====Field of View====
**I.Definition**\\
The **field of view (FOV)** describes the extent of the observable scene captured by an imaging system. In photography, the terms **field of view (FOV)** and **angle of view (AOV)** are often used interchangeably to refer to the maximum angular extent of a scene observable by a camera. \\
Depending on the measurement direction, the field of view may be specified as the **horizontal field of view (HFOV), vertical field of view (VFOV), or diagonal field of view (DFOV).**
|  {{ yanding:成像基础知识:成像系统:成像质量问题:企业微信截图_17604081943519_1_.png?420 |}}  |
^  Figure 1. HFOV, VFOV, and DFOV illustration(Image source: https://commons.wikimedia.org/w/index.php?curid=5294848)  ^

From an optical perspective, the **angle of view** is defined as the angle subtended by the **entrance window** at the center of the **entrance pupil**. The field stop limits the field of view, while the entrance window is the image of the field stop formed by the optical system in object space.\\
|  {{ :en:yanding:image_quality_evaluation:image_quality_factors:fov-1.png?550 |}}  |
^  Figure 2. Optical definition of field of view (FOV)  ^

**II.Impact Factors**\\
The field of view (FOV)  of a camera is determined by both the focal length of the lens and the size of the image sensor.\\
**1. Focal Length**\\
The focal length is the distance between the optical center of the lens and the focal plane of the image sensor. For a given sensor size, a longer focal length results in a narrower angle of view, while a shorter focal length produces a wider angle of view.\\

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|  **Figure 3.** Field of view with focal lengths of 24 mm, 28 mm, 35 mm, 50 mm, and 72 mm.（Image source: https://commons.wikimedia.org/wiki/File:24-72mm_zoom_demo.jpg)  |

**2. Sensor Size**\\
For a given focal length, a larger sensor produces a wider angle of view because it captures a larger portion of the image projected by the lens. Conversely, a smaller sensor results in a narrower angle of view. This relationship is commonly expressed by **the crop factor**, which quantifies the difference in field of view between sensor formats.
|  {{ :en:yanding:image_quality_evaluation:image_quality_factors:fov2.png?700 |}}  |
|  Figure 4. Field-of-view cropping caused by different sensor sizes.  |


**III.Calculation**\\
The effective focal length of the lens and the size of the image sensor fully determine the field of view (FOV) of a camera. The general formula for the angle of view is:\\
$$\alpha = 2\arctan\left(\frac{d}{2f}\right)$$
where $d$ is the dimension of the sensor in the measurement direction, and $f$ is the effective focal length.\\

If the sensor has a horizontal dimension $d_{h}$ for width and a vertical dimension $d_{v}$ for height, the horizontal, vertical, and diagonal fields of view can be calculated as:

$$HFOV=2arctan\frac{d_{h}}{2f}$$

$$VFOV=2arctan\frac{d_{v}}{2f}$$

$$DFOV = 2 \arctan\left( \frac{\sqrt{{d_{h}}^2 + {d_{v}}^2}}{2f} \right)$$
where **HFOV, VFOV, and DFOV** denote the horizontal, vertical, and diagonal angles of view, respectively.