Iterative Fourier Transform Unit for Light Waveform Control
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Solution Overview
Problem
Existing methods for modulating light pulses using spatial light modulators often lead to local solutions rather than optimal results, particularly when trying to achieve arbitrary temporal waveforms, due to limitations in iterative Fourier transform methods.
Innovation Solution
The proposed solution involves an iterative Fourier transform unit that performs a Fourier transform on a waveform function including intensity and phase spectrum functions, followed by replacements in both the time and frequency domains to constrain these spectra, using a coefficient that minimizes the difference between the transformed waveform and the desired waveform, thereby preventing local solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the iterative Fourier method is used to calculate the modulation pattern, then the calculation can be performed, but the solution may be led to a local solution and an optimal solution is not necessarily obtained
Solution Approach 1:
The patent changes the parameter of the replacement operation by introducing a coefficient (initially 0.1) that controls the extent to which the desired waveform replaces the calculated waveform. This parameter adjustment prevents the algorithm from converging to local solutions by gradually adapting the replacement strength, allowing the system to escape suboptimal solutions and achieve better waveform accuracy.
2Productivity
If a large difference exists between the desired waveform and the waveform after Fourier transform, then the iterative method may converge faster, but the solution is more likely to be led to a local solution
Solution Approach 1:
The patent introduces dynamics into the iterative process by making the replacement coefficient variable rather than fixed. The coefficient starts at 0.1 and increases progressively (e.g., 0.1, 0.2, 0.3, ..., 1.0) across iterations. This dynamic adjustment allows fast initial convergence while preventing premature convergence to local solutions, ultimately achieving both speed and accuracy.
3Measurement precision
If the desired waveform and the waveform after Fourier transform are greatly different, then the replacement operation may be more effective, but the iterative Fourier operation may still lead to a local solution
Solution Approach 1:
The patent applies preliminary action by introducing a small coefficient (0.1) at the beginning of the iterative process. This preliminary gentle replacement prevents large abrupt changes that could lead to local solutions, while still progressing toward the desired waveform. The gradual increase of the coefficient ensures optimal solution attainment.
Data Source
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Figure 3(a)~3(b)
AI summary
An iterative Fourier transform unit 22a in a modulation pattern calculation apparatus 20 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 22a performs the replacement using a result of multiplying a function representing the desired waveform by a coefficient, and the coefficient has a value in which a difference between the function after the multiplication and the temporal intensity waveform function after the Fourier transform is smaller than a difference before the multiplication of the coefficient. As a result, a modulation pattern calculation apparatus, a light control apparatus, a modulation pattern calculation method, and a modulation pattern calculation program capable of preventing a solution from being led to a local solution during an iterative Fourier operation and accurately calculating an intensity spectrum or a phase spectrum to bring a temporal waveform of light close to a desired waveform are realized.