Chromatic and Spherical Aberrations

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Spherical aberration

A simple spherical lens focuses light from its edge to a slightly different point from light passing through its centre. This difference blurs the image, and it is called spherical aberration. It is most visible wide open, because the outer zones of the lens carry the most light at that aperture.

Designers reduce spherical aberration by combining elements with different shapes and glass types, and by using aspheric surfaces that depart from a sphere in a controlled way. Stopping down also reduces its effect, because the outer zones are blocked.

Chromatic aberration

The refractive index of glass varies with wavelength. Blue light is bent more strongly than red light, so the two colours focus at different distances. This is longitudinal chromatic aberration. A related effect, lateral chromatic aberration, shifts the colours sideways, so that the edges of high-contrast detail show coloured fringes.

The standard correction is an achromatic doublet: a positive crown glass element combined with a negative flint glass element. The two glasses have different dispersion, so their colour errors partly cancel. More demanding designs use low-dispersion materials to reduce the residual colour error further.

Balancing the corrections

Correcting one aberration often affects another. A design that corrects spherical aberration well may leave more colour error, and the reverse can also be true. Designers balance these against cost, weight, size and manufacturing tolerance. The final design is a compromise chosen for its intended use.

How to recognise them in images

Spherical aberration softens the whole image, often most noticeably in high-contrast detail, and it is reduced by stopping down. Chromatic aberration produces coloured fringes along high-contrast edges. It can be reduced in software, but software correction does not restore lost detail.

Common mistakes

Assuming a sharp centre means no spherical aberration at the edges. Assuming colour fringes are only a software problem. Comparing aberration performance at different apertures or focus distances without stating the conditions.

Correcting spherical aberration with aspheres

An aspheric surface departs from a sphere in a controlled way, so that rays from the edge of the lens are bent to focus at the same point as rays from the centre. Aspheric elements can reduce spherical aberration with fewer elements than an all-spherical design, which saves weight and cost. They are harder and more expensive to manufacture, and their performance depends on accurate production and alignment.

Apochromatic correction

Achromatic doublets bring two colours to a common focus. Apochromatic designs bring three colours to a common focus and reduce the remaining colour error across the spectrum. They usually use low-dispersion glass with a high Abbe number or specialised materials. Apochromatic lenses are common in demanding applications, where colour fringing must be minimised without relying on software.

Reading the effect in a real photograph

Photograph a high-contrast edge, such as a black line on white paper, at several apertures. Coloured fringes that persist when stopped down suggest lateral colour or residual chromatic error. Blur that shrinks when stopped down suggests spherical aberration. Testing in the centre and at the edges of the frame distinguishes these effects from focus error.

Field curvature and distortion

Aberrations are not limited to spherical and chromatic errors. Field curvature makes the image plane curved, so the edges focus at a different distance from the centre. Distortion changes the shape of straight lines, with barrel and pincushion as the common forms. Coma makes off-axis points look like comets. Each error is controlled by a different choice of element shape, glass or spacing.

Measuring chromatic error

A simple test uses a high-contrast target with black and white edges, photographed at a fixed aperture. Coloured fringes that increase towards the edge of the frame indicate lateral chromatic aberration. Fringes that change sign on either side of focus indicate longitudinal chromatic aberration. Repeating the test at several apertures helps separate the two effects.

The role of computation

Lens designers use ray tracing to calculate where each ray from an object point lands in the image plane. The spread of those landing points gives the spot diagram, which shows the aberrations quantitatively. Modern designs are optimised by software that adjusts curvatures, spacings and glass choices to minimise a merit function. Human judgement remains part of the process, particularly in deciding what compromises are acceptable.

Software correction

Cameras and raw processors can correct distortion, lateral colour and vignetting using stored lens profiles. These corrections improve the image but do not restore detail that the lens failed to record. Corrections also depend on accurate profiles for the specific lens and focus setting.

Practical advice for choosing a lens

When comparing lenses for colour fringing, use test shots of high-contrast edges in the same light and at the same focus. When comparing for softness, test the corners as well as the centre, because spherical aberration is visible across the frame while field curvature is most visible at the edges. Both tests should be repeated at the apertures you actually use.

Why corrections trade against each other

Correcting colour with an extra element adds glass, weight and surfaces, each of which can add reflection and other errors. Designers accept some residual colour error to keep the lens compact, or accept some extra size to reduce colour error further.

Reading a test result

Test results with coloured fringes should be checked against the test chart itself, because some charts have colour fringes of their own. Compare the result with a reference lens if one is available, and note whether the fringes are visible in the centre, the edges or both.

Going further

Both aberrations are part of every lens, and a good design keeps them small enough that they do not dominate the image. Knowing how each one looks in a photograph makes it easier to decide whether a lens problem is the cause of a poor result.

Summary

The key point of this article is the one stated at its start. Check the formula, use the stated assumptions, and confirm any result with a test before relying on it in practice.

Sources

Eugene Hecht, Optics, Pearson (any current edition).
Max Born and Emil Wolf, Principles of Optics, Cambridge University Press (any current edition).
ISO 12233: Photography, Electronic still picture imaging, Resolution and spatial frequency responses.

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General information only. This page explains optical principles and does not replace lens design work, lens testing or advice from a qualified optical engineer.