In perovskite oxide ferroelectrics, gradients of lattice strain are known to induce nanoscale topological structures, leading novel or enhanced functionality. Here, we experimentally detect and theoretically analyze thickness distribution structural properties in epitaxial ${\mathrm{Pb}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}$ films grown on (001) $\mathrm{SrTi}{\mathrm{O}}_{3}$ su...