Page 114 - The Indian Optician Digital Edition March-April 2021

two sliding components to enable them to slide
without making contact with one another. This THE THICKNESS AT ANY
form of construction is employed in several
commercially available adjustable spectacles. POINT ON AN ASTIGMATIC
LENS IS MADE UP
A good understanding of the way in
which the Alvarez lens works can be obtained FROM A CONTRIBUTION BY
from Figure 5 which shows the components THE SPHERICAL ELEMENT
centred to form an afocal plate. The power
across the surfaces varies smoothly, but it AND A CONTRIBUTION BY
can be supposed that the power varies across THE CYLINDRICAL ELEMENT
each component as indicated in the Figure. In OF THE LENS
reality, the power varies point by point across
the surface of each element, but if each of the
above small areas is considered as a point, the
comparison remains valid. It will be noted that when the elements are
At the very centre of the combination placed together to form an Alvarez lens (as
the power is zero. The top left-hand area of shown in the lower diagram) the sum of the
the component on the left is marked -2,4, powers in each of the numbered areas is zero.
which means that the power at some point The powers in a few of the areas are shown in
in this area is -2.00 DC x 90/+2.00 DC x 180 (or red and as has just been stated, the powers in
-2.00/+4.00x180), whereas the power in the same these areas all sum to zero.
area of the component on the right is +2.00 Now consider the powers which result from
DC x 90/-2.00 DC x 180 (+2.00/-4.00x180). The sliding the left hand component up by one area
powers in this area neutralize one another. as shown in Figure 6. The powers in the areas
which are now opposite to one another are
shown in red, as before, and it can be seen that
the powers in the corresponding areas sum to
+1.00 D.

The geometry of the Alvarez lens will
now be considered in detail. The thickness at
any point on an astigmatic lens is made up
from a contribution by the spherical element
and a contribution by the cylindrical element
of the lens.

Thus for the spherical element of the lens
Figure 4. Alvvarez lens withh a curved contact suurface shown in Figure 7(a), the thickness at a point,
n
P, whose co-ordinates are (x, y) is given by t - z,
C
where, from the approximate sag relationship,
2
z = a /2r.
2
2
2
Since, a = x + y and r = 1000(n - 1) / S, where
S is the spherical power of the lens, we can write
the thickness of the spherical element as
t SPH = t - (x + y ) S / 2000(n - 1)
2
2
C
The thickness variation from the centre, t ,
C
is, therefore,
a
c
Figure 5. Alvaarez lens arrannged to form an afocal leens
2
2
t - t = ୿t SPH = -((x + y ) S / 2000(n - 1))
C
S
| MAR-APR 2021 | 110 LENS TALK
Mar-Apr 2021 SK.indd 58 26-04-2021 13:32