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,

\(d\Omega = sin(\theta)d\theta d\phi\), where
\(\theta\) is the colatitude (angle from the North Pole) and
\(\phi\) is the longitude