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Doubly positive functions in coherent and partially coherent optics
Optics Letters
|December 8, 2017
Summary
Doubly positive functions are non-negative and their Fourier transforms are also non-negative. This study explores their properties and applications in optics, providing methods to construct new examples.
Area of Science:
- Optics and Photonics
- Mathematical Physics
Background:
- Coherent and partially coherent fields are fundamental in wave phenomena.
- Understanding the properties of functions and their transforms is crucial in signal processing and physics.
Purpose of the Study:
- To define and investigate doubly positive functions.
- To explore the applications of these functions in the context of coherent and partially coherent fields.
- To develop methods for constructing new classes of doubly positive functions.
Main Methods:
- Definition of doubly positive functions based on non-negativity of the function and its Fourier transform.
- Analysis of mathematical properties of these functions.
- Exploration of applications in optical fields.
Main Results:
- Established the definition and key properties of doubly positive functions.
- Demonstrated their relevance and application in coherent and partially coherent fields.
- Provided procedures for devising new classes of such functions.
Conclusions:
- Doubly positive functions offer a unique mathematical framework with practical implications in optics.
- The study provides tools for generating and understanding these functions for future research and applications.
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