The document describes the process of transposing a lens prescription from plus cylinder notation to minus cylinder notation, detailing the importance and steps involved. It outlines different types of transposition, including simple and toric transpositions, with examples to illustrate algebraic manipulation of sphere and cylinder powers. Additionally, it emphasizes the significance of maintaining axes alignment and provides procedures for transforming various lens types.

1. Shishir Shukla
Optometrist, Ocularist
TRANSPOSITION

2. Transposition
Definition :- The process of changing a lens from
one form to another equivalent form .
Transposing a glass prescription is simply
converting the prescription from plus cylinder
notation to minus cylinder notation.

3. Importance of transposition
1.Prescribe cylinder in minus form .
(So as easy for manufacture )
2.Maintain axes of cylinder in two eyes in
approx.same direction .
3.To avoid rubbing of lashes against
posterior surface of glass.

4. Principal Meridian
• One of the two mutually perpendicular
meridians of an astigmatic power lens.
• Power meridian denoted by ---- @
• Axis meridian denoted by ---- X
Ex:
90
180
135
45

5. 90
(-1.00D)
Ex :
•Power meridian denoted by ---- @
-1.00 @ 180°
•Axis meridian denoted by ---- X
-1.00 X 90°
180

6. Types of transposition
• Simple transposition
• Toric transposition

7. Steps for transposition
Three steps :-
1)Algebraically add the cylinder power to the
sphere power to arrive at the new sphere
power.
2) Change the sign of the cylinder power.
3) Add or subtract 90 from the axis.
( add 90 if < 90°
subtract 90 if > 90 °)
_

8. Transposition
1. Sphero-cylinder
2. Simple cylinder to sphero- cylinder
3. Cross cylinder to sphero- cylinder

9. 1. Sphero-cylinder
• Add algebrically sphere and cylinder as
sphere .
• Change sign of cylinder
(- form to + form )
( + form to – form )
• Change axis of cylinder
( add 90 if < 90°
subtract 90 if > 90° )
_

10. Procedure
Add algebraically
sphere and cyl. For
sphere .
Ex
+4.00D / +3.00 X 90 °
+4.00 + ( +3.00)
+7.00 Dsp

11. Procedure
Change sign of cylinder
Ex
+4.00D / +3.00 X 90°
+7.00D / -3.00

12. Procedure
Add or subtract 90 from the axis.
( add 90 if < 90°
subtract 90 if > 90° )
Ex
+4.00D / +3.00 X 90°
+7.00D / -3.00 X 180°

13. 1. Sphero-cylinder
Example + 6.00D/ + 4.00 X 90°
Change sign of cylinder
Change axis 90 degree apart
•Add algebrically sph & cyl
+ 6.00 +(+ 4.00) = + 10 Dsp
•(From – to +) ( From + to - )
+10 Dsp /- 4.00
•( add 90 if < 90, subtract 90 if > 90 )
+ 10Dsp /-4.00 X 180°_

14. 1. Sphero-cylinder
For sphere
Add : -4.00 + (+2.00 ) = -2.00Dsp
For cylinder ,Change the sign
-2.00 Dsp /-2.00 cyl.
For axis ( add 90 if < 90, subtract 90 if > 90 )
-2.00 Dsp /-2.00 cyl X 45°
-4.00 / +2.00 X 135

15. 2. Simple cylinder to sphero-
cylinder
• Turn simple cylinder
• Applying zero sphere
Example Plano / +1.00 cyl. X 90°
0.00 / + 1.00 cyl. X 90°
For sphere
Add : 0 + (+1.00 ) = +1.00Dsp
For cylinder ,Change the sign
+ 1.00 Dsp/ -1.00 cyl
For axis ( add 90 if < 90, subtract 90 if > 90 )
+1.00 Dsp /-1.00 cyl X 180°

16. • Example
0.00 /-3.00 X 45°
2. Simple cylinder to sphero-
cylinder
For sphere
Add : 0.00 + (-3.00) = -3.00 Dsp / -3.00 cyl
For cylinder ,Change the sign
-3.00Dsp / + 3.00 cyl
For axis ( add 90 if < 90, subtract 90 if > 90 )
-3.00Dsp / +3.00 cyl X 135°

17. 3.Cross cylinder to Sphero-
cylinder
1. Use the cylindrical power encounter first
as the spherical power.
Ex:
+3.00
+2.00
Spherical = +3.00D

18. 2. For cylindrical power change the sign of the
spherical & add it algebraically to the second
cylinder power.
3. For cylindrical axis use the axis of the second
cylinder or power meridian of sphere.
or
spherocylinder power = +3.00 /-1.00 X 90°
-3.00 + (+2.00) = -1.00D Cyl
axis of second cylinder = 90 (+2.00X 90)
power meridian of sphere = 90 (+3.00 @ 90)

19. +4.00
-3.00
Example
Spherical = + 4.00Dsp
1. Use the cylindrical power encounter
first as the spherical power.

20. 2.For cylinder change sign of sphere & add
algebrically to sec. Cylinder
-4.00 + (-3.00 ) = -7.00 cyl
3. For cylindrical axis use the axis of the second
cylinder or power meridian of sphere.
Axis of second cyl = 90 ( -3.00X 90)
0r
power meridian of sphere = 90 (+ 4.00 @90)
spherocylinder power = +4.00Dsp/-7.00cyl X 90°

21. Toric Transposition
• sphere curve
• Base Curve/cylinder Curve.
• Transpose the equation to get same sign of the BC.
• Sphere is given by subtracting the Base power .
Toric lens is one in which one surface is spherical and
the other is cylindrical. The surface in which both
meridians having different power is called ‘Toric
surface’.
Toric form=

22. •Take BC opposite axis of the first cyl.
•Add BC to cyl.with its axis 90°. to that of BC.
Always take the sign of the BC
( ie if BC is – then change to –
if BC is + then change to +)

23. Toric transposition
• Example
+ 3.00Dsp/-1.00cyl.90° (BC –6)
+3.00 –(-6) = +9.00Dsp.
-6.00 X 180°
•Sphere is given by subtracting the Base
power from sphere written as numerator.
•Fix cylinder BC with its axis 90 deg.to the cyl.

24. Toric transposition
• Add BC to cyl.with its
axis 90° to that of BC.
(-6.00 + (-1.00) = -7Dcyl X90
This gives on combination on one surface
of -6.00 cyl X 180 + -7.00 cyl X 90°
-6.00 cyl X180° / -7.00 cyl X 90°
+9.00Dsp