Math 2.0

Optics, electromagnetic theory Definition

Optical aberration

Builds on Paraxial approximationOptical path lengthGeometric optics

Definition

Consider an optical system with an exit pupil, in a medium of refractive index nn on the image side. Let PP be an object point and let P′P' be its Gaussian image point, that is, its image under the paraxial approximation. Let Σ\Sigma be the reference sphere: the sphere centred at P′P' through the centre of the exit pupil.

  1. The wave aberration W(x,y)W(x, y) at a point (x,y)(x, y) of the exit pupil is an optical path length. It is measured along the ray from PP through (x,y)(x, y), from the reference sphere Σ\Sigma to the actual wavefront through the centre of the pupil.
  2. The transverse ray aberration of that ray is the vector from P′P' to the point where the ray meets the Gaussian image plane.
  3. The system has an aberration at PP when WW is not identically zero on the exit pupil.

Remarks

If the system images PP perfectly at P′P', the wavefront leaving the pupil is exactly the sphere Σ\Sigma, so W≡0W \equiv 0 and all ray aberrations vanish. A single converging lens with spherical surfaces fails this for points on its axis. Rays through its rim focus closer to the lens than paraxial rays, and WW has a nonzero term in the fourth power of the pupil radius. To first order the two measures are linked: the transverse ray aberration is −(R/n)∇W-(R/n) \nabla W, where RR is the radius of Σ\Sigma (the sign depends on the convention). Aberrations that occur for light of one wavelength are monochromatic; aberrations caused by the dependence of the refractive index on the wavelength are chromatic.

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Geometric optics, concept, no evidence levelGeometric opticsconceptOptical path length, concept, no evidence levelOptical path lengthconceptParaxial approximation, concept, no evidence levelParaxial approximationconceptOptical aberration, definition, no evidence levelOptical aberrationdefinition
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  1. Geometric optics concept
  2. Optical path length concept
  3. Paraxial approximation concept
  4. Optical aberration definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Optical_aberration
About this page
TagNMBRMSR3D3
URIm2://NMBRMSR3D3
Kinddefinition
WritingW0 stub
MSC78A05, 78A10
DefinesOptical aberration
UsesParaxial approximation, Optical path length, Geometric optics
Changed3 November 2026

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