![]() ![]() The best focused spot for a camera lens is called the Airy disk:į is the focal length, is the wavelength, and d is the diameter of the lens. Even a perfect lens convolutes images, as they have unique diffraction patterns. Deconvolution is very important in astronomy, since all data comes from optical based systems. A perfect PSF is impossible to determine, so accounting for this function requires good approximations (4). Extracting the pure image is much more difficult since every blurring variable needs to be taken into account. This requires an understanding of the blurring function, which requires understanding the system that is causing the distortion. Deconvolution is the reverse process, in which you have a convolution and you want to extract the desired image. ![]() Convoluting two functions is simple since the individual functions are known. This function is also called ‘point-spread function’ (PSF). The file name is called ‘Update’.Ĭonvolution has applications in imaging, in that a blurry image is simply the convolution of the image and a lens or instrumental function. ![]() If you are not using a Mac, please open the file from the Google Drive folder located at the end of this post. If, then through both methods I yield this plot: A Fourier transform of a Fourier transform is not necessarily the same as the inverse Fourier transform of a Fourier transform. I should have used the ‘InverseFourierTransform’ function instead. When I computed the convolution the long way by taking the Fourier transform of the product of Fourier transforms, I used the ‘FourierTransform’ function. That may be so with relatively obscure functions, but I was wrong in my example. I concluded in my preliminary data post that the ‘Convolve’ function has its limitations and will not work properly with complicated functions. ![]()
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