Isotropic transverse covariance spectrum
= Isotropic transverse covariance spectrum
{title2=$C(\rho)=\frac1{2\pi}\int_0^\infty\Phi(\kappa)J_0(\kappa\rho)\kappa\,d\kappa$}
For the <Fourier transform> convention $C(\mathbf s)=\int\Phi(\boldsymbol\kappa)e^{i\boldsymbol\kappa\cdot\mathbf s}d^2\kappa/(2\pi)^2$, angular integration of an isotropic <power spectrum> gives the displayed <Hankel transform>. A purely radial Hankel transform without the prefactor corresponds to defining its spectrum as $\Phi/(2\pi)$.