I read that Fourier transform is a mathematical tool to deconstruct a wave taken from a source into basic sine and cosine waves, since visible light coming from the M87 accretion disk will be obscured by the dust and gas but radiowave will penetrate easily through all that with ease. My question is why is it necessary to process the image of M87 using Fourier transform? particular what information do we hope to get from the processed image? I doubt it will improve the resolution or to turn it into false colour image right?
When an optical lens focuses light, it converts the incoming wave front into an image by performing a Fourier transform. See: Lens as a Fourier Transform Engine. With radio telescopes, there is no "lens", so, to obtain an image, a Fourier transform must be performed on a computer.