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.

  • $\begingroup$ The apparent size of the object inside the water drop will be a sensitive function of the distance to the surface as well as of the curvature of the surface. How do you intend to determine the distance? $\endgroup$
    – Floris
    Commented Jul 15, 2016 at 14:28
  • $\begingroup$ @Floris, I can take multiple images at different focal planes, with a relatively shallow depth of field. Though I imagine this gets a bit tricky, as the apparent focal surface inside the drop is probably curved? To keep things simple initially, I'll assume the object is relatively flat and resting on the bottom surface of the drop. $\endgroup$
    – Dan Bryant
    Commented Jul 15, 2016 at 14:45

1 Answer 1


The curvature of the drop is influenced by the liquid-solid, solid-air and liquid-air interface forces. It can be determined by the Young-Laplace equation. For more details see this article


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