Single closed fringe pattern phase demodulation in alignment of nanolithography

The single closed fringe pattern that occurs in two superposed grating marks applied in the previously designed moiré alignment scheme based on dual-grating for lithography is processed and analyzed using a frequency domain method based on two-dimensional (2-D) analytic wavelet transform (AWT) and 2-D wavelet ridge algorithm. The sign ambiguities, which always occur in the process of single closed fringe pattern analysis, are removed through the discontinuities of the angle in the 2-D wavelet ridge. Theoretical analysis regarding application of 2-D AWT and 2-D wavelet ridge to the interference fringe in alignment is performed. Verification of this process is carried out through numerical simulation and experiment. Results indicate that the background and noise in the fringes can be filtered effectively through our method, and the phase information can be obtained successfully.