**Each issue, Tech Tips will explore some interesting aspect of optical technology. This month we look at transposition.**

Changing a prescription’s cylinder sign is easily done.

Transposition is one of the things you learn early in your optical studies. While it’s a handy skill to have, understanding transposition means you have a good knowledge of lens powers and how they are expressed for ophthalmic lenses.

Transposition is used to convert a lens prescription from one cylinder notation to another, for example from plus cylinder to minus cylinder or vice versa. If a lens has a minus cylinder, how can you arbitrarily change it to plus cylinder? The answer is that a lens’ powers are placed on it during surfacing and cannot be altered. Lens prescriptions express those powers as either plus or minus cylinder and either one is correct.

**FOLLOWING THE RULES**

Here’s a rule that comes in handy when learning transposition: Every cylinder lens has two names: a plus cylinder name and minus cylinder name. Here’s why.

Consider the lens cross in Fig. 1. You’ll notice that the total power in the 180th meridian is +1.00D while the power in the 90th is +3.00D. These are the powers you would obtain on the power drum of your lensometer when reading this lens’ power.

While these powers are useful for reading the lens’ power in your lensometer, they don’t express the prescription. In order to create an ophthalmic lens prescription, you need three pieces of information: sphere power, cylinder power, and axis. None of that information is found in the lens cross in Fig. 1 so how do you obtain it?

**THREE BOXES**

Think of an ophthalmic lens prescription as having three boxes: a sphere box, a cylinder box, and an axis box. You have to fill in each box to have a proper prescription. To create the prescription, start with one of the meridians in Fig. 1 and write its power down, for example, +1.00D. This will be the sphere power and it will go into the “sphere box.” Note the axis for the +1.00D power because that’s the value you’ll place in the “axis box.” To establish the cylinder power, determine the difference between the meridian you started with and the other meridian 90Âº away. In this example, the difference is +2.00D. That’s the cylinder power. Your prescription for this lens is +1.00D +2.00D x 180.

What if you started with the other meridian? Here’s how it would come out. Your sphere box would have +3.00D in it since that’s the power you’re starting with. The meridian in which +3.00D is found is 90 so that goes into the axis box. To determine the cylinder power, calculate the difference between +3.00D and +1.00D. That difference is -2.00D. Why? Because you went from +3.00D down to +1.00D, a difference of -2.00D. If you use a manual lensometer, you will experience this as you turn the power drum and watch the diopter numbers dropping. This is a move in the minus direction. The prescription obtained writing it this way is: +3.00D -2.00D x 90.

**ONE CYLINDER TO ANOTHER**

The lens in Fig. 1, like all cylinder lenses, has two names: a plus cylinder name and a minus cylinder name. The cylinder power notation you obtain is based on which of the two powers you begin with. If you want minus cylinder, the first power reading should be the weakness minus or strongest plus power of the lens. If you want plus cylinder, the first reading should be the strongest minus power or weakest plus power on the lens.

To transpose from one cylinder form to another, follow these rules:

- Add the sphere and cylinder powers algebraically.
- Change the cylinder sign to the opposite.
- Change axis 90º.

Here’s an example: -1.00D -3.00D x 90

- -1.00D plus -3.00D becomes -4.00D.
- -3.00D cylinder becomes +3.00D.
- 90º axis changes to 180º.

Transposing often creates a prescription that looks pretty different from the one you started with. The example above had a -1.00D sphere power but its transposed version had a -4.00D sphere power. That’s a pretty radical difference, and yet the two prescriptions express the same lens. Remembering that every cylinder lens has two names will make you feel more comfortable about this seemingly odd situation.

Understanding transposition is a vital step in learning how lens powers and lens prescriptions relate.

*Ed De Gennaro is Director, Professional Content of First Vision Media Group.*