Transposition involves rewriting lens prescriptions while maintaining the same optical power. There are two types: simple transposition and toric transposition. Simple transposition involves algebraically adding/subtracting/changing the sign of sphere and cylinder powers and rotating the cylinder axis by 90 degrees. Toric transposition first uses simple transposition then derives the toric lens formula by separating powers into the spherical and cylindrical base curve components. The spherical equivalent of a prescription is the equal sphere power, calculated as the sphere plus half the cylinder. Crossed cylinder form involves writing two cylinders placed at perpendicular axes to each other.

1. TRANSPOSITION
OPTOM FASLU MUHAMMED

2. TRANSPOSITION
 It implies transfer of lens power from one
form to another so as to their meridian values
remain the same in both the forms.
 It means rewrite the expressions of its power
without actually changing them.

3. TRANSPOSITION
 Simple Transposition
 Toric Transposition

4. SImPle TRANSPOSITION
Three simple steps
1.SUM :The new spherical surface is given by
adding algebraically the power of the sphere
and cylinder.
2.SIGN :Retain the power of the cylinder but
change the sign.
3.AXIS:Rotate the axis of the cylinder through
90º

5. SImPle TRANSPOSITION
 +2.00 DS /+1.00 DC 180º
+3.00DS/-1.00DC 90º
 -5.00DS/ -3.00 DC 90º
-8.00DS/+3.00DC 180º

6. SImPle TRANSPOSITION
 +3.00 DS/-1.50 DC 90º
+1.50 DS /+1.50 DC180º
 -4.00 DS /- 2.25 DC 70º
-6.25 DS /+2.25 DC 160º

7. SImPle TRANSPOSITION
 +1.00 DS /+0.25 DC 130º
 -2.50 DS /-1.75 DC 40º
 +6.00 DS / -2.75 DC 10º
 -3.00 DC 120º

8. TORIc TRANSPOSITION
 Toric formula is written as fraction, the
numerator and the denominator comprises
both the base curve and the cylinder necessary
to give the required combination.

9.  A toric astigmatic lens is made with one
spherical surface and one toric surface .
 The principal meridian of weaker power of the
toric surface is known as the base curve of the
lens.

10. The sTeps of Toric TransposiTion
1.Transpose the given prescription to one having
a cylinder of the same sign as the base curve
which to be used. (SIMPLE Transposition )
2.The spherical surface is given by subtracting
the base power from the sphere in(1) .This is
written as the numerator of the fraction.

11. 3.Fix the cylindrical base curve with its axis at
right angle to the cylinder in (1)
4. Add to the base curve the cylinder in (1) with
its axis at right angles to that of the base
curve

12. Toric TransposiTion
 An example
+3.00 DS +1.00 DC 90º BC -6.00
1.Simple Transposition
+4.00 DS /-1.00 DC 180º

13. 2. The spherical surface is given by subtracting
the base power from the sphere in(1) .This is
written as the numerator of the fraction
+4.00 –(-6.00) =+10.00 DSph

14. 3. Fix the cylindrical base curve with its axis at
right angle to the cylinder in (1)
-6.00 DC 90º

15. 4. Add to the base curve the cylinder in (1) with
its axis at right angles to that of the base curve
-6.00 +(-1.00) =-7.00 DC 180º
+10.00 DSph/ -6.00 DC 90º -7.00 DC
180º

16. Toric TransposiTion
 +3.00 DS /-1.00 DC 90º BC -6.00
+9.00 DSph / -6.00 DC 180º -7.00 DC 90º

17.  +3.00 DS /+2.00 DC 90º
-3.00 DSph / +6.00 DC 180 +8.00 DC 90º

18. Spherical equivalent (S.e)
 A spherocylinder lens will correct for
astigmatism and myopia or hyperopia. If it
was necessary to correct a nearsighted or
farsighted person who also has astigmatism,
but there were no cylinder lenses available,
what would be the best correction using only a
sphere lens?

19. how to Find the Spherical equivalent ?
1. Take half the value of the cylinder and
2. Add it to the sphere power.

20.  In other words, as a formula the spherical
equivalent
Spherical Equivalent =
Sphere + (Cylinder)/2

21.  What is the spherical equivalent for this lens?
+3.00 − 1.00 × 180º
spherical equivalent = +3.00 + (-1.00) /2
= +2.50D

22.  What is the spherical equivalent for a lens
having a power of −4.25 −1.50 × 135º ?
S.E = -4.25 + (-1.50) /2
= -5.00 D

23.  +3.00 DS /-1.50 DC 85º
 -2.50 DS / -2.50 DC 35º
 +7.50 DS / +3.00 DC 10º
 -6.75 DS / +2.50 DC 125º

24. Crossed-Cylinder Form
 Another possible abbreviated form of
prescription writing is the crossed-cylinder
form.
 This form is never used to write a prescription
for spectacle lenses. However, an understanding
of this form of prescription writing aids in a
more complete understanding of lenses.

25.  The crossed-cylinder form of prescription
writing is also the way that keratometer
readings are written when measuring the front
surface power of the cornea for contact lens
purposes.

26.  To understand the crossed-cylinder form of
prescription writing, think through the following:
• If two spherical lenses are placed together, a
new sphere power results from the sum of the two.
• If a sphere and a cylinder are placed together, a
spherocylinder results.
• If two cylinders are placed together with axes
90 degrees apart from one another, a sphere, a
cylinder, or a spherocylinder may result.

27. An AlternAte Crossed-
Cylinder Form
 The normal way of writing a lens prescription
in crossed cylinder form is done just like
writing a plano cylinder.
 When the +1.00 × 180 and +2.00 × 90 lenses
were placed together in the example just given,
the crossed-cylinder combination was written
as
+1.00 × 180/+2.00 × 90

29.  Suppose, for example, +1.00 × 180 and +2.00
× 90 lenses are placed together. These are both
cylinders and their axes are “crossed” in
relationship to one another.
 In abbreviated crossed-cylinder form this
reads
+1.00 × 180( )+2.00 × 90

30.  This form is seen in contact lens practice when
reading or writing the keratometer reading of
the front surface of the cornea.
 Of course the powers are considerably higher
and might look something like this:
+42.50 @ 90/+43.75 @ 180