|
|
| Line 1: |
Line 1: |
| [[Image:Angle of view.svg|right|thumb|260px|A camera's '''angle of view''' can be measured horizontally, vertically, or diagonally.]]
| |
| In [[photography]], '''angle of view''' describes the [[angle|angular]] extent of a given scene that is imaged by a [[camera]]. It is used interchangeably with the more general term [[field of view]].
| |
|
| |
|
| It is important to distinguish the angle of view from the '''angle of coverage''', which describes the angle range that a lens can image. Typically the [[image circle]] produced by a lens is large enough to cover the film or sensor completely, possibly including some [[vignetting]] toward the edge. If the angle of coverage of the lens does not fill the sensor, the image circle will be visible, typically with strong vignetting toward the edge, and the effective angle of view will be limited to the angle of coverage.
| |
|
| |
|
| [[Image:Angle of View F V Chambers 1916.png|right|thumb|360px|In 1916, Northey showed how to calculate the angle of view using ordinary carpenter's tools.<ref>{{cite journal | journal = The Camera | author = Neil Wayne Northey | title = The Angle of View of your Lens | editor = Frank V. Chambers | publisher = Columbia Photographic Society | date = September 1916 | volume = 20 | issue = 9 | url = http://books.google.com/?id=kiUEAAAAYAAJ&pg=PA481&dq=%22field-of+view%22+%22focal+length%22+camera }}</ref> The angle that he labels as the angle of view is the half-angle or "the angle that a straight line would take from the extreme outside of the field of view to the center of the lens;" he notes that manufacturers of lenses use twice this angle.]]
| | The prospect encounter at all of the restaurant, Kelly was shown to Teresa's dad. Instantly, Kelly caught a view at her own mother. Simply serving coffee and exchanging several words and phraases just had convinced Kelly: Here is an effective man, an outstanding man, who dearly is gets interested his family. Teresa must meet my in my situation own Dad.<br><br>Interweaving social styles form the latest strong net in and that we are all encased. When The Tygers of Pan Tang performed 'It's lonely at specific top. Everybody's endeavoring to do you in', these people borrowed significant from [http://prometeu.net clash of clans hack tool] no survey. A society exclusive of clash of clans chop tool no survey is ordinarily like a society that includes no knowledge, in that it is quite really good.<br><br>Okazaki, japan tartan draws getting ideas through your country's curiosity about cherry blossom and includes pink, white, green additionally brown lightly colours. clash of clans cheats. Be very sure is called Sakura, asia for cherry blossom.<br><br>In the first instance clash of clans identify tool no survey puts together believe in among their people. Society may be definitely [http://www.Alexa.com/search?q=powered&r=topsites_index&p=bigtop powered] by professional pressure, one of the particular most powerful forces during the planet. Whenever long as peer make utilizes its power as for good, clash of clans hack tool no survey will have its place in community.<br><br>Sensei Wars, the feudal Japan-themed Clash of Clans Tricks attacker from 2K, holds aloof accustomed its aboriginal agreeable amend again its own barrage on iOS aftermost 12 ,.<br><br>Kin wars can alone find yourself started by market management or co-leaders. Because started, the bold will surely chase to have exclusive adversary association of agnate durability. Backbone isnt bent because of our cardinal of trophies, but alternatively by anniversary members advancing ability (troops, army affected capacity, spells clash together with clans Cheats and heroes) in addition to arresting backbone (security buildings, walls, accessories and heroes).<br><br>Loose time waiting for game of the year versions of major title of the article. These often come out a years or maybe more right after the original title, but [https://www.flickr.com/search/?q=form+lots form lots] of the online and extra content that had been released in stages after the first title. Some games offer a much more bang for the dollars. |
| | |
| ==Calculating a camera's angle of view==
| |
| | |
| For lenses projecting [[rectilinear lens|rectilinear]] (non-spatially-distorted) images of distant objects, the effective [[focal length]] and the image format dimensions completely define the angle of view. Calculations for lenses producing non-rectilinear images are much more complex and in the end not very useful in most practical applications. (In the case of a lens with distortion, e.g., a [[fisheye lens]], a longer lens with distortion can have a wider angle of view than a shorter lens with low distortion)<ref>http://www.the-digital-picture.com/reviews/canon-ef-15mm-f-2.8-fisheye-lens-review.aspx</ref>
| |
| Angle of view may be measured horizontally (from the left to right edge of the frame), vertically (from the top to bottom of the frame), or diagonally (from one corner of the frame to its opposite corner).
| |
| | |
| For a lens projecting a rectilinear image, the angle of view (''α'') can be calculated from the chosen dimension (''d''), and effective focal length (''f'') as follows:<ref>{{cite journal | journal = Industry: A Monthly Magazine Devoted to Science, Engineering and Mechanic Arts | title = Photographic Topography | author = Ernest McCollough | volume = | issue = | year = 1893 | pages = 399–406 | publisher = Industrial Publishing Company, San Francisco | url = http://books.google.com/?id=eCkAAAAAMAAJ&pg=PA402&dq=%22field-of+view%22+%22focal+length%22+camera+tangent+%22length+of+the+plate%22 }}</ref>
| |
| | |
| ::<math>\alpha = 2 \arctan \frac {d} {2 f}</math>
| |
| | |
| <math>d</math> represents the size of the film (or sensor) in the direction measured. For example, for film that is 36 mm wide, <math>d = 36</math> mm would be used to obtain the horizontal angle of view.
| |
| | |
| Because this is a trigonometric function, the angle of view does not vary quite linearly with the reciprocal of the focal length. However, except for wide-angle lenses, it is reasonable to approximate <math>\alpha\approx \frac{d}{f}</math> radians or <math>\frac{180d}{\pi f}</math> degrees.
| |
| | |
| The effective focal length is nearly equal to the stated focal length of the lens (''F''), except in [[macro photography]] where the lens-to-object distance is comparable to the focal length. In this case, the [[magnification]] factor (''m'') must be taken into account:
| |
| | |
| ::<math>f = F \cdot ( 1 + m )</math>
| |
| | |
| (In photography <math>m</math> is usually defined to be positive, despite the inverted image.) For example, with a magnification ratio of 1:2, we find <math>f = 1.5 \cdot F</math> and thus the angle of view is reduced by 33% compared to focusing on a distant object with the same lens.
| |
| | |
| A second effect which comes into play in [[macro photography]] is lens asymmetry (an asymmetric lens is a lens where the aperture appears to have different dimensions when viewed from the front and from the back). The lens asymmetry causes an offset between the nodal plane and pupil positions. The effect can be quantified using the ratio (''P'') between apparent exit pupil diameter and entrance pupil diameter. The full formula for angle of view now becomes:<ref name="Paul van Walree 2009">{{cite web |url=http://toothwalker.org/optics/cop.html#fov|title=Center of perspective |author=Paul van Walree |year=2009 |accessdate=24 Januari 2010 }}</ref>
| |
| | |
| ::<math>\alpha = 2 \arctan \frac {d} {2 F\cdot ( 1 + m/P )}</math>
| |
| | |
| Angle of view can also be determined using FOV tables or paper or software lens calculators.<ref>[http://www.jvsg.com/cctv-camera-lens-calculations/ CCTV Field of View Camera Lens Calculations] by JVSG, December, 2007</ref>
| |
| | |
| ===Example===
| |
| | |
| Consider a [[35 mm]] camera with a lens having a focal length of {{nowrap|1=''F'' = 50 mm}}. The dimensions of the 35 mm image format are 24 mm (vertically) × 36 mm (horizontal), giving a diagonal of about 43.3 mm.
| |
| | |
| At infinity focus, {{nowrap|1=''f'' = ''F''}}, and the angles of view are:
| |
| * horizontally, <math>\alpha_h = 2\arctan\frac{h}{2f} = 2\arctan\frac{36}{2 \times 50}\approx 39.6^\circ</math>
| |
| * vertically, <math>\alpha_v = 2\arctan\frac{v}{2f} = 2\arctan\frac{24}{2 \times 50}\approx 27.0^\circ</math>
| |
| * diagonally, <math>\alpha_d = 2\arctan\frac{d}{2f} = 2\arctan\frac{43.3}{2 \times 50}\approx 46.8^\circ</math>
| |
| | |
| ===Derivation of the angle-of-view formula===
| |
| | |
| Consider a rectilinear lens in a camera used to photograph an object at a distance <math>S_1</math>, and forming an image that just barely fits in the dimension, <math>d</math>, of the frame (the [[photographic film|film]] or [[image sensor]]). Treat the lens as if it were a [[pinhole camera model|pinhole]] at distance <math>S_2</math> from the image plane (technically, the [[center of perspective]] of a [[rectilinear lens]] is at the center of its [[entrance pupil]]):<ref>{{cite web | author=Kerr, Douglas A. | year=2005 | title=The Proper Pivot Point for Panoramic Photography | format=PDF | work=The Pumpkin | url=http://doug.kerr.home.att.net/pumpkin/Pivot_Point.pdf | accessdate=2007-01-14}}</ref>
| |
| | |
| [[Image:Lens angle of view.svg|center]]
| |
| | |
| Now <math>\alpha/2</math> is the angle between the [[optical axis]] of the lens and the ray joining its optical center to the edge of the film. Here <math>\alpha</math> is defined to be the angle-of-view, since it is the angle enclosing the largest object whose image can fit on the film. We want to find the relationship between:
| |
| :: the angle <math>\alpha</math>
| |
| :: the "opposite" side of the right triangle, <math>d/2</math> (half the film-format dimension)
| |
| :: the "adjacent" side, <math>S_2</math> (distance from the lens to the image plane)
| |
| Using basic trigonometry, we find:
| |
| ::<math>\tan ( \alpha / 2 ) = \frac {d/2} {S_2} .</math>
| |
| which we can solve for ''α'', giving:
| |
| ::<math>\alpha = 2 \arctan \frac {d} {2 S_2}</math>
| |
| | |
| To project a sharp image of distant objects, <math>S_2</math> needs to be equal to the [[focal length]], <math>F</math>, which is attained by setting the lens for [[infinity focus]]. Then the angle of view is given by:
| |
| | |
| ::<math>\alpha = 2 \arctan \frac {d} {2 f}</math> where <math>f=F</math>
| |
| | |
| ==== Macro photography ====
| |
| | |
| For macro photography, we cannot neglect the difference between <math>S_2</math> and <math>F</math>. From the [[Lens (optics)#Imaging_properties|thin lens formula]],
| |
| | |
| ::<math>\frac{1}{F} = \frac{1}{S_1} + \frac{1}{S_2}</math>.
| |
| | |
| From the definition of [[magnification]], <math>m = S_2/S_1</math>, we can substitute <math>S_1</math> and with some algebra find:
| |
| ::<math>S_2 = F\cdot(1+m)</math>
| |
| | |
| Defining <math>f=S_2</math> as the "effective focal length", we get the formula presented above:
| |
| | |
| ::<math>\alpha = 2 \arctan \frac {d} {2 f}</math> where <math>f=F\cdot(1+m)</math>.
| |
| | |
| A second effect which comes into play in macro photography is lens asymmetry (an asymmetric lens is a lens where the aperture appears to have different dimensions when viewed from the front and from the back). The lens asymmetry causes an offset between the nodal plane and pupil positions. The effect can be quantified using the ratio (''P'') between apparent exit pupil diameter and entrance pupil diameter. The full formula for angle of view now becomes:<ref name="Paul van Walree 2009"/> | |
| | |
| ::<math>\alpha = 2 \arctan \frac {d} {2 F\cdot ( 1 + m/P )}</math>
| |
| | |
| == Measuring a camera's field of view ==
| |
| | |
| [[Image:FOV test Optics apparatus.PNG|thumb|300px|Schematic of [[collimator]]-based optical apparatus used in measuring the FOV of a camera.]]
| |
| | |
| In the optical instrumentation industry the term ''field of view'' (FOV) is most often used, though the measurements are still expressed as angles.<ref>Holst, G.C. (1998). Testing and Evaluation of Infrared Imaging Systems (2nd ed.). Florida:JCD Publishing, Washington:SPIE.</ref> Optical tests are commonly used for measuring the FOV of [[UV]], [[Visible spectrum|visible]], and [[infrared]] (wavelengths about 0.1–20 µm in the [[electromagnetic spectrum]]) sensors and cameras.
| |
| | |
| The purpose of this test is to measure the horizontal and vertical FOV of a lens and sensor used in an imaging system, when the lens focal length or sensor size is not known (that is, when the calculation above is not immediately applicable). Although this is one typical method that the [[optics]] industry uses to measure the FOV, there exist many other possible methods.
| |
| | |
| UV/visible light from an [[integrating sphere]] (and/or other source such as a [[black body]]) is focused onto a square test target at the [[focal plane]] of a [[collimator]] (the mirrors in the diagram), such that a virtual image of the test target will be seen infinitely far away by the camera under test. The camera under test senses a real image of the virtual image of the target, and the sensed image is displayed on a monitor.<ref>Mazzetta, J.A.; Scopatz, S.D. (2007). Automated Testing of Ultraviolet, Visible, and Infrared Sensors Using Shared Optics. Infrared Imaging Systems: Design Analysis, Modeling, and Testing XVIII,Vol. 6543, pp. 654313-1 654313-14</ref>
| |
| | |
| [[Image:FOV Target on Monitor.png|thumb|250px|Monitor display of sensed image from the camera under test]]
| |
| | |
| The sensed image, which includes the target, is displayed on a monitor, where it can be measured. Dimensions of the full image display and of the portion of the image that is the target are determined by inspection (measurements are typically in pixels, but can just as well be inches or cm).
| |
| | |
| ::<math>D</math> = dimension of full image
| |
| ::<math>d</math> = dimension of image of target
| |
| | |
| The collimator's distant virtual image of the target subtends a certain angle, referred to as the angular extent of the target, that depends on the collimator focal length and the target size. Assuming the sensed image includes the whole target, the angle seen by the camera, its FOV, is this angular extent of the target times the ratio of full image size to target image size.<ref>Electro Optical Industries, Inc.(2005). EO TestLab Methadology. In ''Education/Ref''. http://www.electro-optical.com/html/toplevel/educationref.asp.</ref>
| |
| | |
| The target's angular extent is:
| |
| | |
| ::<math>\alpha = 2 \arctan \frac {L} {2 f_c}</math>
| |
| | |
| ::where <math>L</math> is the dimension of the target and <math>f_c</math> is the focal length of collimator.
| |
| | |
| The total field of view is then approximately:
| |
| | |
| ::<math>\mathrm{FOV} = \alpha \frac{D}{d}</math>
| |
| | |
| or more precisely, if the imaging system is [[rectilinear lens|rectilinear]]:
| |
| | |
| ::<math>\mathrm{FOV} = 2 \arctan \frac {LD} {2 f_c d}</math>
| |
| | |
| This calculation could be a horizontal or a vertical FOV, depending on how the target and image are measured.
| |
| | |
| ==Lens types and effects==
| |
| === Focal length ===
| |
| | |
| [[Image:Focal length.jpg|thumb|How [[focal length]] affects perspective: Varying focal lengths at identical [[Shot_(filmmaking)#By_field_size|field size]] achieved by different camera-subject distances. Notice that the shorter the focal length and the larger the angle of view, [[perspective distortion (photography)|perspective distortion]] and size differences increase.]]
| |
| | |
| Lenses are often referred to by terms that express their angle of view:
| |
| *[[fisheye lens]]es, typical focal lengths are between 8 mm and 10 mm for circular images, and 15–16 mm for full-frame images. Up to 180° and beyond.
| |
| **A [[fisheye lens#Circular|circular fisheye lens]] (as opposed to a full-frame fisheye) is an example of a lens where the angle of coverage is less than the angle of view. The image projected onto the film is circular because the diameter of the image projected is ''narrower'' than that needed to cover the widest portion of the film.
| |
| *[[Ultra wide angle lens]] is a [[rectilinear lens|rectilinear]] which is less than 24mm of [[focal length]] in 35mm film format, here 14mm is 114° and 24mm is 84° .
| |
| * [[Wide-angle lens]]es (24–35mm in 35mm film format) cover between 84° and 64°
| |
| * [[normal lens|Normal, or Standard lenses]] (36–60mm in 35mm film format) cover between 62° and 40°
| |
| * [[Long focus lens]]es (any lens with a focal length greater than the diagonal of the film or sensor used)<ref>[http://books.google.com/books?id=cuzYl4hx-B8C&pg=PA294&dq=%22long+focus+lens%22&hl=en&ei=6Yb6TPPZCoGdlgf9y7yaDA&sa=X&oi=book_result&ct=result&resnum=3&ved=0CDEQ6AEwAg#v=onepage&q=%22long%20focus%20lens%22&f=false Sidney F. Ray, Applied photographic optics: lenses and optical systems for photography, page 294]</ref> generally have an angle of view of 35° or less.<ref>Lynne Warren, Encyclopedia of 20th century photography, page 211</ref> Since photographers usually only encounter the [[telephoto lens]] sub-type,<ref>[http://books.google.com/books?id=mj60n3uH4eMC&lpg=PA83&dq=%22long%20focus%22%20telephoto&pg=PA83#v=onepage&q=%22long%20focus%22%20telephoto&f=false Michael Langford, Basic photography, page 83]</ref> they are referred to in common photographic parlance as:
| |
| * "Medium telephoto", a focal length of 85mm to 135mm in 35mm film format covering between 30° and 10°<ref name="photographywebsite.co.uk">[http://www.photographywebsite.co.uk/lens-types-explained-c487.html photographywebsite.co.uk – Lens Types Explained ]</ref>
| |
| * "Super telephoto" (over 300mm in 35mm film format) generally cover between 8° through less than 1°<ref name="photographywebsite.co.uk"/>
| |
| | |
| [[Zoom lens]]es are a special case wherein the focal length, and hence angle of view, of the lens can be altered mechanically without removing the lens from the camera.
| |
| | |
| === Characteristics ===
| |
| <!-- not sure what this has to do with angle of view ... -->
| |
| For a given camera–subject distance, longer lenses magnify the subject more. For a given subject magnification (and thus different camera–subject distances), longer lenses appear to compress distance; wider lenses appear to expand the distance between objects.
| |
| | |
| Another result of using a wide angle lens is a greater apparent [[Perspective distortion (photography)|perspective distortion]] when the camera is not aligned perpendicularly to the subject: parallel lines converge at the same rate as with a [[normal lens]], but converge more due to the wider total field. For example, buildings appear to be falling backwards much more severely when the camera is pointed upward from ground level than they would if photographed with a normal lens at the same distance from the subject, because more of the subject building is visible in the wide-angle shot.
| |
| | |
| Because different lenses generally require a different camera–subject distance to preserve the size of a subject, changing the angle of view can indirectly [[Perspective distortion (photography)|distort]] perspective, changing the apparent relative size of the subject and foreground. | |
| | |
| If the subject image size remains the same, then at any given aperture all lenses, wide angle and long lenses, will give the same depth of field.<ref>{{cite web|last=Reichmann|first=Michael|title=Do Wide Angle Lenses Really Have Greater Depth of Field Than Telephotos?|url=http://www.luminous-landscape.com/tutorials/dof2.shtml}}</ref>
| |
| | |
| === Examples ===
| |
| | |
| An example of how lens choice affects angle of view.
| |
| | |
| {| align="center"
| |
| |-
| |
| | [[Image:Angleofview 28mm f4.jpg|frame|28 mm lens, 65.5° × 46.4°]]
| |
| | [[Image:Angleofview 50mm f4.jpg|frame|50 mm lens, 39.6° × 27.0°]]
| |
| |-
| |
| | [[Image:Angleofview 70mm f4.jpg|frame|70 mm lens, 28.9° × 19.5°]]
| |
| | [[Image:Angleofview 210mm f4.jpg|frame|210 mm lens, 9.8° × 6.5°]]
| |
| |}
| |
| | |
| == Common lens angles of view ==
| |
| This table shows the diagonal, horizontal, and vertical angles of view, in degrees, for lenses producing rectilinear images, when used with 36 mm × 24 mm format (that is, [[135 film]] or [[Full-frame digital SLR|full-frame 35mm digital]] using width 36 mm, height 24 mm, and diagonal 43.3 mm for ''d'' in the formula above).<ref>However, most interchangeable-lens digital cameras do not use 24x36 mm [[image sensor]]s and therefore produce narrower angles of view than set out in the table. See [[crop factor]] and the subtopic '''digital camera issues''' in the article on [[wide-angle lens]]es for further discussion.</ref> Digital compact cameras sometimes state the focal lengths of their lenses in 35mm equivalents, which can be used in this table.
| |
| | |
| For comparison, the human eye has an angle of view of about 160° by 75°.
| |
| | |
| {| class="wikitable"
| |
| |-
| |
| ! Focal Length (mm)
| |
| | 0 || 2 || 12 || 14 || 16 || 20 || 24 || 35 || 50 || 70 || 85 || 100 || 200 || 300 || 400 || 500 || 600 || 700 || 800 || 1200
| |
| |-
| |
| ! Diagonal (°)
| |
| | 180.0 || 169.4 || 122.0 || 114.2 || 107.1 || 94.5 || 84.1 || 63.4 || 46.8 || 34.4 || 28.6 || 23.3 || 12.4 || 8.25 || 6.19 || 4.96 || 4.13 || 5.72 || 3.10 || 2.07
| |
| |-
| |
| ! Vertical (°)
| |
| | 180.0 || 161.1 || 90.0 || 81.2 || 73.9 || 61.9 || 53.1 || 37.8 || 27.0 || 19.5 || 16.1 || 13.0 || 6.87 || 4.58 || 3.44 || 2.75 || 2.29 || 1.96 || 1.72 || 1.15
| |
| |-
| |
| ! Horizontal (°)
| |
| | 180.0 || 166.9 || 111.1 || 102.7 || 95.1 || 82.4 || 73.7 || 54.4 || 39.6 || 28.8 || 23.9 || 19.5 ||10.3 || 6.87 || 5.15 || 4.12 || 3.54 || 2.86 || 2.58 || 1.72
| |
| |}
| |
| | |
| {{wide image|24-72mm zoom demo.jpg|600px|Five images using 24, 28, 35, 50 and 72mm equivalent zoom lengths, portrait format, to illustrate angles of view <ref>The image examples uses a 5.1–15.3mm lens which is called a 24mm 3x zoom by the producer ([http://www.ricoh.com/r_dc/caplio/gx100/ Ricoh Caplio GX100])</ref>}}
| |
| {{wide image|24-72mm zoom demo horizontal.jpg|600px|Five images using 24, 28, 35, 50 and 72mm equivalent step zoom function, to illustrate angles of view}}
| |
| | |
| ==Three-dimensional digital art== | |
| {{Unreferenced section|date=August 2009}}
| |
| | |
| Displaying [[3d graphics]] as [[3d projection]] of the models onto a 2d surface uses a series of mathematical calculations to render the scene. The angle of view of the scene is thus readily set and changed; some renderers even measure the angle of view as the focal length of an imaginary lens. The angle of view can also be projected onto the surface at an angle greater than 90°, effectively creating an ultra-wide lens effect.
| |
| | |
| ==Cinematography and video gaming==
| |
| {{Unreferenced section|date=August 2009}}
| |
| | |
| Modifying the angle of view over time, or ''zooming'', is a frequently used [[cinematic techniques|cinematic technique]].
| |
| | |
| For a [[visual effect]], some [[first person video games]] (especially [[racing game]]s), widen the angle of view beyond 90° to exaggerate the distance the player is travelling, thus exaggerating the player's perceived speed and giving a [[tunnel]] effect (like [[pincushion distortion]]). Narrowing the view angle gives a [[zoom lens|zoom in]] effect. Also see [[Field of view in video games]].
| |
| | |
| ==References and notes==
| |
| | |
| <references/>
| |
| | |
| ==See also==
| |
| *[http://www.txstockphotos.com/blog/understanding-focal-length-and-angle-of-view-what-is-a-digital-lens-effective-focal-length-crop-factor-sensor-size Simple Explanation of Angle of View and Focal Length]
| |
| *[[35 mm equivalent focal length]]
| |
| *[[Camera angle]]
| |
| *[[Camera coverage]]
| |
| *[[Camera operator]]
| |
| *[[Cinematic techniques]]
| |
| *[[Field of view]]
| |
| *[[Filmmaking]]
| |
| *[[Multiple-camera setup]]
| |
| *[[Single-camera setup]]
| |
| *[[Video production]]
| |
| | |
| ==External links==
| |
| *[http://www.acapixus.dk/photography/angle_of_view.htm Angle of View on digital SLR cameras with reduced sensor size]
| |
| *[http://www.usa.canon.com/app/html/EFLenses101/focal_length.html Focal Length and Angle of View]
| |
| | |
| {{photography subject}}
| |
| | |
| {{DEFAULTSORT:Angle Of View}}
| |
| [[Category:Science of photography]]
| |
| [[Category:Optics]]
| |
| [[Category:Angle]]
| |