Abstract
Due to Fourier transforms nature between the field detected on the image and its corresponding input, astronomical imaging can be modelled mathematically. In exoplanetary imaging, we aim to detect exoplanets whose typical contrast are approximately one over a million times dimmer compared to their parent stars. Among the possible approaches to accomplish that is optical apodization, a technique to purposely modify the input signal profile such that the ‘Airy rings’ on the resulting image are suppressed while keeping the central brightness high. In the paper, we pedagogically describe this technique applying Fourier transforms of radially-symmetric functions; and investigate potential future uses at Timau National Observatory.
Highlights
The existence of worlds other than the earth has always been a great interest for humankind
Due to Fourier transforms nature between the field detected on the image and its corresponding input, astronomical imaging can be modelled mathematically
We aim to detect exoplanets whose typical contrast are approximately one over a million times dimmer compared to their parent stars
Summary
The existence of worlds other than the earth has always been a great interest for humankind. The first detection of an exoplanet around a Sun-like star follows not so long after, using radial velocity method. Mayor and Queloz observed a periodic variation on the radial velocity of 51 Pegasi Another detection method is called transit method, first performed by Charbonneau et al, which measures periodic dimming of the starlight during the planetary transit across the host star [2]. When a function in the pupil plane has a circular symmetry, so does its resulting image, since they are related through Fourier transforms and Fourier transforms preserve the symmetry If this is true, suppressing 360 degrees of starlight halo would require patterns with circular symmetry, which suggests the use of polar coordinates. Plugging equation (2.8) into (2.7), we get the general expression of Fourier transforms in polar coordinates. We refer Fourier transforms for radially symmetric functions as Radial Fourier Transforms (RFT)
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