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Updated: Jun 2, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
On the inter-conversion between Hermite and Laguerre local image expansions
Elio D Di Claudio1, Giovanni Jacovitti, Alberto Laurenti
1Department of Information Engineering, Electronics and Telecommunications (DIET), University of Rome La Sapienza, I-00184 Rome, Italy. dic@infocom.uniroma1.it
Abstract:
The nice relationship existing among the Hermite-Gauss and the Laguerre-Gauss image expansions, whose basis functions span the same signal space, is investigated. As a result, a novel efficient method for Cartesian to polar coordinate inter-conversion, especially suited for dedicated hardware realization, is proposed. Applications to local image rotation, based on the simple steerability of the Laguerre-Gauss expansion, and to local image analysis, based on Gaussian derivatives, are considered in detail. A possible fixed-point realization of the proposed inter-conversion scheme is discussed.
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