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Published on: August 30, 2013
Analysis of digital images into energy-angular momentum modes
Luis Edgar Vicent1, Kurt Bernardo Wolf
1Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Unidad Altamira Instituto Politécnico Nacional, Altamira, Tamaulipas, 89600 México.
Summary
This study introduces Laguerre-Kravchuk functions, a new orthonormal basis for analyzing digital sensor data. This method precisely decomposes and reconstructs sampled optical beams based on energy and angular momentum modes.
Area of Science:
- Optics and Photonics
- Digital Signal Processing
- Mathematical Physics
Background:
- Digital sensors measure continuous wave fields, enabling beam quality assessment via formant modes.
- Laguerre-Gauss functions analyze sampled fields into energy and angular momentum (E-AM) coefficients.
- Existing sampled E-AM modes lack orthogonality, complicating analysis.
Purpose of the Study:
- To introduce a novel, orthonormal basis for analyzing sampled continuous wave fields.
- To provide a convenient mathematical tool for decomposing and synthesizing digital beam images.
- To address the limitations of non-orthogonal modes in E-AM analysis.
Main Methods:
- Development and proposal of the 'Laguerre-Kravchuk' discrete functions as an orthonormal basis.
- Application of these functions to analyze sampled continuous wave fields represented on a Cartesian grid.
- Utilizing the new basis to decompose beams into E-AM polar modes.
Main Results:
- The proposed Laguerre-Kravchuk functions form a properly orthonormal basis.
- This basis allows for the exact synthesis of the input image from its decomposed modes.
- Demonstration of a convenient method for analyzing sampled beams into E-AM polar modes.
Conclusions:
- The Laguerre-Kravchuk functions offer a significant improvement for analyzing digital beam quality.
- This new basis simplifies the decomposition and reconstruction of optical fields sampled by digital sensors.
- The method provides an exact synthesis of images, enhancing beam analysis capabilities.
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