The Many Facets of Prism in Ophthalmic Lenses – Part 2

By Kai Rands, ABO-AC

Learning Objectives

Upon completion of this course, participants will be able to:

1. Determine the magnitude and direction of the prism base in a lens.
2. Analyze the effects of prism in ophthalmic lenses through examples.
3. Describe the process of verifying the prescribed prism in a lens.

Faculty/Editorial Board

Kai Rands is a North Carolina licensed and ABO/NCLE-certified optician at Ocutech, which manufactures vision enhancing systems such as bioptic telescopes. Kai received a Durham Tech Opticianry AAS Degree, and holds a B.S. a Masters of the Arts and a Doctorate of Philosophy and Education. Kai has experience as a vision neuroscience researcher as well as extensive expertise in education higher education, public schools, and community programs. Kai also works as an independent scholar and educational service provider.

Credit Statement
This course is approved for one (1) hour of CE credit by the American Board of Opticianry - ABO, Ophthalmic Technical Level 3, Course STWJHI086-3

Support:
This course is supported by an educational grant from ZEISS

This free CE course is sponsored by ZEISS through an educational grant. ZEISS has a strong commitment to the education of opticians dating back as early as 1908, when the Carl Zeiss Foundation approached the German Association of Ophthalmic Opticians (DOV) with the proposal that a specialist school should be set up for ophthalmic opticians. The profession of “ophthalmic optician” came into being in Germany in the late 1920s and is inextricably linked to ZEISS’ quest for improved and standardized training for opticians. ZEISS recognizes that the evolving and highly technical advancement in ophthalmic lens science requires the modern optician to have a solid background in basic optics while keeping abreast of the newest technologies available in the casting and manufacture of lenses for eyeglasses.

PRISMATIC EFFECT IN OPHTHALMIC LENSES TO CORRECT AMETROPIA

Hyperopes’ internal optical systems converge light so that the light focuses as if behind the retina. Converging light adds positive vergence shortening the focal length of light inside the eye, compensating for the too-long focal length of the hyperopic eye. Myopes’ internal optical systems are the opposite. Light rays inside the eye converge too soon to focus in front of the retina. Diverging light with a minus lens increases the focal length of light inside the eye, compensating for the too-short focal length of the internal optical system relative to the length of the myopic eye.

Ophthalmic lenses focus rays of light by deviating the light toward the thickest part of the lens just as a prism deviates rays toward the thickest part of a prism, aka prism base. Lenses can be modeled as prisms conjoined at the lens center. To model a plus power lens, consider two prisms with the same apical angle conjoined at their bases. Parallel rays strike the surface of the lens and bend toward the base (in) upon entering the lens. Rays traveling through a plus lens converge light rays. Conversely, a minus lens can be modeled with two prisms with the same apical angle conjoined at their apexes. If the rays pass through the two opposing prisms, the light will deviate toward the prism bases. Since the bases are out in a minus lens, light deviates out toward the bases, and the rays diverge (Fig. 1). The only point on the lens with zero prism is at the lens’ optical center (OC), which aligns with the focal point. As the distance from the optical center increases, the greater the deviation of the ray. Rays of light deviate more the further the distance from the optical center of the lens so that the rays can continue to pass through the focal point (Fig. 2). The prismatic effect can be described with the Prentice’s Rule, where the amount of prism at any point on a lens is proportional to the power of the lens by the given point’s distance from the optical center. Prentice’s rule describes this relationship: Prism = Distance × Power, where the distance is the decentration in centimeters.

Understanding Prentice’s Rule helps us understand the unwanted prismatic effect experienced when the patient is not looking through the lens’ optical center due to decentration errors. Alternatively, the lens can be intentionally decentered when mounted in the frame to induce the amount of prism prescribed.

Unwanted prism in a lens occurs when the patient’s visual axis is not aligned with the lens optical axis, causing a prismatic effect. Properly centered eyeglass lenses are decentered from the geometric center of the frame opening to align with the patient’s interpupillary distance (PD), emphasizing the importance of correct decentration and PD measurements for the correct alignment of mounted ophthalmic lenses. Using this same rule, the amount and direction of the prescribed prism can be accomplished by decentering the optical center of a spherical stock lens to induce the desired prism amount and base direction if the lens has sufficient power to produce the prism power prescribed. Note: Aspheric lenses cannot be used to induce prism through decentration.

PRISMATIC EFFECT IN SPHERICAL LENSES

Spherical ophthalmic lenses have radially symmetrical gradual smooth curves across their surfaces rather than the flat surfaces of our triangular prism models. For a spherical lens, the optical center is the location on the lens that does not deviate light, therefore it is the point on the lens with zero prism. In an uncut spherical lens, the geometric center and the optical center of the lens are the same. The prismatic effect gradually changes from zero at the optical center to the edge of the lens. As previously stated, two factors influence the prismatic power at any given point of a spherical lens: the dioptric power of the lens and the distance from the optical center. The dioptric power of the lens tells us how quickly the gradual change in the apical angle is. The distance from the optical center tells us how much of the gradual change is in effect at the given point.

Mathematically, the magnitude of the prismatic power in prism diopters at a given point on a spherical lens is the product of the distance from the optical center and the absolute value of the dioptric power of the lens. Represented mathematically as:
P=dD
P is prism in prism diopters
d is the distance from the geometric center in centimeters
D is the absolute value of the dioptric power of the lens.

To avoid using decimal centimeters, another version of the Prentice’s Rule equation keeps the distance, d, in millimeters. In this version, the product of the distance in millimeters and the dioptric power of the lens is divided by 10, as seen in Fig. 3.

To illustrate this, imagine a +3.00 D uncut lens blank. We mark (dot) the geometric (optical) center of the blank. We draw concentric circles around the mark at radii of 3 mm, 5 mm,10 mm and 15 mm apart, as shown in Fig. 2. Then we find the prismatic power along the circumference of each of these circles.

All of the points on the innermost circle are 3 mm from the center of the uncut lens blank. In centimeters, the distance is 0.3 cm, so d = 0.3. The absolute value of +3.00D is 3.00. We do not use power signs in prism calculations. Applying Prentice’s Rule, we have: P=(0.3)(3.00)=0.9Δ. The prismatic power at all of the points around the circumference of the innermost circle is 0.9Δ. The next innermost circle has a radius of 5 mm or 0.5 cm. The absolute dioptric power of the lens is still 3.00. Applying Prentice’s Rule, we have: P=(0.5)(3.00)=1.5Δ. So, the prismatic power at all of the points around the circumference of the second innermost circle is 1.5Δ. The next circle has a radius of 10 mm or 1.0 cm. The absolute dioptric power of the lens is still 3.00. Applying Prentice’s Rule, we have: P=(1.0)(3.00)=3Δ. Finally, the outer circle has a radius of 15mm or 1.5 cm. The absolute dioptric power is still 3.00. Applying Prentice’s Rule, we have: P = (1.5)(3.00) = 4.5Δ.

Now, let’s consider a -3.00 D uncut lens blank. We draw concentric circles in the same way as with the +3.00 D lens: mark the geometric (optical) center of the lens as the center of concentric circles with radii of 3 mm, 5 mm, 10 mm and 15 mm. The only difference is that the lens is a minus lens instead of a plus lens. Will this change the prismatic effect at each of the circumferences of the circles? Answer: NO!

The prismatic powers match those in the plus lens. The magnitude of the prismatic effect is unaffected by whether the lens is a plus or minus lens. Note also that the prismatic power on all points on the circumference of a given circle is the same. This is because the dioptric power along all meridians is the same for a spherical lens. This would not be true on a spherocylindrical lens.

FROM SPHERICAL UNCUT LENS BLANKS TO MOUNTED LENSES

In determining the prismatic power at any given point on a spherical lens blank, we need only consider the distance from the distance from the geometric center of the lens in centimeters times the dioptric power of the lens. Mounted lenses typically decenter the lens geometric center to align with the patient’s visual axis for prism free vision. However, when prism is prescribed, the geometric center of the lens blank is decentered to align the patient’s visual axis with the desired amount of prism in the desired prism base direction. Since light deviates toward the base, and the image is displaced toward the apex, where the base and apex are located makes a difference in how the prism affects the patient. Prism in mounted lenses is described by the direction of its base: BI for base in, BO for base out, BU for base up and BD for base down. Less commonly, eyecare professionals prescribe oblique prism. In oblique prism, the prescriber indicates a vertical and a horizontal component such as 5 BU and 3 BO.

How can the lab place the correct amount of prism in front of the patient’s visual axis? Consider this case: Patient Amari has a prescription of +3.00 D OU with no prescribed prism. The dispensing optician guides the patient to choose a frame that centers her eyes within the eyewire. The lab edges the lenses to mount in the eyewire so that the optical center of the lens aligns with the patient’s pupils. The patient experiences no prismatic effect when looking directly ahead, as desired.

A year later the patient returns with a new prescription. The sphere power remains the same for each eye, +3.00 D OU, but this time the patient has 1.5Δ of base in (BI) prescribed prism for each eye. When considering uncut lens blanks, we saw that to achieve 1.5Δ on a +3.00 lens, the distance from the optical (geometric) center of the lens blank must be 0.5 cm=5 mm. To achieve a prismatic effect of 1.5Δ in a finished/mounted lens we need to decenter the optical center of the uncut lens blank 5 mm from the position of the patient’s visual axis behind the lens.

Next we need to determine the direction to move this plus powered lens OC to achieve the desired base-in direction. We can use our conjoined prism triangle concept illustrated in Fig. 1 to determine which way to decenter the optical center of the lens blank for plus and minus lenses. In our scenario for Amari, the lens is a plus power, so it can be represented as two triangles conjoined at their bases. Where the bases meet is the optical center. We want Amari’s eyes to look through one of the triangles so that the base of that triangle is in, toward the nose. The eyes need to be temporal to the optical centers to produce base in prism, so we must move/decenter each lens in, meaning that the OC positions will be narrow compared to the patient interpupillary distance. See Fig. 4, example 3. We must decenter the optical center of each lens in, by 5 mm.

Let’s consider another case with a patient, Beverly, whose prescription is -3.00 D OU without prescribed prism. The optical center aligns with her pupil. A year later the patient comes back with the same spherical correction but with 1.5Δ BI prescribed prism. Again, we know from our experiment with spherical uncut lenses that 5mm in any direction from the optical center of a -3.00 D lens has 1.5Δ of prismatic power. Which direction do we need to decenter the optical center, so the prismatic effect is base in? The diagram for a minus lens in Fig. 4, fourth example, can be thought of as two triangles conjoined at their apexes in the center of the lens. We want the patient’s eye to look through the triangle so that the base of that triangle is in toward the nose. If the eye looks through the nasal side of the two triangles of a minus lens, the base is in toward the nose–which is what we want. On the other hand, if the eye is looking through the temporal of the two triangles, the base of that triangle would be out toward the ear–which is what we don’t want. So, we want the eye to look through the nasal of the two triangles for base in prism in a minus lens. We decenter the optical center of each lens out toward the ear, by 5 mm, to align the patient’s visual axis with the 1.5Δ diopters

CANCELING AND COMPOUNDING PRISM (PAIRS OF LENSES)

Coordinated eye movements in the same direction (left, right, up, or down) are called versions. Imagine a patient with no refractive error and typical binocular vision (no tropias or binocular vision dysfunction) looking straight ahead (primary gaze) with both eyes. If we wanted the patient to look up with both eyes (supraversion), we could place base down prisms in front of each eye. Since the prisms prompt eye movement in the same direction (up), it is fairly easy for the eyes to respond with supraversion. The same is true if we want the patient to look down (infraversion). We could insert base up prisms in front of each eye. What if we wanted the patient to easily look to the right (dextroversion)? This time the right eye would need to look toward the ear, and the left eye would have to look toward the nose. This means that instead of using prisms with bases in the same direction as with vertical gaze change, we need to use prisms with bases in opposite directions: base in for the right eye and base out for the left eye. Similarly, to stimulate the eyes to easily turn to the left (levoversion), we need to use prisms with opposite base directions. This time we need base out prism for the right eye and base in prism for the left eye. The term canceling prism is used for combinations of prism base directions that make it easy for the eyes to move in the same direction (up, down, left or right). For someone with typical binocular vision, compounding prism pulls the eyes in different directions: base up paired with base down, base down paired with base up, base out paired with base out, and base in paired with base in. These relationships are summarized in Table 1. The base directions of prism in a pair of lenses have a binocular effect as the brain interprets the way light deviates through both prisms.

CALCULATING NET PRISMATIC EFFECT

We can quantify the net prismatic effect of a pair of lenses using the concepts of canceling and compounding prism along with Prentice’s Rule. Consider the following case:
Carlos' prescription is as follows:
OD -2.00 DS
OS -3.00 DS
Carlos' monocular PDs are as follows:
OD 34mm
OS 35mm

After you mark/dot the lenses, the measured distance between the dotted OC on the right lens to the center of the bridge is 30 mm, and the distance between the dotted OC on the left lens to the center of the bridge is 32 mm. Let’s determine whether the net prismatic effect will be canceling or compounding so that we will know whether we will be subtracting or adding the prism amounts from each lens. Carlos’ monocular PD for each eye is wider than the distance from the center of the bridge to the OC. The lenses are minus lenses on the horizontal axis. Referring back to Fig. 4, we see that if the patient’s PD is wider than the OC position for each lens, then the base direction is out for both lenses. This is compounding prism so we will add the prismatic amounts to find the net prismatic effect.

Now let’s calculate the net prismatic effect for Carlos using Prentice’s Rule, recalling the equation: P=dD.
Find the prismatic effect on the right eye by finding the distance between the horizontal position of the OC and his monocular
PD: d = 34-30 = 4mm = 0.4cm
Next, find the refractive power on the horizontal meridian, taking the absolute value:
D = |-2.00| = 2.00
Now we are ready to apply Prentice’s Rule:
P = (0.4)(2.00) = 0.8Δ
So, the prismatic effect for the right eye is 0.8Δ base out.
Similarly, we can calculate the prismatic effect for the left eye.

P = dD
d = 35 - 30 = 5mm = 0.5cm
D = |-3.00| = 3.00
P = (0.5)(3.00) = 1.5Δ

We already figured out that the net prismatic effect is compounding so we will add the amount of prism for the right eye to the amount of prism for the left eye: Net Prism = 0.8 + 1.5 = 2.3ΔBO. This amount of unwanted prism would likely lead Carlos to experience diplopia aka double vision. As another example, consider Derek’s prescription below:
OD + 4.00 DS
OS + 5.00 DS
Derek's monocular PDs:
OD 30mm
OS 34mm
You find that the distance between the OC position of the right lens and the center of the bridge is 32 mm. The distance between the OC position of the left lens and the center of the bridge is 33 mm. Using Fig. 4, we can see that since Derek’s OD monocular PD is narrower than the horizontal position of the OC, and Derek is viewing through a plus lens, the base direction for the right lens will be base out. For the left lens, Derek’s monocular PD is wider than the horizontal position of the OC. In a plus lens, this means that the base direction is base in. The combination of base out prism in one lens and base in prism in the other lens is canceling prism, so the net prismatic effect will be subtractive. Now let’s find the prismatic effect for each lens. For the right lens, we have the following calculations of the distance from the OC position to Derek’s monocular PD, which is represented by d; the magnitude of the refractive error, D; and the prismatic effect, P:
OD (right lens)
d = 32-30 = 2mm = 0.2cm;
D = |+4.00| = 4.00;
P = (0.2)(4.00) = 0.8Δ BO
We can follow the same process for the left lens:
OS (left lens)
d = 34-33 = 1 mm = 0.1cm;
D = |+5.00| = 5.00;
P = (0.1)(5.00) = 0.5Δ BI
We already determined that the net prismatic effect is canceling, so we will subtract the amount of prism for the left lens from the amount of prism for the right lens: Net Prism = 0.8-0.5 = 0.3Δ

A net prismatic effect of 0.3Δ would likely not cause diplopia but the brain would interpret the light deviating toward the right in each lens (since the base is right of the OC in each lens). The image would be displaced (shift) to the left. Instead of turning his eyes toward the left (levoversion) to align with the image, it is more likely that he would turn his head slightly to the left to compensate for the image shift. With such small amounts of prism, the head turn would likely not have practical significance.

SPLITTING PRISM

Net prismatic effect shows that prismatic effect for one eye is relative to the prismatic effect of the fellow eye. When prismatic correction is placed in front of one eye, it affects both eyes because the brain applies the effect binocularly. For this reason, the prism can be applied in just one lens or split between the lenses. Let’s say we have a patient, Emma, who has the following prescription:
OD -4.00 DS 8Δ BU
OS -2.00 DS
So, we want Emma to experience 8Δ base up for the right eye. Using compounding prism, we can combine different amounts of base-up prism in the right lens with different amounts of base-down prism in the left lens. Let’s use PR to represent the prism amount for the right lens and PL for the prism amount for the left lens. So, we have:
Net prism = P_R + P_L = 8Δ
Consider what this would look like in a frame. Without considering the prism component of the prescription, the right lens will already be thicker than the left lens, especially on the top and bottom, because the right lens has twice the dioptric power. The 8Δ base up prism will add a large amount of thickness to the top of the lens since prism is thicker toward the base. The right lens will be heavier than the left lens, causing the distribution of weight to be uneven, leading to discomfort. The disparity in the upper lens thickness between the two lenses will also cause distortion. Alternatively, we could put all of the prism in the right lens.
P_R = 8Δ BU and P_L = 0Δ: Net prism = 8Δ BU + 0Δ = 8Δ BU

Ah! We can have the same net prism effect by distributing the amount of prism in different combinations between the lenses, as long as the base up prism in the right lens, and the base down prism in the left lens add to 8Δ BU for the right lens. For example, we can use any of the combinations listed in Table 2 to achieve the net prismatic effect of 8Δ BU for the right lens.
Although all of these combinations achieve the same net prism, splitting the prism equally between the lenses would have the best weight distribution, cosmesis and optics. Sometimes the prescriber has a reason to prescribe all of the prism for one lens or to use a specific way to split prism between the two lenses. It is important to check with the prescriber before splitting the prism in a different way than what is listed on the prescription.

To summarize, splitting prism always uses compounding prism, not canceling prism, to achieve the desired prismatic effects. Maintain the prism base direction for the eye originally prescribed prism. For example, if the left eye was prescribed base out prism, and you split prism between the lenses, the left lens should still include base out prism. Discuss options for splitting prisms with the prescriber before making any decisions on how to split prisms.

RECTANGULAR OR POLAR PRISM COORDINATES

The Prism base direction is not restricted to in, out, up or down (or a combination of up, down, in or out). Referring to Fig. 3, we saw that at any point on one of the concentric circles on a spherical lens, the amount of prism was the same 360 degrees. When two separate amounts of prism are prescribed in different directions in the same eye, it can be noted as rectangular or polar coordinates. Optometrists typically use rectangular coordinates, and labs typically use polar coordinates. For example, a prism base out and a prism base down in the same eye is ground as a given amount between the axis of the originally prescribed prism bases. So, how could we describe the direction of the base when it is the result of two base directions one vertical and one horizontal? For example, the base direction is at a 70-degree angle from the horizontal axis for OD +3.00 D 3Δ @ 70 (prism notation in polar coordinates). This is the resultant prism found by resolving the vertical and horizontal prism rectangular coordinates Rx OD +3.00 DS 2.8Δ BU 1.0Δ BI. We can graph this on a polar coordinates graph example shown in Fig. 5 or use trigonometric functions formulas. Resultant and resolving prism will be covered in a separate course.

VERIFYING LENSES WITH PRESCRIBED PRISM

The major reference point (MRP) is the point on the lens through which we want the patient to look. When the patient is not prescribed prism, the OC is the MRP. When a patient is prescribed prism, we want the patient to look through a point on the lens other than the optical center. In this case, the MRP becomes the prism reference point (PRP) and is the point on the lens with the desired prismatic power and direction.

Part of the verification process involves checking whether the MRP/PRP is in the correct location. As with ANSI tolerance ranges for sphere powers, cylinder powers and the cylinder axis, ANSI recommends tolerance ranges for vertical prism and horizontal prism (Table 3). The ranges reference the relationship between the two lenses. The balance of prism between the lenses must also be within a specified tolerance range. As seen before, the brain interprets prism binocularly, so the amount of prism must be balanced properly between the two eyes.

The lensometer is designed to make it fairly easy to position a lens so that it is ready for verifying the amount and base direction of prism. If a patient does not have prescribed prism, the crosshairs of the sphere and cylinder lines should be positioned directly in the center of the reticle. If the patient has prescribed prism, you will need to move the stage up or down and slide the lens left and right, so that the crosshairs center on the vertical and horizontal components of the prescribed prism. Fig. 7 shows the location of the crosshairs in relation to the reticle for several prescriptions with prescribed prism.The following example will help us understand how to verify vertical and horizontal prism.
Rx:
OD -5.00 DS
OS -6.50 DS
PDs
OD 29.5 mm
OS 31 mm
First, we begin by placing the lens with the stronger correction on the vertical axis (in this case, the right lens) on the lensometer stage. Since there is no prescribed prism, we center the sphere and cylinder crosshairs in the center of the reticle and dot the lens. We keep the stage at the same height and switch the left lens to in front of the lens stop, center the crosshairs horizontally in the reticle and dot the lens. Now we check whether the vertical prism reading is less than or equal to 0.33Δ. If the amount of vertical prism is within 0.33Δ, either base up or base down, the lenses are within tolerance. But what if the prism reads as 0.5ΔBD? Now, the lens gets a “second chance to pass.” We adjust the height of the stage so that the crosshairs are in the center of the renticle and dot lens again. We check the vertical distance between the two dots on the right lens. To fall within the ANSI tolerance range, the distance must be 1 mm or less. In this case, the distance is exactly 1 mm, and the vertical imbalance between the lenses is within ANSI tolerance ranges.

After verif ying vertical imbalance, we move on to verifying horizontal prism. We already dotted the horizontal distances between MRPs on the lenses when verifying vertical prism. Greg’s binocular PD is 60.5 mm. We measure the distance between the dots—the distance is 63.5 mm. To be within ANSI tolerance for a single vision lens, these two measurements must be 2.5 mm or less. Since 63.5-60.5 = 3.0 mm, we “give the lenses another chance.” The “se cond chance” range for horizontal prism is up to 0.67Δ binocularly. It seems like we will need to use Prentice’s Rule and calculate distances based on the dioptric power of the lens and the prismatic amount. Fortunately, there is an easier way in the lensometer using logic.

The logic goes as follows. The measurements between dots were too wide—too far temporal. We want to know if the prismatic effect caused by the distance between the location of Greg’s PDs and the actual lens OCs is more or less than 0.33Δ per lens. We can simply slide each lens toward the nasal until 0.33Δ reads on the lensometer reticle and dot the lenses again. Imagine we use a lens marker to draw Xs to mark Greg’s PDs. If these marks fall between the inner and outer dots for each lens, the amount of prism caused by the inaccurate OC placement must be less than 0.67Δ binocularly. In practice, we do not need to mark the location of the patient’s PDs—instead, we can compare the measurement between the second set of dots and the patient’s listed PD. In Greg’s case, when we induce 0.33Δ for each lens, the second set of dots is still too wide compared to his PDs, so the lenses fail the ANSI horizontal prism requirement. In general, if the first set of dots are too wide, slide each lens nasally for the second set of dots; if the first dots are too narrow, slide each lens temporally for the second set of dots.

DEVELOPING PRISM EXPERTISE

Prism, wanted or unwanted, has powerful effects on our interpretation of the world. As we saw in Part 1 of this continuing education course, prescribed prism can be used to benefit patients with various ocular, neurological and systemic conditions. Part 2 delved into the underlying optics and involved in the way prisms work in ophthalmic lenses whether prescribed or unwanted. Prism expertise allows us as opticians to apply optics to prevent adverse effects of unwanted prism while leveraging the positive effects to best benefit our patients.