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Paul Schlyter: "Re: Glory on the Ground" (Nov 14, 14:10):
>
>
> Heligenschein requires water drops ON THE GROUND. It works like
> this: the water drops focuses incident sunlight on the grass (or
> whatever) below. The grass reflects this focused light diffusively,
> but the reflected light is then once again focised by the water drops,
> towards a direction opposite the original direction.
>
> Heligenschein can be simulated quite neatly if you buy a number of
> small glass balls about 1 cm in diameter (of the kind that can be
> found in many toy shops) and then spread them out on e.g. a piece of
> paper. Illuminate this with a lamp and look at it as close to the
> lamp as you can get, then look at it more from the side. There'll be
> a quite dustinguishable difference in brightness, and it"ll be obvious
> why it gets so brighter when viewed as near the lamp as possible.
>
>
> There's still another effect to consider, which I call the
> "opposition effect". This effect requires no water drops neither on
> the ground nor in the air above the ground, but it does require a
> rough surface. This rough surface will produce a lot of small
> shadows when illuminated from a direction different from directly
> behind. These shadows are not individually visible, but they
> decrease the brightness. When illuminated directly from behind, all
> these small shadows disappear and the brightness increases quite
> noticeably. This effect can be very obvious when flying over a forest
> and the shadow of the airplane falls on the forest.
Thank you for clearing this matter, I was under impression that
Heligenshein is exactly what you call "opposition effect", that is, due
to disappearance of shadows when viewed from the direction of incident
light.
>
> This "opposition effect" is also responsible for the full moon being
> about ten times brighter than the half moon, and not merely twice as
> bright as could be naively expected, or PI times as bright as if it
> would be if the lunar surface was a perfect diffusor (˙"Lambertian"
> reflector).
>
I must disagree here a bit. The opposition effect on moon is only partly
caused by disappearance of shadows. There is also significant
contribution from coherent backscattered light due to multiple
scattering at the lunar surface. Geometrically, you can consider two
dust grains lying on the surface close each other. The light scattered
from each grain is incident on the other, and small amount of this light
is scattered back towards the light source. The amplitudes of these
backscattered waves are small compared to the original incident wave,
but due to geometry, they have the same phase, thus constructive
interference occurs. This is propably not that interesting, but it is
important factor explaining the opposition effect of moon (the sudden
increase in brightness at the opposition), so I thought to mention it.
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