Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant

Area of Science:

• Optics and Photonics
• Wave Propagation
• Optical System Characterization

Background:

• Traditional optical system analysis often separates ray tracing from wave propagation effects.
• Accurate characterization requires methods that preserve both geometric and diffractive properties.
• Existing methods may not simultaneously provide precise ray trajectories and complex wave-amplitude distributions.

Purpose of the Study:

• To introduce and describe the Fresnel Gaussian Shape Invariant (FGSI) technique for optical system characterization.
• To demonstrate a method that combines ray tracing with wave propagation analysis.
• To enable high-precision calculation of complex wave-amplitude distribution in optical systems.

Main Methods:

• Representing object plane complex amplitude as a superposition of complex Gaussian wavelets.
• Propagating these wavelets through the optical system using the Fresnel Gaussian Shape Invariant (FGSI).
• Simultaneously tracking ray trajectories and the complex wave-amplitude field distribution.

Main Results:

• The FGSI method allows for full characterization of optical systems, including diffractive and geometric aspects.
• It enables precise calculation of complex wave-amplitude distribution at any observation plane.
• The technique successfully preserves the undulatory behavior of the field distribution alongside ray tracing.

Conclusions:

• The FGSI technique offers a unified approach to optical system analysis, integrating ray and wave optics.
• This method is applicable across a broad spectral range, including visible light, X-rays, and acoustic waves.
• The described technique provides a powerful tool for detailed optical system evaluation.