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Middle East African Journal of Ophthalmology Middle East African Journal of Ophthalmology
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Year : 2015  |  Volume : 22  |  Issue : 3  |  Page : 265-270  

Optical issues in measuring strabismus

Laboratory of Ophthalmic Instrument Development, The Wilmer Eye Institute, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA; Clinical Investigation Center - CIC 1423 INSERM, Quinze-Vingts National Eye Hospital, Paris, France

Date of Web Publication1-Jul-2015

Correspondence Address:
Kristina Irsch
The Wilmer Institute 233, The Johns Hopkins Hospital, 600 N. Wolfe Street, Baltimore, MD 21287-9028, Maryland, USA

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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0974-9233.159691

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Potential errors and complications during examination and treatment of strabismic patients can be reduced by recognition of certain optical issues. This articles reviews basic as well as guiding principles of prism optics and optics of the eye to equip the reader with the necessary know-how to avoid pitfalls that are commonly encountered when using prisms to measure ocular deviations (e.g., during cover testing), and when observing the corneal light reflex to estimate ocular deviations (e.g., during Hirschberg or Krimsky testing in patients who do not allow for cover testing using prisms).

Keywords: Angle kappa, angle lambda, frontal plane position, minimum deviation position, Prentice position, Prentice′s rule, prism diopters

How to cite this article:
Irsch K. Optical issues in measuring strabismus. Middle East Afr J Ophthalmol 2015;22:265-70

How to cite this URL:
Irsch K. Optical issues in measuring strabismus. Middle East Afr J Ophthalmol [serial online] 2015 [cited 2022 Oct 3];22:265-70. Available from: http://www.meajo.org/text.asp?2015/22/3/265/159691

   Introduction Top

It is important to keep certain optical issues in mind when examining and treating strabismic patients. Common pitfalls are encountered when measuring and correcting ocular deviations using prisms, such as during the positioning, stacking, or measuring through corrective spectacle lenses, and when observing the corneal light reflex during the estimation of ocular deviations. Understanding some basic as well as guiding principles of prism optics and optics of the eye enables us to prevent and minimize the effect of potential mistakes in patient care.

   Quantification of Strabismic Deviations: Prism Diopters Versus Degrees Top

Ophthalmic prisms are made of two nonparallel refracting surfaces that intersect at the apex and deflect (refract) light rays passing through them, with the rays always bending toward the base (opposite to the apex) of the prism. Strabismic deviations are commonly quantified in prism diopters, a measure of the power of an ophthalmic prism, which is quite different from degrees. The power of an ophthalmic prism (glass or plastic) in prism diopters (Δ) is equal to the deviation, in centimeters (cm), of a light ray passing through the prism, measured one meter, or 100 cm, away from the prism [Figure 1]. [1],[2],[3] Note that one should not refer to 15Δ as 15 "diopters." Although one may occasionally come across 15 "prisms," the correct term is 15 prism diopters.
Figure 1: Light path through a 15Δ prism. The amount of deflection (in cm) of a light ray that is caused by a prism, measured 1 m (100 cm) away from the prism, is equal to the power of the prism in prism diopters (Δ). Thus, a 15Δ prism, as in this illustration, deviates a light ray 15 cm toward the base of the prism, when measured 1 m away from it

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Degrees of deviation are related to prism diopters of deviation not in a linear but a trigonometric manner (degrees = tan -1 (Δ/100) ×180/π). For angles smaller than 45° (or 100Δ), each degree equals approximately 2Δ. For angles larger than 45° (or 100Δ), however, this approximation of 2Δ per degree is no longer valid; as one approaches 90°, the number of prism diopters per degree rises to infinity [Figure 2]. [1]
Figure 2: Relationship between prism diopters and degrees. For angles smaller than 45° (or 100Δ), the number of prism diopters per degree is about 2. For angles larger than 45° (or 100Δ), this approximation becomes invalid, and as one approaches 90°, the number of prism diopters per degree goes up to infinity

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   Measurement of Strabismic Deviations: Positioning of Prisms Top

The amount of strabismic deviation produced or measured by a prism depends on the position in which it is held. It is thus critical to understand how to hold prisms correctly. Ophthalmic prisms made of glass are calibrated for use in the Prentice position and should be held with one surface, usually the back surface perpendicular to the patient's line of sight [Figure 3]a. Plastic prisms, including plastic prism bars, on the other hand, are calibrated for use in the minimum deviation position, in which, as the name implies, the least amount of total deviation is produced, with equal amounts of bending occurring at each prism surface [Figure 3]b. In clinical practice, it may be difficult to position prisms accurately according to the angle of minimum deviation, but holding them in the frontal plane position, with the back surface flat to the face of the patient, closely approximates the minimum deviation position for distant fixation objects [Figure 3]c. [4] For near fixation objects, the back prism surface should be angled in slightly, so that it is perpendicular to the fixation object. [5] In general, if plastic prisms are held with the back surface perpendicular to the direction of the fixation object, essentially equal angles of bending occur at both surfaces, serving as an ideal surrogate for the minimum deviation position at all times.
Figure 3: Positioning of prisms. (a) Prentice position. Glass prisms are calibrated for use in this position, so the line of sight makes a right angle with one of the surfaces. (b) Minimum deviation position. Plastic prisms, including plastic prism bars, are calibrated in this position, so the line of sight makes an equal angle with each prism surface. (c) Frontal plane position. Holding plastic prisms in this position, with the back surface flat to the face of the patient, closely approximates the minimum deviation position, which would otherwise be difficult to estimate in clinical practice

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What if one holds a prism wrong? This may induce large errors in the amount of produced or measured strabismic deviation by the prism, especially for high power prisms. For example, holding a 40Δ glass prism in the frontal plane rather than the Prentice position, gives a 32Δ effect rather than 40Δ. [4] When a plastic prism is held the way one should hold a glass prism (in the Prentice position), the error is even worse; a 40Δ plastic prism, for example, held in the Prentice position gives 72Δ of effect.

   Measurement of Strabismic Deviations: Stacking Prisms Top

Stacking prisms together in the same direction, especially if one is of high power, when measuring large strabismic deviations may also result in large errors. For example, adding a 5Δ prism to a 40Δ prism, results in 58Δ of effect, and a 10Δ prism added to the 40Δ prism can result in more than 100Δ of effect. [4] This can be understood by looking at the interface between two stacked prisms [Figure 4]. Even if the first prism is held in its proper position, the second prism is nowhere near its calibrated position, leading to a stronger prism effect than simply the sum of the two prisms. Therefore, prisms do not add linearly and should never be held in contact with each other in that manner.
Figure 4: Interface between two stacked prisms. While the first glass prism is in the Prentice position, with the light ray being perpendicular to the first surface of the prism, the second glass prism is nowhere near the Prentice position, with the light ray going in at an angle far from perpendicular (adapted from reference 4)

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When measuring large strabismic deviations, it is thus preferred to split the prisms between the two eyes. There is still some error in adding the powers together; however, the induced additivity error is much less than when stacking prisms together in the same direction before one eye and has been tabulated by Thompson and Guyton. [4] Beware that this only works, however, when dealing with comitant strabismic deviations.

Note, in stacking prisms that one can, in fact, stack a horizontal and vertical prism together, as they do not interfere significantly with one another, and this is common clinical practice when measuring a combined horizontal and vertical strabismic deviation. The combination of a horizontal and vertical prism may be prescribed in spectacle lenses as a single prism at an oblique angle. Other than using a prism nomogram [2] and trigonometric calculations (Pythagorean theorem), the power and base direction of such an oblique prism may be determined by a simple method. Prisms add as ordinary vectors, and this vector addition may be sketched on a piece of paper, by first marking off proportional distances from one corner (down is base-down, and right is base-in or base-out depending on which eye the oblique prism is intended for), then connecting the two measurement marks using a ruler. The length of the connecting line (the hypotenuse of the formed triangle) is proportional to the power of oblique prism required. Last, the direction of the oblique prism base can be determined by folding the paper along the hypotenuse and measuring the appropriate acute angle of the triangle using a protractor (such as on your phoropter or trial frame).

When prescribing oblique prism, attention should be paid to the orientation of the prism base, especially in countries such as the United States, where prism base is specified from 0 to 180 degrees. Each meridian has two choices as far as prism base directions are concerned: For example up and out or down and in. Thus, the direction of the prism base should be specified either as "base up and in at the appropriate meridian" or as "base down and out in the appropriate meridian" to avoid ambiguity.

   Measuring Strabismic Deviations Through Glasses Top

Glasses have an effect on the measurement of strabismus, which becomes clinically significant especially with high power spectacle lenses. [6] This is because in a strabismic patient, only one line of sight at a time passes through the corresponding spectacle lens at its optical center (where there is no prismatic power). The other line of sight, on the other hand, passes through the corresponding spectacle lens at a position away from its optical center, where it encounters prismatic power (that is equal to the distance of that point from the optical axis in centimeters multiplied by the power of the lens in diopters, Prentice's rule), causing a prismatic change of the deviation as measured in front of the glasses.

Plus lenses may be thought of as acting somewhat like two prisms base to base, and minus lenses may be thought of as acting somewhat like two prisms apex to apex. [3] Thus, plus lenses decrease the measured ocular deviation, as they cause base-in effect for exotropia and base-out effect for esotropia, and base-down effect for hypertropia and base-up effect for hypotropia. Minus lenses have the opposite effect; they increase the measured deviation ("minus measures more"), as they cause base-out effect for exotropia and base-in effect for esotropia, and base-up effect for hypertropia and base-down effect for hypotropia. Beware, however that cosmetically the effect of glasses is just the opposite because of magnification considerations; plus lenses increase the cosmetic deviation, and minus lenses decrease the cosmetic deviation. The true deviation (at distance) in front of the glasses is changed by a percentage of approximately 2.5 × D, where D is the bilateral spectacle lens power. [1],[6] For example, an exotrope of 40Δ wearing -10.00 glasses will measure (2.5) × (10) =25% more exotropia for a total of 50Δ.

One consequence of this is that a strabismic patient with anisometropic glasses will measure an incomitant deviation in front of the glasses; even a straight-eyed patient will measure an incomitant deviation with various gazes in front of anisometropic glasses. So before you start thinking of a nerve palsy or similar, make sure that you are not simply dealing with a measurement artifact due to the different power glasses in front of the two eyes.

Likewise, if a patient without strabismus but with anisometropia reads below the optical centers of his or her single vision glasses, different vertical prismatic effect is induced by the different lens powers in the glasses. Most patients physiologically adapt or learn to fuse small vertical deviations. If not, however, the most common way to compensate for the problem is to incorporate vertical prism in the lower portion of one spectacle lens to lessen or eliminate the induced diplopia, in the form of slab-off or reverse-slab prisms, without changing the power of the spectacle lens. When prescribing slab-off or reverse-slab prisms, it is recommended to measure (by prism and cover test in the reading position) rather than calculate, the amount of prism required, [1] which takes into account that the patient may have already partially compensated for the differential vertical prismatic effect.

Note that even patients without ocular misalignment or anisometropia will be given strabismus by their glasses when their spectacle lenses are decentered.

   Measuring the Amount of Prism Ground into, Applied to, or Caused by Decentration of Spectacle Lenses Top

It is imperative to measure the effective amount of prism, at the center of the patient's pupil (at the patient's line of sight when looking straight ahead), when quantifying the prism caused by decentration of spectacle lenses, as well as prism ground into or applied to spectacle lenses. To facilitate this, the part of the lens through which the patient is looking can simply be marked with a water-based maker or a triangular piece of tape.

The amount and orientation of prism can then be roughly estimated by inspection (for example by judging the continuity/discontinuity of a horizontal or vertical edge through the lens, at the marked center of the patient's pupil), [3] as well as more exactly determined by means of the lensmeter (by centering the pupil mark on the nosecone).

When measuring with the lensmeter, any horizontal and vertical displacement of the cross-line target away from the center of the reticle indicates presence of horizontal and vertical prism respectively, with the decentration in the direction of the prism base [Figure 5]. The number of rings on the reticle between the displaced center of the cross-line target and the reticle center reveals the amount of prism in prism diopters, with the first ring corresponding to 0.5Δ, which is usually not labeled in most lensmeters.
Figure 5: Detection of prism with lensmeter. Displacement of the cross-line target away from the reticle center indicates presence of prism, with the decentration in the direction of the prism base. In this illustration, the cross-line target is displaced 4 rings to the right, indicating the presence of 2Δ base-in or-out prism if dealing with a spectacle lens for the right eye or left eye respectively

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If the displacement goes off scale, adding neutralizing prism of a known power anywhere between the spectacle lens and the telescope of the lensmeter aids in bringing the cross-target back onto the scale.

   Measuring Incomitant Strabismic Deviations Top

When measuring incomitant deviations with either eye fixing (first with the prism over one eye and then with the prism over the other eye), we must define the fixing eye by the eye that is looking in the intended direction, in other words the eye not looking through the prism. [7] If the prism is not switched, the same deviation will be measured, no matter which eye the cover is placed over first.

   Estimating Strabismic Deviations by Corneal Light Reflex Observation Top

While the measurement of strabismic deviations using prisms and cover testing is the preferred clinical practice, [8] in some patients, in particular, young children, one may have to resort to an estimation of ocular deviations by observing only the position of the corneal light reflex within the pupil instead (i.e., the Hirschberg and Krimsky tests). Displacement of the light reflex from its normal position with respect to the pupillary center or margin landmarks can provide a fair estimation of strabismic deviations in many instances when the patient will not cooperate for cover testing [Figure 6].
Figure 6: Schematic representation of angle lambda and corneal light reflex positioning. (a) Normal angle lambda (λ) between the patient's line of sight (directed at the examiner's handlight) and pupillary axis is associated with slight nasalward positioning of the corneal light reflex (the reflection of the handlight from the anterior surface of the cornea) with respect to the pupillary center. (b) Eye with normal angle lambda (λ) is not fixating on the handlight, with strabismic deviation (δ), showing nasalward displacement of the corneal light reflex from the pupillary center. Note the imaginary string that connects the corneal center of curvature (CR) with the handlight. (c) Large angle lambda (λ+) caused by a temporally dragged, but fixating fovea, showing the same amount of nasalward displacement of the corneal light reflex from the pupillary center as in (b) with the deviated eye with normal angle lambda (λ) not fixating on the handlight

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The corneal light reflex that is observed clinically is a virtual image (the first Purkinje image of your handlight, for example) formed by the front surface of the cornea that acts like a convex mirror. This virtual image is located at half the radius of curvature behind the corneal front surface, which in the Gullstrand schematic eye, [9] with a radius of curvature of 7.7 mm, is 3.85 mm behind the cornea and 0.8 mm behind where one notes the iris/pupil plane to be (the entrance pupil). The entrance pupil (located 3.05 mm posterior to the cornea) is the image of the actual pupil (located 3.6 mm behind the cornea) formed by the front surface of the cornea.

One may think of the corneal light reflex as being located about 4 mm behind the cornea and near the entrance pupil plane, on an imaginary string that connects your handlight with the center of curvature of the cornea (not the center of rotation of the eye). The shift of the iris margin landmarks or center of the pupil with respect to this first Purkinje image (still in line with your handlight via the imagined string connecting the light with the corneal center of curvature; see [Figure 6]b) during eye rotations provides the ability to estimate degrees or prism diopters of ocular deviation.

Errors from parallax however can occur during corneal light reflex observation (such as with Hirschberg or Krimsky testing). The examiner may avoid potential over- or under-estimation of the strabismic deviation from such parallax errors by positioning his or her own eye directly behind/over the handlight.

Another potential pitfall in the estimation of strabismic deviations by corneal light reflex observation is individual variability in the angle kappa (κ). This angle results from the fact that the pupillary axis (the line passing through the center of the entrance pupil orthogonal to the cornea) and the visual axis (the line passing from the fovea through the nodal points of the eye, about 7 mm behind the cornea, to the fixation object) do not coincide - the pupillary axis projects onto the posterior pole slightly nasal to the fovea [Figure 6]a - and is responsible for the slight nasalward position of the corneal light reflex with respect to the pupil center in a normal eye without strabismus. This displacement is about 0.5 mm in an average (normal) adult, or 1 mm, in a neonate eye, which, when computed with respect to the nodal point of the (reduced schematic) eye would correspond to about 5° (about 10Δ) in the adult or 10° (about 20Δ) in the neonate. [10] To be precise, what we actually estimate clinically under monocular viewing conditions is not the angle kappa (κ) but the angle lambda (λ), formed at the center of the entrance pupil by the patient's line of sight (the line passing from the fovea through the centers of the entrance and exit pupils to the fixation object, which may be considered a clinical approximation of the visual axis) and the pupillary axis [Figure 6]a. This is because we cannot see the nodal point(s) of an eye but the center of the entrance pupil (that approximates the pupillary axis) and the proximate corneal light reflex (that approximates the line of sight), [10] both of which are images formed by the anterior surface of the cornea. Both angles, kappa and lambda, are nearly identical, and the terms are often confused and used interchangeably. While these angles (kappa or lambda) are normally equal and symmetrical in the two eyes, the presence of a true strabismus may be over- or under-estimated when relying on Hirschberg or Krimsky testing alone, and when such angles are asymmetric between the two eyes, a strabismus may be diagnosed when none is actually present. This may occur most frequently in premature children with a history of retinopathy of prematurity where the fovea may be dragged further temporally [Figure 6]c in one eye compared with the other. As illustrated in [Figure 6], such a displaced fovea in one eye [Figure 6]c may give the impression of an eye not fixating on your handlight, as would be the case with strabismus [Figure 6]b. To avoid measurement errors from asymmetric foveas during Hirschberg or Krismky testing, the examiner is therefore advised to first estimate the value of the angle lambda monocularly in each eye. Aside from judging the displacement of the corneal light reflex within the patient's pupil (as shown in [Figure 6]a and c), an even better, more accurate way of measuring the angle lambda is by centering the corneal light reflex in the patient's pupil. To do so, you have the patient fixate on your finger moving off to the side, away from your handlight, until you see the corneal light reflex centered in the pupil. Then, the corneal light reflex (via the imagined string) is aligned with the patient's pupillary axis, and the patient's line of sight is aligned with your finger. Thus, the angle between the two is lambda, a function of how far away you moved your finger.

When both foveas are displaced more temporally symmetrically, such as in albinism where there is increased decussation of nasal nerve fibers, this will give the appearance of a pseudoexotropia. Conversely, when there are fewer nasal decussating fibers, such as with a congenitally present suprasellar mass such as a craniopharyngioma, the foveas may be located more nasally bilaterally according to Parsa CF (personal communication) giving the appearance of a pseudoesotropia. Since the light reflexes remain symmetric between the two eyes, such deviations of the angles lambda or kappa should not give rise to significant clinical misdiagnoses unless a true strabismic deviation is also present, in which case inadvertent errors in measurement may be made if monocular light reflexes are not also assessed.

   References Top

Guyton DL, West CE, Miller JM, Wisnicki HJ. Ophthalmic Optics and Clinical Refraction. Baltimore: Prism Press; 1999.  Back to cited text no. 1
Guyton DL, Miller JM, West CE. Optical pearls and pitfalls. In: Wright KW, Spiegel PH, editors. Pediatric Ophthalmology and Strabismus. New York: Springer-Verlag; 2003.  Back to cited text no. 2
Gutmark R, Guyton DL, Irsch K. Prescribing prisms. Focal points: Clinical modules for ophthalmologists. Am Acad Ophthalmol 2011;XXIX:10 (Module 1 of 3). Available from: http://store.aao.org/focal-points-2011-module-prescribing-prisms.html.   Back to cited text no. 3
Thompson JT, Guyton DL. Ophthalmic prisms. Measurement errors and how to minimize them. Ophthalmology 1983;90:204-10.  Back to cited text no. 4
Thompson JT, Guyton DL. Ophthalmic prisms. Deviant behavior at near. Ophthalmology 1985;92:684-90.  Back to cited text no. 5
Scattergood KD, Brown MH, Guyton DL. Artifacts introduced by spectacle lenses in the measurement of strabismic deviations. Am J Ophthalmol 1983;96:439-48.  Back to cited text no. 6
Repka MX, Kelman S, Guyton DL. Prism measurement of incomitant strabismus. Binocul Vis 1985;1:45-9.  Back to cited text no. 7
Choi RY, Kushner BJ. The accuracy of experienced strabismologists using the Hirschberg and Krimsky tests. Ophthalmology 1998;105:1301-6.  Back to cited text no. 8
Bennett AG, Francis JL. The eye as an optical system. In: Davson H, editor. The Eye: Visual Optics and the Optical Space Sense. Vol. 4. New York: Academic Press; 1962. p. 101-15.  Back to cited text no. 9
Available from: http://schorlab.berkeley.edu/passpro/oculomotor/html/chapter_4.html. [Last accessed on 2015 May 14].  Back to cited text no. 10


  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]

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