ref{sec:basic_chromatic} discusses problems arising from `traditional' atmospheric dispersion, i.e. the change in apparent zenith distance of celestial objects from atmospheric refractivity and its likely impact on image quality in the md-IR. It then goes on to describe in more detail the effect of chromaticity on AO correction, for example where wavefront sensing and science wavelengths are different. Section~\ref{sec:wvturb} shows the importance of turbulence caused by water vapour fluctuations on the performance of a mid-IR instrument on an ELT.

The work is being carried out in the context of METIS (the \underline{M}id-infrared \underline{E}-EL\underline{T} \underline{I}mager and \underline{S}pectrograph). A Phase A study for METIS is currently being carried out by an international collaboration of scientists and engineers from the Netherlands, Germany, France, Belgium and the United Kingdom. A detailed description of the project, science case and instrument parameters can be found in Brandl et al.\cite{brandl_metis08}. The AO issues listed above form an important part of the study.

\section{Atmospheric refractivity in the infrared}\label{sec:dispersion}
Atmospheric dispersion has long been known to affect the results of astronomical observations; its effects are commonly described in standard texts\cite{astrophysical}. Several papers\cite{filippenko82, reardon06, arribas99} describe the impact of atmospheric dispersion on particular observation methods or science cases. More recently, atmospheric dispersion has discussed in the context of adaptive optics, where it can contribute significantly to the wavefront error budget\cite{mette06, roe02, helminiak08}. Because of the steep dispersion of the refractive index of air at optical and NIR wavelengths, atmospheric dispersion mostly affects optical/NIR observations. Indeed, the vast majority of available literature only extends its treatment of the phenomenon to NIR wavelengths; a noted exception is found in Hawarden et al.\cite{hawarden06}, where the authors' discussion is extended to the thermal IR regime. However, a thorough understanding of all atmospheric phenomena affecting mid-IR observations is required to achieve diffraction-limited performance on the one hand, and to define any potential dispersion correction needs for the instrument on the other.

To understand chromatic errors introduced by atmospheric dispersion in the infrared, we should revisit the theory of the refractive index of air. This quantity in itself has been the subject of a large volume of work spanning many decades; the availability of large spectral line databases such as HITRAN\cite{hitran} for common atmospheric constituents has enabled a substantial improvement of its accuracy over extended wavelength ranges. The knowledge of the refractive index at IR wavelengths, however, is still lagging behind that for the visible and radio ranges.  Valuable work was published by Hill et al.\cite{hill80, hill86}, and in more recent years by  Mathar\cite{mathar_ao04,mathar07a}.

Two formulae for the refractive index of air are commonly found in the (astronomical) literature. The first is based on early work by Edl\'en\cite{edlen53}, with subsequent revisions by both Edl\'en\cite{edlen66} and other authors in the 1990s\cite{birchdowns93, birchdowns94}. The second, by Ciddor\cite{ciddor96}, is the equation officially accepted by the International Association of Geodesy (IAG). In the equation's validity range to $\lambda=$1.7 $\mu$m, it agrees with the older Edl\'en expression to $1$ part in $10^8$. As the effect of water vapour at visible/NIR wavelengths is smaller, it is often ignored~\cite{bonsch98}. In the infrared, the refractive index of air has contributions from both a slow-varying continuum and strong infrared resonances resulting from absorption by water, CO$_2$ and other atmospheric constituents, giving rise to a complex spectrum that varies significantly with atmospheric temperature, pressure and composition. This makes a simple extrapolation of the refractivity at visible/NIR wavelengths to longer wavelengths unsuitable for precision modelling. Mathar~\cite{mathar_ao04, mathar07a} gives a detailed description of the effect of IR resonances on the refractivity and we use his models thoughout this paper for refractivity calculations. A different method is described by Colavita et al.~\cite{colavita04}, however the authors note that their method is in agreement with that of Mathar.

In our subsequent discussion of atmospheric effects, we concentrate on atmospheric characteristics at two sites, Cerro Paranal (2400 m) and Cerro Macon (5000 m), representing a `standard' good site and a `high and dry site', respectively. Semi-empirical atmospheric profiles in temperature, pressure and water vapour mixing ratio were obtained in collaboration with ESO and the European Centre for Medium Range Weather Forecast\cite{profiles_ulli}. A summary of the relevant median parameters used in this paper for both sites is shown in Table~\ref{tab:atm_params}. The refractivity at these two sites is plotted in Fig.~\ref{fig:refractivity}, for both the Ciddor and Mathar formulations. The Mathar data show the location and effect on refractivity of the water and CO$_{2}$ resonances. The absolute water content at the `high and dry' site is smaller, causing a smaller slope (dispersion) of the refractivity. The relative humidity for the Macon parameters is nevertheless higher, 14.1 \%, compared to Paranal's 10.1 \%, because the water vapour saturation curve drops significantly over the 20 $^\circ$C difference between the two characteristic temperatures.

\begin{figure}
\centering
\includegraphics[width=8cm]{figs/spie2008Par.ps}
\includegraphics[width=8cm]{figs/spie2008Mac.ps}
\caption{Refractivity at the 2 representative site, Paranal (left) and Macon (right), using the parameters listed in Table~\ref{tab:atm_params}. The solid line follows Mathar, showing the water and CO$_{2}$ resonances. The dashed line shows the  extrapolation of the Ciddor formula to mid-IR wavelengths.}\label{fig:refractivity}
\end{figure}

\bigskip
\begin{table}[h]
\centering
\begin{tabular}{|l|c|c|c|c|}
\hline
Site & h (m) & T (K) & P (mbar) & W.v. mixing ratio (g/kg)\\
\hline
Paranal & 2400 & 286.3 & 760.1 & 1.16\\
Macon & 5000 & 267.0 & 552.4 & 0.466\\
\hline
\end{tabular}
\caption{Median atmospheric parameters for the two representative sites, used as input for the calculations in this paper.}\label{tab:atm_params}
\end{table}

\section{Chromatic effects in adaptive optics correction}\label{sec:basic_chromatic}

In this section we discuss several problems expected to arise from atmospheric chromaticity, applied specifically to mid-infrared wavelengths. For refractivity calculations Mathar's theory is used to account for the resonances that are prominent in the IR refractivity curve of moist air (see Fig.~\ref{fig:refractivity}).

\subsection{Atmospheric dispersion}

The effect of simple atmospheric refraction in astronomical observations is to shift the apparent position of astronomical objects at non-zero zenith positions towards the zenith. This results in a `smearing' of the point spread function (PSF) along the zenith direction. The refraction, defined as the angular distance between apparent and true zenith distance, for a given refractive index $n$ is given by:

\begin{equation}\label{eq:R}
R  \approx 206,265(\frac{n^2-1}{2n^2})\tan(z)
\end{equation}
where $z$ is the true zenith distance in radians and $R$ is in arcseconds. The approximation assumes a spherically symmetric atmosphere and is valid for $z \le 80$\cite{astrophysical}. Full treatment should include the observatory altitude and latitude and target coordinates. From equation~\ref{eq:R} the atmospheric differential refraction between two wavelengths is thus given by:

\begin{equation}\label{eq:adr}
R_1-R_2=206,265(\frac{n_1^2-1}{2n_1^2}-\frac{n_2^2-1}{2n_2^2})\tan(z).
\end{equation}

While the relative flatness of the dispersion curve at mid-IR wavelengths renders this effect largely irrelevant on today's 8-m telescopes, even in broad-band applications, the need for diffraction-limit operation on an ELT combined with the far superior diffraction limit of such telescopes, require revisiting the problem. Using the site parameters listed in Table~\ref{tab:atm_params}, we calculated refractivities for a representative broad-band filter in each of L-, M- and N-band, based on filters currently used on ground-based telescopes (see Table~\ref{tab:filters}). Equation~\ref{eq:adr} then yields the amount of elongation expected in the PSF of a broadband image at the E-ELT. The evolution of this PSF elongation with zenith distance is shown in Fig.~\ref{fig:dispersion_bands}.

The amount of elongation shown in this plot, of the order of 30-35 milli-arcsec(mas) in the worst case at z$=50^{\circ}$ at Paranal, represents almost twice the size of a diffraction-limited PSF core of a 42-m telescope in the L-band. The situation is markedly improved at a higher, drier site in all wavelength bands.

The expected Strehl loss from this level of dispersion, plotted in the bottom row of Fig.~\ref{fig:dispersion_bands},  was computed assuming that the source has a spectrum
that is flat over the specific bandwidth, that the dispersion is linear
over the bandwidth and that the diffraction limited source size is
approximately constant over the band width. The decrease can then be
computed by convolving the diffraction limited PSF by a top-hat function
with a width equal to the atmospheric dispersion and comparing the peak
intensity with the undispersed PSF. While for the M- and N-bands the resulting loss is minimal (of the order of $\sim$1-2\%), at shorter wavelengths its value can be several 10\% even at moderate z, with the value higher but still significantly reduced from 100\% at a high and dry site. Beyond imaging, for long slit spectroscopy dispersion will result in a distortion from wavelength-dependent light losses across the slit.

It would therefore seem that correction of atmospheric dispersion in its simplest form is required for diffraction-limited performance on an ELT, particularly at the shortest wavelengths (L-band). This is a very relevant conclusion given that no full-field compensator is foreseen in the baseline design of the E-ELT. Several schemes for full-field correction of atmospheric dispersion have been proposed in recent years~\cite{goncharov07, mette04,hawarden06}. However, correcting at mid-IR wavelengths using the same optics is not likely to be possible due to the limited transmission of the optics used.

With AO entirely integrated into the telescope's operation, a full treatment of refractive effects should include the dispersion as seen by the wavefront sensor (WFS), depending on WFS wavelength and bandwidth, and how it will affect the quality of the corrected image received by the instrument. This is discussed in the following section.

\begin{table}[h]
\centering
\begin{tabular}{|c|c|c|}
\hline
Band & $\lambda_{centre}$ ($\mu$m) & $\Delta\lambda$ ($\mu$m) \\
\hline
L & 3.78 & 0.70\\
M & 4.68 & 0.20\\
N & 10.5 & 1.50\\
\hline
\end{tabular}
\caption{Centre wavelengths and bandwidths for three representative filters used to calculate the effect of atmospheric dispersion in the mid-IR on the 42-m E-ELT.}\label{tab:filters}
\end{table}

\begin{figure}
\centering
\includegraphics[width=13cm]{figs/dispersion_corrected.eps}
\includegraphics[width=13cm]{figs/disp_strehl_ljo.eps}
\caption{Effect of atmospheric dispersion across the bandwidths of typical broad-band filters, as defined in Table~\ref{tab:filters}, as a function of zenith distance, around 3.8, 4.7 and 10.5 $\mu$m (L-, M- and N-bands) and for the 2 representative sites. Top row: dispersion across the bands in arcseconds. Bottom row: resultant Strehl loss from uncorrected dispersion. The solid line is for a regular site (Paranal), the dashed line for a high and dry site (Macon).}\label{fig:dispersion_bands}
\end{figure}

\subsection{Refractivity and wavefront sensing}

Further degradation of the image quality due to differential refraction in the atmosphere is expected where WFS is carried out at a different wavelength to the AO correction. Several reasons exist for such a strategy:

\begin{itemize}
\item Use of monochromatic laser guide stars (LGS) at 589 nm;
\item Different colour of the natural guide star (NGS) to the science target;
\item If the science target is used as reference source, it may be better to conserve photons in the science band by sensing the wavefront at another wavelength .
\end{itemize}

We examine here two issues specifically related to wavefront sensing, when sensing wavelength differs from science wavelength.

\subsubsection{Time dependent differential refraction}

Because of the dispersion in the refractive index of air between visible and IR wavelengths, as shown in Fig.~\ref{fig:refractivity}, the pointing centres in the visible, in the WFS, and IR, at the science detector, are not coincident. While this instantaneous displacement is not necessarily a problem for an AO system, over long exposures with significant changes in zenith distances the offset will change. If the AO system holds fixed the visible pointing centre of the guide star, the IR image will gradually trail with respect to the science instrument, giving rise to a broadening of the PSF. If left uncorrected, this can impose a limitation on maximum exposure time. Roe~\cite{roe02} gives a comprehensive discussion of this effect, including the effect of observatory altitude and latitude and target coordinates, for a number of representative targets observed in H-band. His calculations show that the H-band PSF in a 30-m telescope at Mauna Kea is broadened by 25\% of the diffraction-limited core size within just one minute; he reports that the effect has already been observed on the 10-m Keck telescopes.

Potential solutions suggested by Roe are to include a continuous calculated correction into the AO correction, or inserting compensating optics between the telescope and AO system. In the case of the E-ELT, the latter option is unlikely to be feasible, due to the broad wavelength range to be corrected.

Using equations~\ref{eq:R} and~\ref{eq:adr} from the previous section, we can calculate the instantaneous offset between visible WFS and IR science image centres. The results, shown in Fig.~\ref{fig:roecalcs}, give a good indicator of the potential magnitude of the problem when observing at mid-IR wavelengths using AO for correcting atmospheric turbulence effects at both sites. When sensing is carried out in the V-band (left-hand panels), the plots show a displacement of pointing centres of the order of $250 mas$ at moderate $z$, and around $1 arcsec$ at $z=45^{\circ}$, at Paranal. Equivalent numbers at the high and dry site lie $\sim$ 20\% lower. Even without more detailed calculations, it is not unreasonable to expect that this will indeed place a limitation on exposure time of the magnitude described by Roe with a mid-IR ELT instrument. The right-hand panels in Fig.~\ref{fig:roecalcs}, showing the same data in the case of K-band wavefront sensing, seem to indicate that the problem will be much mitigated when wavefront sensing is carried out in the K-band (2.2 $\mu$m). This is expected, given the relative flattening of the refractivity curve beyond the NIR.

\begin{figure}[t]
\centering
(a)\includegraphics[width=6cm]{figs/adr15.0000_lref0.eps}
(b)\includegraphics[width=6cm]{figs/adr15.0000_lref2.eps}
(c)\includegraphics[width=6cm]{figs/adr45.0000_lref0.eps}
(d)\includegraphics[width=6cm]{figs/adr45.0000_lref2.eps}
\caption{Offset between visible and infrared pointing centres due to atmospheric differential refraction, calculated for representative wavelengths in V, H, J, K, L, M and N-bands. Top row: $z=15^{\circ}$, (a) $\lambda_{WFS}=0.5\mu m$, (b)  $\lambda_{WFS}=2.2\mu m$. Bottom row: $z=45^{\circ}$, (c) $\lambda_{WFS}=0.5\mu m$, (d) $\lambda_{WFS}=2.2\mu m$. Symbols: $+$ represents Paranal, $\ast$ Macon.}\label{fig:roecalcs}

\end{figure}

The above calculations assume the AO system makes use of a single natural guide star (NGS), and assume a monochromatic WFS. Telescopes in the ELT generation will however use advanced AO observing modes, such as ground-layer AO (GLAO) and laser tomography AO (LTAO), employing sodium laser guide stars (LGS) in asterism configurations around the science target. As these guide stars are from their very nature monochromatic at $\sim$600 nm, K-band WFS within the instrument will not be possible in these modes. Furthermore, LGS too will be subject to atmospheric refraction; detailed calculations following Roe's template extended to multiple guide star configurations will be needed to help develop a correction scheme.

These preliminary calculations indicate strongly that a solution for differential refraction between WFS and mid-IR science instrument is required for achieving near-diffraction-limited operation at these wavelengths on an ELT. For NGS AO, the problem can be solved to a large extent (though not entirely) by the inclusion of a K-band WFS in the instrument; although a full characterisation of the problem should include the effect of WFS bandwidth and spectral distribution of the NGS. When using LGS, however, WFS at NIR wavelengths is not possible because of their monochromatic nature. One solution would be to develop LGS at NIR wavelengths; we are unaware of such developments in the LGS community. In the absence of such a facility, a mid-IR AO-assisted instrument is likely to have to cope with Strehl losses where LGS observing modes are used. A detailed quantitative assessment is needed to further understand such a refractive effect.

\subsubsection{Chromatic amplitude sensing error}

A further problem arising from different sensing and correction wavelengths is the amplitude error on the WFS measurement. It can be shown that the wavefront can be written as the product of a chromatic function, which depends only on the wavelength, and another function which depends on the turbulent flow structure (temperature, pressure) only. In that case, it is clear that any given turbulent wavefront at a given wavelength can be translated to another wavelength, by simply using the dispersion formula; a wavefront measurement at the sensing wavelength should thus be easily transformable to the correction wavelength. However, this works perfectly only if both sensing and correction are monochromatic. In general, this is not the case, therefore a perfect compensation of this effect cannot be achieved. First order estimates suggest this to be a minor effect, giving rise to a Strehl loss of $<5 \%$ on an ELT at mid-IR wavelengths, and this effect will not be discussed in detail here.

\subsection{Chromatic anisoplanatism}

The dispersion of light of different colours causes them to travel through different paths in the atmosphere, and this gives rise to an anisoplanatic error. This phenomenon has been described in detail by several authors, for example Wallner~\cite{wallner84}, Nakajima~\cite{nakajima06} (who refers to it as `chromatic shear'). More recently, Devaney~\cite{devaney08} studied the effect in the context of ELTs and found that the physical separation of the rays, even between visible and NIR rays where dispersion is steeper, is small compared with the value of $r_0$ at these wavelengths, giving rise to Strehl losses of $< 1\%$ even for high z. We will therefore not provide a further discussion of this effect for mid-IR observations.

\section{Water vapour turbulence}\label{sec:wvturb}

As the air refractive index depends on the temperature, pressure, and air constituents, as well as the wavelength, the refractive index structure constant $C_{N}^{2}$ also depends on these parameters. Therefore, $C_{N}^{2}$ can be split into several subcomponents, one for each atmospheric parameter plus cross-couplings. And each of these subcomponents depends on the wavelength as well. Hill et al.\cite{hill80} argue convincingly that the only parameters with a significant impact on the $C_{N}^{2}$ model are fluctuations in temperature and humidity, with contributions from pressure variations and those arising from other minor constituents, such as CO$_2$ negligible. We therefore get:

\begin{equation}
C_{N}^{2}=A^{2}_{T}\,\frac{C_{T}^{2}}{\left<T\right>^{2}}+
          A^{2}_{Q}\,\frac{C_{Q}^{2}}{\left<Q\right>^{2}}+
          2\,A_{T}\,A_{Q}\,\frac{C_{T,Q}}{\left<T\right>\left<Q\right>}
\end{equation}
where $A_{T}$ and $A_{Q}$ are functions of the pressure, temperature, water vapor pressure, and wavelength. Interestingly, the cross-coupling can have either positive or negative values, in principle, therefore it is possible that in certain conditions the presence of water vapour compensates partially the temperature-based $C_{N}^{2}$. In normal conditions, and in the visible and near-IR, optical turbulence due to temperature fluctuation largely dominates the water-based optical turbulence\cite{roddier81}.

At far-IR and submillimetre wavelengths, and in the interferometry community, the effect of water vapour turbulence is well known to affect the quality of observations. Indeed, phase variance due to atmospheric water vapour fluctuations is an important problem for many present and future facilities, such as the Very Large Telescope Interferometer (VLTI)\cite{mathar_paranal07}, the Keck interferometer\cite{colavita04}, and the Atacama Large Millimetre Array (ALMA)\cite{nikolic08}. The available experimental data largely employs water vapour radiometry or observations of radio beacons from geostationary satellites, and have yielded useful results. Measurements at the ALMA site~\cite{alma_517, alma_543} have shown a Kolmogorov-like power spectrum of water vapour turbulence, with a night-time vertical scale height of approximately 1 km. However, there is a need for more experimental data, particularly relevant to mid-IR observations with an ELT-sized filled aperture, and verification of the atmospheric models used for interpretation of data.

Hill's formula permits the calculation of the $C_{N}^{2}$, as the functions $A_{T}$ and $A_{Q}$ can be computed from a knowledge of the temperature, pressure and humidity vertical profiles, but the $C_{T}^{2}$, $C_{Q}^{2}$ and $C_{T}C_{Q}$ need to be measured on-site. As reliable experimental data are lacking, we perform a first-order estimation of the impact of the additional water vapour-based turbulence.
A rough estimate of the proportion of water vapour and dry air (temperature) optical turbulence can be found in Colavita et al.~\cite{colavita04}: by extrapolating water vapour turbulence data measured by radio interferometers at Mauna Kea (measuring rms phase delay fluctuation over a 100 m baseline) to the visible and mid-IR, and assuming an outer scale (L$_0$) of 40 m, they estimate that the refractive index fluctuation due to water vapor would be about 1/20th of the temperature-based refractive index fluctuation, in the visible and near-IR, and about 1/7th in the mid-IR at 10 microns. Translated into a ratio of $C_{N}^{2}$, these numbers would be respectively 1/400th and 1/49th.

We consider the case where WFS is carried out at a wavelength not sensitive to the presence of water vapour (i.e. visible or NIR), correction is applied at 10 $\mu$m (N-band), and the water vapour turbulence is statistically decorrelated from traditional temperature-based turbulence (i.e. neglecting any cross-coupling). The result is an independent wavefront error in the corrected image that remains uncorrected, as it can not been `seen' at the sensing wavelength. We can thus write the phase variance associated to this unseen wavefront error using the classical expression for uncorrected turbulent phase error:

\begin{equation}
\sigma_{WV}^{2}=1.0324\,\eta(L_0/D)\,(D/r_{0})^{5/3}
\end{equation}
where the Fried parameter is calculated from $C_{N}^{2}$ using

\begin{equation}
r_{0}^{-5/3}=0.4234(2\pi/\lambda)^{2}\int C_{N}^{2}(h)dh,
\end{equation}

L$_0$ is the outer scale, D the aperture diameter, and $\eta(L_0/D)$ is the outer scale attenuation factor (see Jolissaint et al.~\cite{jolissaint04} for an accurate empirical calculation method).

In Table~\ref{tab:watervaporturb}, we show the N-band (10 $\mu$m) Strehl ratio associated to the variance error above for three values of the outer scale L$_0$ (infinite, 60 m and 30 m), three telescope diameters (8, 30 and 42 m), a dry turbulence characterized by a typical $r_{0}$ of 10 cm, and assuming Colavita's values for the refractive index fluctuations ratio (water/temperature). It is found that for large apertures, the Strehl loss can become quite significant, if the outer scale is larger than the typical values encountered at most locations (in the range 20-40 m). For 8-m telescopes the effect is shown to be very small. In the absence of dedicated measurements of the water vapour optical turbulence in the mid-IR, it is difficult to assess the importance of this effect. Our estimation at least shows that it is not negligible, and can become a serious issue for large apertures; given the lack of understanding of water vapour turbulence phenomena, these results should be viewed with caution. Water vapour optical turbulence measurement campaigns, on baselines relevant to observations with an ELT-sized filled aperture, are critically needed to support mid-IR AO performance analysis in the context of the ELT projects.

\begin{table}[htdp]
\centering
\begin{tabular}{|l|c|c|c|}
\hline $L_{0}$  & 8 m  & 30 m & 42 m\\
\hline $\infty$ & 0.93 & 0.50 & 0.30\\
60 m     & 0.97 & 0.90 & 0.88\\
30 m     & 0.98 & 0.96 & 0.95\\
\hline
\end{tabular}
\caption{Estimated N-band Strehl loss in the presence of (uncorrected) water vapour turbulence, based on measurement data from Mauna Kea extrapolated to mid-IR wavelengths.}\label{tab:watervaporturb}
\end{table}

\section{Conclusions}

Atmospheric dispersion is a well known source of error in astronomical observations at visible and near-infrared wavelengths. With the advent of ELTs and their integrated AO facilities, atmospheric refractivity becomes a relevant quantity even in the mid-infrared. This is particularly the case if the traditional refractivity formulations are recalculated to include the effects of IR water and CO$_2$ resonances, which causes the refractivity to deviate substantially from the NIR values extrapolated to longer wavelengths.

The calculations in this paper, though in many places approximate in nature, show the likely magnitude of refractive effects on the AO correction for a mid-IR ELT instrument. While `simple' dispersion will only cause a significant drop in Strehl at the short-wavelength end of the region, differential refraction effects between visible/NIR WFS and mid-IR science instrument may cause a significant image degradation over long exposures, even at moderate zenith distances. This problem in particular will be investigated more closely, taking into account the effect of multiple laser guide stars which can only be sensed in the visisble.

Water vapour turbulence has recently been of interest in the interferometry and submillimetre communities, however, a thorough understanding of the phenomenon and experimental data are lacking (and non-existent in the framework of an ELT-sized filled aperture). Our first order estimates show that the Strehl loss can be significant, if not large, depending on the size of the outer scale. However, given the poor understanding of this type of turbulence both in the spatial and temporal domain, and of its correlation with dry air turbulence, these results show be regarded with caution. Further experimental results, specifically designed for ELT-type observations in the mid-IR, are required to help assess the problem.

The comparison of results between the a Paranal-like site and a `high and dry' location like Cerro Macon is also very important, and reinforces the notion that a high and dry location is more suitable for mid-IR astronomy. However, we expect some of these advantages to apply to NIR also, and would invite NIR colleagues to examine site-related effects more closely.

Correcting atmospheric dispersion on an ELT is a challenging task, even in today's telescopes. Solutions have been suggested for ELTs in recent years, but none have the capability of providing correction over a wide wavelength range (from visible to infrared). The problems will have to be addressed by a combination of technology (e.g. K-band wavefront sensing, NIR laser guide stars) and careful calibration. The first step, however, is a detailed theoretical understanding, and we intend to continue this work to make this possible.

\section{Acknowledgements}

The authors wish to thank John Richer, Henry Roe and Jacques Beckers for informative discussions, and exchange of software routines, papers and data. We are also grateful to the METIS consortium for supporting and participating in this work.

redpajama_set_name: RedPajamaArXiv


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Danny Ings is back in training, Ralph Hasenhuttl unsure if he'll feature against Brighton
Danny Ings hasn't played for Southampton since his knee injury picked up against Aston Villa
By St. Mary's Musings Dec 4, 2020, 12:42pm GMT
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Photo by Matt Watson/Southampton FC via Getty Images
Southampton striker Danny Ings made a return to training yesterday for the first time since picking up a knee injury against Aston Villa in October.
The England international is a key component to the Southampton attack, scoring five goals in seven Premier League games so far this season.
Saints haven't looked awful since he has been sidelined, though, picking up four points from three games against Newcastle United, Wolverhampton Wanderers, and Manchester United.
Having missed those games since his collision at Villa Park and now back in training, there is a chance he could return to action against Brighton & Hove Albion on Monday night.
However, Saints manager Ralph Hasenhuttl says he is unsure of Ings' match fitness and if he will be rushed into playing Brighton at the Amex.
"We must have a look. Yesterday was the first time he was training with the team," Hasenhuttl said in response to whether Ings will make an appearance on Monday night or not.
"He looks good. We must look how his body reacts to the training and then we can say more. But it looked good yesterday, yes."


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