Optical System Aberrations (Un-sharp Images)

The inability of a lens to produce a completely sharp image

Rays of light from subject points are not returned as exact image pointsThere are several different types of aberration which can affect image quality.

Spherical aberration

Spherical aberrationSpherical aberration occurs because spherical surfaces are not the ideal shape with which to make a lens, but they are by far the simplest shape to which glass can be ground and polished and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses. Spherical aberration can be minimized by careful choice of the curvature of the surfaces for a particular application: for instance, a plano-convex lens which is used to focus a collimated beam produces a sharper focal spot when used with the convex side towards the beam source.



comaAnother type of aberration is coma, which derives its name from the comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays which pass through the centre of the lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimized (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimized are called bestform lenses.


Chromatic Aberration

Chromatic aberrationChromatic aberration is caused by the dispersion of the lens material—the variation of its refractive index n with the wavelength of light. Since, from the formulae above, f is dependent upon n, it follows that different wavelengths of light will be focused to different positions. Chromatic aberration of a lens is seen as fringes of color around the image. It can be minimized by using an achromatic doublet (or achromat) in which two materials with differing dispersion are bonded together to form a single lens. This reduces the amount of chromatic aberration over a certain range of wavelengths, though it does not produce perfect correction. The use of achromats was an important step in the development of the optical microscope. An apochromat is a lens or lens system which has even better correction of chromatic aberration, combined with improved correction of spherical aberration. Apochromats are much more expensive than achromats.

Different lens materials may also be used to minimize chromatic aberration, such as specialized coatings or lenses made from the crystal fluorite. This naturally occurring substance has the highest known Abbe number, indicating that the material has low dispersion.

Other types of aberration

Other kinds of aberrationOther kinds of aberration include field curvature, barrel and pincushion distortion, and astigmatism.

Aperture diffraction

Even if a lens is designed to minimize or eliminate the aberrations described above, the image quality is still limited by the diffraction of light passing through the lens' finite aperture. A diffraction-limited lens is one in which aberrations have been reduced to the point where the image quality is primarily limited by diffraction under the design conditions

Low Dispersion Glass

Low dispersion glass (LD glass) is a type of glass with low dispersion. Its chief use is in lenses, where SLD elements minimize the chromatic aberration of the lens assembly. 

Special low dispersion glass (SLD glass) and extraordinary low dispersion glass (ELD glass) are glasses with yet lower dispersion (and yet higher price). Other glasses in this class are extra-low dispersion glass (ED glass), ultra-low dispersion glass (UL glass).

Some glasses have a peculiar property called anomalous partial dispersion. Their use in telephoto lens assemblies was pioneered by Leitz.

Before their availability, calcium fluoride in the form of fluorite crystals were used as material for these lenses; however the low refraction index of calcium fluoride required high curvatures of the lenses, therefore increasing spherical aberration. Fluorite also has poor shape retention and is very fragile.

Glass with addition of thorium dioxide has high refraction and low dispersion and was in use since before WW2, but its radioactivity led to its replacement with other compositions. Even during WW2, Kodak managed to make high-performance thorium-free optical glass, for use in aerial photography, but it was yellow-tinted; as it was used usually with black and white film, this property was actually beneficial for that application.

Leitz laboratories discovered that lanthanum(III) oxide can be a suitable thorium dioxide replacement; other elements however had to be added to preserve the amorphous character of the glass and prevent crystallization that'd cause striae defects.

Another high-performance glass contains high content of zirconium dioxide; however its high melting point requires use of platinum lined crucibles to prevent contamination with crucible material.

A good high-refraction replacement for calcium fluoride as a lens material can be a fluorophosphate glass, where a proportion of fluorides is stabilized with a metaphosphate, with addition of titanium dioxide. 

The high cost of such high-performance glasses is mainly dependent on availability of sufficiently pure chemicals in sufficient quantities, and on associated technological difficulties.

Fluorite / UD / Super UD Glass

When parallel light rays are refracted by a prism, a rainbow-hued spectrum comes out. This phenomenon is called "dispersion". In case of photographic lenses, the dispersion causes color fringes at the edge of subjects, which is called axial chromatic aberration, and as a result, deterioration of image quality of photography. There is a limit to the correction of chromatic aberration, using regular optical glass lens elements only. Some aberrations not corrected by optical glass are called secondary spectrum or residual chromatic aberration or secondary chromatic aberration. The artificial crystal fluorite lens element, featuring very low optical dispersion index, was developed by Canon to eliminate secondary spectrum. Canon succeeded artificially crystallizing calcium fluoride (CaF2) into fluorite at the end of 1960s. Canon EF lenses are the only interchangeable lenses for 35mm SLR at the time that employ fluorite lens elements. In the late 1970s, Canon also developed special optical glass lens elements with very low dispersion index called Ultra-low Dispersion (UD) glass lens elements, and in 1990s an upgrade version of UD glass, called Super UD glass, was developed. Fluorite, UD and Super UD glass lens elements are widely used in EF lens series, for super-telephoto L series lenses, as well as in telephoto zoom and wide angle lenses.

FLD glass is the highest level low dispersion glass available with extremely high light transmission. This optical glass has a performance equal to fluorite glass which has a low refractive index and low dispersion compared to current optical glass. It also benefits from high anomalous dispersion. Using these characteristics gives excellent correction for residual chromatic aberration (secondary spectrum) which cannot be corrected by ordinary optical glass and ensures high definition and high contrast images. FLD glass offers superior optical performance, equal to fluorite, at an affordable price. The density of FLD glass is lower than traditional optical glass, ensuring a lighter construction of large aperture lenses.

FLD glass has been incorporated into some of Sigma's recently announced lenses; 4 elements have been included in the Sigma 8-16mm F4.5-5.6 DC HSM as well as 2 elements in both the Sigma APO 70-200mm F2.8 EX DG OS HSM and the Sigma 17-50mm F2.8 EX DC OS HSM.

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