2.2 Sphere, Cylinder, Axis, and Add

Sphere power

Sphere power has the same power in every meridian of the lens. A plus sphere converges light and is used to correct hyperopia or support near work. A minus sphere diverges light and is used to correct myopia. Plano is zero sphere power. In lensmeter verification, a simple spherical lens gives one power reading regardless of meridian.

Think of sphere as the baseline power. In -3.00 -1.00 x 180, the sphere is -3.00 D. At the axis meridian, the lens power is -3.00 D because cylinder has no effect at its own axis. Ninety degrees away from the axis, the full cylinder is added, so the other principal meridian is -4.00 D.

Cylinder power

Cylinder power corrects astigmatism. A cylindrical surface has power in one meridian and no power in the meridian 90 degrees away. In prescription notation, the cylinder value tells how much additional power exists away from the axis. Cylinder may be written in minus or plus form. The amount of cylinder is the difference between the two principal powers of the lens.

For example, +1.00 -2.00 x 090 has +1.00 D at axis 090 and -1.00 D at meridian 180. The two principal meridians are +1.00 and -1.00, so the cylinder amount is 2.00 D. This prescription is mixed astigmatism because one principal meridian is plus and the other is minus.

Cylinder has practical dispensing consequences. Higher cylinder powers make axis accuracy more important. A small axis error in a low-cylinder lens may be tolerated, while the same axis error in a -4.00 cylinder can cause blur, swim, or distortion. When a patient says, "The letters look shadowed," "the floor tilts," or "one eye feels off," cylinder axis and lens rotation are among the first verification points.

Axis

Axis is a direction, not a power. It is written from 001 to 180 degrees. In minus-cylinder notation, the axis identifies the meridian where only the sphere power is present. The full minus cylinder is found 90 degrees away. In plus-cylinder notation, the same concept applies: the cylinder has no effect at the written axis, and its full plus effect appears 90 degrees away.

A useful phrase is: axis is where the cylinder is absent. This helps avoid the common exam error of placing the cylinder power on the written axis. In -2.00 -1.50 x 180, the power at 180 is -2.00 D, and the power at 090 is -3.50 D. In -3.50 +1.50 x 090, the power at 090 is -3.50 D, and the power at 180 is -2.00 D. These are equivalent forms.

Add power

Add power is extra plus power for near or intermediate tasks. It is algebraically added to the distance sphere. The cylinder and axis usually remain the same when converting a distance Rx with add into a near-only Rx. Formula: near sphere = distance sphere + add.

Worked example: distance Rx OD -2.25 -0.75 x 180 Add +2.00. Near-only sphere is -2.25 + 2.00 = -0.25. Near-only Rx is OD -0.25 -0.75 x 180. If the distance sphere is +1.50 and the add is +2.25, near sphere is +3.75.

The add is not a bifocal height, and it is not the patient's reading PD. It is optical power. Segment height, fitting cross height, near PD, corridor length, and frame choice are dispensing measurements that interact with the add but are not the same thing. On an order form, mixing these fields can create a lens that is optically correct but physically unusable.

Case example: office worker with first add

A 46-year-old accountant brings OD -0.75 -0.50 x 170; OS -0.50 -0.25 x 010; Add +1.25. She says distance is fine but near print is tiring. The optician should recognize early presbyopic support. The add indicates plus power for near, and the final design might be a progressive, lined bifocal, or separate near pair depending on needs analysis and prescriber instructions.

If she chooses a separate computer pair, do not simply use the full reading add unless the working distance matches. Intermediate adds are commonly lower than full near adds, but the optician should follow the prescribed occupational instruction or obtain clarification. ABO Basic optics questions may test the concept that more plus focuses closer, while less plus is often used for farther intermediate tasks.

Practical verification mindset

When reading any Rx, ask four questions. What is the sphere? Is there cylinder? If there is cylinder, what is the axis? Is there an add or prism instruction? This checklist prevents common order-entry mistakes: dropping a cylinder sign, transposing only one eye, entering 090 as 009, or placing the add in the sphere field.

A finished lens must match the intended optical effect. If a patient with high cylinder reports blur after a frame adjustment, verify lens rotation and frame alignment as well as lens power. If a progressive wearer reports near blur, do not blame the add immediately; check fitting height, pantoscopic tilt, vertex position, corridor use, and whether the patient is looking through the near zone correctly. Optics and dispensing geometry work together.