My final year project at Sussex is about teaching neural networks to read the light scattered by droplets in a spray. My supervisor is Cyril Crua, who has spent over twenty-five years developing optical measurements for fuel sprays and other multiphase flows. The technique we are building on is called Phase Rainbow Refractometry, where every droplet crossing a laser beam carries a tiny rainbow that encodes its temperature and size, and the difficulty is extracting those numbers fast enough to be useful, which is where the deep learning comes in.
The measurement problem
Sprays turn up anywhere engineering cares about heat and mass transfer, in fuel injectors, spray dryers in pharmaceutical plants, and agricultural nozzles, and in most of them the quantity you actually want is the evaporation rate, since how fast the droplets shrink controls mixing, combustion, and coating quality.
The trouble is measuring inside a dense spray. The workhorse instrument, phase Doppler anemometry, sizes droplets one at a time as they cross a pair of laser beams, which works well while the spray stays dilute, but in a dense spray the light scattered by one droplet gets scattered again by its neighbours before it reaches the detector, and the single-droplet assumption underneath the measurement falls apart. That happens worst in the near-nozzle region of a real injector, which is exactly the part a measurement most needs to reach. And even where phase Doppler does work, it only measures size and velocity, with nothing about the temperature that drives the evaporation in the first place.
Phase Rainbow Refractometry
When a laser hits a transparent droplet, some of the light enters it, reflects once off the far side internally, and leaves again, concentrating near a specific angle known as the rainbow angle. Two useful things are encoded there. The position of the rainbow peak depends on the droplet's refractive index, which varies with temperature, and the fine fringe pattern superimposed on the peak has a spacing that depends on droplet size, so the one signal carries temperature and size together.
Phase Rainbow Refractometry, introduced by Yingchun Wu and collaborators in 2016, is the part that got me interested. With a fast line camera recording the rainbow, the phase of the fine ripple structure can be tracked over time, and its shift varies linearly with the change in droplet diameter, which resolves diameter changes down to tens of nanometres at sampling rates in the tens of kilohertz, far smaller than anything a camera could see directly. A droplet shrinking too slowly for any imaging system to notice still shows up in the phase, and the result is a direct, time-resolved measurement of evaporation rate for individual droplets.
The inverse problem
Getting numbers back out of a rainbow signal is an inverse problem. The forward physics is Lorenz-Mie scattering theory, an infinite series that converges slowly, and the usual approach is to fit it, or one of its approximations, to each measured signal iteratively. That is fine for a single droplet in a lab, but it gets painful when a high-speed camera is producing tens of thousands of frames a second from a spray full of droplets, and in practice the fitting needs manual supervision and per-case tuning as well. There is also a second bottleneck sitting in front of that one, because conventional processing starts by isolating each droplet's rainbow from the image, and in a dense spray the rainbows overlap.
My project skips the isolation entirely. The aim is a model that takes the full one-dimensional spray image and returns a pixel-wise refractive-index profile across it, which can then support temperature, composition, and evaporation-rate analysis over the whole spray field instead of droplet by droplet. Training data is its own problem, since there is no way to get pixel-level ground truth from a real spray, so training will lean on synthetic signals generated from Lorenz-Mie theory, checked against real measurements from a droplet generator rig where the conventional processing chain can still provide a trusted answer.
There is some encouraging prior work here. A ResNet-based model published in 2024 inverts standard rainbow signals about three times faster than theoretical fitting with comparable accuracy, but as far as I can find, nobody has published deep learning applied to the high-speed phase measurements of PRR specifically.
The choice
I got to engineering through software, and most of my time outside the degree goes into shipping production systems, but until now the two have mostly run in parallel. This is the first piece of work that needs both at once, where the physics sets the constraints and a wrong prediction is a wrong temperature, so the software has to hold up against a method that already works, just slowly.
The machine learning side goes back further than the degree, too. Around GCSE I was writing small neural networks from scratch in Python, mostly to understand what a forward pass actually does, and this project takes that interest somewhere with real physics in the loop, towards physics-informed models and architectures like Kolmogorov-Arnold networks that learn from Lorenz-Mie scattering rather than from a benchmark dataset.
The project runs through my final year, and I will write up how it goes here.