Optimization Technique for Phase-Only Computer-Generated Holograms Based on Gradient Descent Method

2019 ◽  
pp. 1014
Author(s):  
Shujian Liu ◽  
Yuki Nagahama ◽  
Yasuhiro Takaki
Keyword(s):  
Gradient Descent ◽  
Optimization Technique ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Computer Generated Holograms

scholarly journals Optimization of Phase-Only Computer-Generated Holograms Based on the Gradient Descent Method

2020 ◽  
Vol 10 (12) ◽  
pp. 4283 ◽  
Author(s):  
Shujian Liu ◽  
Yasuhiro Takaki
Keyword(s):  
Iterative Algorithm ◽  
Gradient Descent ◽  
Optimization Technique ◽  
Descent Method ◽  
Complex Amplitude ◽  
Gradient Descent Method ◽  
Constant Amplitude ◽  
Computer Generated Holograms

The Gerchberg–Saxton (GS) algorithm is a Fourier iterative algorithm that can effectively optimize phase-only computer-generated holograms (CGHs). This study proposes a new optimization technique for phase-only CGHs based on the gradient descent method. The proposed technique evaluates the intensity distributions of reconstructed images to directly obtain the phase distributions of the CGHs, whereas the GS algorithm equivalently evaluates the amplitude distributions of reconstructed images and extracts phase distributions from complex-amplitude distributions of the holograms using a constant-amplitude constraint. The proposed technique can reduce the errors in the reconstructed images with fewer iterations than the GS algorithm.

Analysis of 2D Coupled Sails: Use of an Optimization Technique Based on Turbulent Viscous Flows

2003 ◽  
Author(s):  
Giovanni Lombardi ◽  
Francois Beux ◽  
Mattia de? Michieli Vitturi
Keyword(s):  
Gradient Descent ◽  
Grid Point ◽  
Optimization Technique ◽  
Viscous Flows ◽  
Descent Method ◽  
Optimum Shape ◽  
Shape Design ◽  
Gradient Descent Method ◽  
Flow Modeling ◽  
America’S Cup

In this study the optimization of a complete 2D flying sails configuration is considered. An optimum shape design problem is then defined considering the maximization of the drive force on the sails, constrained by the heeling force, and complete flow modeling including turbulent effects. The corresponding numerical algorithm is based on a gradient descent method coupled with a discrete shape grid-point parameterization. The descent direction is obtained by an exact computation of an incomplete discrete gradient associated with a multilevel strategy. The numerical behavior of the present formulation has been illustrated by the optimization of real 2D configurations of an America’s Cup yacht.

Two Timescale Analysis of the Alopex Algorithm for Optimization

2002 ◽  
Vol 14 (11) ◽  
pp. 2729-2750 ◽  
Author(s):  
P. S. Sastry ◽  
M. Magesh ◽  
K. P. Unnikrishnan
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Approximation ◽  
Approximation Method ◽  
Gradient Descent ◽  
Optimization Technique ◽  
Descent Method ◽  
Learning Problems ◽  
Gradient Descent Method ◽  
Gradient Information ◽  
Two Timescale Stochastic Approximation

Alopex is a correlation-based gradient-free optimization technique useful in many learning problems. However, there are no analytical results on the asymptotic behavior of this algorithm. This article presents a new version of Alopex that can be analyzed using techniques of two timescale stochastic approximation method. It is shown that the algorithm asymptotically behaves like a gradient-descent method, though it does not need (or estimate) any gradient information. It is also shown, through simulations, that the algorithm is quite effective.

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