To quantify the sensitivity of diverse implosion designs to laser imprinting, we developed an equivalent perturbation model that maps laser imprinting as the target surface perturbation. By

incorporating imperfections in target fabrication and thermal smoothing in the plasma, the model shows a reduced implosion sensitivity to laser imprinting, extending the analysis beyond geometric irradiation. The imprinting sensitivity threshold is defined as δh_las/δh_tar=0.1. When the imprinting amplitude δh_las is less than one-tenth of the target perturbation amplitude δh_tar, target perturbations dominate. Radiation-hydrodynamics simulations confirm that when δh_las/δh_tar⩽0.1, variations in nonlinear onset time and adiabat remain within 12% of those observed with target perturbations alone. Moreover, the imprinting sensitivity is supported by OMEGA experiments. These results indicate that joint control of laser and target perturbations, improving target quality when δh_las/δh_tar⩽0.1 and laser smoothing otherwise, can support stable implosions for high-gain direct-drive inertial confinement fusion.