OPTICAL CORRECTION

THE ABERRATIONS OF SPECTACLE LENSES (1)

Off-axis images formed by a lens placed before the eye are, in general, afflicted by various aberrations which spoil the image quality. A previous article examined transverse chromatic aberration and curvature of field.

This article will cover oblique astigmatism and distortion. Future articles will examine how these aberrations can be overcome.

OBLIQUE ASTIGMATISM

When a narrow pencil of rays is refracted obliquely by a spherical surface the refracted pencil becomes astigmatic.

Instead of the rays reuniting in a single image point, they form two line foci at right angles to one another with a disk of least confusion, where the refracted pencil has its least cross-sectional area, somewhere between the two foci. The plane containing the optical axis of the surface is referred to as the tangential plane and the plane at right angles to the tangential plane is referred to as the sagittal plane.

The effect of oblique astigmatism is to produce a blurring of the image as though an unwanted sphero-cylinder had been interposed between the lens and the eye.

Figure 2 shows the passage of a narrow pencil of oblique rays through a plus lens mounted before the eye.

The refracted pencil is afflicted with aberrational astigmatism and the tangential focus, Q',, lies closer to the lens than the sagittal focus, Q's. Ideally, the lens should produce a point image of a distant point object on the eye's far point sphere. (The terminology used for off-axis imagery is summarised in the caption.) The vertex sphere is an imaginary reference surface concentric with the eye's centre of rotation, from which the positions of the tangential and sagittal foci are measured. The far point sphere is the imaginary surface, also concentric with the eye's centre of rotation, upon which we can assume the far point to remain as the eye rotates to view through off-axis zones of the lens. The distance between the vertex sphere and the far point sphere measured through the eye's centre of rotation, Z, is constant and equal to the back vertex focal length of the lens, A2F'.

The reduction of oblique astigmatism is very important in the design of spectacle lenses and it will be seen later that this may be achieved by a suitable choice of lens bending or by the use of an aspherical surface.

FIGURE CAPTIONS 1

Distortion in spectacle lenses.

• a) square grid target for the study of distortion.
• b) appearance of target when viewed through strong plus spectacle lens.
• c) appearance of target when viewed through strong minus spectacle lens.
• 2. Oblique vertex sphere powers of spectacle lenses.

M, is the eye's far point, conjugate with the macula, M °. The criterion for a best-form spectacle lens is that it should produce point images of distant point objects on the eye's far point sphere. The focal lengths of the refracted pencils are measured from the point of intersection of the refracted pencil with the vertex sphere, Z, to the line foci, Q's and Q',.

• Back vertex power - 1 / f'v
• Sagittal oblique vertex sphere power, F's = 1 / f 's
• Tangential oblique vertex sphere power, F'1= 1 / f'1
• Oblique astigmatic error = F' - F's
• Mean oblique power, MOP= (F'T + F's) / 2
• Mean oblique error = MOP- F'v

DISTORTION

Distortion affects the shape of the image rather than its sharpness and is caused by the fact that the power of a spherical surface increases towards its periphery. Instead of remaining constant, the magnification increases as the eye uses wider and wider zones of a spherical lens.

Figure 1 shows the effects of distortion on a square- grid target (Figure la) viewed through plus and minus lenses. Plus lenses produce pincushion distortion (Figure lb), the type of distortion typically seen when a strong plus lens is used as a magnifier. Note that the characteristic pincushion-shape image also gives the impression that the object being viewed is concave, the centre of the object being further from the eye than the edges.

Minus lenses produce barrel distortion (Figure lc) and this is often reported by myopes who view through peripheral zones of their lenses. Note the convex appearance of the target afflicted with barrel distortion; the centre of the target appears to be closer than the edges.

When the form of a lens is changed, the amount of distortion that is exhibited by the lens also changes. This is probably the chief cause of the perceptual problems that occur when a client is given new lenses of a different form.

20/20 03/2002