5:15 PM - 5:45 PM
▲ [5p-A413-15] [JSAP-OSA Joint Symposia 2017 Invited Talk] Optimization Strategy for Designing Computer-Generated Holograms and Diffractive Optical Elements
Keywords:diffractive optics, iterative optimization algorithm, computer-generated hologram
A computer-generated hologram (CGH) or diffractive optical element (DOE) is adapted in a free-space optical system to modulate the incident wavefront and then generate a diffractive pattern in a specified output plane. The optical field function of the diffractive pattern is related to the modulated function of CGH/DOE through an operation based on the Fourier transform. Because of constraints imposed on the input and the output functions, there is in general no solution to exactly fulfill the constraints. To find an approximation to the solution with minimum error, one needs to decide an optimization algorithm and a merit function of CGH performance.
Optimization algorithms are used to find approximations of the solution in scientific and engineering problems that do not have analytic relationships between the inputs and the outputs. Design of CGH and DOE is a typical problem needing optimization approaches to search an approximation which minimizes the difference due to the constraints applied to the input and the output. New optimization algorithms are in a great demand for the CGH/DOEs of millions of pixels due to high performance manufacture techniques and electronic devices recently developed.
Many optimization methods have been developed and applied to design of DOE, including Gerchberg-Saxton algorithm (GSA), error diffusion method, direct binary search method, simulated annealing algorithm, generic algorithm, and hybrid methods. They are categorized into the direct and inverse methods. A direct method begins with perturbations in the CGH domain, in which CGH pixels or element parameters are selected to change. Most approaches belong to the direct optimization method. A typical inverse method is GSA which is more effective than the direct methods. The main drawback is the poor image quality of the resultant CGH.
Merit function is critical in the optimization processing even before the optimization evolution begins. A merit function is a combination of weighted device parameters (indices) to identify the approximate solution of minimum error. Frequently used parameters include the root-mean- squared error, the diffraction efficiency, the signal-to-noise ratio, and the signal variation of the diffractive image. They help to determine the minimum error and thus the best approximation in the optimization process.
To obtain a solution to CGH/DOE with minimum error in a free-space optical system, one needs to select an optimization algorithm and realize the details of the algorithm based on the merit function of performance parameters.
Optimization algorithms are used to find approximations of the solution in scientific and engineering problems that do not have analytic relationships between the inputs and the outputs. Design of CGH and DOE is a typical problem needing optimization approaches to search an approximation which minimizes the difference due to the constraints applied to the input and the output. New optimization algorithms are in a great demand for the CGH/DOEs of millions of pixels due to high performance manufacture techniques and electronic devices recently developed.
Many optimization methods have been developed and applied to design of DOE, including Gerchberg-Saxton algorithm (GSA), error diffusion method, direct binary search method, simulated annealing algorithm, generic algorithm, and hybrid methods. They are categorized into the direct and inverse methods. A direct method begins with perturbations in the CGH domain, in which CGH pixels or element parameters are selected to change. Most approaches belong to the direct optimization method. A typical inverse method is GSA which is more effective than the direct methods. The main drawback is the poor image quality of the resultant CGH.
Merit function is critical in the optimization processing even before the optimization evolution begins. A merit function is a combination of weighted device parameters (indices) to identify the approximate solution of minimum error. Frequently used parameters include the root-mean- squared error, the diffraction efficiency, the signal-to-noise ratio, and the signal variation of the diffractive image. They help to determine the minimum error and thus the best approximation in the optimization process.
To obtain a solution to CGH/DOE with minimum error in a free-space optical system, one needs to select an optimization algorithm and realize the details of the algorithm based on the merit function of performance parameters.