Nice looking machining.
You can see the relative response effect of various sized APE ball attachments here:
https://www.dpamicrophones.com/mic-university/acoustic-modification-accessoriesYour 20mm ball is 10mm smaller in diameter than the smallest of the three shown on that page, but the general trend is apparent. Expect the
on-axis response bump to be centered around 5-7kHz, with a bit less emphasis than what is shown for the 30mm APE.
When viewing those, remember that the polar response diagrams are normalized to a flat on-axis response, so the effect of the response bump is sort of buried in the polars by the normalization. One take away of that is the true polar response is actually wider than indicated in the region where the on-axis response is bumped up. In other words, you don't see the "bump" directly in the polars, and the off-axis polar angle responses are affected just like the on-axis normalization so if trying to determine the response at say 90-degrees by looking at the polar graph, you sort of need to look at the plot lines and shift them outward by a few dB within the range of the "bump". So if you point the microphone upward with ball attachment installed, the clarity enhancement effect of the response bump will be applied to the pickup of sound arriving from the ceiling direction. At 90 degrees off-axis, the response bump and off-axis roll-off more or less cancel each other out, leaving just the higher frequency roll-off where the "presence range" bump response tapers back down again. Beyond 90-degrees pickup will be somewhat less present and less bright.
With the attachment in place, the change in response will be tied to the direction in which you orient the microphone. The increased clarity effect will be apparent on-axis, while moving off-axis the response will transition the opposite way. Averaged across all directions, overall sensitivity remains about the same with and without the ball attachment in place. In essence use of the attachment shifts the balance of high frequency sensitivity toward on-axis by simultaneously reducing sensitivity in that range from off-axis directions. With the ball attachment, sounds arriving on-axis will "see" the response bump, whereas sounds arriving from off-axis will see a corresponding roll-off that increases with off-axis angle, generally.
Most of the time when APE spheres are used the microphones are pointed toward the source, causing on-axis pickup of the source to become somewhat brighter and clearer, due to the bump in the "clarity presence" range on-axis. However, you can "tune" how much of that high-frequency emphasis is imparted to the source by pointing the microphone more toward or away from the source. The ball attachment amplifies that effect. With an omni as small as the 4090 is without the ball attachment installed on it that angular response tuning effect may not be apparent. With the ball attachment in place it should be.
The farther away the omni is from the source, the more likely it will be that pointing the microphone at the source with the ball attachment installed is appropriate.
The ball attachments can be used simply as an on-axis response modifier (in combination with microphone angle as mentioned), but the most productive use of ball attachments in my way of thinking is in combination with EQ across the same frequency range that the attachment modifies. In that way you can un-link the frequency response modification aspect of the attachment from its polar modification aspect. Point the microphone with the polar-response modification aspect in mind, then alter the frequency-response aspect of the direct sound pickup form the source as needed. In that way you gain some degree of control over both both frequency response and directionality in the high frequency range.