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The radiation of large antennas and those operating at low frequencies can be determined efficiently by near-field measurement techniques and a subsequent near-field far-field transformation. Various approaches and algorithms have been researched but for electrically large antennas and irregular measurement contours advanced algorithms with low computation complexity are required. In this paper an algorithm employing plane waves as equivalent sources and utilising efficient diagonal translation operators is presented. The efficiency is further enhanced using simple far-field translations in combination with the expensive near-field translations. In this way a low complexity near-field transformation is achieved, which works for arbitrary sample point distributions and incorporates a full probe correction without increasing the complexity.