Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform

Area of Science:

• Optics and Photonics
• Computational Imaging
• Digital Holography

Background:

• Digital Holography (DH) applications often require only a few wavefield samples for image reconstruction.
• Current methods like direct and spectral discrete Fresnel transforms can lead to excessive sampling rates.
• Existing wavefield computation methods necessitate multiple 2D discrete Fourier transforms (2D-DFT), increasing computational cost.

Purpose of the Study:

• To develop a more efficient numerical method for computing down-sampled wavefields in DH.
• To reduce the computational load associated with wavefield propagation and sampling in DH.
• To enable precise control over down-sampling rates without compromising image quality.

Main Methods:

• Introduction of an aliasing operator for controlled wavefield down-sampling.
• Utilization of a single 2D discrete Fourier transform (2D-DFT) instead of multiple transforms.
• Integration of the aliasing operator with the Fresnel transform for efficient wavefield computation.

Main Results:

• The proposed method significantly reduces computational complexity compared to existing techniques.
• Achieves efficient down-sampling of wavefields obtained through Fresnel transform.
• Demonstrates the feasibility of using a single 2D-DFT for down-sampled wavefield calculation.

Conclusions:

• The novel approach offers an efficient solution for down-sampling wavefields in Digital Holography.
• This method lowers the computational burden, making DH applications more accessible.
• The use of an aliasing operator and a single 2D-DFT is a promising advancement in holographic imaging.