1.
Dispensing BSc (4)
Dr. Atif Babiker Mohamed Ali
Faculty of Optometry
2014 -2023

2.
The crossed or compound cylinder
form
• To transpose a sphero-cylinder to crossed
cylinders:
• A- the sphere power (S) become the power of
one cylinder (C1) with axis at right angle to
that of original cylinder ( C ).
• B- the sum of the sphere (S) and cylinder ( C)
becomes the power of the second cylinder
(C2) with axis parallel of original cylinder ( C).

3.
• Example: transpose - 1.0sph/- 2.0 CX90 to
crossed cylinder form.
• A- -1.0 CX 180
• B- - 3.0 CX 90
• The form is
− 1.0 𝐶𝑋 180
− 3.0𝐶𝑋90
• Transpose - 2.0sph/+3.0 CX30 to crossed
cylinder form.
• A- -2.0 CX 120
• B- +1.0 CX 30
• The form is -2.0 CX 120/ +1.0 CX 30.

4.
• To transpose crossed cylinder to sphero-
cylinder.
• A- select any of cylinders (e.g. C1) to become
sphere (S).
• B- The difference between the two cylinders
(C2 - C1) become the new cylinder (C) with axis of
second cylinder (C2 ).
• E.g. Transpose + 1.0 CX 180/+1.5 CX90 to sphero-
cylinder form.
• A - + 1.0 sph
• B - + 1.5 – (+1.0) = +0.5 CX 90
• +1.0 sph/+ 0.5 CX 90

5.
• For example: transpose - 1.50CX90/ - 2.50CX
180 to sphero-cylinder form.
• A- - 1.50 Sph
• B- - 1.0CX 180
• Result: - 1.50 Sph/ - 1.0CX 180.
• Or select C2 instead of C1 to become the sph.
• A- - 2.50 sph
• B- - 1.5 – (-2.5) = + 1.0 CX90
• Result – 2.5sph/ + 1.0 CX 90

6.
Toric lenses
• Like meniscus lenses, torics have one convex
and one concave surface, but only one of
these is spherical. The other surface which
required to correct astigmatism is known as
toroidal surface.
• The base curve is the surface power in the
meridian of least curvature.
• The cross curve is the surface power in the
meridian of maximum curvature.

7.
• E.g. if the base curve were +6.0D and the
cross curve +7.50D, this toric surface could be
specified as +1.50D cylinder.
• There is a simple rule can be used to express
the power of a toric lens in the usual sphero-
cylinder or cylinder notation.
• Sphere power = Base curve + power of
spherical surface.
• Cylinder power = Cross curve – base curve
• Sph = BC + SC
• Cyl = CC - BC

8.
Toric transposition
• In case of toric transposition if the spherical
surface is given. Transpose the cylinder of
sphero-cylinder form to opposite sign of
spherical.
• In case of toric transposition if the Base curve
is given. Transpose the cylinder of sphero-
cylinder form to same sign of Base curve .

9.
• Transpose – 1.0/ - 0.5 CX 180 to toric form
given base curve – 6.0D.
• Sph = BC + SC
• Cyl = CC - BC
• - 1.0 = - 6.0 + SC or (SC = + 5.0)
• - 0.5 = CC - ( -6.0) or (CC = - 6.5)
•
𝑆𝐶
𝐵𝐶/𝐶𝐶
•
+5.0𝑆𝑝ℎ
−6.0𝐶𝑋90/−6.5𝐶𝑋180

10.
• Transpose +2.0/+1.5 CX 30 to toric form given
spherical surface +9.0Dsph.
• Transpose to opposite cyl sign +3.5/ - 1.5 CX 120
• Sph = BC + SC
• Cyl = CC – BC
• +3.5 = BC + (+9.0) or (Bc = - 5.5)
• - 1.5 = CC – (-5.5) or (CC = - 7.0)
•
𝑆𝐶
𝐵𝐶/𝐶𝐶
•
+9.0𝑆𝑝ℎ
−5.5 𝐶𝑋30/−7.0𝐶𝑋120