Eyeglass prescription

Positive meniscus lenses provide positive diopters, while negative meniscus lenses provide negative diopters.

Every corrective lens prescription includes a spherical correction in diopters. Convergent powers are positive (e.g., +4.00 D) and condense light to correct for farsightedness/long-sightedness (hyperopia) or allow the patient to read more comfortably (see presbyopia and binocular vision disorders). Divergent powers are negative (e.g., −3.75 D) and spread out light to correct for nearsightedness/short-sightedness (myopia). If neither convergence nor divergence is required in the prescription, "plano" is used to denote a refractive power of zero.

The term "sphere" comes from the geometry of lenses. Lenses derive their power from curved surfaces. A spherical lens has the same curvature in every direction perpendicular to the optical axis. Spherical lenses are adequate correction when a person has no astigmatism. To correct for astigmatism, the "cylinder" and "axis" components specify how a particular lens is different from a lens composed of purely spherical surfaces.

Patients with astigmatism need a cylindrical lens, or more generally a toric lens to see clearly. The geometry of a toric lens focuses light differently in different meridians. A meridian, in this case, is a plane that is incident with the optical axis. For example, a toric lens, when rotated correctly, could focus an object to the image of a horizontal line at one focal distance while focusing a vertical line to a separate focal distance.

The power of a toric lens can be specified by describing how the cylinder (the meridian that is most different from the spherical power) differs from the spherical power. Power evenly transitions between the two powers as you move from the meridian with the most convergence to the meridian with the least convergence. For regular toric lenses, these powers are perpendicular to each other and their location relative to vertical and horizontal are specified by the axis component.

There are two different conventions for indicating the amount of cylinder: "plus cylinder notation" and "minus cylinder notation". In the former, the cylinder power is a number of diopters more convergent than the sphere power. That means the spherical power describes the most divergent meridian and the cylindrical component describes the most convergent. In the minus cylinder notation, the cylinder power is a number of diopters more divergent than the sphere component. In this convention, the sphere power describes the most convergent meridian and the cylinder component describes the most divergent. Europe typically follows the plus cylinder convention while in the US the minus cylinder notation is used by optometrists and the plus cylinder notation is used by ophthalmologists. Minus cylinder notation is also more common in Asia, although either style may be encountered there. There is no difference in these forms of notation and it is easy to convert between them:[1]

• Add the sphere and cylinder numbers together to produce the converted sphere
• Invert the sign of cylinder value
• Add 90° to axis value, and if the new axis value exceeds 180°, subtract 180° from the result

For example, a lens with a vertical power of −3.75 and a horizontal power of −2.25 could be specified as either −2.25 −1.50 × 180 or −3.75 +1.50 × 090.

This phoropter is set to an axis of 180 for each eye. This can be seen by noticing the tiny white arrows that are horizontal as they point to the tiny numbers that line the opening the patient looks through. Click the image to see a full resolution version where the individual axis markings become more visible.

The axis defines the location of the sphere and cylinder powers. The name "axis" comes from the concept of generating a cylinder by rotating a line around an axis. The curve of that cylinder is 90° from that axis of rotation. When dealing with toric lenses, the axis defines the orientation of the steepest and flattest curvatures relative to horizontal and vertical. The "3 o'clock" position is defined as zero, and the 90th meridian is a vertical line. A horizontal line passes through both zero and the 180th meridians. By convention, a horizontal axis is recorded as 180.

In a regular toric lens, the flattest and steepest curvatures are separated by 90°. As a result, the axis of the cylinder is also the meridian with the same power as the recorded sphere power. The cylinder power, as defined above is the power that is most different from the sphere power. Because they are defined relative to each other, it is important to know if the lens is being described in minus cylinder notation, where the sphere power is the most convergent / least divergent power. When using plus cylinder notation, the opposite is true.

If the lens is spherical (there is no cylinder component) then there is no need for an axis. A prescription like this is written with D.S. (diopters sphere) after the sphere power (e.g., −3.00 D.S.). This verifies that the prescription is truly spherical rather than the cylinder power being omitted in error.

• correction power is measured in diopters
• by convention, an axis of 90° is vertical, 0° or 180° are horizontal
• if the cylinder power is positive, the lens is most convergent 90° from the axis
• if the cylinder power is negative, the lens is most divergent 90° from the axis
• if the cylinder power is zero, the lens is spherical and has the same power in every meridian

A prescription of −1.00 +0.25 × 180 describes a lens that has a horizontal power of −1.00 D and a vertical power of −0.75 D. Only ophthalmologists write prescriptions in + cylinder. An optometrist would write a prescription in - (minus) cylinder. All spectacle and contact lenses would be made in minus cylinder. Therefore, the above prescription would be written as −0.75 −0.25 × 90.