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# 1 The Inspiration

It has always amazed me the way the light interacts with the environment, so for this project my plan was to play with some of these interactions to create an interesting XMAS light show. My inspiration to develop this project was the observation of caustics generated by the surface of the water at the bottom of the swimming pool. So what are caustics? Here there are two examples:

Caustics are the envelope of light rays through either refraction of reflection, that causes patterns of concentrated light as seen in the images. In the first image the light "statically" bends when it refracts in the glass. In the second image the pattern is dynamic as it is affected by the water surface. Caustic patterns are notoriously visible when the light comes from a point source or is collimated, which is the reason why the sun generates sharp patterns when interacting with the water surface (when its not covered by clouds).

# 2 The Design

## 2.1 Layout

I tried a couple of approaches on how to achieve an effect similar to the one caused by the sun and  water surface interaction. As I wanted the pattern to be dynamic, I decided that I would need to use liquid to generate the pattern, so I used water. There are different ways light could be used to illuminate the water surface, Initially I thought about using a light over the surface (A), under the surface (B) and under the transparent recipient that holds the water (C). Ideally I wanted to illuminate the ceiling and the walls, so illumination would have to be under the water surface or under the transparent recipient. Keeping light under water requires water proofing, so I discarded it. To illuminate from the bottom of the recipient I would have to hang it or build a structure that could hold the recipient and leave space for the light, so I discarded those solutions as well. Finally I decided to illuminate from the top to a submerged mirror (D), this would also have the effect of increasing the caustic effect as light would have to cross two times the water surface.

## 2.2 Illumination

As explained before, without divergent (point source) or collimated light the caustics degrade considerably and their edges get blurry. In my first attempts I tried some high power small LEDs, but the results were mediocre. The closer the LED illuminated the water surface, the bigger the solid angle, and the less it acted as a point light source, leading to blurry caustics. Moving the LED farther from the liquid surface decreased the solid angle, but increased the light leak (light that does not hit the water surface). The alternative of course was to use lasers, as they are collimated. Initially I tried inexpensive 5 mW lasers and they produced very sharp edged caustics, but there were two drawbacks to this approach, light was very faint (as the lasers were low power), and the projected caustic was small, (as collimated light does not diverge). Finally I figured out that I needed more powerful lasers, so I removed some from DVD drives. These lasers could be used at 400 mW and without a collimator, they projected a divergent beam, making the projected caustic effect much bigger.

## 2.3 Liquid surface agitation

Caustics can be observed in swimming pools when water is agitated, usually by swimmers or the wind. If water stands still, caustics disappear and as my project would not have wind or swimmers to agitate the water I had to look for alternatives. I found that blowing the water surface with a fan would produce long wavelength waves, which would require me to build everything in a bigger scale. To keep everything small I decided to use a 12 W salvaged PC speaker and a small recipient which was placed over it. This also allowed me to tightly control the water motion by sending any kind of signal patterns to the speaker, which in turn allowed me to produce interesting effects like standing waves or pulsed water motion.

## 2.4 The Circuit

The circuit is pretty straightforward and very inefficient, but it was relatively fast to build with components I had at hand. The circuit was built for an ESP32 microcontroller, some advantages of this microcontroller are that it is very fast, can source or sink up to 40 mA, and has a very fast and customizable PWM which allowed me to set it to 5 khz and 13 bits of resolution. One not so great feature of the microcontroller is that its DAC has 8 bits of resolution and is relatively slow, still both constraints did not have any negative impact in the project.

Some notes on the circuit:

• There is no decoupling between the DAC and the NPN base, this allowed me to generate signals up to sub-Hz frequencies. It also had the detrimental effect of reducing the effective DAC resolution as 0.7 V of the full 3.3 V swing could not be used because of the base-emitter voltage drop.
• Even though the speaker is driven by DC and current flows all the time (unless the transistor is shut down), the speaker power rating is far higher than the power its dissipating.
• Lasers are driven at around 400 mW with PWM signals at 5 khz.
• The maximum power consumption is around  3 W

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## 2.5 Getting everything together

As the liquid recipient I used a small lens that I salvaged from a projector.  As it can be seen, it is very shallow, and this gave me greater flexibility at choosing the illumination angle. The mirror was also salvaged from a projector and glued to the recipient (lens) with hot glue.

The 3 laser diodes were glued together with hot glue and fixed to the speaker through a PC power supply cable braid. As expected, this was far from the ideal solution, but I would not have finished the project in time if I spent more time in holding the lasers more firmly.

# 3 Results

As this project relies on the physiology of the visual system, the photos or the film look quite different to how the light effects are perceived by a human. More specifically, the dynamic range of the eyes is far higher than that of the camera, doesn't produce aliasing or flickering effects and doesn't struggle to focus correctly. At to all this that Youtube's agressive compression is very mean to red monochromatic videos. So to put it simple, the light effects look far better through the eyes than through the camera.

## 3.1 Standing waves

Standing waves occur as waves get reflected back and forth when they hit the recipient border. This effect occurs only at specific resonant frequencies and produces beautiful light patterns as it can be seen in the images and videos (which sadly don't look like the real thing). The small points that move around in the first video are floating dust particles. The second video shows how these floating particles move within the recipient.

## 3.2 Chaotic stationary waves

When some conditions are met, the standing waves don't converge to a defined pattern, instead the pattern keeps changing in a chaotic way, producing at the same time higher spatial frequency patterns, as it can be seen in the image and video.

## 3.3 Laser modulation

The reason that I used 3 lasers connected to 3 PWM outputs was to individually control them to produce visually appealing effects. In the next video I controlled the intensity of the 3 lasers sinusoidally, and at the same I constantly modified their phase difference.

## 3.4 XMAS Illumination

Here we can see how the illumination blends with the Christmas tree.

# 4 Closing Words

I had this project in mind long ago, but this Project14 was a good excuse to actually develop it. The complete project was developed in 4 days, which did not give me much time to play with the system. I found that the generated patterns are affected by multiple factors such as intensity of the vibration, the amount of water, its viscosity, the form of the recipient, etc. There are probably many interesting effects that could be achieved through the manipulation of the lasers and the water, I just scratched the surface of the possibilities. This idea could be extended further in many different ways, more colors, more lasers, different pointing directions, different layouts, mirrors, lenses, etc, I hope the project inspires others to develop interesting light effects.