Analytic design of a spherochromatic singlet

Area of Science:

• Optical engineering
• Lens design
• Aberration correction

Background:

• Spherochromatic lenses exhibit aberrations that limit optical performance.
• Achieving diffraction-limited performance requires precise control over chromatic and spherical aberrations.

Purpose of the Study:

• To derive an analytic formula for the output surface of a spherochromatic lens.
• To minimize spherical aberration for a wide range of wavelengths.
• To enable diffraction-limited performance in singlet lenses.

Main Methods:

• Analytic formula derivation for lens surface.
• Ray-tracing simulations.
• Spot diagram analysis for multiple wavelengths (Abbe numbers).

Main Results:

• The derived analytic formula successfully minimizes spherical aberration.
• All rays for a broad spectrum of wavelengths focus within the Airy disk.
• Ray-tracing confirmed satisfactory performance, meeting diffraction-limited criteria.

Conclusions:

• The analytic solution provides a method for designing high-performance spherochromatic lenses.
• This approach is suitable for singlet lenses requiring minimal aberrations.
• The results demonstrate the potential for diffraction-limited optical systems.