Research On Inverse Diffraction Grating Problem Based On Neural Network

Diffraction grating is an important optical component with periodic structure,which is widely used in medical X-ray imaging,crystalline silicon solar cells,optical communication and gas sensors.The diffraction grating problem refers to determining the scattering field according to the periodic structure of the given incident wave and grating,and the inverse problem refers to the shape of the grating inverted by the given incident wave and scattering field.The numerical solution of the inverse diffraction grating problem is of great significance in the design and manufacture of optical elements.In practical problems,it is challenging to solve numerically due to its ill-posedness and nonlinearity,Therefore,it is of extraordinary practical significance to develop a simple and efficient numerical method to solve the inverse diffraction grating problem.In this paper,a fast solution method is proposed for the inverse diffraction grating problem.Aiming at the shape reconstruction problem in the inverse diffraction grating problem,a neural network method based on encoder-decoder structure is proposed.Firstly,considering that in the near-field region where the measurement distance b above the grating is much smaller than the wavelength λ,the measured near-field data is used to transform the grating shape reconstruction problem into a shape parameter inversion problem by the Fourier expansion method.Secondly,the inversion model of grating shape parameters is constructed based on neural network and gating idea(GIMNN).The network model takes the near-field data as the input and the shape parameters of the grating as the output.First,the encoder is used to extract the features of the input near-field data,and then the Adam algorithm is used to update the model weight iteratively.Finally,the decoder is used to invert the grating shape parameters of the grating,and then the grating shape is reconstructed.The numerical experiments demonstrate that the model can reconstruct the shape of the grating effectively,and has a certain robustness under the interference of noise.In this paper,the neural network method is applied to the reconstruction of boundary figure in the inverse diffraction grating problem.The feasibility of GIMNN neural network method is verified by numerical experiments.The numerical experiments demonstrate that the neural network method can improve the inversion accuracy of grating shape.