The angle of view is the decisive variable for the visual perception of the size or projection of the size of an object.
The perceived size of an object depends on the size of the image projected onto the 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 glasses or binoculars, microscope and 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 visual angle)
In photography, angle of view (AOV)describes the 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.
A camera's angle of view depends not only on the lens, but also on the sensor. Digital sensors are usually smaller than 35 mm film, and this causes the lens to have a narrower angle of view than with 35 mm film, by a constant factor for each sensor (called the crop factor). In everyday digital cameras, the crop factor can range from around 1 (professional digital SLRs), to 1.6 (consumer SLR), to 2 (Micro Four Thirds ILC) to 6 (most compact cameras). So a standard 50 mm lens for 35 mm photography acts like a 50 mm standard "film" lens on a professional digital SLR, but would act closer to an 80 mm lens (1.6 x 50mm) on many mid-market DSLRs, and the 40 degree angle of view of a standard 50 mm lens on a film camera is equivalent to an 80 mm lens on many digital SLRs.
For lenses projecting 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)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 derivation), the angle of view (α) can be calculated from the chosen dimension (d), and effective focal length (f) as follows:
represents the size of the film (or sensor) in the direction measured (see below: sensor effects). For example, for 35 mm film which is 36 mm wide and 24 mm high, mm would be used to obtain the horizontal angle of view and mm 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 radians or 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:
(In photography is usually defined to be positive, despite the inverted image.) For example, with a magnification ratio of 1:2, we find 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.
Consider a 50 mm camera with a lens having a focal length of 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, f = F, the angles of view are:
Consider a rectilinear lens in a camera used to photograph an object at a distance , and forming an image that just barely fits in the dimension, , of the frame (the film or image sensor). Treat the lens as if it were a pinhole at distance from the image plane (technically, the center of perspective of a rectilinear lens is at the center of its entrance pupil):
Now is the angle between the optical axis of the lens and the ray joining its optical center to the edge of the film. Here 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:
Using basic trigonometry, we find:
which we can solve for α, giving:
To project a sharp image of distant objects, needs to be equal to the focal length, , which is attained by setting the lens for infinity focus. Then the angle of view is given by:
Note that the angle of view varies slightly when the focus is not at infinity (See breathing (lens)), given by rearranging the lens equation.
For macro photography, we cannot neglect the difference between and . From the thin lens formula,
From the definition of magnification, , we can substitute and with some algebra find:
Defining as the "effective focal length", we get the formula presented above:
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:
In the optical instrumentation industry the term field of view (FOV) is most often used, though the measurements are still expressed as angles. μm in the electromagnetic spectrum) sensors and cameras.Optical tests are commonly used for measuring the FOV of UV, visible, and infrared (wavelengths about 0.1–20
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.
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).
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.
The target's angular extent is:
The total field of view is then approximately:
or more precisely, if the imaging system is rectilinear:
This calculation could be a horizontal or a vertical FOV, depending on how the target and image are measured.
Lenses are often referred to by terms that express their angle of view:
Zoom lenses 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.
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 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 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.
An example of how lens choice affects angle 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 35 mm digital using width 36 mm, height 24 mm, and diagonal 43.3 mm for d in the formula above). Digital compact cameras sometimes state the focal lengths of their lenses in 35 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°.
|Focal length (mm)||Diagonal (°)||Vertical (°)||Horizontal (°)|
As noted above, a camera's angle of view depends not only on the lens, but also on the sensor used. Digital sensors are usually smaller than 35 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 mm film, by a constant factor for each sensor (called the crop factor). In everyday digital cameras, the crop factor can range from around 1 (professional digital SLRs), to 1.6 (mid-market SLRs), to around 3 to 6 for compact cameras. So a standard 50 mm lens for 35 mm photography acts like a 50 mm standard "film" lens even on a professional digital SLR, but would act closer to a 75mm (1.5×50 mm Nikon) or 80mm lens (1.6×50 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 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 mm × 14.8 mm format (that is Canon's DSLR APS-C frame size) and a diagonal of 26.7 mm.
|Focal length (mm)||Diagonal (°)||Vertical (°)||Horizontal (°)|
|Ratio||1080p resolution||Common name||Video format / lens|
|64:27||2560x1080p||Ultra-Widescreen||Cinemascope / Anamorphic|
|32:9||3840x1080p||Super Ultra-Widescreen||Ultra-Widescreen 3.6 / Anamorphic 3.6|
Modifying the angle of view over time (known as zooming), is a frequently used cinematic technique, often combined with camera movement to produce a "dolly zoom" effect, made famous by the film Vertigo . Using a wide angle of view can exaggerate the camera's perceived speed, and is a common technique in tracking shots, phantom rides, and racing video games. See also Field of view in video games.
For many cameras, depth of field (DOF) is the distance between the nearest and the farthest objects that are in acceptably sharp focus in an image. The depth of field can be calculated based on focal length, distance to subject, the acceptable circle of confusion size, and aperture. A particular depth of field may be chosen for technical or artistic purposes. Limitations of depth of field can sometimes be overcome with various techniques/equipment.
The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power.
A camera lens is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically.
In photography and cinematography, a wide-angle lens refers to a lens whose focal length is substantially smaller than the focal length of a normal lens for a given film plane. This type of lens allows more of the scene to be included in the photograph, which is useful in architectural, interior and landscape photography where the photographer may not be able to move farther from the scene to photograph it.
An optical telescope is a telescope that gathers and focuses light, mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct view, or to make a photograph, or to collect data through electronic image sensors.
The field of view (FoV) is the extent of the observable world that is seen at any given moment. In the case of optical instruments or sensors it is a solid angle through which a detector is sensitive to electromagnetic radiation.
A fisheye lens is an ultra wide-angle lens that produces strong visual distortion intended to create a wide panoramic or hemispherical image. Fisheye lenses achieve extremely wide angles of view. Instead of producing images with straight lines of perspective, fisheye lenses use a special mapping, which gives images a characteristic convex non-rectilinear appearance.
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. The objective lens or mirror collects light and brings it to focus creating an image. The eyepiece is placed near the focal point of the objective to magnify this image. The amount of magnification depends on the focal length of the eyepiece.
A digital single-lens reflex camera is a digital camera that combines the optics and the mechanisms of a single-lens reflex camera with a digital imaging sensor.
Advanced Photo System type-C (APS-C) is an image sensor format approximately equivalent in size to the Advanced Photo System film negative in its C ("Classic") format, of 25.1×16.7 mm, an aspect ratio of 3:2. It is therefore also equivalent in size to the Super 35 motion picture film format, which has the dimensions of 24.89 mm × 18.66 mm.
In digital photography, the crop factor, format factor, or focal length multiplier of an image sensor format is the ratio of the dimensions of a camera's imaging area compared to a reference format; most often, this term is applied to digital cameras, relative to 35 mm film format as a reference. In the case of digital cameras, the imaging device would be a digital sensor. The most commonly used definition of crop factor is the ratio of a 35 mm frame's diagonal (43.3 mm) to the diagonal of the image sensor in question; that is, CF=diag35mm / diagsensor. Given the same 3:2 aspect ratio as 35mm's 36 mm × 24 mm area, this is equivalent to the ratio of heights or ratio of widths; the ratio of sensor areas is the square of the crop factor.
A full-frame DSLR is a digital single-lens reflex camera (DSLR) with a 35 mm image sensor format. Historically, 35 mm was considered a small film format compared with medium format, large format and even larger.
In digital photography, the image sensor format is the shape and size of the image sensor.
This article is about photographic lenses for single-lens reflex film cameras (SLRs) and digital single-lens reflex cameras (DSLRs). Emphasis is on modern lenses for 35 mm film SLRs and for DSLRs with sensor sizes less than or equal to 35 mm ("full-frame").
In photography, the 35 mm equivalent focal length is a measure that indicates the angle of view of a particular combination of a camera lens and film or sensor size. The term is useful because most photographers experienced with interchangeable lenses are most familiar with the 35 mm film format.
A telecompressor or focal reducer is an optical element used to reduce focal length, increase lens speed, and in some instances improve optical transfer function (OTF) performance. It is also widely known under the name “Speed Booster”, which is the commercial name of a line of telecompressors by the manufacturer Metabones. Popular applications include photography, videography, and astrophotography. In astrophotography, these qualities are most desirable when taking pictures of nearby large objects, such as nebulae. The effects and uses of the telecompressor are largely opposite to those of the teleconverter or Barlow lens. A combined system of a lens and a focal reducer has smaller back focus than the lens alone; this places restrictions on lenses and cameras that focal reducer might be used with.
The Nikkor 13mm f/5.6 is an ultra-wide angle rectilinear lens which was manufactured by Nikon for use on Nikon 135 film format SLR cameras until 1998, at which time it was discontinued. It has been dubbed 'The Holy Grail', for its low-distortion ultra-wide capabilities. The lens was produced by Nikon only upon receipt of an order, thus making it one of the Nikon lenses with the least number manufactured.
Afocal photography, also called afocal imaging or afocal projection is a method of photography where the camera with its lens attached is mounted over the eyepiece of another image forming system such as an optical telescope or optical microscope, with the camera lens taking the place of the human eye.
The Sigma 8–16mm lens is an enthusiast-level, ultra wide-angle rectilinear zoom lens made by Sigma Corporation specifically for use with APS-C small format digital SLRs. It is the first ultrawide rectilinear zoom lens with a minimum focal length of 8 mm, designed specifically for APS-C size image sensors. The lens was introduced at the February 2010 Photo Marketing Association International Convention and Trade Show. At its release it was the widest viewing angle focal length available commercially for APS-C cameras. It is part of Sigma's DC line of lenses, meaning it was designed to have an image circle tailored to work with APS-C format cameras. The lens has a constant length regardless of optical zoom and focus with inner lens tube elements responding to these parameters. The lens has hypersonic zoom autofocus.
Lightfieldmicroscopy (LFM) is a scanning-free 3-dimensional (3D) microscopic imaging method based on the theory of light field. This technique allows sub-second (~10 Hz) large volumetric imaging with ~1 μm spatial resolution in the condition of weak scattering and semi-transparence, which has never been achieved by other methods. Just as in traditional light field rendering, there are two steps for LFM imaging: light field capture and processing. In most setups, a microlens array is used to capture the light field. As for processing, it can be based on two kinds of representations of light propagation: the ray optics picture and the wave optics picture. The Stanford University Computer Graphics Laboratory published their first prototype LFM in 2006 and has been working on the cutting edge since then.