On Monday, January 31, 2022 at 7:51:23 PM UTC-6, RichA wrote:
> https://phys.org/news/2022-01-universe-sharper-focus-algorithms-supercomputers.html
<
If one knew the precise PSF (point spread function) associated at each pixel* in the image,
there are correlation(*) algorithms that can remove even the diffraction effects converting
the typical Airy 2-D wave into a Lawrencian spread function. The problem is that the calculations
are "very time consuming". Requiring a 2-D Fourier Transform, a height×width conjugate multiply
for every pixel in the image, and an 2-D inverse Fourier Transform. height×width is the size where
the PSF function is greater than ¼ the noise level in that area of the image.
<
If the PSF is identical across the whole image (like from a Three Mirror Anastigmat) this
calculation can be performed with a 2-D Fourier transform, a conjugate multiply, and an
inverse Fourier transform.
<
* the PSF is identical at each radial offset from the center of the image.
(*)Correlation is a close relative of convolution.
<
I used to do this kind of stuff for an fast sweep NMR machine just out of college more
than 45 years ago in 1-D. For a 4096×1 pixel "image" the calculations took more than
7 seconds on a Sigma 5 minicomputer. When setup correctly, we could correct even the
phase of the detector and remove the oscillations of the resonant exponential decay.
This allows us to take (thousands) of images (sometimes hours), add them up, and the
make the image "look" like the sweep took infinitely long (no ringing). A PSF in in the
same class of data/image as a ringing Lawrencian line.
<
But still, you cannot improve the image more that the Lawrencian without inducing ringing,
but you can add other filtering functions to the calculation almost for free.