How many cameras one needs to measure a particle Lagrangian trajectory? In some cases, one camera is enough:
Obviously what we get is a 2D projection of the 3D trajectory. In this particular case, we study settling particles and their main motion is vertical, while the horizontal motions exist, but they're smaller and do not have any preferential direction. Thus, studying the horizontal motion in one direction, we can infer the statistics also for the out-of-plane motion in another horizontal direction.
But in most cases you will need at least two cameras
or three
of better four cameras :)
Well, there is really a long story why would you need four cameras. Two cameras are needed theoretically to obtain the depth information in a single media (air, water). Three cameras are needed to solve the non-linear part in case you have index of refraction changes along the imaging path, e.g. air - glass - water. And four cameras are needed when you have multiple particles and they simply interfere and at any given frame only some of the cameras can see the particle. This redundancy is also saving us from the strong noise effects.
In this particular case we also have air - glass - water - glass - water - perspex - water. So, wish us luck calibrating this thing ;)
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