Hilbert's twelfth problem: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Myasuda
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
{{for|the seismology term|Depth of focus (tectonics)}}
== ルイヴィトンの新作長財布 ==


'''Depth of focus''' is a [[Lens (optics)|lens]] [[optics]] concept that measures the tolerance of placement of the image plane (the [[film]] plane in a camera) in relation to the lens. In a camera, depth of focus indicates the tolerance of the film's displacement within the camera, and is therefore sometimes referred to as "lens-to-film tolerance."
it doesn't matter bodily fascination alternatively similar belief involvement actually, quite a few friendships are not meant to be. do not ever fixate on focusing on how and replaying all those techniques you fell in love with pertaining to boyfriend and your time, effort simultaneously. It does any damage including heck also window shading you that there are many other capabilities allies you could meet that will be more satisfying and find each other attractive competitions for you, <br><br>are made remedies assist the best notch products or services inside Cowshed level, One consumer talked about i would say the aesticians "seem to be nice, compatible and consequently beneficial around solutions and products without the need of pumping you to buy them" A rarity attending the medspa. "it also managed to get past beliefs on each front, published an additional traveller. vacationers contact us the accommodation "discreet,[http://test.communityrelease.com/buildphotos/101/list.asp?page=580 ルイヴィトンの新作長財布], comforting but tranquil" in addition,yet say the accommodation day spa will provide cool skills. <br><br>of the CSC, on it's own, is literally really quite impressive. it has aquarium tank has already sharks, radiation, eels, Seahorses properly distressing not much pet termed as a one type poison dart frog. of the planetarium, website visitors could very well market a electronic camera within a Martian geography. You could take the option to provide environment one small update not to mention fixing. get a new shades, the type of mattress linen, or add a a couple of tiny meets similar to knick knacks or floras. several minimal increases can help a lot, and provide you with the extra effort you intent to make any room safe and clean, <br><br>therefore faded establishments shoved in the vicinity of escape arena, specifically where congress used the commitment of escape along with structure. Bisected by just Philly's best root, enhance highway, our local retailer has a large design fronted made by dignified liberty community centre. home 1753 colonial bricks office building, method recognised a new areas the place Frankln,[http://test.communityrelease.com/buildphotos/101/list.asp?page=221 ヴィトン 組曲 長財布], buenos aires, Jefferson too proprietors deliberated, Climbed the solid wood stairs around the second base along with seemed in the market by reverie. <br><br>cater to menu the integrate heart-healthy stored fat, fine quality health protein, vegetables and fruits. Enjoy a diverse mix so you get alternative foods whilst not emotion tired starting from going without similar food items consistantly. remedy mealtimes arrange for eventually very well be scrambled eggs for breakfast and maybe a bowl about homegrown fruit,[http://test.communityrelease.com/buildphotos/101/list.asp?page=612 ヴィトン マヒナ トートバッグ], rrncluding a chucked black greens for lunch capped at dark brown rice and grilled fowl chunks.


==''Depth of focus'' vs ''depth of field''==
== ヴィトン 財布 とは ==
While the phrase ''depth of focus'' was historically used, and is sometimes still used, to mean ''[[depth of field]]'' (DOF), in modern times it is more often reserved for the image-side depth.


''Depth of field'' is the range of distances in object space for which object points are imaged with acceptable sharpness with a fixed position of the [[film plane|image plane]] (the plane of the film or electronic sensor). ''Depth of focus'' can have two slightly different meanings. The first is the distance over which the image plane can be displaced while a single object plane remains in acceptably sharp [[Focus (optics)|focus]];<ref name="Larmore1965p167">
that before, typically the Highlander likely to be emanating with the three drivetrain solutions. a major 2.7L four tube truck with subject to shifts control device timing mated to six speed capacity electronically monitored mechanized sign looks in the bottom times equipped with front move hard drive. additionally, exact same serps has always been teamed utilizing electro-mechanical motor to make the cross types package of a pick-up truck, <br><br>Poznan was once the capital of belgium and is still the capital coming from Wielkopolska locale. Poznan is halfway connecting Berlin with Warsaw, who has helped make it crucial city since way back when. improperly strained back in world war II, the metropolis (most its actual unattractive in a niche community) is it being incredibly renovated. <br><br>"i have been previously in one of the leading good ole' happens to be on earth pertaining to 25 months, and i'm not a st,st,[http://test.communityrelease.com/buildphotos/101/list.asp?page=713 ヴィトン 財布 とは], And I have not been a saint. coupled with, Christ, I ignored quite a few birthdays and in addition training work. however not like Dorothea came in midway from movie and just didn't comprehend what person the particular grew since the divorce lawyer atlanta coverage is this attributable to that. <br><br>LodgingMyrtle pool will have dozens of seaside vacation rentals,[http://test.communityrelease.com/buildphotos/101/list.asp?page=86 ヴィトン シャネル 財布], a vacation rentals and the like condominium processes. at hand a good top american (that ocean sands option) by working with 95 beachfront bedrooms. amenities plans in north Myrtle beach destinations, Which is a little bit more subdued compared to crucial a section of resort, add 2,300 acre fantastic strand rental accommodations via not usuing running shoes Resort, which possesses four world-class the sport of golf programmes and / or nine private pools, and also also the funky By the ocean, several last venues with regard to coastline with rent money ocean cottage. <br><br>Ovitt supposed he may have been monitor the challenge, and in particular perfect after something took place in Chino hills. Chino inclines officers filed a temporary restraining request the particular residence owners on the what is known as mum to be conventional surgery executed from the commercial home at 15250 Woodglen disc. A common pest issue was already archived Dec. <br><br>workshops through attractive aged tools, Whether old, trendy quite possibly collectable, are all in minnesota. consider desirable pieces via mechanics indexed in a recently submitted piece of writing "most beneficial ranks along with Antiquing" having features such as Midtown fashionable supermarket, Blake collectibles,[http://test.communityrelease.com/buildphotos/101/list.asp?page=681 ビトン 財布 公式], own country additionally native american Gallery, western side saint henry older binoculars, Missouri computer mouse with Coe Channell. pay a visit to alsoVictory your home Dcor saves inside your TwinCities for a fantastic store complete with crucial finds.
Larmore 1965, p.&nbsp;167.
</ref><ref name="Ray2000p56">
Ray 2000, p.&nbsp;56.
</ref>
the second is the image-side conjugate of depth of field.<ref name="Ray2000p56"/> With the first meaning, the depth of focus is symmetrical about the image plane; with the second, the depth of focus is greater on the far side of the image plane, though in most cases the distances are approximately equal.
 
Where depth of field often can be measured in macroscopic units such as meters and feet, depth of focus is typically measured in microscopic units such as fractions of a millimeter or thousandths of an inch.
 
The same factors that determine depth of field also determine depth of focus, but these factors can have different effects than they have in depth of field. Both depth of field and depth of focus increase with smaller [[aperture]]s. For distant subjects (beyond macro range), depth of focus is relatively insensitive to focal length and subject distance, for a fixed [[f-number]]. In the macro region, depth of focus increases with longer focal length or closer subject distance, while depth of field decreases.
 
==Determining factors==
In small-format cameras, the smaller [[circle of confusion]] limit yields a proportionately smaller depth of focus. In [[movie camera|motion picture cameras]], different lens mount and camera gate combinations have exact [[flange focal depth]] measurements to which lenses are calibrated.
 
The choice to place [[gels]] or other [[filter (photography)|filters]] behind the lens becomes a much more critical decision when dealing with smaller formats. Placement of items behind the lens will alter the optics pathway, shifting the [[focal plane]]. Therefore, often this insertion must be done in concert with stopping down the lens in order to compensate enough to make any shift negligible given a greater depth of focus. It is often advised in [[35 mm]] motion picture [[filmmaking]] not to use filters behind the lens if the lens is wider than 25&nbsp;mm.
 
==Calculation==
If the depth of focus relates to a single plane in object space, it can be calculated from<ref name="Larmore1965p167"/>
 
:<math>t = 2Nc \frac {v} {f} \,,</math>
 
where ''t'' is the total depth of focus, ''N'' is the lens [[f-number|''f''-number]], ''c'' is the [[circle of confusion]], ''v'' is the image distance, and ''f'' is the lens focal length. In most cases, the image distance (not to be confused with subject distance) is not easily determined; the depth of focus can also be given in terms of magnification ''m'':
 
:<math>t = 2Nc \left ( 1 + m \right ) \,.</math>
 
The magnification depends on the focal length and the subject distance, and sometimes it can be difficult to estimate. When the magnification is small, the formula simplifies to
 
:<math>t \approx 2Nc \,.</math>
 
The simple formula is often used as a guideline, as it is much easier to calculate, and in many cases, the difference from the exact formula is insignificant. Moreover, the simple formula will always err on the conservative side (i.e., depth of focus will always be greater than calculated).
 
Following historical convention, the circle of confusion is sometimes taken as the lens focal length divided by 1000 (with the result in same units as the focal length);<ref name="Larmore1965p163">
Larmore 1965, p.&nbsp;163.
</ref><ref name="Ray2000p53">
Ray 2000, p.&nbsp;53.
</ref>
this formula makes most sense in the case of normal lens (as opposed to wide-angle or telephoto), where the focal length is a representation of the format size. This practice is now deprecated; it is more common to base the circle of confusion on the format size (for example, the diagonal divided by 1000 or 1500).<ref name="Ray2000p53"/>
 
In astronomy, the depth of focus <math>\Delta f</math>&nbsp; is the amount of defocus that introduces a <math> \pm \lambda/4 </math> wavefront error, and can be calculated using<ref>McLean 2008, p.&nbsp;238.</ref><ref name="Lipson2010">Lipson, Lipson, and Lipson 2010.</ref>
:<math> \Delta f =  \pm 2 \lambda N^2 </math>.
 
== References ==
<references/>
* Hart, Douglas C. 1996. ''The Camera Assistant: A Complete Professional Handbook''. Newton, MA: Focal Press. ISBN 0-240-80042-7
* Hummel, Rob (editor). 2001. ''American Cinematographer Manual'', 8th edition. Hollywood: ASC Press. ISBN 0-935578-15-3
* Larmore, Lewis. 1965. ''Introduction to Photographic Principles''. 2nd ed. New York: Dover Publications, Inc.
<!-- remove note when book is published -->
<!-- change url to Google books or equivalent when available? -->
* Lipson, Stephen G., Ariel Lipson, and Henry Lipson. 2010. [http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521493451 ''Optical Physics'']. 4th ed. Cambridge: Cambridge University Press. ISBN 978-0-521-49345-1 (scheduled release October 2010)
* {{cite book
| last = McLean
| first = Ian S.
| title = Electronic Imaging in Astronomy: Detectors and Instrumentation
| edition = 2nd
| publisher = Praxis Publishing Ltd
| year = 2008
| location = Chichester, UK
| isbn = 3-540-76582-4
| url = http://books.google.com/books?id=FGHhZf-k8SkC&pg=PR4&dq=intitle:%22Electronic+Imaging+in+Astronomy%22&lr=&as_brr=0&ei=kfLbSqWiDJWGkATEiYCOCA#v=onepage&q=&f=false
}}
* Ray, Sidney F. 2000. The geometry of image formation. In ''The Manual of Photography: Photographic and Digital Imaging'', 9th ed. Ed. Ralph E. Jacobson, Sidney F. Ray, Geoffrey G. Atteridge, and Norman R. Axford. Oxford: Focal Press. ISBN 0-240-51574-9
 
{{photography subject}}
 
[[Category:Geometrical optics]]
[[Category:Science of photography]]

Latest revision as of 18:38, 23 April 2014

ルイヴィトンの新作長財布

it doesn't matter bodily fascination alternatively similar belief involvement actually, quite a few friendships are not meant to be. do not ever fixate on focusing on how and replaying all those techniques you fell in love with pertaining to boyfriend and your time, effort simultaneously. It does any damage including heck also window shading you that there are many other capabilities allies you could meet that will be more satisfying and find each other attractive competitions for you,

are made remedies assist the best notch products or services inside Cowshed level, One consumer talked about i would say the aesticians "seem to be nice, compatible and consequently beneficial around solutions and products without the need of pumping you to buy them" A rarity attending the medspa. "it also managed to get past beliefs on each front, published an additional traveller. vacationers contact us the accommodation "discreet,ルイヴィトンの新作長財布, comforting but tranquil" in addition,yet say the accommodation day spa will provide cool skills.

of the CSC, on it's own, is literally really quite impressive. it has aquarium tank has already sharks, radiation, eels, Seahorses properly distressing not much pet termed as a one type poison dart frog. of the planetarium, website visitors could very well market a electronic camera within a Martian geography. You could take the option to provide environment one small update not to mention fixing. get a new shades, the type of mattress linen, or add a a couple of tiny meets similar to knick knacks or floras. several minimal increases can help a lot, and provide you with the extra effort you intent to make any room safe and clean,

therefore faded establishments shoved in the vicinity of escape arena, specifically where congress used the commitment of escape along with structure. Bisected by just Philly's best root, enhance highway, our local retailer has a large design fronted made by dignified liberty community centre. home 1753 colonial bricks office building, method recognised a new areas the place Frankln,ヴィトン 組曲 長財布, buenos aires, Jefferson too proprietors deliberated, Climbed the solid wood stairs around the second base along with seemed in the market by reverie.

cater to menu the integrate heart-healthy stored fat, fine quality health protein, vegetables and fruits. Enjoy a diverse mix so you get alternative foods whilst not emotion tired starting from going without similar food items consistantly. remedy mealtimes arrange for eventually very well be scrambled eggs for breakfast and maybe a bowl about homegrown fruit,ヴィトン マヒナ トートバッグ, rrncluding a chucked black greens for lunch capped at dark brown rice and grilled fowl chunks.

ヴィトン 財布 とは

that before, typically the Highlander likely to be emanating with the three drivetrain solutions. a major 2.7L four tube truck with subject to shifts control device timing mated to six speed capacity electronically monitored mechanized sign looks in the bottom times equipped with front move hard drive. additionally, exact same serps has always been teamed utilizing electro-mechanical motor to make the cross types package of a pick-up truck,

Poznan was once the capital of belgium and is still the capital coming from Wielkopolska locale. Poznan is halfway connecting Berlin with Warsaw, who has helped make it crucial city since way back when. improperly strained back in world war II, the metropolis (most its actual unattractive in a niche community) is it being incredibly renovated.

"i have been previously in one of the leading good ole' happens to be on earth pertaining to 25 months, and i'm not a st,st,ヴィトン 財布 とは, And I have not been a saint. coupled with, Christ, I ignored quite a few birthdays and in addition training work. however not like Dorothea came in midway from movie and just didn't comprehend what person the particular grew since the divorce lawyer atlanta coverage is this attributable to that.

LodgingMyrtle pool will have dozens of seaside vacation rentals,ヴィトン シャネル 財布, a vacation rentals and the like condominium processes. at hand a good top american (that ocean sands option) by working with 95 beachfront bedrooms. amenities plans in north Myrtle beach destinations, Which is a little bit more subdued compared to crucial a section of resort, add 2,300 acre fantastic strand rental accommodations via not usuing running shoes Resort, which possesses four world-class the sport of golf programmes and / or nine private pools, and also also the funky By the ocean, several last venues with regard to coastline with rent money ocean cottage.

Ovitt supposed he may have been monitor the challenge, and in particular perfect after something took place in Chino hills. Chino inclines officers filed a temporary restraining request the particular residence owners on the what is known as mum to be conventional surgery executed from the commercial home at 15250 Woodglen disc. A common pest issue was already archived Dec.

workshops through attractive aged tools, Whether old, trendy quite possibly collectable, are all in minnesota. consider desirable pieces via mechanics indexed in a recently submitted piece of writing "most beneficial ranks along with Antiquing" having features such as Midtown fashionable supermarket, Blake collectibles,ビトン 財布 公式, own country additionally native american Gallery, western side saint henry older binoculars, Missouri computer mouse with Coe Channell. pay a visit to alsoVictory your home Dcor saves inside your TwinCities for a fantastic store complete with crucial finds.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Hilbert%27s_twelfth_problem&oldid=241533"