Light intensity profile along all radial distances

[XLAYZ]

Hello,

I have an ordinary light (not laser) collimated to produce a parallel beam. After traveling a distance in air, the beam has diverged significantly. The intensity decreases as the radial distance increases. Now I need to estimate the intensity profile along all radial distances inside the beam. All what I found was about laser beam and Gaussian beam, it is not the same thing. Could anyone please show me what theory and which formula I need to use?

Thank you in advance!

 

[tech99]

Once we are more than a certain distance from the source (the boundary of the Radiation Near Field), the intensity falls with the inverse square law. This applies along any radial.
The boundary of the radiation Near Field is quite indistinct, and for a collimated beam is sometimes given as the Rayleigh Distance = diameter of source^2 / 2 lambda.
The same applies to laser beams, radio beams and microwave beams, water waves etc.

 

[kuruman]

When you say "radial" which radius do you mean? The radius $R$ of a sphere centered at the source or the radius $r$ of the circular spot of collimated light at distance $R$ from the source?

 

[XLAYZ]

When you say "radial" which radius do you mean? The radius $R$ of a sphere centered at the source or the radius $r$ of the circular spot of collimated light at distance $R$ from the source?

Sorry, I mean the radial distance from the axis of the beam with circular cross section.

 

[tech99]

Sorry, I had misunderstood the meaning of"radius". If the radiating aperture is circular and uniformly illuminated, we see a tapered central lobe, followed by a succession of nulls and gradually diminishing peaks, known as sidelobes. This is called an Airy pattern, named after the former Astronomer Royal. See Wiki, https://en.wikipedia.org/wiki/Side_lobe
Close to the antenna, within the radiation near zone, the beam is essentially parallel.