So I got some time to set up some simplified Optical models of a transparent leader sun illuminated that I can ray trace and see what happens. I haven't put it under water yet, but I've already learned some things which may be different from what we all may have thought about this problem.
I started out by first of all setting up a uniform clear sunlight field to illuminate the setup. I moved the sun to just an inch (25 mm) away from the leader, which I arbitrarily set at 5 mils in diameter. So yeah I know the sun was way too big so I shrunk it too down to the same scale as I shrunk the distance, so it is still the exact same 0.5 degree angular diameter source, and I sent out a beam which is about three times the leader diameter when it reaches the leader. This was to give a background illumination that matched the sunlight (in air) falling on any ground level surface. Then I adjusted the sun power until the spot I got was 1,000 Watts per square meter, which is about what ground level sunlight is, starting at 1362 W/m^2 outside the atmosphere. So that's about 100 milliWatts per squ cm.
So I could set the leader index to 1.000 to match the air, and thus disappear the leader, and plot the normal sun background.
Next I turned the leader index up to 1.576, by putting in SAN for the material, which is a copolymer much like Nylon; BUT, I turned off the ray splitting and polarisation, so that I could see what happens sans any reflections.
And voilla !!, the problem may not be the reflections at all. The cylindrical leader acts like a shadower, blocking light from the space behind it to leave a dark hole in the sunlight; but then the light that does hit the leader, and is transmitted, gets focussed by the cylindrical lens effect, to make a line image of the sun's disk, that is just a short distance outside the far side of the leader from the sun, right in the middle of the leader shadow black hole.
In air, that sun image is 12 times brighter than the ambient sunlight, so it is very bright, and more like 1.2 W/cm^2 than 100 mW/cm^2. That focussed sun image is formed by a quite wide angle focussed beam, which then diverges, so the sun line image is visible over a wide angle on the opposite side of the leader.
When I turned the polarisation and ray splitting back on, then I got a broad scattered reflected beam off the sun side of the leader, and in a couple of directions almost perpendicular to the sun, the reflected rays appear to form a virtual sun image inside the leader, so looking from those two directions, you would again see a sun image, which will be reduced by the reflection coefficient, but also brightened by the apparent magnification of that virtual image. I haven't looked at that image yet; simply noticed that it is present.
The forward beam of focussing rays, that form the bright sun image on the far side of the leader, also reflects off the concave inside of the leader, and create another real focussed image of the sun inside the leader, which of course will be reduced in brightness, by the reflection coefficient, and further modified in magnification by the optics of the leader as a concave mirror, rather than a doublle convex lens.
Now all of this will change in values; but not in concept, when I put the thing in water. The lowest index material I can find is 1.45, which is not as low as Seaguar's 1.42 fluoro-carbon; but I think we will get a pretty good idea of what is really happening.
To post the data results, I will have to photograph the plots off the screen, and then compress the photos, to present as a slide show. But the transmitted light image may turn out to be the big problem; which just might support the notion of a more opaque leader, to attenuate the transmitted light rather than worry about reflections. I'm also suspecting (WAG)) that matte surfaces won't impact the transmitted focussing effect as much as they affect reflections, So I don't think that solution flies.
More later.
George |