Field of view

As one of the world's leading manufacturers of precision optics, Schneider-Kreuznach attaches great importance to ensuring that only first-class products leave the company. For this reason, every finished lens undergoes a three-stage test procedure. In the 3D precision measurement, computer-controlled measuring devices check the accuracy of the mechanical components. Optical engineers then use MTF measurements to determine whether the assembled optical system deviates from the calculated values. At the end of the testing chain, each lens is visually inspected by Schneider experts. This includes evaluation of the optical performance in the projection test as well as cosmetic aspects (dust, scratches).

Field of view vsangleof view

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.

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.

In photography, angle of view (AOV)[1] 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.

field ofview中文

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 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 75 mm (1.5×50 mm Nikon) or 80 mm lens (1.6×50mm Canon) 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 a 28–35 mm lens on many digital SLRs.

The target's angular extent is: α = 2 arctan ⁡ L 2 f c {\displaystyle \alpha =2\arctan {\frac {L}{2f_{c}}}} where L {\displaystyle L} is the dimension of the target and f c {\displaystyle f_{c}} is the focal length of collimator.

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).[16] Digital compact cameras sometimes state the focal lengths of their lenses in 35 mm equivalents, which can be used in this table.

Focal length

The focal length of a lens determines two interrelated characteristics: magnification and angle of view.

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 macro photography, we cannot neglect the difference between S 2 {\displaystyle S_{2}} and F {\displaystyle F} . From the thin lens formula, 1 F = 1 S 1 + 1 S 2 . {\displaystyle {\frac {1}{F}}={\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}.}

Consider a 35 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.

A specific MTF curve is also only valid for a specific point of view. In general, the MTF curves for different image points are different, so a large number of curves would be required to describe the entire image field. Therefore, another representation is used in which the modulation is plotted over the image height, starting from the center of the image, for reasonably selected spatial frequencies. This is the basis of the data sheets.

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.

In the optical instrumentation industry the term field of view (FOV) is most often used, though the measurements are still expressed as angles.[8] Optical tests are commonly used for measuring the FOV of UV, visible, and infrared (wavelengths about 0.1–20 μm in the electromagnetic spectrum) sensors and cameras.

To project a sharp image of distant objects, S 2 {\displaystyle S_{2}} needs to be equal to the focal length, F {\displaystyle F} , which is attained by setting the lens for infinity focus. Then the angle of view is given by:

Spherical aberration occurs when light rays at or near the edge (or margin) of the lens focus at a different location than those that enter the lens at or near ...

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fov和焦距的关系

Consider a rectilinear lens in a camera used to photograph an object at a distance S 1 {\displaystyle S_{1}} , and forming an image that just barely fits in the dimension, d {\displaystyle d} , of the frame (the film or image sensor). Treat the lens as if it were a pinhole at distance S 2 {\displaystyle S_{2}} from the image plane (technically, the center of perspective of a rectilinear lens is at the center of its entrance pupil):[6]

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The total field of view is then approximately: F O V = α D d {\displaystyle \mathrm {FOV} =\alpha {\frac {D}{d}}} or more precisely, if the imaging system is rectilinear: F O V = 2 arctan ⁡ L D 2 f c d {\displaystyle \mathrm {FOV} =2\arctan {\frac {LD}{2f_{c}d}}}

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)[3] 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 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.

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).

Using basic trigonometry, we find: tan ⁡ ( α / 2 ) = d / 2 S 2 . {\displaystyle \tan(\alpha /2)={\frac {d/2}{S_{2}}}.} which we can solve for α, giving: α = 2 arctan ⁡ d 2 S 2 {\displaystyle \alpha =2\arctan {\frac {d}{2S_{2}}}}

In addition, the beam path in the lens becomes increasingly asymmetric for pixels outside the center. Therefore, the MTF also depends on the orientation of the line pairs in the image field. Two perpendicular orientations are selected from the large number of possible orientations, as shown in the adjacent figure.

(In photography m {\displaystyle m} is usually defined to be positive, despite the inverted image.) For example, with a magnification ratio of 1:2, we find f = 1.5 ⋅ F {\displaystyle f=1.5\cdot F} and thus the angle of view is reduced by 33% compared to focusing on a distant object with the same lens.

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 (1.6×50mm) 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.

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 α ≈ d f {\displaystyle \alpha \approx {\frac {d}{f}}} radians or 180 d π f {\displaystyle {\frac {180d}{\pi f}}} degrees.

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.

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Defining f = S 2 {\displaystyle f=S_{2}} as the "effective focal length", we get the formula presented above: α = 2 arctan ⁡ d 2 f {\displaystyle \alpha =2\arctan {\frac {d}{2f}}} where f = F ⋅ ( 1 + m ) {\displaystyle f=F\cdot (1+m)} .

The ideal lens is one that faithfully reproduces all the coarse and fine structures in an object. This means that differences in the brightness of the object must be reflected in the image in the same way for a wide variety of structures.      For physical reasons alone, this requirement cannot be strictly met. Contrast losses occur to a greater or lesser extent in the entire range from coarse to fine structures. This entire structure range is now measured numerically by the number of line pairs per millimeter (spatial frequency R [1/mm]).

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: f = F ⋅ ( 1 + m ) {\displaystyle f=F\cdot (1+m)}

FOV tofocal lengthcalculator

Note that the angle of view varies slightly when the focus is not at infinity (See breathing (lens)), given by S 2 = S 1 f S 1 − f {\displaystyle S_{2}={\frac {S_{1}f}{S_{1}-f}}} rearranging the lens equation.

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.[9]

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From the definition of magnification, m = S 2 / S 1 {\displaystyle m=S_{2}/S_{1}} , we can substitute S 1 {\displaystyle S_{1}} and with some algebra find: S 2 = F ⋅ ( 1 + m ) {\displaystyle S_{2}=F\cdot (1+m)}

In addition, the modulation transfer function depends on the f-number set, the image scale used, and the weighting of the individual spectral components. Therefore, additional MTF curves are needed to characterize the image quality. Insensitivity to changes in scale is also a quality criterion that must be taken into account.

As you can see, the modulationdeteriorates for finer structures and drops to zero at a certain number of line pairs per millimeter. The impression of sharpness is therefore not determined by this highest spatial frequency, but by the highest possible contrast reproduction over the entire spatial frequency range, up to a maximum spatial frequency depending on the application.

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.

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The focal length of a lens is a number, measured in millimeters, which determines how wide angle or telephoto a lens is. A diagram showing different subjects ...

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.[10]

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:[7] α = 2 arctan ⁡ d 2 F ⋅ ( 1 + m / P ) {\displaystyle \alpha =2\arctan {\frac {d}{2F\cdot (1+m/P)}}}

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:[4] α = 2 arctan ⁡ d 2 f {\displaystyle \alpha =2\arctan {\frac {d}{2f}}}

For extreme wide-angle designs with large image angles, it should be noted that the modulation in the image field decreases with the cosine for sagittal structures and with the cube of the cosine of the image angle for tangential structures.

fov参数

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.

The MTF curves valid for the two orientations are shown in the diagrams as dashed (tangential) and solid (sagittal) in the diagrams.

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.[15]

d {\displaystyle d} 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, d = 36 m m {\displaystyle d=36\,\mathrm {mm} } would be used to obtain the horizontal angle of view and d = 24 m m {\displaystyle d=24\,\mathrm {mm} } for the vertical angle.

The figure on the left illustrates this using the example of a diffraction-limited (i.e. perfect) lens for 20 line pairs per mm and f-number k = 22 at a wavelength of 546 nm. The relative illuminance is plotted as a function of image angle.

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Now α / 2 {\displaystyle \alpha /2} is the angle between the optical axis of the lens and the ray joining its optical center to the edge of the film. Here α {\displaystyle \alpha } 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:

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