Problem 1: Simulating Optical Density Measurements¶

Assume bacteria are shaped like spheres of a certain radius $r > 0$. Further, assume that if light hits a bacteria, it is scattered into a random direction.

Write code that allows you to:

  1. Initalize a certain number of non-overlapping spheres in a 2D volume of size $1 \times 1$. Make sure that spheres do not overlap.
  2. Simulate scattering of light by following ray traces emitted form the left in parallel.
  3. Simulate capturing of these traces through a hole of size $h > 0$ within distance $\ell > 0$ to the testing volume.

Experiment with:

  1. The OD that you measure as a function of the number of spheres.
  2. Think of experiments for $r$, $h$, and $\ell$ and what you would expect. Then test your hypothesis.

Limitations:

  1. What are limitations of our simplified model?