View source for 3D Modelling/Create 3D Models/Hugin/Angle of view

[[File:Hugin User Interface.png|300px|thumb|concatenation 24 image in Hugin - Result in Aframe - [https://niebert.github.io/HuginSample/ Link to interactive HuginSample(s)]]]
[[File:Angle of view 4.png|thumb|400px]]

== From Angle of View to 360 degree View ==
The '''angle of view''' is the decisive variable for the [[w:en:visual perception|visual perception]] of the size or projection of the size of an object. The angle of view determines how many images you need to cover the full 360 degree circle for an equirectangular image.

=== Remark - Overlap of Images ===
Keep in mind that [[3D Modelling/Create 3D Models/Hugin|Hugin]] need overlap of images to identify matching points in several images. Matching points can be identified by [[3D Modelling/Create 3D Models/Hugin|Hugin]] much better if show e.q. unique elements in the overlap area. An homogeneous overlap area with almost no structure or just area with leaves of trees are not ideal for overlap areas of the images, while a unique tree trunk with unique branching pattern, a car, a door, ... is a better selection for overlap areas.

== Angle of view and perception of size ==
[[File:Angle of view 1.png|thumb|]]

The perceived size of an object depends on the size of the image projected onto the [[w:en:retina|retina]]. The size of the image depends on the angle of vision. A near and a far object can appear the same size if their edges produce the same angle of vision. With an optical device such as [[w:en:glasses|glasses]] or [[w:en:binoculars|binoculars]], [[w:en:microscope|microscope]] and [[w:en:telescope|telescope]] the angle of vision can be widened so that the object appears larger, which is favourable for the resolving power of the eye (see [[w:en:visual angle|visual angle]]).<ref>''[https://www.univie.ac.at/mikroskopie/1_grundlagen/optik/Grundlagen%20der%20Optik.pdf Light microscopy online theory and application - Optics]'' page 24</ref><ref>Georg Eisner: ''[http://www.eisner-georg.ch/Andere/Perspektive/Perspektiven.pdf Perspektive und Visuelles System]'' page 134</ref>

== Angle of view in photography ==
[[Image:Angle of view.svg|right|thumb|260px|A camera's '''angle of view''' can be measured horizontally, vertically, or diagonally.]]
In [[w:en:photography|photography]], '''angle of view''' ('''AOV''')<ref>{{cite book | author = Tim Dobbert | title = Matchmoving: The Invisible Art of Camera Tracking, 2nd Edition | page = 116 | publisher = John Wiley & Sons | date = November 2012 | isbn = 9781118529669 | url = https://books.google.com/books?id=Jr4YsaTrIBgC&q=AOV+angle+of+view&pg=PA116 }}</ref> describes the [[w:en:angle|angular]] extent of a given scene that is imaged by a [[w:en:camera|camera]]. It is used interchangeably with the more general term [[w:en:field of view|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 [[w:en:image circle|image circle]] produced by a lens is large enough to cover the film or sensor completely, possibly including some [[w:en:vignetting|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.


[[File:Camera focal length distance house animation.gif|thumb|right|In this simulation, adjusting the angle of view and distance of the camera while keeping the object in frame results in vastly differing images. At distances approaching infinity, the light rays are nearly parallel to each other, resulting in a "flattened" image. At low distances and high angles of view objects appear "foreshortened".]]

A camera's angle of view depends not only on the lens, but also on the sensor. Digital sensors are usually smaller than [[w:en:35mm format|35&nbsp;mm film]], and this causes the lens to have a narrower angle of view than with 35&nbsp;mm film, by a constant factor for each sensor (called the [[w:en:crop factor|crop factor]]). In everyday digital cameras, the crop factor can range from around 1 (professional [[w:en:digital SLR|digital SLR]]s), to 1.6 (consumer SLR), to 2 ([[w:en:Micro Four Thirds|Micro Four Thirds]] ILC) to 6 (most [[w:en:compact camera|compact camera]]s). So a standard 50&nbsp;mm lens for 35&nbsp;mm photography acts like a 50&nbsp;mm standard "film" lens on a professional digital SLR, but would act closer to an 80&nbsp;mm lens (1.6 x 50mm) on many mid-market DSLRs, and the 40 degree angle of view of a standard 50&nbsp;mm lens on a film camera is equivalent to an 80&nbsp;mm lens on many digital SLRs.

== Calculating a camera's angle of view ==

For lenses projecting [[w:en:rectilinear lens|rectilinear]] (non-spatially-distorted) images of distant objects, the effective [[w:en:focal length|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 [[w:en:fisheye lens|fisheye lens]], a longer lens with distortion can have a wider angle of view than a shorter lens with low distortion)<ref>{{cite web|url=http://www.the-digital-picture.com/reviews/canon-ef-15mm-f-2.8-fisheye-lens-review.aspx| title=Canon EF 15mm f/2.8 Fisheye Lens Review|website=The-Digital-Picture.com|access-date=1 May 2018|url-status=live|archive-url=https://web.archive.org/web/20170807005837/http://www.the-digital-picture.com/Reviews/Canon-EF-15mm-f-2.8-Fisheye-Lens-Review.aspx|archive-date=7 August 2017}}</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 (focused at infinity, see [[w:en:#Derivation of the angle-of-view formula|derivation]]), 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 | year = 1893 | pages = 399–406 | publisher = Industrial Publishing Company, San Francisco | url = https://books.google.com/books?id=eCkAAAAAMAAJ&q=%22field-of+view%22+%22focal+length%22+camera+tangent+%22length+of+the+plate%22&pg=PA402 }}</ref>
<math display="block">\alpha = 2 \arctan \frac {d} {2 f}</math>

<math>d</math> represents the size of the film (or sensor) in the direction measured ''(see [[#Crop factor|below: sensor effects]])''. For example, for 35&nbsp;mm film which is 36&nbsp;mm wide and 24&nbsp;mm high, <math>d = 36\,\mathrm{mm}</math> would be used to obtain the horizontal angle of view and <math>d = 24\,\mathrm{mm}</math> for the vertical angle.

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 [[w:en:macro photography|macro photography]] where the lens-to-object distance is comparable to the focal length. In this case, the [[w:en:magnification|magnification]] factor (''m'') must be taken into account:
<math display="block">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.

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] {{webarchive|url=https://web.archive.org/web/20080822113350/http://www.jvsg.com/cctv-camera-lens-calculations/ |date=2008-08-22 }} by JVSG, December, 2007</ref>

{{wide image|camera focal length vs crop factor vs angle of view.svg|600px|Log-log graphs of focal length vs crop factor vs diagonal, horizontal and vertical angles of view for film or sensors of 3:2 and 4:3 aspect ratios. The yellow line shows an example where 18&nbsp;mm on 3:2 APS-C is equivalent to 27&nbsp;mm and yields a vertical angle of 48 degrees.}}

=== Example ===

Consider a 50&nbsp;mm camera with a lens having a focal length of {{nowrap|1=''F'' = 50 mm}}. The dimensions of the 35&nbsp;mm image format are 24&nbsp;mm (vertically) × 36&nbsp;mm (horizontal), giving a diagonal of about 43.3&nbsp;mm.

At infinity focus, {{nowrap|1=''f'' = ''F''}}, 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 [[w:en:photographic film|film]] or [[w:en:image sensor|image sensor]]). Treat the lens as if it were a [[w:en:pinhole camera model|pinhole]] at distance <math>S_2</math> from the image plane (technically, the center of perspective of a [[w:en:rectilinear lens|rectilinear lens]] is at the center of its [[w:en:entrance pupil|entrance pupil]]):<ref>{{cite web | author=Kerr, Douglas A. | year=2008 | title=The Proper Pivot Point for Panoramic Photography | work=The Pumpkin | url=http://dougkerr.net/Pumpkin/articles/Pivot_Point.pdf | access-date=2014-03-20}}</ref>

[[Image:Lens angle of view.svg|center]]

Now <math>\alpha/2</math> is the angle between the [[w:en:optical axis|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 display="block">\tan ( \alpha / 2 ) = \frac {d/2} {S_2} .</math>
which we can solve for ''α'', giving:
<math display="block">\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 [[w:en:focal length|focal length]], <math>F</math>, which is attained by setting the lens for [[w:en:infinity focus|infinity focus]]. Then the angle of view is given by:

<math display="block">\alpha = 2 \arctan \frac {d} {2 f}</math> where <math>f = F</math>.

Note that the angle of view varies slightly when the focus is not at infinity (See [[w:en:breathing (lens)|breathing (lens)]]), given by <math>S_2 = \frac{S_1 f}{S_1 - f}</math> rearranging the lens equation.

==== Macro photography ====

For macro photography, we cannot neglect the difference between <math>S_2</math> and <math>F</math>. From the [[w:en:Lens (optics)#Imaging properties|thin lens formula]],
<math display="block">\frac{1}{F} = \frac{1}{S_1} + \frac{1}{S_2}.</math>

From the definition of [[w:en:magnification|magnification]], <math>m = S_2/S_1</math>, we can substitute <math>S_1</math> and with some algebra find:
<math display="block">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 display="block">\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">{{cite web |url=http://toothwalker.org/optics/cop.html#fov |title=Center of perspective |author=Paul van Walree |year=2009 |access-date=24 January 2010 |url-status=dead |archive-url=https://web.archive.org/web/20090430094706/http://toothwalker.org/optics/cop.html#fov |archive-date=30 April 2009 }}</ref>
<math display="block">\alpha = 2 \arctan \frac {d} {2 F\cdot ( 1 + m/P )}</math>

== Measuring a camera's field of view ==
[[Image:FOV test Optics apparatus.svg|thumb|300px|Schematic of [[w:en:collimator|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 [[w:en:UV|UV]], [[w:en:Visible spectrum|visible]], and [[w:en:infrared|infrared]] (wavelengths about 0.1–20&nbsp;μm in the [[w:en:electromagnetic spectrum|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 [[w:en:optics|optics]] industry uses to measure the FOV, there exist many other possible methods.

UV/visible light from an [[w:en:integrating sphere|integrating sphere]] (and/or other source such as a [[w:en:black body|black body]]) is focused onto a square test target at the [[w:en:focal plane|focal plane]] of a [[w:en:collimator|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.svg|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''. {{cite web | url=http://www.electro-optical.com/html/toplevel/educationref.asp |title=Education and Reference |access-date=2008-05-22 |url-status=dead |archive-url=https://web.archive.org/web/20080828124035/http://www.electro-optical.com/html/toplevel/educationref.asp |archive-date=2008-08-28 }}.</ref>

The target's angular extent is:
<math display="block">\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 display="block">\mathrm{FOV} = \alpha  \frac{D}{d}</math>
or more precisely, if the imaging system is [[w:en:rectilinear lens|rectilinear]]:
<math display="block">\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 [[w:en:focal length|focal length]] affects perspective: Varying focal lengths at identical [[w:en: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, [[w:en:perspective distortion (photography)|perspective distortion]] and size differences increase.]]

Lenses are often referred to by terms that express their angle of view:
*[[w:en:Fisheye lens|Fisheye lens]]es, typical focal lengths are between 8&nbsp;mm and 10&nbsp;mm for circular images, and 15–16&nbsp;mm for full-frame images. Up to 180° and beyond.
**A [[w:en: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.
*[[w:en:Ultra wide angle lens|Ultra wide angle lens]] is a [[w:en:rectilinear lens|rectilinear]] which is less than 24&nbsp;mm of [[w:en:focal length|focal length]] in 35&nbsp;mm film format, here 14&nbsp;mm gives 114° and 24&nbsp;mm gives 84° .
* [[w:en:Wide-angle lens|Wide-angle lens]]es (24–35&nbsp;mm in 35&nbsp;mm film format) cover between 84° and 64°
* [[w:en:normal lens|Normal, or Standard lenses]] (36–60&nbsp;mm in 35&nbsp;mm film format) cover between 62° and 40°
* [[w:en:Long focus lens|Long focus lens]]es (any lens with a focal length greater than the diagonal of the film or sensor used)<ref>{{cite book|url=https://books.google.com/books?id=cuzYl4hx-B8C&q=%22long+focus+lens%22&pg=PA294|title=Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging|first=Sidney F.|last=Ray|date=1 May 2018|publisher=Focal|isbn=9780240515403|access-date=1 May 2018|via=Google Books}}</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 [[w:en:telephoto lens|telephoto lens]] sub-type,<ref>{{cite book|url=https://books.google.com/books?id=mj60n3uH4eMC&q=%22long+focus%22+telephoto&pg=PA83|title=Basic Photography|first=Michael|last=Langford|date=1 May 2018|publisher=Focal Press|isbn=9780240515922|access-date=1 May 2018|via=Google Books}}</ref> they are referred to in common photographic parlance as:
* "Medium telephoto", a focal length of 85&nbsp;mm to 250&nbsp;mm in 35&nbsp;mm film format covering between 30° and 10°<ref name="photographywebsite.co.uk">{{cite web|url=http://www.photographywebsite.co.uk/lens-types-explained-c487.html|title=Your Site|website=www.photographywebsite.co.uk|access-date=1 May 2018}}</ref>
* "Super telephoto" (over 300&nbsp;mm in 35&nbsp;mm film format) generally cover between 8° through less than 1°<ref name="photographywebsite.co.uk"/>

[[w:en:Zoom lens|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 [[w:en: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 [[w:en:normal lens|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 [[w:en: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 [[w:en:depth of field|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|url-status=dead|archive-url=https://web.archive.org/web/20110610032235/http://www.luminous-landscape.com/tutorials/dof2.shtml|archive-date=2011-06-10|access-date=2011-07-08}}</ref>

=== Examples ===

An example of how lens choice affects angle of view.

{| align="center"
|-
| [[Image:Angleofview 28mm f4.jpg|frame|28&nbsp;mm lens, 65.5° × 46.4°]]
| [[Image:Angleofview 50mm f4.jpg|frame|50&nbsp;mm lens, 39.6° × 27.0°]]
|-
| [[Image:Angleofview 70mm f4.jpg|frame|70&nbsp;mm lens, 28.9° × 19.5°]]
| [[Image:Angleofview 210mm f4.jpg|frame|210&nbsp;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&nbsp;mm × 24&nbsp;mm format (that is, [[w:en:135 film|135 film]] or [[w:en:Full-frame digital SLR|full-frame 35&nbsp;mm digital]] using width 36&nbsp;mm, height 24&nbsp;mm, and diagonal 43.3&nbsp;mm for ''d'' in the formula above).<ref>However, most interchangeable-lens digital cameras do not use 24×36&nbsp;mm [[w:en:image sensor|image sensor]]s and therefore produce narrower angles of view than set out in the table. See [[w:en:crop factor|crop factor]] and the subtopic '''digital camera issues''' in the article on [[w:en:wide-angle lens|wide-angle lens]]es for further discussion.</ref> Digital compact cameras sometimes state the focal lengths of their lenses in 35&nbsp;mm equivalents, which can be used in this table.

For comparison, the human visual system perceives an angle of view of about 140° by 80°.<ref>{{cite conference| url=http://www.hitl.washington.edu/publications/p-93-2/index.html |first=Joel S. |last=Kollin |date=1993 |title=A Retinal Display for Virtual-Environment Applications |work=Proceedings of Society for Information Display |volume=XXIV |pages=827  |access-date=2014-04-27 |url-status=dead |archive-url=https://web.archive.org/web/20130704143409/http://www.hitl.washington.edu/publications/p-93-2/index.html |archive-date=2013-07-04 }}</ref>

{| class="wikitable" style="text-align:center;margin:0px;"
|- 
! style="width:6em;" | Focal length (mm) || style="width:6em;" | Diagonal (°) || style="width:6em;" | Vertical (°) || style="width:6em;" | Horizontal (°) 
|-
| 0 || 180.0 || 180.0 || 180.0 
|-
| 2 || 169.4 || 161.1 || 166.9 
|-
| 12 || 122.0 ||  90.0 || 111.1 
|-
| 14  || 114.2 ||  81.2 || 102.7 
|-
| 16  || 107.1 ||  73.9 ||  95.1 
|-
| 20  || 94.5  ||  61.9 ||  82.4 
|-
| 24  || 84.1  ||  53.1 ||  73.7 
|-
| 35  || 63.4  ||  37.8 ||  54.4 
|-
| 50  || 46.8  ||  27.0 ||  39.6 
|-
| 70  || 34.4  ||  19.5 ||  28.8 
|-
| 85  || 28.6  ||  16.1 ||  23.9 
|-
| 105 || 23.3  ||  13.0 ||  19.5 
|-
| 200 || 12.3  ||  6.87 ||  10.3 
|-
| 300 || 8.25  ||  4.58 ||  6.87 
|-
| 400 || 6.19  ||  3.44 ||  5.15 
|-
| 500 || 4.96  ||  2.75 ||  4.12 
|-
| 600 || 4.13  ||  2.29 ||  3.44 
|-
| 700 || 3.54  ||  1.96 ||  2.95 
|-
| 800 || 3.10  ||  1.72 ||  2.58 
|-
| 1200|| 2.07  ||  1.15 ||  1.72
|}

{{wide image|24-72mm zoom demo.jpg|600px|Five images using 24, 28, 35, 50 and 72&nbsp;mm equivalent zoom lengths, portrait format, to illustrate angles of view<ref>The image examples uses a 5.1–15.3&nbsp;mm lens which is called a 24&nbsp;mm 3× zoom by the producer ([http://www.ricoh.com/r_dc/caplio/gx100/ Ricoh Caplio GX100] {{webarchive|url=https://web.archive.org/web/20090601152604/http://www.ricoh.com/r_dc/caplio/gx100/ |date=2009-06-01 }})</ref>}}
{{wide image|24-72mm zoom demo horizontal.jpg|600px|Five images using 24, 28, 35, 50 and 72&nbsp;mm equivalent step zoom function, to illustrate angles of view}}

== {{anchor|Crop factor}} Sensor size effects ("crop factor") ==
{{Main|w:en:Crop factor}}

As noted above, a camera's angle level of view depends not only on the lens, but also on the sensor used. Digital sensors are usually smaller than 35&nbsp;mm film, causing the lens to usually behave as a longer focal length lens would behave, and have a narrower angle of view than with 35&nbsp;mm film, by a constant factor for each sensor (called the [[w:en:crop factor|crop factor]]). In everyday digital cameras, the crop factor can range from around 1 (professional [[w:en:digital SLR|digital SLR]]s), to 1.6 (mid-market SLRs), to around 3 to 6 for [[w:en:compact camera|compact camera]]s. So a standard 50&nbsp;mm lens for [[w:en:35 mm photography|35 mm photography]] acts like a 50&nbsp;mm standard "film" lens even on a professional digital SLR, but would act closer to a 75mm (1.5×50&nbsp;mm Nikon) or 80mm lens (1.6×50&nbsp;mm Canon) on many mid-market DSLRs, and the 40 degree angle of view of a standard 50mm lens on a film camera is equivalent to a 28–35&nbsp;mm lens on many digital SLRs.

The table below shows the horizontal, vertical and diagonal angles of view, in degrees, when used with 22.2&nbsp;mm × 14.8&nbsp;mm format (that is Canon's [[w:en:APS-C|DSLR APS-C frame size]]) and a diagonal of 26.7&nbsp;mm.
{| class="wikitable" style="text-align:center;margin:0px;"
|- 
! style="width:6em;" | Focal length (mm) || style="width:6em;" | Diagonal (°) ||style="width:6em;" |  Vertical (°) || style="width:6em;" | Horizontal (°)	 
|-
| 2   || 162.9 || 149.8 || 159.6 	       		 
|-
| 4   || 146.6 || 123.2 || 140.4 	       		 
|-
| 7   || 124.6 || 93.2  || 115.5 	       		 
|-
| 9   || 112.0 || 78.9  || 101.9 	       		 
|-
| 12  || 96.1  || 63.3  || 85.5 	       		 
|-
| 14  || 87.2  || 55.7  || 76.8 	       		 
|-
| 16  || 79.6  || 49.6  || 69.5 	       		 
|-
| 17  || 76.2  || 47.0  || 66.3 	       		 
|-
| 18  || 73.1  || 44.7  || 63.3 	       		 
|-
| 20  || 67.4  || 40.6  || 58.1 	       		 
|-
| 24  || 58.1  || 34.3  || 49.6 	       		 
|-
| 35  || 41.7  || 23.9  || 35.2 	       		 
|-
| 50  || 29.9  || 16.8  || 25.0 	       		 
|-
| 70  || 21.6  || 12.1  || 18.0 	       		 
|-
| 85  || 17.8  || 10.0  || 14.9 	       		 
|-
| 105 || 14.5  || 8.1   || 12.1 	       		 
|-
| 200 || 7.6   || 4.2   || 6.4  	       		 
|-
| 210 || 7.3   || 4.0   || 6.1  	       		 
|-
| 300 || 5.1   || 2.8   || 4.2  	       		 
|-
| 400 || 3.8   || 2.1   || 3.2  	       		 
|-
| 500 || 3.1   || 1.7   || 2.5  	       		 
|-
| 600 || 2.5   || 1.4   || 2.1  	       		 
|-
| 700 || 2.2   || 1.2   || 1.8  	       		 
|-
| 800 || 1.9   || 1.1   || 1.6
|}

== Cinematography and video gaming ==
{|  class="wikitable"
!Ratio
!1080p resolution
!Common name
!Video format / lens
|-
!32:27
|1280x1080p
|
|[[w:en:DV#DVCPRO HD|DVCPRO HD]]
|-
!4:3
|1440x1080p 
|
|
|-
!16:9
|1920x1080p 
|Widescreen
|
|-
!2:1
|2160x1080
|18:9
|[[w:en:Univisium|Univisium]]
|-
!64:27
|2560x1080p 
|Ultra-Widescreen
|[[w:en:Cinemascope|Cinemascope]] / [[w:en:Anamorphic format#2.35, 2.39 or 2.40?|Anamorphic]]
|-
!32:9
|3840x1080p
|Super Ultra-Widescreen
|[[Aspect ratio (image)#36:10 (3.6:1)|Ultra-Widescreen 3.6]] / [[w:en:Anamorphic format|Anamorphic]] 3.6
|}

Modifying the angle of view over time (known as [[w:en:zooming (filmmaking)|zooming]]), is a frequently used [[w:en:cinematic techniques|cinematic technique]], often combined with camera movement to produce a "[[w:en:dolly zoom|dolly zoom]]" effect, made famous by the film ''[[w:en:Vertigo (film)|Vertigo]]''. Using a wide angle of view can exaggerate the camera's perceived speed, and is a common technique in [[w:en:tracking shot|tracking shot]]s, [[w:en:phantom ride|phantom ride]]s, and [[w:en:racing video game|racing video game]]s. See also [[w:en:Field of view in video games|Field of view in video games]].

== See also ==
{{div col}}
* [[w:en:equirectangular projection|equirectangular projection]]
* [[w:en:35 mm equivalent focal length|35 mm equivalent focal length]]
* [[w:en:Camera angle|Camera angle]]
* [[w:en:Camera coverage|Camera coverage]]
* [[w:en:Camera operator|Camera operator]]
* [[w:en:Cinematic techniques|Cinematic techniques]]
* [[w:en:Field of view|Field of view]]
* [[w:en:Filmmaking|Filmmaking]]
* [[w:en:Multiple-camera setup|Multiple-camera setup]]
* [[w:en:Single-camera setup|Single-camera setup]]
* [[w:en:Video production|Video production]]
* [[w:en:Image sensor format|Image sensor format]]
* [[w:en:Crop factor|Crop factor]]
* [[w:en:Ultrawide formats|Ultrawide formats]]
{{div col end}}

== Notes and references ==
<references/>

== External links ==
* [https://web.archive.org/web/20130110002548/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]
* [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]


[[Category:Science of photography]]
[[Category:Geometrical optics]]
[[Category:Angle]]

== Page Information ==
This page was based on the following [https://en.wikipedia.org/wiki/Angle%20of%20view wikipedia-source page]:
* [https://en.wikipedia.org/wiki/Angle%20of%20view Angle of view] https://en.wikipedia.org/wiki/Angle%20of%20view
* Datum: 12/11/2022
* [https://niebert.github.com/Wikipedia2Wikiversity Wikipedia2Wikiversity-Converter]: https://niebert.github.com/Wikipedia2Wikiversity