Étendue’s Final Battle

Dear optical wizard, the time has come! Do you have what it takes to take out evil Étendue once and for all?

After wrestling étendue for longer than you can remember, you meet him for one final battle. You come prepared: You use your new laser wand upgrade to send a powerful, perfectly collimated beam toward his wand to take it out for good. Unfortunately, evil Étendue expected this, and came with the same upgrade. The power from your two beams meet in the middle and magically form an intensely glowing ring situated in a ball of smoke.

You both exert your maximum powers to push the magical glowing ring towards the opponent, which makes it move back and forth during your duel.

Your one remaining spell is your final hope to land the victory: You can cast mirrors of any geometry into existence. With these mirrors, you can capture the intense glow from the magical ring and send it onto evil Étendue's wand to overheat and destroy it.

Unfortunately your powers are wearing down from the intense battle, and you only have the energy to cast your optical design spell once. This means that your fixed optical system must be able to redirect the light onto evil Étendue’s wand from every position of the glowing ring.

Your weakened spell also has a limited reach. It can only create mirrors in the corridor of air between the two of you: a box that rests on the floor of the hall, stretches out to the far ends of both of your wands, and is 4 000 mm across.

The challenge

Create a fixed specular mirror geometry that redirects as much power as possible onto evil Étendue's wand, from all possible source positions.

System geometry

The optical axis is $z$. The centres of both cylindrical wands lie on this axis, and the source surrounds it at different positions along the optical axis. The inner tip of your wand is at $z=-5\,000\,\mathrm{mm}$; the inner tip of evil Étendue’s target wand is at $z=+5\,000\,\mathrm{mm}$. The five source positions are $z \in \{-1\,000,-500,0,+500,+1\,000\}\,\mathrm{mm}$, with the origin at the centre of the middle source position, halfway between the two wands.

The reach of your spell

Your mirror-casting spell has a limited reach in the duelling hall. Every part of your geometry has to sit inside the dashed box in the figures above, measuring 4 000 mm wide × 4 000 mm tall × 12 000 mm long:

• $-2\,000\,\mathrm{mm} \le x \le +2\,000\,\mathrm{mm}$
• $-1\,500\,\mathrm{mm} \le y \le +2\,500\,\mathrm{mm}$ (floor to ceiling)
• $-6\,000\,\mathrm{mm} \le z \le +6\,000\,\mathrm{mm}$ (between the outer ends of the two wands)

Note that some CAD tools and STL exporters shift the geometry so that all coordinates are positive, placing the corner of its bounding box at the origin. If your design appears offset in the upload portal, you can use the position controls to move it back into place, or export to STEP, which preserves the original coordinate system.

The source

The power from the two laser wands forms a Lambertian glowing torus with major radius 100 mm, minor radius 5 mm, and constant radiance 1 W cm⁻² sr⁻¹ (total power: 620 W). The torus is perfectly absorbing, so light that later returns to it is lost.

Smoke model

The torus is centred inside a spherical smoke volume of radius 200 mm. While a ray is inside the sphere, the distance to its next scattering event is sampled from an exponential distribution with mean free path $\ell=100\,\mathrm{mm}$.

Scattering is isotropic: at every scattering event, the ray leaves in a uniformly random direction, independent of its incoming direction.

To help you get started, below are instructions for setting up this source surrounded by smoke in common optical design software packages. Alternatively, you can download a ready-made model from Getting started.

The target

The laser wands are perfectly absorbing cylinders with radius 20 mm and length 1 000 mm, centred on and oriented along the optical axis. Power intercepted by any part of evil Étendue’s wand, including either circular end, counts towards your score. Your own wand absorbs whatever hits it, but that power is not counted.

Optical evaluation

Optical evaluation is performed by sampling rays from the torus source at each source position, propagating them through a scene containing the torus, the surrounding sphere of smoke, the laser wands, and your provided geometry. The power carried by the rays that land on evil Étendue's wand is then summed up.

Light can be reflected back to the ball of smoke where it will again be scattered by that smoke, but if it reaches the magical ring it will be absorbed and lost.

Submitted surfaces are ideal specular mirrors with 95% reflectivity. Both cylindrical wands are perfectly absorbing. Each ray carries its remaining power after mirror losses when it reaches a wand.

Merit function

The performance of your optics is decided by how it performs at its weakest point: evil Étendue only needs one weak point to be able to escape your attack and you must prevent him from finding such a weak point.

The optical power on evil Étendue’s wand is calculated independently for each of the five source positions. The competition score is the lowest of those five powers. Power is reported in watts, and higher scores are better.

Specific rules

• You will not be able to redirect the original collimated light from the laser wands (it is so powerful that it would immediately burn a hole in your optics). Your optics work purely on the light emitted from the magical glowing ring.
• Submitted surfaces are ideal specular mirrors with 95% reflectivity.
• Your optic-casting spell is limited to mirror files smaller than 100 MB.

Instructions

1. Design your optical system using any optical design or CAD software of your choice, keeping it within the reach of your spell.
2. Export your design as an STL or STEP file, no larger than 100 MB.
3. Upload the file in our online portal and get an immediate score for your design.
4. Sign in with your email address and submit your design. You may submit as many designs as you like; the best one counts.

Submission deadline: April 1, 2027

Getting started

To help you get started, we have prepared models of the competition setup for common optical design software. Each model contains the glowing torus, the smoke, both wands and a simple test reflector, so you only have to replace the test reflector with your own design.

Are you ready?