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We present an experimental scheme to calculate the inner product of two arbitrary scalar optical fields. The scheme is based on using an interferometer to generate superpositions of the optical fields with a relative phase difference between the two fields. The intensity observed permits the calculation of the inner product using numerical integration. The experimental results obtained for the inner product of a few common optical fields are presented along with comparison with simulations.
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Rohan Ramesh, Benjamin Perez-Garcia, Raul I. Hernandez-Aranda, Thomas Konrad, "Inner product of arbitrary scalar optical fields," Proc. SPIE 11486, Laser Beam Shaping XX, 114860L (20 August 2020); https://doi.org/10.1117/12.2568886