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Field of View
1. Concept of Field of View
In the field of photography, Angle of View (AOV) and Field of View (FOV) are often used interchangeably, both referring to the maximum angular extent of the scene that a camera can “see.” Specifically, AOV refers to the angular measurement of this extent, while the concept of FOV is broader and can be expressed in terms of angles, physical dimensions, or other measures; however, in photography, it specifically denotes the angular range.
From an optical perspective, the angle of view is the angle subtended by the entrance window at the center of the entrance pupil, as shown in the figure above. Here, the field stop is the aperture that limits the field of view (i.e., the frame of the image sensor in the figure), and the entrance window is the image of the field stop formed by the optical system between it and the object.
2. Classification of Field of View
Based on the direction of measurement, the field of view can be classified into horizontal field of view (HFOV), vertical field of view (VFOV), and diagonal field of view (DFOV).
The horizontal field of view (HFOV) refers to the angle of view in the horizontal direction.
The vertical field of view (VFOV) refers to the angle of view in the vertical direction.
The diagonal field of view (DFOV) refers to the angle of view along the two diagonals. The specific measurement ranges are illustrated in the figure below.
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| (Image source: https://commons.wikimedia.org/w/index.php?curid=5294848) |
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3. Factors Affecting Field of View
The size of the field of view depends on the focal length of the lens and the size of the image sensor.
1. Focal Length
Focal length refers to the distance from the optical center of the lens to the focal plane of the sensor (the plane where the image is sharply focused). For a given image sensor size, the longer the focal length of the lens, the smaller the field of view. Conversely, the shorter the focal length, the larger the field of view.
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| Five images captured with cameras using different focal lengths of 24, 28, 35, 50, and 72 mm, but with the same image sensor |
Image source: https://commons.wikimedia.org/wiki/File:24-72mm_zoom_demo.jpg)
2. Image Sensor Size
The size of the image sensor affects the camera's crop factor. For a given lens focal length, the larger the image sensor, the larger the field of view. Conversely, the smaller the image sensor, the smaller the field of view.
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| Field of view cropping in cameras with different sensor sizes but the same lens focal length |
(Image source: https://commons.wikimedia.org/wiki/File:LensCropFactor.png)
4. Calculation Principle of FOV
The effective focal length and sensor size of a camera completely define the field of view. The formula for calculating the field of view is as follows:
$$ \alpha=2arctan\frac{d}{2f} $$
where d is the dimension of the sensor in the measurement direction, and f is the effective focal length.
Assuming the horizontal dimension (i.e., width) of the sensor is $d_{h}$, and the vertical dimension (i.e., height) is $d_{v}$.
$HFOV=2arctan\frac{d_{h}}{2f}$
$VFOV=2arctan\frac{d_{v}}{2f}$
$DFOV = 2 \arctan\left( \frac{\sqrt{{d_{h}}^2 + {d_{v}}^2}}{2f} \right)$