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Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization

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Published on: July 5, 2016

Fresnelets: new multiresolution wavelet bases for digital holography.

Michael Liebling¹, Thierry Blu, Michael Unser

¹Biomedical Imaging Group, STI, BIO-E, Swiss Federal Institute of Technology, Lausanne (EPFL), CH-1015 Lausanne, Switzerland. michael.liebling@epfl.ch

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|February 2, 2008

Summary

This summary is machine-generated.

We introduce Fresnelets, new wavelet-like bases for processing digital holograms. This method efficiently reconstructs holograms and suppresses unwanted terms, improving digital hologram analysis.

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Area of Science:

Optics
Digital Signal Processing
Wavelet Theory

Background:

Traditional methods for digital hologram reconstruction face challenges with noise and image artifacts.
Wavelet transforms offer powerful tools for signal analysis but require adaptation for holographic data.

Purpose of the Study:

To develop novel wavelet-like bases (Fresnelets) for efficient reconstruction and processing of optically generated Fresnel holograms.
To introduce a multiresolution algorithm, the Fresnelet transform, for enhanced digital hologram analysis.

Main Methods:

Construction of new wavelet-like bases by applying a unitary Fresnel transform to existing wavelet bases.
Derivation of a Heisenberg-like uncertainty relation to determine optimal basis functions (Gabor functions).
Development of an efficient multiresolution Fresnelet transform algorithm for hologram reconstruction.

Main Results:

Fresnelet bases, particularly those derived from polynomial spline wavelets, exhibit optimal localization and approximation properties.
The Fresnelet transform enables wavelength-independent reconstruction of complex scalar waves at multiple resolutions.
Subband decomposition effectively separates desired images from zero-order and twin image terms, facilitating their suppression.

Conclusions:

Fresnelets provide a robust framework for digital hologram processing, enhancing reconstruction accuracy and efficiency.
The Fresnelet transform algorithm significantly simplifies the removal of artifacts in digital holography.
This work integrates Gabor function properties into wavelet analysis for advanced holographic data processing.