Cylindrical Lenses Explained

by Ariel Seafish
(Tulsa OK)

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Q: Greetings, everyone!

Two years back, an eye examination revealed the following prescription with cylindrical lenses:

OD: (SPH /) (CYL+0.25) (Ax 70)
OS: (SPH +0.5) (CYL+0.5) (Ax 100)

Initially, I was uncertain whether to use these glasses for reading, distance, or both. Strangely, the glasses for my right eye caused significant discomfort, leading me to stop wearing them in under two weeks.

Yesterday, a visit to a different eye doctor resulted in this prescription:

OD: (SPH +0.75) (CYL 0.5) (Ax 150)
OS: (SPH +1.00) (CYL /) (Ax /)

The doctor advised that I wear these glasses constantly. He indicated that my reading difficulties were due to issues with my distance vision, which resonated with me as I often struggle to read street signs at night.

I'm left with several questions:

1. Is it possible for someone to have eyeglasses with "+" for distance vision?
2. Can the prescription change from cylinder (OS: +0.5) to no cylinder (OS) and from Ax 70 (OD) to Ax 150 (OD)?
3. Can the spherical measurement increase from none to 0.75 in just two years?
4. Is it true that wearing unnecessary eyeglasses can permanently impair one's vision?

Thank you for your insights!
Ariel


A: Hi Ariel,

To clarify from the start, the two prescriptions you have with cylindrical lenses are formatted differently.

The initial prescription is noted with (+) cylinder, while the second utilizes (-) cylinder notation. When reframing both prescriptions using (+) cylinder, the latter would convert to:

OD: (sph +0.25) ( cyl +0.50) (ax 60)

The variation between the first and second prescriptions is minimal.

Now, let’s address your inquiries:

1. Yes, having a (+) for distance vision is possible; this condition is known as Hyperopia or farsightedness.

2. No, when a cylinder is present, it indicates astigmatism, a condition that does not resolve itself. Typically, if the cylinder power is under 1 diopter (0.25; 0.50), correction may not be essential unless it notably enhances vision. You mentioned discomfort with the right eye while wearing glasses, so the doctor likely opted not to include the cylinder in the new prescription.

3. Yes, it is feasible for the spherical measurement to evolve over two years, influenced by factors such as eye fatigue, reading habits, and exposure to screens.

4. If the prescription strength is high and not needed, it may cause issues like dizziness, blurred vision, or headaches, resulting in difficulty wearing them. For smaller diopters, as in your case, the primary consequence would be eye fatigue, not lasting damage.

Best Regards,
Arpi

In essence, most lenses consist not of angular prismatic surfaces but rather of curved designs. A foundational form of these curves is the sphere. If you envision the curve on a spherical lens extended in all directions, it would create a perfect sphere. The size of the sphere varies according to the curve's steepness; a steeper, higher power curve results in a smaller sphere with a reduced radius, while a flatter, lower power curve results in a larger sphere with an increased radius.

Aside from their power or radius, spherical curves also possess a directional aspect. An inward curve is referred to as concave, while an outward curve is labeled convex. To illustrate, a minus lens, which diverges light, necessitates a concave surface, conversely, a plus lens, which converges light, requires a convex surface. Therefore, we denote concave curves with a minus (-) and convex curves with a plus (+) sign, using the term "plano" for a flat or zero curve.

A lens encompasses two significant curved surfaces concerning the wearer’s vision: the front surface and the back surface. Common lens shapes produced by optical wholesale labs, based on these surface curves, can be visualized in the accompanying figure.

The corrective power of a lens is calculated by combining the front curve with the back curve, expressed in the equation: F1 + F2 = FTotal. It's worth noting that for any specific corrective power, a myriad of curve combinations can be utilized to achieve the same outcome.

For example:

+6.00 D + -2.00 D = +4.00 D

+4.00 D + 0.00 D (plano) = +4.00 D

+2.00 D + +2.00 D = +4.00 D

In practical terms, labs have a finite array of curve combinations available. Lens blanks originate from manufacturers with limited selections of front curves, also known as base curves, along with suggested ranges for each power. Furthermore, given that aberrations arise as the eye deviates from the lens's optical center, the lab selects curves designed to minimize these aberrations. Lenses crafted to mitigate aberrations are termed "corrected curve" or "best form" lenses.

The chart below provides basic guidelines for selecting base curves that minimize peripheral aberrations.

Sphere Power Base Curve > +12.25 +16.00 D +10.75 to +12.25 +14.00 D +9.00 to +10.50 +12.00 D +5.50 to +8.75 +10.00 D +2.25 to +5.25 +8.00 D -1.75 to +2.00 +6.00 D -2.00 to -4.50 +4.00 D -4.75 to -8.00 +2.00 D -8.00 to -9.00 +0.50 D < -9.00 plano or minus

Bear in mind that these serve as guidelines for selecting base curves, with many additional factors influencing base curve choices, including: manufacturer recommendations, frame selection, aesthetics, lens material, and patient history.

Beyond the spherical curve, numerous prescriptions include a cylinder curve designed to correct for astigmatism. The cylinder curve exhibits curvature along a unique axis, remaining flat along its perpendicular axis. Furthermore, the focus of a spherical curve converges at a single point, while the focus of a cylinder curve aligns as a line. The cylinder axis refers to the meridian devoid of cylinder power within the lens, denoting the cylindrical focus. This cylinder axis is measured in degrees, ranging from 0 to 180.

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Usually, prescriptions comprise various combinations of spherical and cylinder curves. A lens merging spherical and cylinder curves is labeled a compound lens or toric lens. The conceptual framework of the power cross aids in visualizing the compound lens scenario. The power cross represents the two primary meridians of the lens surface. An uncomplicated case to envision involves a plano combined with a +4.00 D cylinder.

The preceding examples illustrate the cylinder curve positioned at right angles. Notice how the power at the meridian of the cylinder axis remains plano, while the meridian perpendicular to the cylinder axis carries a +4.00 D power. To fully comprehend the cylinder curve, however, it is vital to examine the lens form at angles other than 90° and 180° from the cylinder axis.

The illustration above depicts the +4.00 D cylinder curve situated at 45°. Observe that the powers at 90° and 180° are now +2.00 D, while the +4.00 D curve is positioned at 135°. As you rotate the meridian away from the cylinder axis, the curve subtly transitions from 0 to the full cylinder curve power (+4.00 D in this example) when the meridian is perpendicular to the cylinder axis. A simple formula can ascertain the cylinder power across any meridian: F = Fcyl*(SIN(ϴ))^2, where Fcyl designates the cylinder power and ϴ represents the angle between the cylinder axis and the new meridian. It’s also straightforward to recall key angles such as 30°, 45°, 60°, and 90° as 25%, 50%, 75%, and 100% of the cylinder power, respectively.

As a spherical curve retains uniformity across all meridians, if combined with a -2.00 D spherical curve and a +4.00 D cylinder at 45°, the outcome manifests as a compound lens articulated through the power cross below.

The curves along the lens surface can be conveniently gauged through an instrument termed a lens measure or lens clock.

A lens measure utilizes three points of contact, positioned on the lens surface to ascertain its curvature. The outer points remain stationary while the inner point adjusts in or out to measure the sagittal depth of the lens. Using the sagittal depth, the device displays the curve in diopters, where plus (+) curves indicate one direction and minus (-) curves the opposite. The lens measure can also assist in distinguishing between spherical and toric surfaces by situating the tool at the optical center of a lens and rotating it around the center. If the indicator remains static during rotation, the surface is spherical. Conversely, if the indicator shifts upon rotation, it reveals a toric lens surface, with minimum and maximum readings correlating with the power meridians.

Bear in mind, when utilizing a lens measure, that it is calibrated to yield readings for lens materials with a refractive index of 1.53, implying that higher index materials will exhibit true power exceeding indicated measurements.

The power cross, complemented by the total power equation (F1 + F2 = FTotal), enables the determination of the nominal power of both spherical and toric lenses. For instance, should we use the lens measure to ascertain the front surface curve of a lens to be +4.00 D across all meridians, and the back surface curve shows as -2.00 D across all meridians, the spherical curves confirm their total lens power as follows:

If the front surface measurement reveals +6.00 D while the back surface is identified as toric with measurements of -8.00 D at the 90° meridian and -5.00 D at the 180° meridian, our power determination would manifest as follows:

Should you wish to delve deeper into this topic, please visit our page on Cylindrical Lens Glasses.