Relating vector ray-tracing equations for holograms of arbitrary shape and thickness

Area of Science:

• Optics and Photonics
• Holographic Imaging
• Mathematical Modeling

Background:

• Latta's ray-tracing equations are established for holograms of arbitrary thickness.
• Welford's vector ray-tracing equation applies to holograms of arbitrary shape.
• Existing models may not fully account for medium deformation during holographic processes.

Purpose of the Study:

• To derive Latta's ray-tracing equations from Welford's vector equation.
• To extend holographic ray-tracing capabilities to include changes in recording medium shape and thickness.
• To provide a unified framework for analyzing holographic systems with deformable media.

Main Methods:

• Utilized Welford's vector ray-tracing approach as the foundational method.
• Modified the derivation to incorporate variations in the hologram's shape and thickness.
• Applied principles of geometrical optics and vector analysis.

Main Results:

• Successfully derived Latta's equations for arbitrary thickness holograms starting from Welford's arbitrary shape equation.
• The derivation explicitly accounts for physical changes in the holographic medium.
• The resulting equations offer a more comprehensive model for ray tracing in holography.

Conclusions:

• The unified derivation demonstrates the interconnectedness of holographic ray-tracing formalisms.
• This work provides a more robust theoretical basis for analyzing complex holographic optical elements.
• The findings are applicable to advanced holographic designs where medium deformation is a factor.