Up until a couple years ago, I just assumed that with any paraboloid dish, that signals coming in at different angles (ie from different sats) would just focus at different points. That is, until I set up my first small dish, a Fortec 90CM (up until then, I had only used a BUD). I documented some experiments I did before setting it up, at FC90-sg2100.html. But the part of that process that relates to this thread, is down near the bottom of that page, where I did an experiment by putting several small mirrors on the dish, and aimed the dish at the sun. An example of an image from that is below (sorry for not putting it in thumbprint, but I wanted to wrap text around it)
In the above picture, you can see the spots from 4 different mirrors. I found out later, that the Fortec 90CM's lnbf arm was off by about 2" position wise. Anyway, doing this experiment was really educational for me. No matter what direction you moved off aim, those spots from the mirrors danced around in all directions, not just having the focus move right or left as you aimed right or left of the central aim. Ie if aimed so as to have all the spots at the focal point, then move say to the left a bit, one spot might move up, another right, another left, another down, then as you move further, they all change directions, and do a little dance all over the area. I later put up a bigger screen to observe the dance of the spots. This convinced me that with a regular dish, there was truely only one focal point, and anything off center is a compromise, even though obviously people, including myself, have put lnbfs off center to pick up nearby satellites.
Some day, perhaps at the next solar outage period, I may try that mirror experiment on my 3 sat DirecTV dish, and watch the spots for a couple hours as the sun goes from 101-110-119, just to see if that dish is optimized at those 3 positions, and see how it performs in between these 3 sats. If I do that, I think I'll put a dozen or so mirrors instead of just 5.
Re doing theoretical calculations to show the off axis reflection patterns, that was way beyond my capability, but I did look at how 3 or 4 off axis rays would reflect off a parabola, and it's pretty clear that they don't focus.
Seems like antenna theory using things like mininec or something similar, might show directions where off axis reception might be favorable, but I don't think (I don't really know enough about mininec to know ) that it can really show the pattern of an off axis signal. (I'm not sure I said that clearly.)
{EDIT: ie I think mininec would show the pattern of the antenna, not the pattern of an incoming off axis signal. I think optical theory would be more useful here. End EDIT.}
Anyway, I agree that this is an interesting topic, but for me, using mirrors is the only way I can visualize what's going on.
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