In this work, we study the tomography of the spatial structure of light. We develop a simple technique that allows one to perform tomography over the space of fixed-order modes. The technique is based on two spatially resolved intensity measurements, the second of which is performed after the light field has undergone an astigmatic transformation implemented by a tilted lens. We demonstrate that this method is informationally complete within the considered subspaces, and this is experimentally verified in both the intense and photocount regimes. We also study the effect of obstructions on our ability to reconstruct the states. The work presented is expected to help the development of characterization techniques in the field of structured light and in its application to both classical and quantum information protocols.

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• Angular momentum of light
• Optical quantum information processing
• Quantum communication, protocols & technology
• Quantum information theory
• Quantum tomography
• Structured light
• Lenses
• Spatial light modulators