Configuring WiFi can be an extra step that's just one more possible point of failure when using a...
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Instead of getting it on the same WiFi network, @wmacfarl suggested configuring it as an ethernet "linux gadget". Where's some documentation on how to do this, and would it make it as simple as plugging the Raspberry Pi into your laptop or phone with a USB cable and navigating to http://raspberrypi.local?
It would use the USB port. The zero is wired to draw power through it as well as data.
I've just enabled it on the Pi zero i'm using at work. You can edit the relevant files over ssh and then reboot it. Saved me having to disassemble the whole spectrometer to get the micro-sd out.
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I got this running -- it was pretty simple to change a couple files in the boot drive. But I found that it wasn't easy to just connect via a web browser -- you have to configure your laptop to connect properly to the Pi's network, which isn't easy for everyone.
Instead, i'm going to try to get the Pi to produce a WiFi hotspot, called "Microscope" (for this application) which you connect to and it auto-directs you to the microscope page.
Then as a next step, if you still need internet access, it's apparently possible for a 2nd wifi interface on the Pi to connect in turn to another wifi network. I want to make it possible to configure that connection from the hotspot welcome page... !!! Meta, but it could be pretty seamless once it works.