The time derivative of a transit light curve during ingress or egress is a Radon transform of the planet's attenuation map, so a single transit gives at most two Fourier-space slices and a large null space.
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A Radon-Transform Perspective on Exoplanet Transits
The time derivative of a transit light curve during ingress or egress is a Radon transform of the planet's attenuation map, so a single transit gives at most two Fourier-space slices and a large null space.