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.

Figure 1-33 Power-versus-meridian graph (PVMG) of a toric lens. There is only 1 PVMG for any toric lens. To read the spherocylinder power in plus cylinder form (red arrows), look at the trough (lowest point on the graph). The (vertical) distance between the trough and the horizontal axis is the sphere power PS; the cylinder axis is the meridian of the trough. The (positive) cylinder power is the distance from the trough to the peak (highest point on the graph). For minus cylinder form, the distance of the peak from the horizontal is the sphere power PS; the cylinder axis is the meridian of the peak. The (negative) cylinder power is the distance from the peak to the trough.

(Courtesy of Edmond H. Thall, MD.)

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.