Solid angle

• Used to measure FOV
• Unit: steridians

$\Omega =\frac{A}{r^2}$

• Solid angle from a person’s view to the moon is about the same as that of the sun, which is evident during a solar eclipse
• Solid angle of a sphere measured from any point in its interior is $4\pi$ steridians.
• Solid angle subtended by a face of a cube to its centre is 1/6th of that, or $\frac{2\pi }{3}$ steridians.
• Solid angle can also be measured in square degrees

1 sr = $(\frac{180}{\pi }{)}^2$ square degrees

• It can also be measured in square minutes, square seconds or fractions of sphere ($\frac{1}{4\pi }$) sr, also known as spat

1 sp = $4\pi$ sr

• In spherical coordinates, $d\Omega =sin(\theta )d\theta d\varphi$, where $\theta$ is the colatitude (angle from the North Pole) and $\varphi$ is the longitude