Fig. 5: The correlation comparison between images in Cartesian and log-polar coordinates.
From: All-optical geometric image transformations enabled by ultrathin metasurfaces
The correlations for the input airplane shapes \({f}_{i}\left(x,\, y\right)\) in the Cartesian coordinate (a–c). The correlation function is \({R}_{{f}_{1}{f}_{i}}={{{{{{\mathcal{F}}}}}}}^{-1}\{{[{{{{{\mathcal{F}}}}}}({f}_{1})]}^{*}{{{{{\mathcal{F}}}}}}({f}_{i})\}\), where \(i\)=1, 2 or 3. The correlations for the transformed images \({g}_{i}\left(X,\, Y\right)\) in the log-polar coordinate (d–f). The correlation function is \({R}_{{g}_{1}{g}_{i}}={{{{{{\mathcal{F}}}}}}}^{-1}\{{[{{{{{\mathcal{F}}}}}}({g}_{1})]}^{*}{{{{{\mathcal{F}}}}}}({g}_{i})\}\), where \(i\) = 1, 2 or 3.
