A unitary transformation between Cartesian and polar pixellations of finite two-dimensional images is obtained from the $\mathsf{su}\left(2\right)$ model for discrete and finite signals. This transformation analyzes the original image into its finite Cartesian “Laguerre–Kravchuk” modes (involving Wigner little-d functions) and synthesizes it back using a polar mode basis with the same set of mode coefficients. The polar basis is derived from the quantum angular momentum theory, and its modes are given by Clebsch–Gordan coefficients.

© 2008 Optical Society of America

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