Optical Aberrations

Aberrations are the departures of a real optical system from ideal paraxial imaging, blurring or distorting the image away from the axis or for non-paraxial rays.

Definition

Imperfections in image formation by which an optical system fails to map each object point to a single sharp image point, classified as monochromatic aberrations from the geometry of non-paraxial rays and chromatic aberrations from the wavelength dependence of refractive index.

Scope

This topic covers the systematic deviations from perfect image formation that arise when the paraxial approximation breaks down or when light of different wavelengths is involved. It includes the five primary (Seidel) monochromatic aberrations of spherical aberration, coma, astigmatism, field curvature, and distortion, as well as chromatic aberration arising from dispersion. It treats the wavefront description of aberrations, their dependence on aperture and field, and the strategies used to balance or correct them in lens design.

Core questions

• Why do real lenses fail to form perfect images of off-axis or wide-aperture object points?
• What are the distinct types of primary aberration and how does each distort the image?
• How does chromatic aberration arise from dispersion and how is it corrected?
• How can a multi-element design balance aberrations against one another?

Key concepts

• spherical aberration
• coma
• astigmatism
• field curvature
• distortion
• chromatic aberration
• wavefront error
• Abbe number

Key theories

Seidel (third-order) aberration theory

Expanding the wavefront error to third order in aperture and field angle yields five primary monochromatic aberrations, spherical aberration, coma, astigmatism, field curvature, and distortion, each with a characteristic dependence on aperture and field.

Chromatic aberration and achromatization

Because refractive index varies with wavelength, focal length depends on colour; combining lenses of complementary dispersion in an achromatic doublet brings two or more wavelengths to a common focus.

Clinical relevance

Aberrations of the human eye, both lower-order refractive errors and higher-order aberrations, are measured by wavefront aberrometry and corrected with spectacles, custom contact lenses, or refractive surgery; controlling aberrations is also essential to high-resolution microscopes and astronomical instruments.

History

Seidel published the third-order theory of the five primary aberrations in 1856, giving lens designers a systematic vocabulary. Earlier, Fraunhofer and others had developed achromatic doublets to tame chromatic aberration, and Abbe later placed lens design on a firmer theoretical and metrological footing in the manufacture of microscope optics.

Key figures

• Ludwig von Seidel
• Ernst Abbe
• Joseph von Fraunhofer

Seminal works

• bornwolf1999
• smith2007

Frequently asked questions

What is the difference between spherical and chromatic aberration?

Spherical aberration is a monochromatic defect in which rays through different zones of a spherical surface focus at different distances, while chromatic aberration arises because different wavelengths of light are refracted by different amounts and so focus at different points.

Can aberrations be eliminated completely?

No single lens is free of all aberrations, but careful choice of element shapes, materials, and spacings, and the use of aspheric surfaces, can reduce the residual aberrations to a level negligible for a given application.