Research On Reverse Prediction Methods For Designing Diffractive Optical Elements

The Diffractive Optical Elements(DOEs)are widely used because of their compactness and ability to control light distribution accurately.With the continued development of nanoimprint technology,the DOEs have been widely used in consumer electronics due to its lower production cost.However,normal methods for designing DOE require a fixed set of parameters such as beam waist radius,beam outer radius,wavelength,image plane size,diffraction plane and input plane distance.When these parameters change,new phase data need to be re-optimized,which again takes a lot of time.In order to overcome the limitations of traditional design methods,which require re-optimization when parameters change,in this thesis the machine learning algorithms are employed to design the DOE phase design and analyze the tolerances.A modified DOE phase design algorithm is proposed,which combines the energy mapping method,the G-S algorithm and the Ant-lion optimization algorithm.The phase calculated by energy mapping method is taken as the initial phase of G-S algorithm.With the initial phase,the G-S algorithm can calculate the new phase data.The new phase data is unwrapped and then fitted to a polynomial.The coefficients of the fitted polynomial are further optimized by the ant-lion optimization algorithm(ALO).The DOE phase designed in this way is smooth with no abrupt points.The DOE designed by the modified algorithm can generated a spot with highly uniform distribution.With a set of system parameter,the DOE designed by the modified algorithm can generate highly uniform intensity distribution on target plane with a uniformity of 0.91 and diffraction efficiency of 96.1%,respectively.The DOE phase coefficients generated by the modified algorithm are taken as the output data,and system parameters are taken as input data.One-dimensional convolutional neural network(1D-CNN)is used for data training.After250 iterations,the root mean square error is reduced to 0.33 and the loss function is reduced to0.05.The 10 groups of system parameters were randomly selected from the sample data to test the prediction accuracy.The results show that the prediction accuracies of 10 group of phase coefficients are all up to 97% using the well-trained CNN.The effect of DOE fabrication errors on the uniformity of the intensity distribution on target plane is analyzed.Tolerance analysis includes manufacturing tolerance and assembly tolerance.For manufacturing tolerances,a set of error data is added to the ideal DOE phase data.The error data is generated by an error function.The magnitude of the added error can be simulated by changing several coefficients in the error function.The influence of the error coefficient on the uniformity of the optical intensity are plotted,and the maximum allowed height profile error for the DOE is obtained.Given a set of system parameters,the maximum allowed fabrication error for the DOE edges is-177.2 nm to 73.3 nm.The mapping between the error coefficients and the uniformity is constructed using a machine learning algorithm,which can directly predict the uniformity of the intensity distribution on the target plane generated by the DOE with the phase errors.The simulation results show that the relative errors are all within 2.2% compared to the actual and predicted uniformity of the light intensity distribution by this method.Finally,the effect of the assembly tolerance of the DOE on the uniformity of the light intensity is analyzed.The analysis results show that the installation position error relative to the optical axis should be controlled within ±30 μm and the rotation error should be controlled within ±0.3°.