4
Astigmatic Lenses
In an astigmatic lens, all the meridians do not have the same curvature and a point image of a point object cannot be formed. The lens effectively gives a minimum power in one direction, gradually changing to a maximum power in the other, at right angle to the first. These meridians of minimum and maximum power are referred to as the principal meridians of the lens. There are two types of astigmatic lenses, namely cylindrical and toric lenses.
CYLINDRICAL LENSES (FIG. 4.1)
Cylindrical lenses have one plane surface and the other curved surface forming the part of a cylinder. Thus, in one meridian the lens has no vergence power which is known as the axis of the cylinder. In the meridian at right angle to the axis, the cylinder acts as a spherical lens. The total effect is the formation of a line image of a point object. This is called focal line. It is parallel to the axis of the cylinder (Fig. 4.2).
Fig. 4.1: Cylindrical Lens
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Fig. 4.2: Image formation by convex cylindrical lens of point object O
NOTATION FOR CYLINDER LENSES AND ORIENTATION OF AXIS
Fig. 4.3: Axis direction of astigmatic lens
A lens with purely cylinder power would be described as, say – 4.00Dcyl (diopter cylindrical) in order to differentiate from the spherical one, which is described as – 4.00Dsph (diopter spherical). As cylindrical surface is not rotationally symmetrical about the midpoint, a notation is required for their positioning in front of the eye. This is achieved by specifying the angle between the axis of symmetry of the cylinder and the horizontal. The universally used “standard” axis notation uses a protractor that reads anticlockwise when looking at the face of the lens wearer. Angles upto 180 are
Fig. 4.4: Standard axis notation
Astigmatic Lenses 35
used for the axis of cylinder, the full 360° protractor is only required for the base direction of prism. When describing a horizontal cylindrical axis, it is conventional to use the angle 180°, rather than zero. The orientation of cylindrical axis is opposite the dispenser’s side as compared with viewing the axis from the subject’s side (Figs 4.3 to 4.5).
Fig. 4.5: Orientation of cylindrical axes on a protractor
A good way to recognize cylindrical axes from dispenser’s side is to view the back of your left hand; the thumb will point to the zero degree (Fig. 4.6).
Fig. 4.6: Thumb will point to zero degrees
TORIC LENSES
Toric lenses, also known as sphero-cylinder lenses can be explained as spherical lens that has been placed in contact with a plano-cylinder lens (Fig. 4.7).
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Fig. 4.7: Convex spherical surface combined with plano-convex cylindrical surface
Since a plano-cylinder lens has no power along its axis meridian, the power along the axis meridian of the combination must result from spherical element alone. The power along the other principal meridian of the lens, at right angles to the axis meridian of the cylinder surface, is the sum of the sphere and cylinder. Under the rotation test, it exhibits scissor movement in the same way as a plano-cylindrical lens and under the movement test; it exhibits movement along each of its principal meridians. The power of a sphero-cylindrical lens is expressed by stating the power of the spherical component first, followed by the power of the cylindrical component, and finally the direction of the cylindrical axis. Thus, the specification:
– 3.00/– 2.00 × 90º
It signifies that spherical component of the lens is – 3.00D, the cylindrical component is – 2.00D and the axis of the cylindrical surface lies along the 90º meridian. On representing the power of the sphero-cylindrical lens by means of optical cross, the principal meridians show – 3.00D on vertical meridian and – 5.00D on the horizontal meridian as shown in Figure 4.8.
Fig. 4.8: Optical cross representation of – 3.00/– 2.00 × 90°
The pencil of light that results from refraction at an astigmatic lens is depicted in the Figure 4.9. Since the light does not focus as a point, the interval between two line foci is called the ‘Interval of Sturm’. The best focusing occurs somewhere inside the interval of Sturm. This point is called the ‘Circle of least confusion’, and the complete envelop of the light near the circle of least confusion is called the ‘Sturm’s Conoid’, named after the mathematician CF Sturm.
Astigmatic Lenses 37
Fig. 4.9: Pencil of light results from retraction at an astigmatic lens
Figure 4.10 illustrates the toroidal surface of the sphero-cylinder lens. The lower power is usually referred to as the base curve of the surface and the higher power as the cross curve. In the plano-cylindrical surface, the base curve is along the axis meridian which is zero and the cross curve is simply the power of the cylindrical surface. In case of the toroidal surface, the “axis meridian” is curved and the cylindrical power of the surface is the difference between the cross curve and the base curve.
Fig. 4.10: Toroidal surface of the sphero-cylinder lens
DETECTION OF CYLINDRICAL LENS
Cylinder lenses are often referred to as cylinder or toric lens because of their out of round surfaces. In order to determine the cylinder lens and to detect its dioptric strength, hold the lens a few inches away from your eyes; sight a straight lined object, such as window or the door frame. Rotate the lens slowly as you would turn a steering wheel – first to the right
38 Ophthalmic Lenses
(clockwise), then to the left (anti-clockwise). If a section of the door frame appears slanted, it establishes that the lens under examination is a cylindrical lens. This is called “scissors like movement”.
Fig. 4.11: Looking through a plano-cylinder, a section of the door’s frame appears to be slanted
Fig. 4.12: Upon rotating the lens, a position will be found in which the door frame appears straight
Next step is to find out two principal meridians of the lens. To do so continue rotating the lens and at one position on rotation, the frame of the door would not look slanted. This is one of the principle meridians. The meridian opposite to this is the other principal meridian. They are at 90 degree to each other. Now, neutralize both the meridians separately. If the movement in one meridian is nil, it is a plano-cylindrical lens and nil movement meridian is taken as the axis of the lens. Contrarily, if both the meridians show movement, it is a sphero-cylindrical lens. The weaker movement meridian is taken as the axis of the lens under observation. Now, neutralize both the meridians as before to determine exact spherical and cylindrical elements.
Astigmatic Lenses 39
Fig. 4.13
Fig. 4.14
Fig. 4.15
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Lensometer can also be used to determine the lens power of an astigmatic lens. The procedure is as under:
•Place the lens on the lens stage and start from zero.
•Focus the target image by rotating the dioptre power knob.
•Read the dioptre power scale when the target image is cleared. This is taken as either plano for a plano-cylinder lens or spherical for a toric lens.
•Now focus the target for other meridian by rotating the knob.
•The difference between the second absolute value and the first is taken as cylinder.
•Align the cross line with the second focused point by rotating the axis wheel. The angle of the indicator shows the axis.