Why does increasing sampling density in the frequency domain separate overlapping artifacts in the spatial domain?
edited for more depth &amp; clarity to avoid artifacts, pun intended 

You can control your artifacts with an improved "anti-alias" filter to eliminate all content of signals above the Nyquist rate. This is often more critical if the image has been digitized already by another system at some unknown pixel rate.  


  For example a high  resolution scan of magazine photo without the appropriate anti-alias filter setting will result in herringbone artifacts that are much worse than the original. This is a similar effect to the stripes of a shirt on TV with harmonic pixel interference herringbone patterns or the fringing patterns of lenses on a digital camera or camcorder in the presence of infrared light and similar resolution subject matter above the pixel resolution of the camera.


How you implement the anti-alias filter depends on the original signal. 


In the more general sense, if the original signal is natural light to be captured for 2D imaging, you might use an AA optical "blur filter". 
If the original signal is light reflected from a digital printed object in a scanner, you might tune the alias digital blur filter to match the resolution of the original print and synchronously if possible. e.g. 100 dpi for fax content  
If the original signal is a 3D scan using magneto-resonant imaging then you need to determine is it from stop-band remnant signals or pass-band group delay distortion.


The quality factors of low artifacts depend on the relative levels of interference from each to avoid alias artifacts. 


  Over-sampling makes the job of ideal bandstop filtering easier but ends up with huge file sizes so this can be followed by undersampling to achieve easier brick wall filters with desired blur filter in pass band.


Wiki has a more examples of various anti-alias filters and also spacial filtering
applications.