How to determine the angle range of the surveillance camera?

How to calculate the monitoring range of the webcam? The following is the calculation method given by a security engineer of Xueba:
The main parameters:
1. Image sensor: 1 / 2.7 '' 2 million pixel progressive scan CMOS;
2. Focal length: 3.3mm ~ 12mm;
3. Viewing angle range:
96 ° ~ 35 ° (16: 9) 79.3 ° ~ 27.2 ° (4: 3)
Let's take this camera as an example, the relationship between the lens and the scene.
The main test installation environment is as follows:
The installation height of the hemisphere camera is: H = 3m, and the width W of the corridor is: 2m;
The installation angle of the camera lens is 0 ° (that is, the lens is horizontal);
Monitor display ratio: 4: 3, camera mode setting: 4: 3;
The main monitoring target W '* H' = 2m wide * 3m high complete corridor range.
Since it is an algorithm, there must be a basis for calculation:
Calculation formula horizontal field angle: α = 2arctan (w / 2f),
Vertical field of view: β = 2arctan (h / 2f),
Where w is the field width, h is the field height, and f is the focal length of the lens.
Although the calculated field of view angle is smaller than the actual field of view, the difference can be ignored. Here we describe the surveillance range of the camera with the calculated field angle.
1 / 2.7 '' CMOS imaging size is:
w * h = 5.27mm * 3.96mm.
So we calculated that:
When the focal length is 3.3mm:
Horizontal field angle: α1 = 2arctan (5.27mm / 2 * 3.3mm) = 77.2 °
Vertical field angle: β1 = 2arctan (3.96mm / 2 * 3.3mm) = 61.9 °
① In the vertical direction, the minimum distance (the horizontal distance from the camera) to see the complete corridor is: dvmin = H / tan (β1 / 2) = 3000mm / tan (61.9 ° / 2) = 5000mm = 5 meters
â‘¡ In the horizontal direction, the minimum distance to see the complete corridor (horizontal distance from the camera) is:
dhmin = W / 2 * tan (α1 / 2) = 2000mm / 2 * tan (77.2 ° / 2) = 1253mm = 1.25 meters.
Since dvmin> dhmin, when the focal length is 3.3mm, the monitoring range is the corridor area 5 meters away from the camera monitoring direction.
When the focal length is 12mm:
Horizontal field angle: α2 = 2arctan (5.27mm / 2 * 12mm) = 24.8 °
Vertical field angle: β2: = 2arctan (3.96mm / 2 * 12mm) = 18.7 °
â‘  In the vertical direction, the minimum distance (horizontal distance from the camera) to see the complete corridor is:
dvmin '= H / tan (β2 / 2) = 3000mm / tan (18.7 ° / 2) = 18220mm≈18 meters;
â‘¡ In the horizontal direction, the minimum distance to see the complete corridor (horizontal distance from the camera) is:
dhmin '= W / 2 * tan (α2 / 2) = 2000mm / 2 * tan (24.8 ° / 2) = 4548mm≈4.5 meters;
Thanks to dvmin '
The above algorithm is based on the fact that the camera lens is at a horizontal angle. If it is installed in this way, half of the image will be the ceiling. So this kind of situation rarely occurs, and most of them are the camera lens tilted downward, offset by a horizontal angle.
Then let's calculate the monitoring range when the downtilt angle is half of the vertical field angle. This is the maximum downtilt angle when the installation height of the camera and the height of the monitored object are the same.
(1) When the focal length is 3.3mm:
â‘  In the vertical direction, the minimum distance (horizontal distance from the camera) to see the complete corridor is:
dvmin = H / tanβ1 = 3000mm / tan61.9 ° ≈1.6m
â‘¡ In the horizontal direction, the field of view angle can be considered approximately unchanged, dhmin is still 1.25 meters.
Since dvmin> dhmin and the focal length is 3.3mm, the monitoring range is the corridor area 1.6 meters away from the camera monitoring direction.
(2) When the focal length is 12mm:
① In the vertical direction, the minimum distance (horizontal distance from the camera) to see the complete corridor is: dvmin = H / tanβ2 = 3000mm / tan18.7 ° ≈8.86 meters
â‘¡ In the horizontal direction, the field of view angle can also be considered to be approximately unchanged, dhmin 'is still 4.5 meters;
Since dvmin '> dhmin' and the focal length is 12mm, the monitoring range is the corridor area 8.86 meters away from the camera monitoring direction.
to sum up:
I do n’t know if you understand it. In fact, no matter the calculation method and method, the purpose is one. The field of view to be monitored must be matched with the choice of camera lens. We must remember this picture below!

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