Why the difference come of 2D Fourier Transforms from two similar image?
Here is some code that will let you interactively make a mask and see the difference.

For the first image the dark edges and the bright centres are about the same width, so there is only one ring. For the second image, the dark edges are half the size of the bright centres, hence two rings.

I1 = imread('sefft1.jpg');
I2 = imread('sefft2.jpg');

I1g = rgb2gray(I1);
I2g = rgb2gray(I2);

I1gFFT = fft2(I1g);
I2gFFT = fft2(I2g);

imagesc(log(abs(fftshift(I1gFFT))))
imagesc(log(abs(fftshift(I2gFFT))))

% FFT coordinates
[rows,cols] = size(I1gFFT);

[ux, uy] = meshgrid(([1:cols]-(fix(cols/2)+1))/(cols-mod(cols,2)), ...
    ([1:rows]-(fix(rows/2)+1))/(rows-mod(rows,2)));
ux = ifftshift(ux);   % Quadrant shift to put 0 frequency at the corners
uy = ifftshift(uy);

% Convert to polar coordinates
th = atan2(uy,ux);
r = sqrt(ux.^2 + uy.^2);

% Centred versions
rc = fftshift(r);
thc = fftshift(th);

% Interactive selection of filter
imagesc(log(abs(fftshift(I1gFFT))));
title('Image 1: Press enter to select max and min freq');
pause;
title('select max and min freq');
[x,y] = ginput(2);
y = round(y)
x = round(x)
r1 = rc(y(1),x(1));
r2 = rc(y(2),x(2));
rmin = min(r1,r2);
rmax = max(r1,r2);
mask = (r &gt; rmin) &amp; (r &lt; rmax);
maskc = (rc &gt; rmin) &amp; (rc &lt; rmax);

imagesc(log(abs(fftshift(I1gFFT).*maskc))); title('Masked area'); pause;
imagesc(ifft2(I1gFFT.*mask)); title('Result of ifft of masked area'); pause;
imagesc(ifft2(I1gFFT.*(1-mask))); title('Result of ifft of non-masked area'); pause;

% Interactive selection of filter
imagesc(log(abs(fftshift(I2gFFT))));
title('Image 2: Press enter to select max and min freq');
pause;
title('select max and min freq')
[x,y] = ginput(2);
y = round(y)
x = round(x)
r1 = rc(y(1),x(1));
r2 = rc(y(2),x(2));
rmin = min(r1,r2);
rmax = max(r1,r2);
mask = (r &gt; rmin) &amp; (r &lt; rmax);
maskc = (rc &gt; rmin) &amp; (rc &lt; rmax);

imagesc(log(abs(fftshift(I2gFFT).*maskc))); title('Masked area'); pause;
imagesc(ifft2(I2gFFT.*mask)); title('Result of ifft of masked area'); pause;
imagesc(ifft2(I2gFFT.*(1-mask))); title('Result of ifft of non-masked area'); pause;