Focal-shift formula in apodized nontelecentric focusing systems

Area of Science:

• Optics and Photonics
• Optical Engineering
• Mathematical Physics

Background:

• Apodization and nontelecentric setups are crucial in optical system design.
• Understanding focal shift is essential for precise optical focusing.
• Existing methods for focal shift evaluation can be complex and setup-specific.

Purpose of the Study:

• To develop a universal analytical formulation for focal shift evaluation.
• To simplify the analysis of focal shift in apodized nontelecentric focusing systems.
• To demonstrate the formulation's applicability to paraxial beams.

Main Methods:

• Derivation of a single analytical formulation for focal shift.
• Analysis of the formulation's dependence on pupil filter characteristics.
• Application of the formulation to various focusing configurations.

Main Results:

• A unified analytical formulation for focal shift is presented.
• The focal shift magnitude is shown to depend on a single parameter related to the pupil filter's effective width and axial position.
• The formulation is validated across different focusing setups and for paraxial beams.

Conclusions:

• The developed formulation provides a simplified and universal approach to evaluate focal shift.
• This work offers a valuable tool for optical system design and analysis.
• The findings contribute to a deeper understanding of focusing behavior in optical systems.