Calculation of vectorial three-dimensional transfer functions in large-angle focusing systems

Area of Science:

• Optics and Photonics
• Electromagnetic Theory
• Image Science

Background:

• The optical transfer function (OTF) is crucial for characterizing imaging system performance in the Fourier domain.
• Calculating the OTF for large-aperture systems is complex due to the vectorial nature of light, which disrupts traditional cylindrical symmetry assumptions.
• Existing methods struggle with the vectorial light effects in high-aperture imaging.

Purpose of the Study:

• To develop a simplified method for calculating the vectorial three-dimensional OTF of large-aperture imaging systems.
• To extend the formalism to account for imaging across interfaces between media with different refractive indices.
• To provide a general framework for computing the Fourier transform of electromagnetic field products within pupil functions.

Main Methods:

• Derivation of a line integral solution for the vectorial three-dimensional OTF.
• Extension of the formalism to include imaging through planar interfaces with mismatched refractive indices.
• Development of a general approach for calculating the Fourier transform of arbitrary vector component products of the electromagnetic field.

Main Results:

• A novel, simplified line integral solution for computing the vectorial 3D OTF.
• The method successfully extends to analyze imaging through interfaces of differing refractive indices.
• The formalism accommodates arbitrary pupil function modifications, including phase and amplitude.

Conclusions:

• The derived line integral solution offers a significant advancement in calculating vectorial OTFs for complex imaging systems.
• This approach simplifies the analysis of large-aperture systems and imaging through refractive interfaces.
• The generalized formalism provides a powerful tool for analyzing various electromagnetic field interactions within imaging systems.