Definition
The act of converting the prescription of an ophthalmic spectacle lenses to other forms from its original form without changing its property is called transposition
Simple transposition
Toric transposition
Optical cross
An optical cross is a diagram which shows the direction of principle meridians of astigmatic lens
It also helps in understanding the actual power of astigmatic lens
Properties of cross cylinders 1
Two cylinders placed together in axis with their axis parallel to one another can be replaced by a simple cylinder equal to the sum of two cylindrical power
Example
+1.0 Dcyl x 180/+2.0 Dcyl x 180
can be written
+3.0 Dcyl x 180
Properties of cross cylinders 2
Two cylinder of equal power but opposite sign placed together neutralize one another
Example :
+2.0 Dcyl x 180/-2.0 Dcyl x 180
Neutralizes
Properties of cross cylinder 3
Two identical cylinders placed together with their axis at right angles to each other can be replaced with a sphere of same power
Example :
+1.0 Dcyl x 180/+1.0 Dcyl x 90
Can be written
+1.0 Dsph
Properties of cross cylinder 4
Any single cylinder can be replaced by a sphere of the same power as the cylinder combine with a cylinder of equal but opposite power to that of the original cylinder with its axis perpendicular to the axis of the first
+2.00DCyl x 90 = +2.00DSph / -2.00DCyl x 180
Properties of cross cylinder 5
2 unequal cylinders placed together with their axes at right angles to one another can be replaced by a sphere and a cylinder.
Example :
+2.00DC x 90 +4.00DC x 180
+2.00DS +2.00DC x 180 (Plus sherocyl form)
+4.00DS - 2.00DC x 90 (minus sherocyl form)
Sphero cylinder from cross cylinder
Given:+1.00DC x 90 + 4.00DC x 180
Procedures:
write either cross cyl as the sphere. +1.00DS
subtract the cylinder chosen as the sphere from other cylinder to find the cylinder power. 4 – 1 =+3.00DC
Axis of the cylinder is the same as the axis of cross-cyl that was not chosen as the sphere. Axis : 180
The sphero-cyl form is : +1.00DS +3.00DC x180 or
+4.00DS -3.00DC x 90
Alternative spherocylindrical form
Given: +2Dsph/+4Dcyl x 180
New sphere: algebraic sum of old sphere and cylinder
new sph: 6Dsph
new cylinder : Old cyl, change the sign and axis i,e new angles will be right angles to old
new cyl: -4Dcyl x 90
Alternative spherocylindrical form:
6Dsph/-4Dcyl x 90
Crosscylinder from spherocylinder
Given: +2Dsph/+4Dcyl x 180
Sphere in the spherocylindrical form is written as first cylinder with axis right angle to the cylinder:
2Dcyl x 90
2nd cylinder is the algebraic sum of sph and cyl: 6Dcyl x 180
Cross cylinder:
+2Dcyl x 90/+6Dcyl x 180
Toric transposition
Step 1 : Transpose the prescription to spherocylindrical form which has the cyl sign of the base curve
Step 2 : Write the base curve as cyl component with the axis opp to transposed spherocyl
Step 3 : Cross curve = base curve + cyl component x opp of b.c
Step 4 : Sphere curve = sph component - base curve
Step 5 : Inference = TTP
positive components
Negative component
Uses of transposition
Transposition techniques are used by opticians during times of unavailability of lenses
Can be used to convert or transpose a Plano concave/convex lens to meniscus lens
Used in manufacturing unit to find base curve and also in selecting tools for surfacing process.