Astigmatic prescriptions may be written in plus- or minus-cylinder form. The numbers can look very different even when the optical result is equivalent, so prescription comparisons should first use the same cylinder convention.
01 · TWO MERIDIANS
A sphero-cylinder describes powers in two perpendicular principal meridians
SPH can be viewed as the power in the axis meridian, while CYL is the additional difference acting 90° away. AXIS identifies the meridian where cylinder power is zero.
The same two meridian powers can therefore be represented from either principal meridian, producing plus- or minus-cylinder notation.
02 · TRANSPOSITION
Add CYL to SPH, reverse the CYL sign and rotate AXIS by 90°
For example, -2.00 -1.00 ×180 transposes to -3.00 +1.00 ×90. The first notation gives -2.00 D in the 180° meridian and -3.00 D in the 90° meridian; the second describes the same pair.
Axis is normalized within 1–180°, with 0° and 180° representing the same orientation.
03 · COMPARE
Put both prescriptions into the same cylinder convention before comparing them
If one prescription is written in minus cylinder and another in plus cylinder, SPH and AXIS can both appear to change dramatically. Transpose one first, then compare the principal powers.
04 · NOT A NEW RX
Transposition changes notation, not the optical prescription
A correctly transposed form is optically equivalent. Moving from +CYL to -CYL does not by itself make the prescription stronger or weaker.
All three steps must be applied together; omitting the sphere addition, sign change or 90° axis shift creates a different prescription.
05 · VERIFY
When uncertain, verify the actual powers in the two principal meridians
Calculate the power along the axis and 90° away. This is especially useful when a prescription, lensmeter printout and manufacturing system use different cylinder conventions.
SOLUTION GUIDE
A practical check order
Check whether each prescription uses plus or minus cylinder.
Add CYL to SPH, reverse CYL, and shift AXIS by 90°.
Verify that the two principal meridian powers remain the same.
Only compare clinical change after both records use the same convention.
GLANOS CHECK
Plus and minus cylinder may be two notations for the same sphero-cylinder rather than two different prescriptions.
Separating notation changes from true power changes makes comparisons more reliable.
CAUTION
Changing only the axis or only the cylinder sign is not a valid transposition.
SPH, CYL and AXIS must all be transformed according to the rule.
GLANOS EYEWEAR
There is usually a reason behind eyewear discomfort.
plus cylinder · minus cylinder · astigmatism prescription · transposition · SPH · CYL · AXIS