Suppose I have a camera that is looking straight down at a single droplet of water resting on a flat surface. The droplet is small enough that surface tension forms it into a rounded shape. Inside the water, there is suspended an object that I'd like to image and measure. Is it possible to somehow calibrate for the lensing effect of the drop and make accurate measurements of objects suspended inside it?
I know how to deal with calibration of the camera itself and measurement of objects in a flat focal plane, with no water surface in the way. So I think the core problem here is figuring out how to 'dewarp' the image seen through the water droplet into an equivalent flat plane image.
If I know the shape of the droplet, I think I can create a model of the optics and use it to calibrate using known reference features positioned under droplets, but I'm uncertain what parameters determine the shape of a water droplet on a flat surface. I'm planning to do some experiments, but I'm interested in identifying prior research to review on the subject.