Normalized parameter relating the spherical aberration of a thin lens to the diffraction limit and fiber coupling...

Area of Science:

• Optics
• Optical Engineering

Background:

• Spherical aberration is a common optical distortion.
• Diffraction limits define the theoretical resolution of optical systems.

Purpose of the Study:

• To define and calculate transverse spherical aberration (TA) for thin lenses.
• To introduce a normalized aberration metric (Y) for assessing lens performance.
• To establish criteria for diffraction-limited performance and efficient Gaussian beam coupling.

Main Methods:

• Calculation of transverse spherical aberration (TA).
• Normalization of TA by the theoretical resolution limit to obtain the aberration metric Y.
• Analysis of lens performance based on Y values.

Main Results:

• A thin lens with only spherical aberration is effectively diffraction-limited if Y < 1.6.
• High coupling efficiency of Gaussian beams to single-mode fibers is achievable even for Y > 1.6.
• Diffraction-limited performance is only required over a radius approximately equal to the Gaussian beam's radius (to the 1/e-point).

Conclusions:

• The normalized aberration metric Y provides a practical tool for evaluating thin lens performance.
• The findings offer guidelines for designing optical systems requiring efficient Gaussian beam coupling.
• Optimized lens design can achieve high performance without strict diffraction-limited conditions over the entire aperture.