I'm a big hop across the big pond. Keep forgetting all of the dish size limitations "over there". I have a 12 foot (however many meters and fractions of that is....it's a 12' dish).
Yes. Most of your off the shelf ku band lnbf's do have the scalar integrated. And they are designed for offset feed dishes.
Further. From my findings, If the lnbf is from a smaller, <1m DBS dish. Putting it on a larger dish and focused for strongest signal. Is still "under illuminating" the dish.
In other words, the integrated scalar was designed with the lnbf, at best placement for strongest signal on a smaller dish, to keep any 'outside the dish rim' interference from infiltrating the satellite signal.
The scalar also serves to reflect those outer rim radio waves back to the dish surface and in to the lnbf throat 'in-phase'.
Lnbf's. Like Inverto has. And others for professional installations. With separate scalar assemblies. Rule is. Conical is for offset dishes and flat if for prime focus.
Those assemblies allow for usage on different sized dishes. And calculations for diameter, dish depth, etc. To determine the f/D. Separate of the actual focal length of the dish.
The throat of the lnbf may be 'wide open' and be subject to any and all signals presented to it. The scalar can be considered a blinder to limit how much it can 'see'.
Limiting it when adjusted properly to not only limit the lnbf from getting extraneous RF interference from beyond the rim of the dish. But also the scalar will capture and re-reflect those signals off of the dish surface and back into the lnbf throat.
In the big dish c band world. Scalar placement is very important. And most of 'ours' are prime focus dishes. You calculate the f/D for scalar placement and then slip the lnbf or orthomode feed assembly into the scalar. Most if not all feed assy's. have markings on them for the f/D. You insert the feed to that depth, and use the set screws to fix it there, or close to. And it gets you into the ballpark. But there is still tweaking and skew adjustments involved.
But just a touch in too far with the scalar and you don't see the entire dish diameter and signal that can be tuned to highest dB is lower than expected.
In a steerable polar mount dish setup. It will be sensitive to movement. And signal versus aim will be very tight. Scalar too far out from the dish and signal can be good but aiming is vague. Kind of a delicate dance. And too far away from the dish you risk getting interference from beyond the dish.
I've put a Geosat Pro ku lnbf on the side of my scalar. "Sidecar". A bit offset due to the geometry of the dish. So it reflects about 5 degrees difference versus the same c band transponders on the same sat.
And since it actually is designed for a 1m offset dish. It is only seeing about that much. I've proven that by moving pieces of aluminum backed foam insulation in from the edge of where the ku lnbf is aimed.
I would need an Inverto type of lnbf and scalar to experience the entire dish diameter. Or, if I had a spare. Try removing some of the Geosat cast scalar length.
If you find my rant interesting of full of errors. It would be interesting to hear feedback.