A method for determining the positions of hologram dislocations relative to the optical axes of entangled Laguerre Gaussian modes is proposed. In our method, the coincidence count rate distribution was obtained by scanning the position of one of the holograms in two dimensions. Then, the relative position of the hologram dislocation was determined quantitatively from the positions of the minimum and maximum coincidence count rates. The validity of the method was experimentally verified, and in addition, an experiment demonstrating the violation of the Clauser-Horne-Shimony-Holt inequality was performed using the well-identified optical axes of the entangled modes.
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