David Grant (smartly not on social media) did an amazing job with this work. I have been dreaming of doing transmission mapping since 2016, but I never got past the hard maths & coding stage. Enter David! He came in with the idea himself & quickly started on how to make it work🙏

This work involved a LOT of maths & new methods David Grant found to make computing Transmission strings fast & precise taking into account other aspects of transits such as limb-darkening. The paper contains 42 equations, resulting in a behemoth table of symbols in the appendix

Harmonica is also incredibly precise! Using a 5-term Transmission string for a typical
@NASAWebb
transit lightcurve (yes we already have typical #JWST lightcurves) & assuming ~1% deviation from a circle Harmonica is orders of magnitude more precise than expected JWST noise floor

Harmonica can calculate transmission strings in fractions of a second and can infer the shape of an occulting object directly from the transit lightcurve in less than one second for any dataset with less than 100,000 data points 🤯 (BTW that is insanely fast 🏎️)

The deviations from a circle can be plotted - here we show the 3000 different transmission strings computed to fit our #JWST-like lightcurve. The degree of change as a function of the angle around the object can tell you about the changes in a feature measured at that wavelength

We tested the idea of Transmission Strings by considering a planet measured with a
@NASAWebb
like transit light curve (465 data points🧐) injecting a shape w/ East/West differences & equator/pole differences. We fit for a 5-parameter string using Harmonica & recover the shape!

For this work David Grant developed a Transmission strings open source package called Harmonica https://harmonica.readthedocs.io/en/latest/
From this you can compute transit lightcurves for irregularly shaped occulter (not just planets!)