@Compro01. Ah! I see. I wasn't aware of this. I don't know very much about peripherals of these kinds of handheld devices, but I guess it makes perfect sense with products like Square's card reader and PaypalHere. I wonder if the noise is approximately the same on phones, and from phone to phone? I know in many laptops the output and input can be very noisey depending on whether it is plugged into a charger or not. If this is a real concern, to print identical objects with identical resolution from multiple devices, more hardware and a filter would be necessary.

@Slayte. Using the phone's camera would largely depend on several things that would be basically impossible to configure identically. Consider the following:
1) Position of the lens is not identical across most phones. You would have to have a way of ensuring the camera was positioned identically every time you began a print. This would mean a physical device to ensure it is physically some defined distance from the printer and oriented identically as well, probably orthogonally. You could attempt to account for the differences in position and orientation through software, but it may not be possible depending on the distance and orientation of the camera. Some extreme examples would be if it was pressed directly to the print area so that the entire reservoir was outside the scope of the image, or if it was turned away. Even neglecting these rather macroscopic concerns, if the resolution of the printer are to approach several hundred micrometers, this is tenths of a millimeter. 200 um = .2mm, so your 10mm markings would have to turn into 0.1mm markings.

2) Quality of the image and/or video is not the same. Most newer smart phones are ~20MP, but not all are this quality and some regular cellular phones are significantly lower. I'm not going to go into a physics and geometry explanation of this particular problem, but basically MP is a measurement of how many millions of pixels a camera produces in a single image. For a given object at a given distance with a given number of MP, you have a resulting actual size pixel dimension. This means, one phone may see 0.1mm where another phone may see 0.2mm depending on all of these things, assuming it is even high enough resolution to see 0.1mm markings and when liquid rises beyond it. The same problem of reading a beaker or graduated cylinder (the miniscus) would be present here as well. The surface tension of the resin would cause the mixture to cling to the sides and this would likely make it very hard to read in 0.1mm increments.

3) Lighting changes reflective properties of objects, especially liquids. As you noted, you may have to use a colored resin for this kind of approach. What if your resin is red and the background is red? What if the lighting is such that the surface of the liquid is very very hard to see? For example, in ultra low light conditions when you turn your lights off and the print continued?

There are too may design problems to correct with this method, in my opinion. Not to mention the same phone, and nearly all phones use this same TRRS connection Compro mentioned. The prints would be wildly unreliable and differ greatly for each camera device used.