Strange FFT spectrum of background noise

[jumpfunky]

Dear list,

I currently have some TEM images with a strange background noise pattern
(background.png). It seems to be "red shifted" noise.  White noise
exhibit the same power for each frequency. Red shifted noise exhibed
lower power for higher frequencies. You can reproduce this kind of
background noise if you create a x*y image, then add gaussian noise and
upscale (bilinear interpolation) it to a (3*x)*(3*y) image. So my guess
is, that the TEM camera simply upscale lower resolution to a higher
resolution image.

But there is one discrepancy:
The fft spectra of these simulated image (spectrumSimulated.png) is
different from the fft spectrum of the background of the TEM image
(spectrum.png). The TEM spectrum shows a radial symmetric sinc pattern
whereas the simulated spectra shows a rough sinc pattern in x and y
direction.

Any idea which interpolation technique can produce this radial symmetric
sinc pattern in the fft spectrum?

Another idea: The sinc function is an ideal reconstruction filter. It is
possible that the camera simply apply a reconstruction filter which
leads to this kind of fft spectum?

Cheers,
Thorsten

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[Zack Gainsforth]

Hi Thorsten,

[I hope I haven’t misinterpreted your question!]

It looks like you have taken a TEM image at a fairly high resolution of an amorphous material.  The FFT you are seeing is the contrast transfer function of the microscope (CTF).  I suggest you look in the book Transmission Electron Microscopy by Williams and Carter, or a similar book for a detailed explanation.  Essentially, the optics column of the microscope acts as a filter transmitting only specific spatial components of the image.  This is normal and part of the TEM design.  By changing your focus, you will change the frequency components to which your TEM is sensitive.  It is a good thing, and using the radial symmetric FFT you see, you can remove astigmatism, ensure you have perfect focus, and select which frequencies you are imaging.  There is a ton of detail about this in any study of HRTEM, so I’ll stop there...

Cheers,

Zack


On Jan 16, 2015, at 8:57 AM, Thorsten Wagner <[hidden email]> wrote:

Dear list,

I currently have some TEM images with a strange background noise pattern
(background.png). It seems to be "red shifted" noise.  White noise
exhibit the same power for each frequency. Red shifted noise exhibed
lower power for higher frequencies. You can reproduce this kind of
background noise if you create a x*y image, then add gaussian noise and
upscale (bilinear interpolation) it to a (3*x)*(3*y) image. So my guess
is, that the TEM camera simply upscale lower resolution to a higher
resolution image.

But there is one discrepancy:
The fft spectra of these simulated image (spectrumSimulated.png) is
different from the fft spectrum of the background of the TEM image
(spectrum.png). The TEM spectrum shows a radial symmetric sinc pattern
whereas the simulated spectra shows a rough sinc pattern in x and y
direction.

Any idea which interpolation technique can produce this radial symmetric
sinc pattern in the fft spectrum?

Another idea: The sinc function is an ideal reconstruction filter. It is
possible that the camera simply apply a reconstruction filter which
leads to this kind of fft spectum?

Cheers,
Thorsten

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ImageJ mailing list: http://imagej.nih.gov/ij/list.html
<spectrum.png><background.png><spectrumSimulated.png>

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[Divakar Ramachandran-2]

Phil Fraundorf shows some examples of simulation of images of amorphous
films and their power spectra at
http://www.umsl.edu/~fraundorfp/epc/index.html.

HTH,
Divakar



Zack Gainsforth wrote on Friday 16 January 2015 11:30 PM:

> Hi Thorsten,
>
> [I hope I haven&#8217;t misinterpreted your question!]
>
> It looks like you have taken a TEM image at a fairly high resolution of an amorphous material.  The FFT you are seeing is the contrast transfer function of the microscope (CTF).  I suggest you look in the book Transmission Electron Microscopy by Williams and Carter, or a similar book for a detailed explanation.  Essentially, the optics column of the microscope acts as a filter transmitting only specific spatial components of the image.  This is normal and part of the TEM design.  By changing your focus, you will change the frequency components to which your TEM is sensitive.  It is a good thing, and using the radial symmetric FFT you see, you can remove astigmatism, ensure you have perfect focus, and select which frequencies you are imaging.  There is a ton of detail about this in any study of HRTEM, so I&#8217;ll stop there...
>
> Cheers,
>
> Zack
>
>
> On Jan 16, 2015, at 8:57 AM, Thorsten Wagner <[hidden email]> wrote:
>
> Dear list,
>
> I currently have some TEM images with a strange background noise pattern
> (background.png). It seems to be "red shifted" noise.  White noise
> exhibit the same power for each frequency. Red shifted noise exhibed
> lower power for higher frequencies. You can reproduce this kind of
> background noise if you create a x*y image, then add gaussian noise and
> upscale (bilinear interpolation) it to a (3*x)*(3*y) image. So my guess
> is, that the TEM camera simply upscale lower resolution to a higher
> resolution image.
>
> But there is one discrepancy:
> The fft spectra of these simulated image (spectrumSimulated.png) is
> different from the fft spectrum of the background of the TEM image
> (spectrum.png). The TEM spectrum shows a radial symmetric sinc pattern
> whereas the simulated spectra shows a rough sinc pattern in x and y
> direction.
>
> Any idea which interpolation technique can produce this radial symmetric
> sinc pattern in the fft spectrum?
>
> Another idea: The sinc function is an ideal reconstruction filter. It is
> possible that the camera simply apply a reconstruction filter which
> leads to this kind of fft spectum?
>
> Cheers,
> Thorsten
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> <spectrum.png><background.png><spectrumSimulated.png>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html

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