In the near future, next-generation telescopes will be able to observe Earth-like exoplanets illuminated by their parent stars for long periods of time. As the distance between exoplanet and observer is enormous, exoplanets will only make up a pixel on our image. However, the observed intensity of this pixel will fluctuate over time as the exoplanet rotates about its axis and orbits around its parent star. These fluctuations in the reflected light contain information about the planet’s surface. Previous researchers have developed a retrieval method known as spin-orbit tomography which uses these intensity fluctuations to construct a surface map of the exoplanet assuming fully diffuse reflection as a model for the reflection of starlight. In this thesis, we aim to build on this method by introducing two new reflection models, namely Fresnel and Lommel-Seeliger reflection, and by using this composite reflection model for the starlight we attempt to reconstruct the surfaces of exoplanets based on their observed light curve. We will derive an analytical expression for the observed intensity of the light reflected off an exoplanet. Next, we will simulate intensity observations along the orbit of an exoplanet with a pseudo-randomly generated surface containing terrain types found on Earth.
As we assign a measure of reflectance for each reflection model, we will construct three distinct reflectance maps for one planet, nd simulate the observed light curve by linearly transforming these maps. Afterward, we attempt to retrieve the reflectance maps from the observed signal by inverting the transformation.
We show that the retrieval of all three maps is successful if the light curve is observed without noise, even when the number of samples is low. If artificial shot noise is imposed on our signal, we are still able to retrieve glossy reflectance maps for Lambertian and Lommel-Seeliger reflection by truncating the transformation matrix. Lastly, we show that even if the original light signal originates from an exoplanet that only reflects according to the Lambertian model, then the composite reflection model still retrieves the Lambertian map accurately. On the other hand, if the original light curve is simulated by the composite reflection model, then the Lambertian method does not retrieve an accurate surface map.