Journal of the Optical Society of America · 1971 · 89 citations · 0 references
Natural SciencesPhysicsBiomedical OpticsOpticsVisual OpticsChromatic AberrationLens SystemsOptical AberrationsPhysical OpticsRefractive IndexSpherical AberrationAberration TheoryChromatic Aberration CorrectionCurvatureLens DesignPetzval CurvatureSpherical Aberration CorrectionThird-order Aberration TheoryThird-order Distortion
Continuously varying indices of refraction offer new degrees of freedom for lens design. The study evaluates how these varying indices can correct third‑order aberrations using Sands’ third‑order theory. They implemented the theory computationally and designed two singlet lenses: an axial‑gradient singlet correcting spherical and chromatic aberrations without distortion, and a radial‑gradient singlet correcting all monochromatic third‑order aberrations except Petzval curvature. Axial gradients perform equivalently to aspheric surfaces for third‑order aberrations, while radial gradients outperform axial gradients and offer greater design potential.
The use of a continuously varying index of refraction provides new degrees of freedom in the design of lens systems. By use of the third-order aberration theory developed by Sands, the effectiveness of these new degrees of freedom in correcting third-order aberrations is determined. After the theory is cast into a form suitable for a computer, two major designs are done. The first is a singlet with an axial gradient that is corrected for third-order spherical and chromatic aberrations and has no third-order distortion. A radial gradient is used in a singlet to correct all third-order monochromatic aberrations except Petzval curvature of field. The results of the study indicate that axial gradients have the same effect as aspheric surfaces for third-order aberrations. The study also shows that radial gradients are more effective in aberration correction than axial gradients and have a greater potential in lens design.