Transposition

Transposition is the conversion of a written lens power from plus-cylinder form to minus-cylinder form or vice
versa. Transposition can be performed by first drawing an optical cross, but in most cases the following three
steps are used.



Step 1. Add the sphere and cylinder power values algebraically. This becomes the new sphere power.
Step 2. Change the sign of the cylinder power. This becomes the new cylinder power.
Step 3. Change the cylinder axis by 90 degrees. This becomes the new cylinder axis. The decision to add or subtract 90 degrees is made with the requirements ofTABO notation in mind. Cylinder axes cannot exceed 180 degrees or be less than zero.

As an example,
transpose a lens power of +2.00 -3.00 x lOO (in minus-cylinder form) to plus-cylinder form.

Step 1. Add the sphere and cylinder values to obtain
the new sphere power. +2.00 - 3.00 = -1.00

Step 2. Change the sign of the cylinder axis. - 3.00 =
+3.00

Step 3. Change the cylinder axis by 90 degrees. 100 -
90 = 10 degrees

Note that 90 degrees should not be added to 100 degrees
to change the cylinder axis because the total would
exceed 180 degrees. Combining the three steps provides
the lens power in plus-cylinder form: -1.00 + 3.00 x 010.