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The spatial distribution of beams with orbital angular momentum in the far field is known to be extremely sensitive to angular aberrations, such as astigmatism, coma and trefoil. This poses a challenge for conventional beam optimization strategies when a homogeneous ring intensity is required for an application. We developed a novel approach for estimating the Zernike coefficients of low-order angular aberrations in the near field based solely on the analysis of the ring deformations in the far field. A fast, iterative reconstruction of the focal ring recreates the deformations and provides insight into the wavefront deformations in the near field without relying on conventional phase retrieval approaches. The output of our algorithm can be used to optimize the focal ring, as demonstrated experimentally at the 100 TW beamline at the Extreme Light Infrastructure - Nuclear Physics facility.