Motivation

Due to the challenging environment found on the moon, the sunlight alters the uppermost surface. One change that has been observed is the formation of iron particles in the rim of the minerals. Their influence is quite prominent in the spectral response in the near-infrared region since it both darkens and reddens the spectrum, and we also see a lack of absorption features. There has yet to be much study regarding their distribution in the rim since we mainly have 2D images using transmission electron microscopy.

This thesis aims to find a way of reconstructing an approximate cluster using those 2D images. One method would be to generate a cluster using fractal algorithms, such as FracVAL. Creating a cluster with a known fractal dimension and taking its cross-section would represent a 2D TEM image. The idea is to train a model and estimate the fractal dimension using only 2D information from a TEM. We can first look at generating multiple clusters and see if any statistics pop out. The model can then be statistically driven and implemented through, let's say, old-school methods, or we can look into utilizing neural networks/tokenizers (used by LLMs such as ChatGPT and so on).

Outline

The main goal is to reconstruct the 3D spatial distribution using a 2D image of a cross-section. A potential approach would incorporate:

1. Generate clusters using a fractal particle aggregation algorithm. Some frameworks will be provided.
   https://github.com/aetherspritee/PyFracVAL

2. Build a pipeline to read cluster data and create cross-sections of those. Substantial here: not every cross-section is usable since sparse clusters (not dense) do not yield “nice” data. Some bias here is welcomed!

3. Transform the cross-section “image” into a suitable data format for further processing, such as a list of all centers (x,y) and the radius of the circle.

4. Process the data with a framework to get statistical information and find a potential correlation between it and the fractal dimension.

5. Derive the information about the cluster using both “old school” and new methods. This includes Neural Networks/Tokenizers, Support Vector Machines, k-means, and nearest neighbors.

6. If possible, get some insights into how TEM images are made, what makes the contract, etc. We can get data from our colleagues at Münster University and try to apply the approach to actual data.