Excellent!Long story short, I slowly added Kenko tubes, from my second set, one ring at a time. Just as I ran out, at 136mm, I hit parfocal on the 4x and got an exact 2.2mm on my frame, side to side.
A few more thoughts to cross all the "T's"and dot the "i's", and get you ready for that spiffy 20X.
While not impossible, it would be extremely unusual (lucky!) to actually hit accurate parfocal with rigid, fixed length extension tubes... close, yes... but "dead-on, I really doubt it. So now that you are, at the very least, quite close, let's talk about fine-tuning things.
Run this procedure again:
1) Set up viewing eyepieces correctly as per microscope manual. Don't change this once set.
2) Get a small, very contrasty subject in the center of the view and focus very carefully through the viewing eyepieces using either a 4X or 10X objective. DO NOT CHANGE THIS FOCUS!
3) Put the camera into live view mode and look at the subject you have just focused on... BUT DO NOT CHANGE THE MICROSCOPE FOCUS YET!
4) Magnify the live view setting on the camera and center the subject (using the controls on the camera body) in the view.
5) Now, while paying very close attention to magnified live-view image, slowly turn the fine focus knob to see if you can improve on the focus as seen in the magnified camera live-view image. If the live view image can be improved by altering the fine-focus any amount at all, the camera is not perfectly "parfocal" with the eyepieces.
At this point you need to make a determination. If you are perfectly "parfocal"... fantastic!... go and buy that lottery ticket! But most likely you are not.
How will you be focusing the microscope for taking pictures? Will you be focusing through the eyepieces, or will you be focusing while looking at the live-view image on a screen or the back of the camera?
If you will be focusing by viewing through the microscope eyepieces then you'll need to work to get the eyepiece view and the camera truly "parfocal". (Let’s call this “Case A”)
If you will be focusing from a monitor image or by observing the live-view image on the camera back (let’s call this “Case B”), you don't need to be quite as obsessive... BUT... there should not be a great difference between eyepiece and camera focus. They should be quite close, with only a modest "tweak" of the fine focus knob to get the "live-view" image in focus after focusing with the eyepieces.
If it’s “Case A” you will need to either raise (more tubes or extension) the camera relative to the microscope, or lower the camera (less tubes or extension) relative to the microscope. Since right now you are using rigid tubes, here’s a way you can determine which the situation is:
Go back and repeat steps 2, 3, and 4 mentioned above. Now, when you perform step 5 pay very close attention to the direction of the fine-focus movement that is needed to achieve accurate focus in the live-view camera image.
If the fine-focus movement that was needed raised the subject up towards the objective, then the camera is positioned too high… you need to lower the camera very slightly (remove tubes/extension).
If the fine-focus movement that was needed lowered the subject away from the objective then the camera is positioned too low… you need to raise the camera very slightly (add tubes/extension).
All of the camera adapters I have made for my microscopes incorporate a means of raising or lowering the camera continuously within at least a ½ inch range. (With the camera on a separate stand it is obviously easy to do. With the camera attached directly to the microscope I incorporate a focusing helical mount in the adapter). So now, with live-view cameras, I do steps 1-4, and then, while viewing the magnified live-view image, raise or lower the camera until the live –view image in perfect focus ( this is done WITHOUT CHANGING THE MICROSCOPE FOCUS DETERMINED IN STEP 2).
Again, you should use a 4x or 10x objective for this setup procedure. It is somewhat counter-intuitive, but the accurate positioning of the camera is far more critical with low power objectives. If you’ve got it nailed down with a 4x you are in good shape with higher power objectives.
(Last point... typically on a binocular microscope one of the eyepieces has a focusing helical so that the binocular can be set for your vision. Occasionally both eyepieces will have this adjustment. I don't think this is the case with yours, but if it is let me know... you might be able to do some "fine-tuning" at that end).