Keith, I do show the ESP8266 in all of the schematics. It's the Wemos D1 Mini, and it's connected as shown.I just re-read the entire thread. You mention a ESP8266 wi-fi microchip but you do not show it in any of your diagrams. How is it connected?
I have one of those. It works very well for the price. Here are the instructions for adjusting the DC offset. It's under Operations / Vpos Alignment.
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I have the instructions for the DS0138, but when I read them, they didn't make any sense to me, in part because I've never used an oscilloscope before so I didn't know about setting the ground level, and in part because they were written by someone who doesn't write very clear documentation. I've finally watched enough videos, and pushed the buttons enough times, to have figured that out on my own. I think I'll make my own video, and document the whole process of using the DSO138, because it's probably being bought by a lot of people like me who need much better instructions than what's currently available.