Wow. I had a nice right up complete with pics on this but it got whacked apparently. The editor on this forum has some serious problems!
I'll dispense with all the neat stuff because I'm not spending another hour just to have it deleted.
Using a short horn like the one in our detectors distorts the microwave wavefront as it passes through the horn which is not good. The sharply tapered side walls of the antenna bends it like this )))))). What you want is for the wavefront to stay flat so as to generate the maximum electric field at the base of the antenna where it connects to the microstrip so it looks like this ||||||. The plano convex lens bends the wave the opposite way of the short horn like this ((((((.
So )))))) + ((((((( = ||||||| which = maximum gain.
If Escort's claim of +40 percent improvement with the X50 black is correct, then that lens is worth about -3db in sensitivity. That is a pretty decent boost but will not be apparent in every scenario.
I suggest doing the same tests with your X50 Black both with and without the lens to see if there is a noticeable difference with that detector. If there is, then we can assume that the lens for the M4 is either not designed properly for the S7 or is not positioned correctly.