By Rich Palmer
The introduction of so-called fashion/performance wrap-around style frames suitable for Rx lenses has given rise to some challenging and very unique ophthalmic fitting and lens power issues both at the dispensing table and in the production laboratory.

Until recently lenses for wrap frames have been fabricated by producing the patient’s Rx using spherical high base lenses, which typically had a nominal front curve of 8.25 diopters. Unfortunately the results oftentimes have been patient discomfort and less than desired visual acuity than that realized through the patient’s so-called dress wear lenses. This has been due in large measure to considerations not adequately being given for the need to compensate or re-calculate Rx powers because of the optical effects associated with large amounts of Face Form Tilt or Panoramic Angle in wrap frames and the induced prism that’s associated with tilting of prescription lenses.

In a high wrap frame the Rx power is rotated about the two primary optical meridians, the tangential meridian along the horizontal plane and the sagittal meridian about the vertical plane. This rotational effect is often referred to as “Radial Astigmatism,” often referred to as “marginal” or “oblique astigmatism.” The sagittal meridian may be considered as the Rx’s spherical component and the tangential meridian equated to the cylinder Rx component.

The greater the degree or severity of the wrap angle of the frame the greater the amount of compensating Rx power that will be required in these meridians to yield proper visual acuity and wearing comfort; i.e. the same visual acuity a wearer experiences with dress wear lenses. This is true not only for a compound Rx, spherocylindrical lens with an oblique axis, but also for a spherical power Rx. As an example consider the following dress wear Rx that is to be placed in a wrap frame having a Face Form (or Panoramic) Wrap angle of 25° with frame (58x16) and patient’s PD (32/32) requiring 5mm decentration. Also, for purposes of illustration, let’s consider vertex distances of 13mm and 11mm refracted and fitting distances respectively. For this example consider a wrap frame’s Pantoscopic tilt angle of 9° also to be considered for the recalculations. However, the effect that these two additional factors, vertex distances both refracted and fitted distances, have on re-calculating an Rx (or the “RA” change factors) plus considerations for lens decentration will be noted and explained in greater detail later.

Patient’s Rx #1:

Rx of -3.00 sphere into a frame with 25° of wrap angle Lens material to be polycarbonate and fabricated using an 8.25 base lens Compensated/Re-calculated Rx: -2.62 – 0.25 x 29° With “Induced Prism” of 0.37° base in & 0.12° base up

Thus far we have an example of only a wrap lens for a spherical Rx. In the case of re-calculating compound Rx powers for wrap lenses, sphereocylindrical lenses at an oblique axis, there will be a change in the cylinder axis as well as a change in the diopters values of the sphere and cylinder power components. At this point in any re-calculation of an Rx for wrap lenses, the calculations will involve considerations for cross cylinder powers. To dramatize this, consider the following Rx example:

Patient’s Rx #2:

Rx of -1.75 – 2.75 x 135 Wrap frame with a 25° Face Form Angle – 5mm decentration-Vertex distances of 13mm for the Refracted distance and 11mm for the Fitting distance Lens material of Polycarbonate Compensated/Re-Calculated Rx” -1.62 – 2.25 x 141 With “Induced Prism” of 0.37° base in & 0.12° base up

As you can see from the resulting calculations, there is little change in the sphere power but a significant change in the cylinder power plus a change in cylinder axis of 6°, not a small amount when considering a cylinder power in excess of 2.00 diopters.

Discussions with Dr. Clifford Brooks of Indiana University School of Optometry and through reference text as that noted in the footnote below, gave rise to recognition of one additional optical consequence, which occurs in prescription lenses for wrap frames. Specifically this additional cause and effect associated with wrap lenses involves the amount and direction of induced prism associated with the tilting of Rx lenses. Because wrap frames inherently have greater amounts of Pantoscopic tilt and Panoramic or Face form angles than dress wear frames, the added factor of this induced prism must be examined.

The amount of the induced prism is dependant upon not only the lens material index of refraction but also lens thickness, the radius or diopter value of the front curve, and respective to this discussion, the number of degrees of the tilt angle. The following formula represents the manner in which the prismatic effect can be calculated:

∆ = 100 tan 0θ t F1 n

∆ = amount of prism induced

θ = tilt angle

t = lens thickness in meters

n = refractive index of lens material

F1 = true front curve of lens

Additionally the direction or base of the induced prism is dependant angle upon where light will enter the Rx wrap lens. Consider first the right Rx lens in a wrap-around frame. The Face Form tilt of the lens causes light to enter the lens essentially from the left of the viewing gaze causing the “base” of the prism to be toward the right-hand or temporal side of the lens; or Base Out. The opposite is true for the left Rx wrap lens.

Additionally because wrap-around frames inherently have a greater degree of Pantoscopic tilt, (tilted inward toward the patient’s face) light will enter the Rx lens in essence nearer the top of the lens causing whatever prism that is induced to be downward or Base Down.

Therefore to neutralize the effect of these induced prism the re-calculated Rx must include opposite and compensating prism amounts to be part of the fabricated lenses for the wrap Rx. These “natural” prisms come with the territory of Wrap Rx’s and are one more factor that defines the differences in dress and performance eyewear.

As is evident from the above brief discussions on a sampling of the optical effects of wrap lenses and the example Rx’s cited, the fitting and production of lenses for fashion and performance wrap frames involves far more detail than is associated with that of so-called regular prescription dress wear.

However, with the ever increasing popularity of wrap performance frames and the inherent effects associated with Rx lenses, the need to properly address and provide the eye wear consumer with maximum visual acuity is the challenge that confronts all within the optical community, dispensers and fabricators alike. The mathematical basis behind the use of these measurements and the subsequent re-calculations of Rx powers are as follows: Panoramic Angle (Face Form Angle) “RA” change factor for the Spherical Component or Sagittal meridian:

Equal to 1 + sin 0 2 n

“RA” change factor for the Cylinder Component or Tangential meridian:

Equal to --- 2n + sin 0 2n + cos 0 For both formulas:

0 equals the angle of Panoramic Angle (Face Form Angle) of the frame n equals the index of refraction of the lens materials utilized

To complete the re-computation of the original lens powers, the “RA” change factors are divided into the original sphere and cylinder diopter values. Specific to the Pantoscopic Tilt, which is rotation about a horizontal axis, there is an alteration or change in one’s effective sphere power while also inducing a cylinder power along the horizontal or 180 meridian. This is in direct contrast to Panoramic Angle (Face Form tilt) in that with Pantoscopic tilt sphere and cylinder powers are altered about the vertical or 90 meridian.

Application of Martin’s Formula will dramatize the effect that this element of frame tilt will have on an Rx thereby further substantiating the rationale for Rx re-calculations of a dress wear prescription into powers necessary for optimum acuity relative to the wrap Rx:

S’ = S [1 + (sin α)^2 / 2n] C’′ = S′’ (tanα)^2 Where:

S’ equals the new sphere power S equals the original sphere power  equals the degrees of tilt n equals the index of refraction of the lens material C’′ equals the induced cylinder on axis of rotation

In like fashion to the previously shown formulations for Panoramic and Pantoscopic angles, the vertex distance of wrap frames compared to those of dress wear frames can also have an effect upon the Rx eventually produced once re-calculation of powers is accomplished.

Again with all respect of reference to Stoner and Perkins, calculations of vertex distance yields an effective power formula of DE = DL (1+dDL) Where:

DE =new effective power DL = original lens power d = change in vertex distance in meters

If the lens is moved toward the eye in that the refracted distance is greater than the fitted distance, the value of “d” is positive. The converse is true if the lens fitted distance is greater than the refracted distance.

In as much as various ophthalmic formulas and their applications can be a bit overwhelming, it is nonetheless important to understand how and in what manner the unique aspects of wrap frame fitting can have on a patient’s Rx as well as to what degree the Rx which will ultimately be produced differs from that originally written by the prescribing doctor.

A study was conducted covering a collection of wrap frames to determine the possibility that an average Pantoscopic tilt and Panoramic or Face Form angle values might exist to assist the laboratory and dispensers in the ordering and fabrication of a wrap Rx.

The findings to these investigations revealed that there were indeed average values that could be made available to the laboratory to assist in the order entry process of wrap lenses for fashion or performance wrap frames.

The results are as noted below:

Average Panoramic Angle = 20° Average Pantoscopic Tilt Angle = 9° Average Vertex fitting distance of the wrap lens = 10mm

It is recommended that the laboratory use these average measurements unless they are confident in their ability to measure customized Panoramic and Pantoscopic values. One other piece of data that is of utmost importance is that of a “Fitting Height” or optical center location to be obtained during the surfacing of wrap lenses. The “Fitting Height” or O.C. placement for single vision wrap lenses is of the same importance and has the same relevance as a segment height for multifocal prescriptions.

When the original doctor’s Rx is re-calculated for wrap production the O.C. placement plays a very critical part in determining the final sphere, cylinder, cylinder axis, and amount(s) of induced prism that will be fabricated. In the event that the dispenser fails to provide this “fitting height / optical center placement location, it is advisable for the laboratory to use a minimum of 50 percent of the frame’s “B” measurement as an optical center default value.

Written by Rich Palmer of Practical Engineering, LLC, Minneapolis, MN


Labtalk June 2020