# Frame Wrap

By Mathew Musladin, ABOM

**Learning Objectives:**

Upon completion of this program, the participant should be able to:

- Describe the aberrations occurring in the lens due to off-axis gaze and tilt.
- Explain the difference in the refractive plane and spectacle plane.
- Picture the effect of tilt and wrap angle on the lens performance.

**Faculty/Editorial Board**

**Mathew “Guy” Musladin, ABOM,** has a Bachelor of Science in Business Administration from Sacramento State University and over ten years in the optical industry. He specializes in staff training, teaching optics, ABO exam preparation, lensometry, and final inspection. In his free time, he studies Hebrew and Koine Greek and enjoys designing chess sets to add to his *Chess Sets by Guy* collection.

**Credit Statement**

**This course is approved for one 1 hour O.D. CE credit by NYSSO**

This course is intended to help the dispensing optician visualize how the frame wrap angle and pantoscopic tilt impact lens optical performance, and how the resulting aberrations can be compensated.

With all of the frame styles available today, it is hard to keep up with the fashion trends, let alone track the “Rxable” factor. However, it is our business to understand the nature of the Rx relative to frame wrap and pantoscopic tilt. Why is this important? Well, let’s see! Most Rxs are for distance. In the case of a distant object, optical infinity is defined as over 20 feet or 6 meters away. This means that the wavefront originating from infinity is on a plane perpendicular to the line of sight by the time it reaches an optical surface. Therefore, when plane waves (from infinity) come into contact with the curved lens, the only point of the lens that is considered plane is the point tangent to the wavefront, the optical center.

ABO study teaches us that curvature is power. Lens curvature introduces the obliquity necessary to apply Snell’s law to the rays from that plane wave through the lens to a focal point. The further away from the optical center, the parallel ray, the greater the induced obliquity at the point of contact. Rays incident on the lens in the periphery form oblique angles to the normal (the axis perpendicular to the center of curvature at the point of contact). This means that a parallel ray of light refracts more at greater oblique angles the further it is from the normal. This is true for every contact point along the surface of the lens. The angles created obey Snell’s law; therefore, ray tracing can simulate the ray path for all points on the lens.

Still, curvature is a relevant factor determined by the center of the spherical wavefront. Therefore, when a lens is tilted relative to the line of sight, the radius of curvature is effectively altered, changing the perceived curvature and thus, the power.

Refraction from a phoropter is determined from a specified back vertex distance (the distance from the back of the lens to the corneal apex), usually around 13 millimeters. Also, the lenses are on a plane that is perpendicular to the line of sight. Therefore, the corrective power of the Rx is measured from this refractive plane versus the as worn spectacle plane.

The phoropter lens does not account for frame wrap or pantoscopic tilt! However, there is an industry standard for these position of wear fac tors. The average standard wrap or “face form” is 10 degrees. The average pantoscopic tilt is 8 degrees. Why? Because human skulls are not designed as flat planes! Eyes rotate about a “bony orbit.” Remember the ABO question regarding how many muscles control the rotation of the eye? The answer is six. They are in the bony orbit, which is not in a flat plane in relation to the line of sight. The industry standard 10 degrees of wrap and 8 degrees of pantoscopic tilt for a spec tacle frame allow the eyes to maintain a consistent vertex when rotating behind properly designed lenses. These are averages, of course, and depend ing on the actual position of wear (POW) frame fit parameters, the relationship between the line of sight and the optical axis of the lens will vary for the individual position of wear parameters. A personalized freeform lens design can compen sate for the tilted lens based on fit parameters so that the wearer experiences the prescribed power.

This begs the question: Why are there all of these high-wrap (over 20 degrees) frames? The answer: Protection! This is especially true for sunwear since the trend for wrap sunwear manufacturers is to design frames with higher wrap angles and pantoscopic tilt.

This now begs another question: What effect does wrap angle and pantoscopic tilt have on the lens optics, and how will it vary from the prescribed power? The mounted lens is no longer in the same plane that the patient’s eye was refracted in. The effective change in power will exhibit the aberration known as radial astigmatism, aka marginal or oblique astigmatism. The effective power perceived by the wearer is altered from the prescribed power. Remember, the effective radius of curvature has been altered relative to that eye.

Since indeed, there is an effect, there must also be some way to counter that same effect. There is, and it’s known as compensation. The calculations for the effects of wrap and tilt angles are inversely related, as well they should be. An optician should understand the basic effects of tilting a lens in front of the patient’s line of sight or when the gaze direction behind the lens is off axis in the periphery of the lens. The perceived power through the lens at that point and obliquity varies from the prescribed power. An optician should be aware that a wrap compensated Rx will read differently on the flat plane of the lensometer than it will on the angular plane of the wearer’s face in a highwrap frame. This is known as the as worn position. Simply stated, a wrap compensated Rx that reads differently from the given Rx in the lensometer will read correctly at the angle the wearer will look through the lens. You can see this effect by holding the lens against the lens stop at the approximate wrap and tilt angles when reading the Rx. Notice how the readings change when you put the lens back on the flat plane on the lens stop.

So, other than frame selection, what is our role as dispensing opticians? After all, doesn’t the lab take care of any needed calculations? Computers do all of the work, don’t they? Guess what? The lab can only perform as well as the data that is input. AND is provided by you. Therefore, the lab depends on your precision and measurement skills! Good precision tools help. Fortunately, most freeform lens design manufacturers provide helpful tools.

Therefore, skill in taking the position of wear and biometric measurements is imperative, especially when in a high-wrap frame. The higher the Rx, the more relevant this becomes. Another consideration is prism; the prismatic effect of the wrap is independent of the Rx. The relevant variables for compensating the prismatic effect for a high-wrap frame consist of the base curve, lens thickness (reduced thickness) and the lens material’s refraction index.

To research this further, I read up on the effects
of radial astigmatism in Keating’s *Geometric,
Physical, and Visual Optics and the Optical Formulas
Tutorial* by Stoner, Perkins and Ferguson.

Keating explains that radial astigmatism is related to off-axis tangential and sagittal meridians. As a person looks away, say downward through the lens, a certain number of degrees, power and cylinder are induced. Induced being the key word! The plane containing the optical axis and chief ray is the tangential plane. In the case of a person looking down, this would constitute the vertical meridian. Thus, the horizontal meridian would constitute the sagittal plane for this case. Again, the planes are altered, changing the effective radius of curvature, thus the effective power through that gaze.

Several formulas are related to calculating and compensating the altered power due to high wrap and pantoscopic tilt angles. There is also a formulation to counter the induced prismatic effect of wrap in relation to PD. These are listed as a reference, as some only apply to either a wrap angle or a pantoscopic tilt angle. The examples will be for conditions where both are relevant.

It is essential to understand that the advanced mathematical methodology used to produce freeform lenses is highly sophisticated and well beyond the rudimentary understanding we glean from basic dispensing principles. However, by familiarizing yourself with the compensation formulas, you will gain an intuition that will help you picture the effects of wrap and tilt angles on the effective power for different points on the lens. Furthermore, your increased skill level will benefit you and your clientele when it comes time to recommend the optimal lens design, material, multifocal style (when applicable) and coatings. The following are formulas related to wrap and pantoscopic tilt compensation. You may recognize certain ones that will be used in the examples.

## FORMULAS

**The Radial Astigmatic Formulas
For either a wrap only or pantoscopic tilt only Rx (where φ is in radians):**

**Compensation factors for an Rx with both
wrap and pantoscopic tilt (where θ is in
degrees):**

**The Prism Compensation Formula
(Due to Wrap Angle)**

This formula calculates the base-in prism required based on the base curve, lens thickness and wrap angle.

This is stated as: one hundred times the reduced
thickness of the lens times the base curve times *φ *(Phi) in radians. It can also be stated as one hundred times the reduced thickness of the lens times
the base curve times sin*θ*** **(Theta) where:

1. The reduced thickness equals the actual thickness of the lens divided by the index of refraction of the lens material.

2. The angle (*φ*) Phi equals the wrap angle in
radians.

3. The angle (*θ*) Theta equals the wrap angle
in degrees.

Remember, this is a factor regardless of the Rx.

**Example**: A patient comes into your dispensary
with an Rx of:

OD: +4.50-2.00 x 155

OS: +5.00-2.50 x 020

A high-wrap sports frame is chosen because the client loves to play softball and enjoys other outdoor activities. You take accurate measurements for monocular PD, frame wrap angle and pantoscopic tilt angle. The index of refraction is

1.50 due to the customer’s desire for clarity, even after you had explained the difference in impact resistance of other materials.

Your high-tech digital devices give the following readings:

1. PD: 64 mm – MONO PD 32 OU

2. Frame wrap: 20 degrees

3. Pantoscopic tilt: 14 degrees

The Rx is single vision. A +8.00-diopter base curve will be used due to the high plus Rx and the high wrap frame. The center thickness has been calculated at 5.5 mm.

Since the frame has both a wrap angle and
pantoscopic tilt, the calculations are more complex. Keating states, “In the more complicated
case of OCR (Oblique Central Refraction) for a
spectacle lens with both the faceform and pantoscopic tilt, there is an effective tilt angle *φ *(Phi)
that is a function of the face-form tilt angle f and
the pantoscopic tilt angle p.”1 The angle *φ *(Phi)
is then converted to degrees to compute the tangential (Tc), sagittal (SC) and torsional (Hc)
compensation factors. The tangential and sagittal planes are also no longer horizontal and
vertical. This means more induced obliquity.
The wrap-compensated Rx will definitely be
different from the prescribed Rx.

An effective rotation of the prescribed cylinder axis moves out of the flat plane of the refraction. The angle A is a degree measure of that rotation’s clockwise or counterclockwise deviation. It must effectively be subtracted from the given Rx axis. That resultant axis will then be used to compute the cylinder power and thus, the total power of the lens in the horizontal x meridian and the vertical y meridian, respectively. The torsional component will also be computed using the new resultant axis. Since the wrap rotation for the OD and OS are counter to each other, the angle A will be straightforwardly calculated for the OD, while the OS will subtract that angle from 90 degrees. The subscript R will be attached to A for the OD and L for the OS. For the current example:

An effective angle must be added back to the resultant matrix calculated Rx to compensate for the initial subtraction of angle A. It is designated as A” (A double prime). For the current example:

**Using A _{R} 36.09^{°}**

**Effective axis (OD) = 155-A _{R} = 155-36.09 =
118.91.**

**Power x axis = sin(118.91)2 x -2.00 = -1.533;
+4.50+(-1.533) = +2.967.**

**Power y axis = cos(118.91)2 x-2.00 = -0.467;+4.50+(-0.467) =
+4.033.**

**Torsion = -sin(118.91)cos(118.91) (-2.00) = -0.846**

The effective power matrix becomes:

When using the tangential, sagittal and torsional compensation factors, the x-axis power is divided by the tangential factor, the y-axis power is divided by the sagittal factor, and the torsion is divided by the torsional factor resulting in the Power matrix (PR) for the OD.

Now that the Power matrix (PR) has been computed, the resultant compensated Rx can be found.

Basic matrix algebra shows:

Now for the OS:

**Effective axis (OS) = 020-AL = 020-53.91 = -33.91 + 180 = 146.09.**

** Power x axis = sin(146.09)****2****x -2.50 = -0.778; +5.00+(-0.778) = +4.22.**

**Power y axis = cos(146.09)****2**** x -2.50 = -1.722; +5.00+(-1.722) = +3.278.**

**Torsion = -sin(146.09)cos(146.09)x(-2.50) = -1.1575**

Since the OS is rotated counter to the OD, the compensation factors for the tangential and sagittal meridians for the OS must be switched.

The x-axis is now divided by the sagittal factor, while the y-axis is divided by the tangential factor.

**Induced Prism Calculation**

And last but not least, the base in prism calculation. Remember, the base curve chosen is +8.00, and the index of refraction is 1.50. The wrap angle (Theta) is 20 degrees. The previously displayed formula is:

All that remains is to “plug in” the data.

This means a 1.0 diopter of base-in prism is needed for each lens. Again, this parameter is independent of the Rx.

So now that your brain and pencil hand are cramping, aren’t you thankful for that sophisticated freeform computer program and the lens designers (optical engineers) that create them? Which, by the way, goes way beyond the calculations I’ve shared. Freeform designs optimize the lens surface point by point to minimize aberrations and compute the ideal surface for best optics. And thanks to the computer numeric code (CNC) multi-axes lathe, these point-by-point surface curves can be applied to within 1/100 of a diopter or with 10 times more precision than standard lap tools. Hopefully, this exercise helps you become more intuitive about how a lens will perform based on the wrap and tilt angle. And hopefully, you now have a better appreciation of how impressive freeform technology is in its ability to optimize the lens and compensate for the position of wear measurement.