Prescription Transposition: Converting Plus and Minus Cylinder | ABO Exam

Why Transposition Matters

Transposition is the process of converting a spectacle prescription between plus cylinder and minus cylinder notation. Both forms describe the identical lens with the same optical properties. The conversion is necessary because different eye care professionals use different conventions:

• Ophthalmologists typically write prescriptions in plus cylinder form.
• Optometrists and opticians typically work in minus cylinder form.
• Optical laboratories process orders in minus cylinder form.

As an optician, you will regularly receive prescriptions in plus cylinder from ophthalmologists and need to convert them to minus cylinder for ordering lenses, verifying with a lensometer, and communicating with labs.

The Three-Step Method

Transposition follows exactly three steps, every time:

1. New Sphere = old sphere + old cylinder (add algebraically)
2. New Cylinder = change the sign of the old cylinder
3. New Axis = change the old axis by 90 degrees

For step 3: if the old axis is 90 or less, add 90. If the old axis is greater than 90, subtract 90. The result must fall between 1 and 180 (never use 0; use 180 instead).

Worked Examples

Example 1: Plus to Minus Cylinder

Original (plus cyl): +1.00 +2.00 x 090

1. New sphere: +1.00 + (+2.00) = +3.00
2. New cylinder: change sign of +2.00 = -2.00
3. New axis: 090 + 90 = 180

Result (minus cyl): +3.00 -2.00 x 180

Example 2: Minus to Plus Cylinder

Original (minus cyl): -4.25 -1.75 x 045

1. New sphere: -4.25 + (-1.75) = -6.00
2. New cylinder: change sign of -1.75 = +1.75
3. New axis: 045 + 90 = 135

Result (plus cyl): -6.00 +1.75 x 135

Example 3: Axis Greater Than 90

Original: +2.50 -1.00 x 160

1. New sphere: +2.50 + (-1.00) = +1.50
2. New cylinder: change sign of -1.00 = +1.00
3. New axis: 160 - 90 = 070

Result: +1.50 +1.00 x 070

Verification Using the Optical Cross

The best way to confirm a transposition is correct is to check that both forms produce the same power at each principal meridian.

Using Example 1:

Both forms give +1.00 D at the 090 meridian and +3.00 D at the 180 meridian. The transposition is verified.

Common Transposition Scenarios

Some special cases are worth noting:

• Sphere only (DS): No transposition needed. -3.00 DS is the same in both forms.
• Plano sphere: Plano +1.00 x 090 transposes to +1.00 -1.00 x 180. (Plano + 1.00 = +1.00 for the new sphere.)
• Axis at 090 or 180: These are the most common axes and the easiest to verify. The two principal powers run along the vertical and horizontal meridians.

Key Takeaways

• Transposition converts between plus and minus cylinder forms of the same prescription.
• Three steps: add sphere+cyl for new sphere, flip cylinder sign, rotate axis by 90°.
• Always verify by checking that power at each principal meridian matches in both forms.
• Ophthalmologists use plus cylinder; optometrists and labs use minus cylinder.
• Axis must remain between 1 and 180 (never 0).
• Practice until transposition is automatic; it appears frequently on the ABO exam.