Relationship between electric field at aperture and field at distance

I'm new to this forum and turned here because I have no other help to turn to. In studying antenna theory and I came across the relationship between E0(Electric field at aperture) and Er(Electric field at distance r). It was stated as follows:

$$|Er| = \frac { |E_0| \times A } { r \times \lambda }$$ where:

$Er$ is the electric field broadside to aperture at distance $r$,

$E_0$ the electric field at aperture,

$A$ the effective aperture of the antenna,

$r$ the distance between the two fields,

$\lambda$ the of radiating filed wave length.

I have tried extensively to find proof to this either mathematically or intuitively but I am really confused, specially how lambda makes an effect on the field intensity change. My only idea is that as r increases, the field varies according to inverse square law which I believe is a very basic view than what is expected.

Any help will be appreciated, or links to sources where I can research myself.

• What have you found so far, get out your EM book and start hashing equations together. Do some units analysis. Commented Jan 8, 2017 at 3:24
• I am currently following Antennas 2nd edition by John D. Kraus and I find the derivation quite difficult to understand. I was hoping to find a simpler explanation somewhere. Unit analysis does verify the equation by doesn't really explain why. Commented Jan 8, 2017 at 3:43
• Hazarding a guess here! Antenna aperture is a function of wavelength. So lambda needs to be included (antennas have less gain as wavelength increases). On Ham.SE: Why is antenna aperture a function of wavelength? Commented Sep 7, 2018 at 16:15