Tomography of Spatial Mode Detectors

Transformation and detection of photons in higher-order spatial modes usually requires complicated holographic techniques. Detectors based on spatial holograms suffer from non-idealities and should be carefully calibrated. We report a novel method for analyzing the quality of projective measurements in spatial mode basis inspired by quantum detector tomography. It allows us to calibrate the detector response using only gaussian beams. We experimentally investigate the inherent inaccuracy of the existing methods of mode transformation and provide a full statistical reconstruction of the POVM (positive operator valued measure) elements for holographic spatial mode detectors.