A singular wave field was shown to have memory of optical vortices that existed in this field. After vortex annihilation, characteristic marks remain in the cross phase distribution. The phase near these marks exceeds essentially the phase in the adjacent area. Besides, vortex backwash manifests itself on the wave-front surface, where the vortex trail holds after vortex annihilation, and such wave front characteristics as the mean and Gaussian wave front curvatures are singular functions within the vortex trail. Some issues concerning the calculation of the phase distributing for singular wave fields are discussed.