The formula to calculate the Vertical Field of View (VFOV) is:
\[ \text{VFOV} = 2 \times \text{atan}\left(\text{tan}\left(\frac{h}{2}\right) \times \text{AR}\right) \]
Where:
A vertical field of view is a measure of the total observable area a person or object can see via an optical device. It’s measured in terms of degrees of total visible angle. This concept is crucial in fields such as photography, videography, and virtual reality, where understanding the extent of the visible area is important for capturing or rendering images accurately.
Let's assume the following values:
Using the formula to calculate the Vertical Field of View:
\[ \text{VFOV} = 2 \times \text{atan}\left(\text{tan}\left(\frac{90}{2}\right) \times 1.7777\right) \]
First, calculate the horizontal FOV in radians:
\[ h_{\text{rad}} = \text{deg2rad}(90) = \frac{\pi}{2} \text{ radians} \]
Next, calculate the tangent of half the horizontal FOV and multiply by the aspect ratio:
\[ \text{tan}\left(\frac{h_{\text{rad}}}{2}\right) \times 1.7777 = 1 \times 1.7777 = 1.7777 \]
Then, calculate the arctangent and multiply by 2:
\[ \text{VFOV}_{\text{rad}} = 2 \times \text{atan}(1.7777) \approx 1.91 \text{ radians} \]
Finally, convert the vertical FOV back to degrees:
\[ \text{VFOV} = \text{rad2deg}(1.91) \approx 109.38 \text{ degrees} \]
The Vertical Field of View is approximately 121.28 degrees.