Why are there moving lights at the bottom of swimming pools? Here comes the Transport of Intensity effect.

Jan 1, 0001

Have ever noticed this typical network of bright-and-dark areas on the bottom of a swimming pool?

You certainly observed that its variations were correlated to how much the water was agitated by swimmers or divers.

But why does this happen? And how can we use this for scientific applications?

Let me show you.

Why do water waves generate a bright and dark network in the swimming-pool

Here is a simplified illustration of the phenomenon using geometrical optics:

Due to refraction, rays of light will converge or diverge depending on the curvature of the change in refractive index between two mediums: air and water for example.

When they converge, the intensity is higher, hence the bright lines. When they diverge, intensity is lower, hence the dark areas.

This is similar to what you can observe with a magnifying lens. Light is concentrated by the lens, enough to set fire to a piece of paper or your skin (don’t burn yourself!).

The waves at the surface of the water act as a multitude of lenses.

If the water is perfectly still, you won’t see any pattern on the bottom of the swimming pool before the surface is flat and there are no differences in light condensation.

You can observe other manifestations of the transport of intensity phenomenon in daily life: see how the view through your windows is deformed when rains fall for example.

But let’s dive a bit deeper into this phenomenon to understand how it works and how we can use it.

The Transport of Intensity phenomenon: a simplified theory

You may have learned that phase is not detectable unless you produce interferences. This typically requires a coherent monochromatic light source like a laser.

*So how can transparent objects generate intensity patterns from incoherent plurichromatic light like the sunlight? *

The theory behind this common phenomenon has been established in 1982 by Teague. It is named the Transport of intensity (TIE) theory.

The TIE equation can be simplified in certain conditions like that:

OK, maybe you don’t find it simple, so let’s make it easier.

Variation of intensity along the direction of illumination = Intensity x the map of refractive index (density of matter).

Let’s try to make it even clearer with our initial question.

We are back at the swimming pool.

The sunlight goes through the air down to touch the surface of the water. In the air, the density is roughly the same (thankfully! I would be uncomfortable to start suffocating depending on where we are).

Thus, the TIE tells us that the intensity variation is 0 (the ∇x,yΦ stuff is 0 on the right-hand side of the equation).

Nothing much happens. (In reality, things happen and that’s why stars are sparkling. Same phenomenon. But let’s stay focused on the swimming pool, shall we?)

When the light reaches the surface of the water, it will experience differences in refractive index due to the high density. If the water is still, nothing much happens either.

The light will travel the same way at each point of the swimming pool and the variation of intensity will be 0 again.

But now that you are swimming (or this kid over here jumps into the water, again), there are waves. So the height of water travelled is not the same depending on where the light enters the water.

Now the variation of refractive index is not 0 anymore, hence the variation of intensity.

That’s why you see this network of shadows and lights at the bottom of the swimming pool.

You’ll never look at a swimming pool the same way now!

But apart from making you smarter in front of your partner or friends at the next dinner or beer party, why does it matter?

Because they are actual applications. I will mention one in the field of life science so you get an idea (and brag even more about your deep scientific knowledge).

Application of the Transport of Intensity to life science

Biological objects are composed of water.

A lot of water: 70% of the mass of each cell composing your body.

When observing unique cells to study them (cell biology), scientists, including me, have to face their transparency.

We struggle to see them. Almost invisible. It doesn’t help us do our job.

So we have to find ways to make them less invisible. There are many methods such as using fluorescent molecules that emit light after exposure to specific illumination.

But it comes with lots of drawbacks and we don’t get all the information we want.

There is another way: using our knowledge of the physics of light to make them more contrasted.

The most commonly used methods are phase contrast or differential interferential contrast (DIC). These are very useful methods based on the work of Zernike who won the Nobel prize for this. Smart guy.

We may not be as smart, but we go to the beach or the swimming pool (take that Zernike!). And we are good observers.

We know that the waves of water generate contrast in intensity, even if the water is as transparent as before.

That’s really cool because biological cells also have “waves” inside them. They have organelles, a nucleus and a lot of stuff that are more or less dense.

This means that we should see a network of shadows and light if we observe carefully.

The difference is the scale. The waves are much smaller. Hence the variations of intensity. Thus, if you collect the intensity of light that goes through a cell, you don’t see the pattern of shadows.

But we can use the TIE equation and measure finely the variations in intensity to recover the variations of refractive index (or density or mass) inside the cells.

That’s the solution: measuring the intensity at different locations along the axis of illumination and compute the map of cellular waves.

The computations are a bit complicated to be shown here, but if you are interested, you can have a good read of this paper by Bostan et al. (This link looks weird but it is safe, don’t worry).

This has been used by scientists to study the evolution of cell density during the cell cycle in yeastfor example.

There are more applications coming, so stay tuned!

Conclusion

Observing how light behaves in a swimming pool brought us to a deeper understanding of the physics of light and how we can use it to study the living matter.

From the sun to the beach to the lab.

Fun stuff, right?