Local demodulation of holograms using the Riesz transform with application to microscopy

Area of Science:

• Optics and Photonics
• Digital Holography
• Image Processing

Background:

• Accurate demodulation of digital holograms is crucial for quantitative phase imaging.
• Existing methods struggle with nonplanar fringes and local orientation variations.
• Quadrature-phase functions are essential for hologram demodulation.

Purpose of the Study:

• To propose a novel Riesz transform-based approach for digital hologram demodulation.
• To develop a method for constructing accurate quadrature-phase functions.
• To achieve aberration-free holographic imaging, particularly for nonplanar wavefronts.

Main Methods:

• Utilized the Riesz transform, a multidimensional extension of the Hilbert transform.
• Constructed a vortex operator using quasi-eigenfunctions to generate accurate quadratures.
• Calibrated the method using a reference hologram and validated on synthesized and real fringe patterns.

Main Results:

• The Riesz transform-based vortex operator successfully generates accurate quadratures.
• The method effectively handles nonplanar fringes and compensates for local orientation.
• High demodulation accuracy was demonstrated on both synthetic and experimental data, including biological samples.

Conclusions:

• The proposed Riesz transform approach provides a robust method for digital hologram demodulation.
• This technique enables aberration-free holographic imaging, overcoming limitations of previous methods.
• The vortex operator offers significant advantages for analyzing complex holographic data.