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Published on: August 30, 2013
Complex signal representation, Mandel's theorem, and spiral phase quadrature transform
1GE Global Research, One Research Circle, Niskayuna, New York 12309, USA. khare@ge.com
Applied Optics
|August 2, 2008
Summary
This study introduces a novel method for creating two-dimensional complex signals, essential for optical processing. The spiral phase quadrature transform minimizes signal envelope fluctuations, improving image analysis.
Area of Science:
- Optics and Photonics
- Signal Processing
- Image Analysis
Background:
- Complex signal representation is crucial in optical signal processing and coherence theory.
- Existing 2D complex signal representations vary based on their quadrature transform choices.
- A standardized method for 2D complex signal representation is needed for advanced optical applications.
Purpose of the Study:
- To determine the optimal complex representation for 2D real signals (images).
- To identify a quadrature transform that minimizes the envelope fluctuations of the complex image.
- To apply a least-squares minimization framework for robust image analysis.
Main Methods:
- Utilized a least-squares minimization framework, building upon Mandel's work.
- Investigated various quadrature transforms for 2D real signals.
- Focused on minimizing ensemble-averaged envelope fluctuations of the complex image.
Main Results:
- Identified the spiral phase quadrature transform as a solution for 2D complex signal representation.
- Demonstrated that this transform yields a complex image with minimal envelope fluctuations.
- The proposed method offers a stable and effective approach to 2D signal analysis.
Conclusions:
- The spiral phase quadrature transform provides an effective method for 2D complex signal representation.
- This approach enhances the analysis of optical fields and image processing.
- The findings contribute to advancements in coherence theory and optical signal manipulation.
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