Curvilinear distortion

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When an iris diaphragm acting as the aperture stop is used to limit the diameter of a camera lens in order to reduce aberrations, it is desirable that it should be located so that it transmits the bundle of rays that surround the primary ray (i.e. the ray that passes through the centre of the lens undeviated). Distortion occurs when a stop is used to control aberrations such as coma. If the stop is positioned for example in front of the lens or behind it, the bundle of rays selected does not pass through the centre of the lens (as is assumed in theory based on thin lenses), but through a more peripheral region, where it is deviated either inwards, for a stop on the object side of the lens ('barrel distortion'), or outwards, for a stop on the image side of the lens ('pincushion distortion') (see

Barrel distortion Pincushion distortion

Barrel distortion Pincushion distortion

Object Images

Object Images

Barrel Pincushion distortion distortion

Barrel Pincushion distortion distortion

Figure 6.10 The effects of curvilinear distortion. (a) The selection of a geometrically incorrect ray bundle by asymmetric location of the aperture stop. (b) Image shape changes caused by barrel and pincushion distortion defects cancel one another. The use of a symmetrical construction eliminates not only distortion but also coma and lateral chromatic aberration. Unfortunately, residual higher orders of spherical aberration limit the maximum aperture of such lenses to about f/4.

Lenses of highly asymmetrical construction, such as telephoto and retrofocus lenses, are prone to residual distortions: telephoto lenses may show pincushion distortion and retrofocus lenses barrel distortion. The effect is more serious in the latter case, as retrofocus lenses are used chiefly for wide-angle work, where distortion is more noticeable. Zoom lenses tend to show pincushion distortion at long-focus settings and barrel distortion at short-focus settings, but individual performance must be determined by the user. General purpose lenses usually have about 1 per cent distortion measured as a displacement error, acceptable in practice. Wide-angle lenses for architectural work must have less than this, while lenses for aerial survey work and photogrammetry must be essentially distortion free, with residual image displacements measurable in micrometres. The use of aspheric lens surfaces may help reduce distortion.

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