Real-Time Laser Beam Propagation Prediction via Fresnel Integral
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional systems and models for predicting laser beam propagation are either slow or inaccurate due to inadequate scalar optical wave control schemes, particularly the Helmholtz wave equation, integral representations, and direct solutions of Maxwell's equations, which struggle with accuracy and computational complexity.
Innovation Solution
A system and method for real-time predictive laser beam propagation using an embedded control scheme that incorporates a scalar Fresnel diffraction integral and Linear Canonical Transform, allowing for accurate and efficient prediction of laser beam parameters through atmospheric conditions over extended distances, with the ability to quantify computational errors and adjust laser system components accordingly.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional scalar optical wave control schemes (Helmholtz wave equation, integral representations, direct solutions of Maxwell's equations) are used for laser beam propagation prediction, then the prediction can be obtained, but the computation is slow and accuracy is difficult to quantify with artifacts introduced
Solution Approach 1:
The patent changes the fundamental parameter of the wave equation from the traditional Helmholtz form to a modified form where the Laplacian operator acts only on the envelope function rather than the complete field. This parameter change in the mathematical formulation enables both faster computation and maintained accuracy by separating the rapidly oscillating carrier from the slowly varying envelope, allowing efficient numerical evaluation without the artifacts of traditional methods
Solution Approach 2:
The patent replaces the conventional mechanical/numerical discretization approach of solving Maxwell's equations or Helmholtz equation with a simplified wave envelope equation that can be solved more efficiently. This substitution of the governing equation itself (rather than just the solution method) enables real-time computation while maintaining prediction accuracy through proper mathematical formulation
2Productivity
If integral representations (Rayleigh-Sommerford, Fresnel-Kirchford) with FFT approach are used, then computation can be performed in frequency domain, but artifacts due to sampling and aliasing are introduced and accuracy quantification is challenging
Solution Approach 1:
The patent extracts and separates the rapidly oscillating carrier wave component from the slowly varying envelope function. By taking out the carrier explicitly and formulating equations only for the envelope, the method avoids the sampling and aliasing artifacts that plague FFT-based integral methods, while still enabling efficient computation through the simplified envelope equation
Solution Approach 2:
The patent introduces the envelope function as an intermediary between the complete electromagnetic field and the observable quantities. This intermediary representation allows computation without direct FFT transformation of the complete field, avoiding aliasing artifacts while maintaining computational efficiency through the simplified envelope propagation equation
3Adaptability or versatility
If direct solution of Maxwell's equations is used, then waveguide problems of different geometries can be handled, but the computation is slow and inaccurate for most cases
Solution Approach 1:
The patent segments the electromagnetic field into a carrier wave component and an envelope function component. This segmentation allows the use of simplified equations for the envelope that are computationally efficient, while still handling diverse geometries through the boundary conditions applied to the envelope equation, achieving both versatility and speed
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly improves the speed and accuracy of laser beam parameter predictions, reducing complexity and enabling faster processing times compared to conventional methods, while minimizing artifacts and aliasing issues, thus providing better performance and user-friendly operation.
Implementation Method 1
A system and model for real-time predictive laser beam propagation using an embedded control scheme that incorporates a scalar Fresnel diffraction integral
Data Source
AI summary
The present invention is a method for real-time predictive laser beam propagation through various atmospheric conditions and over predetermined distances. The invention includes loading input parameters into an embedded control scheme of a laser system. A prediction of one or more laser beam parameters is generated and a computational error is quantified for the generated laser beam parameters. One or more parameters for the laser system are then chosen based on the prediction and based on the quantified computational error. The chosen parameters are within a predetermined tolerance. A laser system is then built or adjusted using the one or more chosen parameters.