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Updated: May 8, 2025
08:42
Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
Published on: September 3, 2021
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Summary
Researchers defined a new class of partially coherent planar sources with structured coherence. This work extends Fourier transforms and Hilbert space kernels, offering new possibilities for optical coherence research.
Area of Science:
- Optics and Photonics
- Mathematical Physics
Background:
- The study builds upon the extension of the Fourier transform (FT) to complex arguments and reproducing kernel theory in Hilbert spaces.
- Existing models for partially coherent sources have limitations in describing structured coherence properties.
Purpose of the Study:
- To introduce a novel class of partially coherent planar sources with a structured degree of coherence.
- To explore the mathematical framework for defining and characterizing these new sources.
Main Methods:
- Extension of the ordinary Fourier transform (FT) to complex arguments.
- Application of results concerning reproducing kernels in Hilbert spaces.
- Development of a mathematical definition for the new class of sources.
Main Results:
- A new class of partially coherent planar sources with structured coherence has been defined.
- These sources exhibit Schell-model characteristics in one transverse coordinate and dependence on the average orthogonal coordinate.
- Specific examples of these sources are detailed.
Conclusions:
- The proposed approach provides a novel method for generating and analyzing partially coherent planar sources.
- The defined sources offer a structured degree of coherence, expanding the toolkit for optical coherence research.
- The methodology is adaptable for defining a wide range of other partially coherent sources.
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