Power-Versus-Meridian Graph
The (paraxial) power of a spherocylinder varies in every meridian according to the equation
Pθ = PS + PC sin2 (θ − ϕ)
Here Pθ is the power in the meridian at angle θ from the horizontal (measured counterclockwise, as seen facing the patient), PS is the power of the spherical component of the spherocylinder, PC is the power of the cylindrical component, and ϕ is the cylinder axis.
For instance, a +3.00 D cylinder with an axis at 020 has a power in the 050 meridian given by
P
050 = +3.00 D [sin2 (50 − 20)] = +0.75 D
A power-versus-meridian graph (PVMG) represents the power in every meridian (Figure 1-33). Like a power cross, a toric lens has only 1 PVMG. Whether specified in plus cylinder or minus cylinder form, the PVMG is the same. However, the PVMG is a more complete representation of a spherocylinder—unlike a power cross, which shows power in only 2 meridians, a PVMG shows power in all meridians. We can use the PVMG to represent the combination of spherocylinders at any axes in a single representation without the need for a separate calculation for cylinders and spheres. We can algebraically add the sin2 formulas for meridional power of 2 thin spherocylindrical lenses in contact and simplify according to the usual rules for trigonometric functions, regardless of whether the cylinder axes coincide.
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.