We prove a local version of recently established theorem by Myroshnychenko, Ryabogin and the second named author. More specifically, we show that if $n\geq 3$, $g:\mathbb{S}^{n-1}\to\mathbb{R}$ is an even bounded measurable function, $U$ open subset $\mathbb{S}^{n-1}$ restriction (section) $f$ onto any great sphere perpendicular to isotropic, then ${\cal C}(g)|_U=c+\langle a,\cdot\rangle$ R}(g)...