4 ms·

> a vertical array of distinctive marks (e.g. rapidly blinking LEDs) This doesn't work, as light beams diverge. Even taking a high-quality laser beam with a di

> a vertical array of distinctive marks (e.g. rapidly blinking LEDs) This doesn't work, as light beams diverge. Even taking a high-quality laser beam with a divergence of 0.1 milliradian (for comparison, a typical laser pointer is about 1-2 mrad), after crossing the 11 meters width of a 9-lane athletics track, you end up with a beam diameter of 2.2 millimeters. At the 10 m/s speed of the athletes and a 40000 fps framerate, they travel 250 micrometers between each frame.

amluto 2y ago
I'm not sure what the issue you're describing is. If I have two devices, each with a camera and a line of marks, if they can each see each other's marks, then they are aligned to within the horizontal spread of the camera pixels. There are no lasers involved -- the marks can be paint, stickers, blinking wide-angle LEDs, etc. -- my suggestion to use blinking LEDs is just so that's it's more obvious when one is in the field of view of the camera.
- Denvercoder9 2y ago
  You don't just need the cameras to see each other, you need them to be perfectly parallel to each other as well, as otherwise they're photographing along a different plane, which may give conflicting results.
  - amluto 2y ago
    Suppose camera A has line L_A on the camera. A’s optics and marks are both on L_A, so A’s image plane contains L_A and camera B’s image plane also contains L_A (you know the latter because you’ve aligned the cameras so camera B sees L_A). And vice versa: camera A sees L_B. In 3D Euclidean space, two distinct lines define a plane, and both camera’s are photographing planes that contain L_A and L_B, so both cameras are photographing the same plane. More concretely, if the cameras are photographing along different but parallel planes, then they won’t see each other.
    - Denvercoder9 2y ago
      Your solution works in a geometric world, where light propagates in a perfect straight line of infinitesimally small width. That's not true in reality, where light propagates in an ever-expanding cone. More concretely, you can have two cameras photographing along different but parallel planes that do see each other.

amluto 2y ago

I'm not sure what the issue you're describing is. If I have two devices, each with a camera and a line of marks, if they can each see each other's marks, then they are aligned to within the horizontal spread of the camera pixels. There are no lasers involved -- the marks can be paint, stickers, blinking wide-angle LEDs, etc. -- my suggestion to use blinking LEDs is just so that's it's more obvious when one is in the field of view of the camera.

Denvercoder9 2y ago
You don't just need the cameras to see each other, you need them to be perfectly parallel to each other as well, as otherwise they're photographing along a different plane, which may give conflicting results.
- amluto 2y ago
  Suppose camera A has line L_A on the camera. A’s optics and marks are both on L_A, so A’s image plane contains L_A and camera B’s image plane also contains L_A (you know the latter because you’ve aligned the cameras so camera B sees L_A). And vice versa: camera A sees L_B. In 3D Euclidean space, two distinct lines define a plane, and both camera’s are photographing planes that contain L_A and L_B, so both cameras are photographing the same plane. More concretely, if the cameras are photographing along different but parallel planes, then they won’t see each other.
  - Denvercoder9 2y ago
    Your solution works in a geometric world, where light propagates in a perfect straight line of infinitesimally small width. That's not true in reality, where light propagates in an ever-expanding cone. More concretely, you can have two cameras photographing along different but parallel planes that do see each other.