Abstract:

 The authors proposed a numerical method to reconstruct  the grating profile. We considered the reconstrution of the grating profile by  the incident plane wave and the scattered waves measured on Γb, which is a straight line above the grating. First, we obtained the normal derivatives of the scattered waves on Γb via the Dirichlet-to-Neumann map. Then we got the total field below Γb by means of solving the Cauchy problem of the  Helmholtz equation, which is changed into an initial value problem. The initial value problem was solved by the spectral method which is used to solve the initial value problem of the elliptic equation. Finally, we used the curve, which is composed of the zeros of the total field, to approximate the grating profile. The numerical results show that the method is effective.

Key words: Helmholtz equation, initialvalue problem, illposed , problem, regularization method, grating