img=imread("fibers01.tif");

%fourier transform
img_sf=fft2(double(img));

% shift, to move the frequency 0 to center 
img_sf_shift=fftshift(img_sf);

%conjuate 
img_sf_shift_conj=conj(img_sf_shift);

%check the friedel symmetry
%img_sf_shift(1,1) should have the same real part and opposite imaginary part 
%compare to img_sf_shift(256,256), and was exactly same with img_sf_shift_conj(256,256).
img_sf_shift(1,1)
img_sf_shift(256,256)
img_sf_shift_conj(256,256)


% the image size is 256x256, the center is (128,128). after shift, if it follows friedel symmetry, then 
%img_sf_shift(125,128) have the same real part and opposite imaginary part with 
%img_sf_shift(131,128)
%img_sf_shift(126.128) --> img_sf_shift(130,128)
%img_sf_shift(127.128) --> img_sf_shift(129,128)

img_sf_shift(125:131,128)