In this paper we propose a system with the piezoelectric actuator by the single neuron adaptive PID controller for the
grating tiling. Then the design of the control system as well as the control method by considering the nonlinearity of
piezoelectric actuators is discussed. At last, close loop position examinations by the capacitive displacement sensor with
nanometer scale precision are performed. The experimental results indicate that the system is working effectively. The
system is provided with the characters of self-learning, easy calculating and adaptability as well as of a simple structure.
This paper proposes a new digital method to compensate for the aberration of electron-objective lens in electron holography. In this method, the object wavefront in the exit pupil plane is numerically reconstructed from digitized electron hologram, and is corrected by multiplying it with the conjugate aberration function of the electron-objective lens. Then, aberration-free image can be obtained by calculating the Fresnel integral of this corrected wavefront. In comparison with traditional methods, this method is much more convenient and accurate.