A total-field/scattered-field (TF/SF) boundary which is commonly used in the finite-difference time-domain (FDTD) method to illuminate scatterers by plane waves, is developed for use in the constrained interpolation profile (CIP) method. By taking the numerical dispersion into account, the nearly perfect TF/SF boundary can be achieved, which allows us to calculate incident fields containing high frequency components without fictitious scattered fields. First of all, we formulate the TF/SF boundary in the CIP scheme. The numerical dispersion relation is then reviewed. Finally the numerical dispersion is implemented in the TF/SF boundary to estimate deformed incident fields. The performance of the nearly perfect TF/SF boundary is examined by measuring leaked fields in the SF region, and the proposed method drastically diminish the leakage compared with the simple TF/SF boundary.