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A probe-compensated near-field-to-far-field-transform algorithm has been developed that can generate far-field patterns from near-field measurements made on an arbitrary surface. We present the concept, the algorithm, and computer-simulated and measured test results for measurements on a conical surface. The prototype conical near-field measurements were made in a planar near-field range on a horn antenna under test (AUT), mounted on an azimuth-over-elevation positioner to produce a conical measurement surface. This system is especially applicable for producing full-hemisphere far-field patterns for antennas mounted on vehicles, where other standard measurement systems may not adapt well to the profile, may not provide full-hemisphere coverage, or may require large, mechanically complex systems.