Design of two-dimensional asymmetric filter in Fourier transform profilometry

In the Fourier transforms profilometry (FTP), the band-pass filter that extracts the fundamental frequency component has a significant influence on the reconstructed accuracy of the 3D profile. For traditional 2D symmetrical filters such as Hanning window or Gaussian window, their cut-off frequencies are limited by the spatial frequency of projection fringe, namely the distance between the fundamental frequency and the zero frequency. This often leads to the incomplete extraction of fundamental frequency components and the loss of useful information. To solve this problem, we designed a 2D asymmetric filter with the elliptical bottom shape on the basis of 2D Hanning filter. It holds different frequency response and cut-off frequency towards different frequency directions and thus one can extract more complete fundamental frequency component. The simulation experiments of step object and array object show that the reconstructed accuracy of the proposed 2D asymmetric filter improves respectively by 39.5% and 55.6% for these two objects compared with traditional Hanning filter.