2D Reflector Simulator

Flashlight Modding and DIY Parts
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I have built on Desmos a simulation for the beam of light produced by a circular emitter in a parabolic reflector. This is an exact simulation that should work for any set of parameters that is physically possible: no small-angle approximations or other simplifications.

Details are written up in the simulation itself, so I will include here just two technical notes.

  1. I have built this simulation for a 2D world because in 3D, the math quickly becomes overwhelming. Since the laws of physics are slightly different in 2D (e.g., many things are proportional to length rather than area), the relative intensity figures in the simulation cannot be expected to be accurate to what we would measure in a 3D world.

However, the geometrical features in the simulation, such as hotspot/corona/spill angle predictions, can be expected to be representative of their 3D counterparts, if one believes that the essence of the beam profile can be captured by a thin slice of the reflector along a diameter.

  1. I was unable to generate an angular beam profile plot from the prediction, for a Desmos-specific technical reason; as a result, simulation data must be manually captured. The issue stems from my using Desmos’s built-in linear regression solver as a solution finder for equations. This regression solver can only accept and output specific numerical values, and cannot output a function of a variable input.

If someone figures out a way to automatically generate an angular intensity plot (represented as the variable I_N in the simulation), please let me know!

For now, I have manually captured simulated data for 3 setups, so that you all can play around and compare, if you happen to own one of the setups.

Setup 1: S2+ SFT42R. S2+ SFT42R 2D simulation | Desmos

Setup 2: S6 SFT25R. S6 SFT25R 2D simulation | Desmos

Setup 3: C8 SFT42R. C8 SFT42R 2D simulation | Desmos

Enjoy, and please let me know what you think, especially if you think you’ve discovered a bug, or have ideas to make it more user-friendly!

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Updates: here is an alternate version that gives a visual breakdown of the entire beam and outputs hotspot/corona/spill angles as its primary purpose. Check it against your lights and see how well it does!

Also patched some minor bugs in the original version: it turns out that extremely deep reflectors and extremely large emitters generate second- and higher-order reflections not captured by the simulation. The patch added a parameter checker to alert the user should this occur.

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Also a helpful tool I like to use:

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I love this and have been using it to check stuff before making my own simulator! I wish it had an option for (1) numerical inputs/outputs and (2) beam breakdown as distance tends to infinity. My simulation aims to address these two missing pieces.

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