Page 115 - The Indian Optician Digital Edition March-April 2021

The thickness due to the cylindrical element
can be deduced as follows. The sag of the plano-
convex cylinder along its power meridian is the
sag of the cylindrical curve at the diameter, 2
q
(Figure 7(b)).
Suppose the cylinder has a power, C, with
axis, ת. The perpendicular distance of the point,
P, from the cylinder axis, q, is given by

q = x sin ת + y cos ת (see §8.15)
a
0
so the thickness contribution at P due to the Figure 6. Alvaarez lens arrannged to form a +1.00 D leens s
cylinder
୿t = - (x sin ת + y cos ת) C / 2000(n - 1)
2
CYL
Hence the variation in thickness
୿t = ୿t SPH + ୿t CYL =
2
2
2
- (x + y )S - (x sin ת + y cos ת) C / 2000(n - 1)
and so it must be possible to produce a
sphero-cylindrical lens by ensuring that its
thickness variation at every point is satisfied
by the above equation. A combination of two
optical elements in contact would produce the
same result if the combined thickness variation
satisfied the expression for ୿t.
If two such identical elements that are
arranged to enable sliding contact, are
P
p
k
combined so that the effect of any relative Figure 7. Thickness of component elemennts at aa point P
transverse movement is always to redistribute
the combined thickness in accordance with the
above expression, they would produce a lens of
variable spherical and cylindrical power. two components, z , the thickness component
X
A single Alvarez element is shown in Figure along the x-axis and z , the thickness
Y
8(a) and its combination with a second identical component along the y-axis.
component to form an afocal block is shown in Figure 9 reproduces Figure 8(a) to a
Figure 8(b). larger scale and it can be seen that the total
thickness, PQ, = t , of the element at point P(x,
The coordinate system which is chosen is P
y), is given by
also shown in Figure 8 where, it has been seen
that movement of either component along the t = t + z + z Y
P
X
C
y-direction produces changes in spherical power
and movement along the x-direction produces Suppose that a section of the surface along
the x-axis is defined by the equation,
changes in cylindrical power.
The movement required to provide a given z = Ayx 2
X
power can be deduced from knowledge of the and that a section along the y-axis takes the
thickness of each Alvarez component. At some form of a simple cubic equation defined by,
point, P(x, y), on each element, the thickness
3
variation from the centre, t , is made up from z = Ay / 3
Y
C
| MAR-APR 2021 | 111 LENSES

Mar-Apr 2021 SK.indd 59 26-04-2021 13:32