A new probe-compensated near-field - far-field (NF-FF) transformation with helicoidal scanning for aperture antennas is presented. Such a technique takes the advantage of the NF data acquisition made according to a very efficient sampling strategy along a helix and exploits a proper aperture field expansion based on the use of the prolate spheroidal wave functions, accounting for the a priori information on shape and size of the antenna under test. Experimental results on a disconnected radiating aperture antenna show the effectiveness of the approach, and how it enables a serious reduction of the measurement points without impairing the FF estimation accurac