http://imagej.273.s1.nabble.com/1D-Fourier-transform-in-macro-tp5009727p5009764.html
test is what is to be expected. There is no need for another FFT-algorithm.
single line (PSF) image. Dividing the value at the origin by n should
> Hi Herbie, Ludovic,
>
> to me it looks like Ludovic wants to do a prodecure as described
> here:
>
>
http://www.irss.ca/documents/CODES%20&%20STANDARDS_02-28-08/ASTM%20Standards/PDF/E1695.PDF>
> The procedure is essentially determining the one-dimensional point
> spread function (PSF) from the derivative of the image of an edge,
> and then taking the Fourier transform of the PSF to find the
> modulation transfer function (MTF).
>
> So it is really just the Fourier transform of the PSF that is
> needed.
>
> For that purpose, I agree with Ludovic that no background should be
> subtracted.
>
> So I tried creating a line with a PSF-like function, replicated it to
> get a 32-bit square image with a size of 2^n, and ran FFT on it. The
> raw power spectrum does not give a single pixel in the center but
> rather a short streak. Then one can do 'Swap Quadrants', run
> Math>Square Root, select a rectangle of only the first row and do a
> profile. This profile should be the FFT required for converting the
> PSF into the MTF.
>
> So one can do it without doing a 1D FFT.
>
>
> Michael
> ________________________________________________________________ On
> Sep 25, 2014, at 11:14, Herbie wrote:
>
>> Ludovic,
>>
>> I must admit that I'm confused!
>>
>> First you wrote: "This is to perform direct _MTF_ evaluation from
>> the profile"
>>
>> Now you write: "It is for _CT_ (reconstruction)"
>>
>> You also wrote: "What I get is a single _colored_ pixel"
>>
>> Now you write: "16bits unsigned _grey_ level"
>>
>> If you are indeed seeking to reconstruct images from CT projections
>> (not profiles) then there exist several methods to do so. I'm quite
>> familiar with CT but not with formal standards and norms.
>>
>> One way of reconstructing images from projections is by first
>> Fourier-transforming all projections (you need at least n * PI/2
>> projections, where n is the number of pixels of the properly
>> sampled projections). The resulting 1D Fourier-spectra are then
>> combined to give a 2D spectrum by properly rotated superposition of
>> the 1D spectra. This 2D spectrum is to be corrected by the
>> so-called rho-filter to compensate its 1/f_r amplitude
>> characteristic. Finally the resulting 2D spectrum is
>> Fourier-retransformed and results in the desired image.
>>
>> Principally you should be able to compute all steps by use of
>> ImageJ and perhaps you will even find an appropriate
>> ImageJ-plugin.
>>
>> In any case, the FFT must lead to complex-valued spectra. Power
>> spectra make no sense in this application.
>>
>> Good luck
>>
>> Herbie
>>
>> :::::::::::::::::::::::::::::::::::::::: On 25.09.14 09:07, Ludovic
>> Pinier wrote:
>>> Herbie,
>>>
>>> the pictures I work with are 16bits unsigned grey level from a CT
>>> machine (raw format). No color. And using a Fourier transform is
>>> the method described in the standard applying to CT I use (ASTM
>>> E-1695). This standard also prevents to remove the mean or alter
>>> the contrast/brightness. To be standard-compliant, profile (the
>>> "Edge Spread Function") is mandatory. You are only allowed to
>>> frequency-filter it, and remove aberrant points. Even the Fourier
>>> transform sampling has to be compliant with the standard
>>> criteria. Concerning the Fourier transform, I am used to
>>> manipulate time-frequency transforms, but not to deal with the
>>> programming aspects. Last, my reason is that the tool built in
>>> the machine is not accurate. And the "slanted edge method" plugin
>>> is inappropriate for the geometry of my targets (which are also
>>> defined according to the standard: material, shape and size). The
>>> standard requires a line profile, and the slanted edge produces
>>> an integration of the profile along the edge. I could use this
>>> plugin with 1pixel-wide areas, but ,that means I need to rotate
>>> the image; and even if is an as-accurate-as-possible
>>> transformation, it is an interpolation that produces a calculated
>>> image. It is not the direct capture from the sensor anymore. That
>>> is also the reason why the slanted edge method was introduced in
>>> the ISO12233. But unfortunately, the target definition in this
>>> standard is inappropriate for my use.
>>>
>>> I know your suggestions could definitely help, but they don't
>>> apply to my need.
>>>
>>> Best regards, Ludovic
>>>
>>> -- ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>
>>
>> -- ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>
> -- ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>