Re: Regarding FFT

[akash verma]

> Hello sir
> I am new user of Imagej . I have to find phase from interferogram can you
> give me an idea about how i will find a pahse and also how filter out the
> first order after taking Fourier transform.
> Thanks in advance
>

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[David M Gauntt]

The instruction below describe how to perform a Fourier Transform on your image, and get the phase of the Fourier transform.  This may not be what your are trying to do, however.

1) Select the command "Process/FFT/FFT Options…".  Select the "Complex Fourier Transform" option.

2) With your image open, select "Process / FFT / FFT".  This will produce a 2 image stack containing the real and imaginary componts of the FT.

3) Display the "Real" image in the stack, and then select "File/Save As/Text image…".  Save the file and name it "Real.txt".

4) Display the "Imaginary" image in the stack, and then select "File/Save As/Text image…".  Save the file and name it "Imaginary.txt".

5) Open Excel, and Import the Real.txt file into Excel as tab delimited text.

6) Import the Imaginary.txt file into Excel as tab delimited text.

7) Create a new Excel spreadsheet, and save it as an Excel spreadsheet named "Phase.xls" (or Phase.xlsx").

8) Enter the following formula in the first cell of phase.xlsx:  =ATAN2(Real.txt!A1,Imaginary.txt!A1)

9) Copy this formula into the rest of the cells of the new spreadsheet.  If your real and imaginary images are 128x128 pixels, then copy into the first 128 rows and 128 columns.

10) Save phase.xls, then save a copy as a text file as "phase.txt".

11) In ImageJ, select "File / Import / Text Image…" to import "phase.txt".

You have now opened the phase image, with the phase in radians.

Hello sir
I am new user of Imagej . I have to find phase from interferogram can you
give me an idea about how i will find a pahse and also how filter out the
first order after taking Fourier transform.
Thanks in advance

--
David M. Gauntt, Ph.D.
Associate Professor,
Division of Medical Physics and Engineering
UAB Department of Radiology

mailto:[hidden email]
205-975-3777



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[Gabriel Landini]

On Tuesday 14 Aug 2012 16:27:52 David M Gauntt wrote:

> The instruction below describe how to perform a Fourier Transform on your
> image, and get the phase of the Fourier transform.  This may not be what
> your are trying to do, however.
>
> 1) Select the command "Process/FFT/FFT Options…".  Select the "Complex
>    Fourier Transform" option.
> 2) With your image open, select "Process / FFT / FFT".  This will produce a
>    2 image stack containing the real and imaginary componts of the FT.
> 3) Display the "Real" image in the stack, and then select "File/Save As/Text
>    image…".  Save the file and name it "Real.txt".
> 4) Display the "Imaginary" image in the stack, and then select "File/Save
>    As/Text image…".  Save the file and name it "Imaginary.txt".
> 5) Open Excel, and Import the Real.txt file into Excel as tab delimited
>    text.
> 6) Import the Imaginary.txt file into Excel as tab delimited text.
> 7) Create a new Excel spreadsheet, and save it as an Excel spreadsheet named
>    "Phase.xls" (or Phase.xlsx").
> 8) Enter the following formula in the first cell of phase.xlsx:
>    =ATAN2(Real.txt!A1,Imaginary.txt!A1)
> 9) Copy this formula into the rest of the cells of the new spreadsheet.  If
>    your real and imaginary images are 128x128 pixels, then copy into the
>    first 128 rows and 128 columns.
> 10) Save phase.xls, then save a copy as a text file as "phase.txt".
> 11) In ImageJ, select "File / Import / Text Image…" to import "phase.txt".
> You have now opened the phase image, with the phase in radians.

That could be made into a macro and save all the file transfer to excel.

Warning - Warning - Warning - Warning - Warning - Warning -

I am not sure the result is correct, so could somebody with some sample data
please check? Maybe this needs some quadrant swapping? Not sure.
I am also not sure if the operands of the atan2 function in excel match the
ones in the macro function.

//---------------
setBatchMode(true);
a=getTitle();
run("FFT Options...", "fft complex");
run("FFT");
selectWindow("Complex of "+a);
run("Duplicate...", "title=phase");
w=getWidth();
h=getHeight();
imag=newArray(w);
for (y=0;y<h;y++){
  selectWindow("Complex of "+a);
  setSlice(2);
  for(x=0;x<w;x++){
      imag[x]=getPixel(x,y);
  }
  selectWindow("phase");
  for(x=0;x<w;x++){
     putPixel(x,y, atan2(getPixel(x,y), imag[x]));
  }
}
setBatchMode(false);
selectWindow("phase");
run("Enhance Contrast", "saturated=0.0");
//---------------

Cheers
Gabriel

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[Gabriel Landini]

On Tuesday 14 Aug 2012 17:31:46 Tom Hennessy wrote:
> I have 16 X-ray grey scale images (8-bit), all of which have been
> taken at different angles.
> I need change the horizontal shift of the images and add them together
> so I can move through the focal plane.
> Here is a link to the 16 images that I am trying to process:
> http://www.sendspace.com/file/cnwzmk

You could try the stack alignment using SIFT in Fiji, but not sure it will do
what you want, because all the x rays appear to have been taken from a
different angles so fiducial points are difficult to find.
Other than that I can only suggest to do it by hand with the align slice
plugin:
http://www.dentistry.bham.ac.uk/landinig/software/align_slice.zip

Cheers
Gabriel

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