Iterative Fourier Transform for Light Waveform Control
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for calculating intensity and phase spectra to control light waveforms, particularly in high-intensity regions, often lead to local solutions and suboptimal results due to uniform evaluation across all time regions, which is not suitable for applications like laser processing or nonlinear optical microscopy.
Innovation Solution
The proposed solution involves a data creation apparatus and method that uses a phase spectrum design unit and an intensity spectrum design unit to calculate phase and intensity spectra. These units perform a Fourier transform, a first replacement based on a desired waveform multiplied by a coefficient, and an inverse Fourier transform, with additional constraints to prevent local solutions. The coefficient is optimized to reduce differences between the desired and transformed waveforms, particularly in high-intensity regions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If uniform evaluation is applied across all time regions in iterative Fourier method, then calculation simplicity is maintained, but manufacturing precision of temporal waveform in high-intensity regions deteriorates
Solution Approach 1:
The patent applies local quality by introducing a weight function that assigns different evaluation weights to different time regions. Specifically, regions with high light intensity are given higher weights in the evaluation function, allowing the iterative Fourier method to focus optimization effort on these critical regions while maintaining calculation efficiency. This resolves the contradiction by making the evaluation process non-uniform without adding complex calculation procedures.
2Adaptability or versatility
If iterative Fourier method is used to calculate phase and intensity spectra, then arbitrary temporal waveform can be obtained, but solution may be led to local solution
Solution Approach 1:
The patent introduces feedback mechanisms through the evaluation function that guides the iterative Fourier method. The evaluation function continuously assesses the quality of the generated temporal waveform and provides feedback to adjust the phase and intensity spectra in subsequent iterations. This feedback loop ensures that the solution converges to a global optimum rather than getting trapped in local solutions, while maintaining the ability to generate arbitrary waveforms.
3Manufacturing precision
If coefficient is optimized to reduce difference in high-intensity regions, then temporal waveform precision in high-intensity parts is improved, but calculation complexity increases
Solution Approach 1:
The patent applies parameter changes by introducing a coefficient that scales the desired temporal waveform before comparison in the evaluation function. This coefficient is optimized to minimize the difference between the generated and desired waveforms in high-intensity regions. By adjusting this single parameter within the evaluation function, the method achieves higher precision in critical regions without fundamentally changing the calculation framework or adding complex computational steps.
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 allows for accurate calculation of intensity and phase spectra, ensuring that the temporal waveform of light, especially in high-intensity parts, is brought closer to the desired waveform with higher precision, while avoiding local solutions and minimizing intensity loss.
Implementation Method 1
a phase spectrum function to be used for creating the data by performing a Fourier transform on a waveform function in a frequency domain including an intensity spectrum function and a phase spectrum function
Data Source
AI summary
An iterative Fourier transform unit of a modulation pattern calculation apparatus performs a Fourier transform on a waveform function including an intensity spectrum function and a phase spectrum function, performs a replacement of a temporal intensity waveform function based on a desired waveform after the Fourier transform, and then performs an inverse Fourier transform. The iterative Fourier transform unit performs the replacement using a result of multiplying a function representing the desired waveform by a coefficient. The coefficient has a value with which a difference between the function after the multiplication of the coefficient and the temporal intensity waveform function after the Fourier transform is smaller than a difference before the multiplication, and a ratio of the difference is smaller when an intensity is higher at each time of the function before the multiplication.