Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space

Area of Science:

• Optics and Photonics
• Computer Graphics
• Computational Imaging

Background:

• Calculating computer-generated holograms (CGHs) is computationally intensive, often requiring significant processing time.
• Existing methods for Fresnel hologram calculation, particularly those using Fourier transforms, can be slow for complex scenes.

Purpose of the Study:

• To propose and validate a novel, accelerated method for calculating object lights for Fresnel holograms.
• To reduce the computational burden associated with generating CGHs for complex objects.

Main Methods:

• Developed a method to calculate object lights for Fresnel holograms without using Fourier transforms.
• Utilized three-dimensional affine transforms to generate object lights for variously shaped patches from a basic object light for a fixed-shape patch.

Main Results:

• The proposed method achieves a computation speed twice as fast as traditional Fourier transform-based methods.
• Computer simulations and optical experiments confirmed the effectiveness and efficiency of the new approach.
• Successfully calculated holograms displaying complex objects composed of patches with diverse shapes.

Conclusions:

• The novel method offers a significant speed improvement for Fresnel hologram computation.
• This technique enables the efficient generation of holograms for complex objects, overcoming limitations of previous methods.
• The approach is effective for creating realistic holographic displays with varied object geometries.