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On the Theory of Optical Hilbert transform for incoherent objects
Optics Express
|June 18, 2009
Summary
This study introduces the Hilbert transform for incoherent imaging for the first time. A novel optical heterodyne scanning system is designed to perform this transform on incoherent objects, validated by simulations.
Area of Science:
- Optics
- Image Processing
- Mathematical Physics
Background:
- The Hilbert transform is widely used in coherent imaging.
- Its application in incoherent imaging has not been previously explored.
Purpose of the Study:
- To investigate the Hilbert transform in the context of incoherent imaging.
- To design an optical system capable of performing the Hilbert transform on incoherent objects.
Main Methods:
- Development of a two-pupil optical heterodyne scanning system.
- Mathematical analysis of pupil design for Hilbert transform implementation.
- Computer simulations to validate theoretical results.
Main Results:
- Successful mathematical design of pupils for incoherent Hilbert transform.
- Computer simulations confirmed the system's capability to perform the Hilbert transform on incoherent objects.
Conclusions:
- The Hilbert transform can be effectively applied to incoherent imaging.
- The proposed optical heterodyne scanning system provides a viable method for incoherent Hilbert transform implementation.
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