How to calculate spatial frequency after taking fft in case of oversampling?

Hi,

I am calculating Fourier transform of an image. Width of each pixel is 0.004 mm. I re-sample my image at every pixel

dx=0.004; %mm
Fs=1/dx; %pixel/mm
f=Fs*(0:L/2-1)/L; %L is the length of signal in unit of pixel

But, now I want to over-sample my signal and want to re-sample at every half pixel,so I choose the following parameters:

dx=0.004/2; 
Fs=1/dx; %pixel/mm
f=Fs*(0:L/2-1)/L; %L is the length of signal in unit of pixel

The Final output I obtain is off by a factor of 2 from the previous case and I think it should not because I am just decreasing re-sampling width and length of the signal is same. I am not sure, if this is correct way of calculating spatial frequency in case of oversampling. Could anyone suggest me in case of oversampling how do we define spatial frequency axis??

Answer 1

[Matt J]

If dx has been cut in half, then L must be doubled in order to cover the same continuous space signal.