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Chapter 4

Key words: visual axis, line of sight, pupillary axis, angle lambda, angle kappa

IV. Measurement of eye position and movement

Next let's consider some of the instruments and techniques available for clinical measurement of eye movements.  Clinical measurements are often made of monocular and binocular fixation, binocular eye alignment in strabismus, phoria, and fixation disparity.  You may also want to quantify reading ability by the number of regressions a person makes while reading a paragraph.  You may want to document the quality of tracking pursuits and saccades and unsteadiness of fixation (nystagmus) in patients receiving orthoptics or ocular calisthenics to train their oculomotor systems to perform better. You may also want to test the development of an infant by the quality of its OKN.  If a patient has a neurological disorder that you detect you may want to send a record of the diagnostic information to the neurologist.  Both subjective and objective techniques are discussed.  Subjective techniques of eye movement measurements require interpretation by the clinician or patient.  Objective techniques rely on a separate device such as a computer and are not influenced by a clinician's bias.

Subjective eye position measurement techniques
Direct Observation
Currently most eye movements are observed directly with the aid of a cover paddle and a small hand held fixation light (i.e. pen light). You sit directly opposite the patient while they look at a fixation point (such as your nose) or track a moving penlight, and you observe the accuracy of fixation and tracking.  These observations are facilitated by observing the position of the corneal reflex with respect to the center of the pupil.
The corneal reflex is one of 4 images reflected from the 4 surfaces of the eye's optics.  These are called catoptric images which means they are reflected.  The four surfaces are the front and back surfaces of the cornea and the front and back surface of the lens.  These reflections are referred to as the Purkinje images.  The first and second are nearly superimposed and can't be distinguished from one image.  They are erect images.  The third is reflected from the front surface of the lens and is also erect and larger than the first and second.  The fourth image is small and inverted.  It is actually brighter than the third and easier to see.  Clinically the first image is used to determine the accuracy of eye fixation. 

Fig 4.1  Purkinje Images


The two most common applications of the first Purkinje image are the angle kappa test and the Hirschberg test.  These tests evaluate the accuracy of monocular and binocular fixation respectively.  To evaluate monocular fixation, you face the patient while he/she attempts to monocularly fixate a small penlight.  You sight the patient's eye directly over the penlight and observe the displacement of the reflected image of the light from the center of the pupil.  Normally the corneal light reflex is displaced about 0.5 mm nasally from the pupil center in an adult and nearly 1mm in an infant.  This displacement corresponds with about 5 degrees or 10 prism diopters angle when computed with respect to the nodal point of the eye.

Fig 4.2
Axes and angles of the human eye

Technically this angular displacement is called angle lambda.  It is the angle formed between the pupillary axis and the subject's line of sight.  The pupillary axis is a line perpendicular to the cornea that passes through the center of the pupil.  The line of sight  is defined as a line passing from the center of the pupil to the object of regard.  The corneal light reflex approximates the line of sight and the center of the pupil approximates the pupillary axis.  This angle lambda is referred to clinically as angle kappa.  Angle kappa is nearly identical to angle lambda.  It is the angle formed between the pupillary axis and the visual axis.  The visual axis is defined as a line passing from the fovea through the nodal point of the eye.   If the pupil of the eye is displaced from the eye's optical axis then the visual axis and line of sight may be different.  When we look at a patient we can't see the nodal point, but we can see the center of their pupil. That's why we measure angle lambda.  There are two other angles that you need to know for National Board Exams.  One is angle alpha which is the angle formed by the intersection between the visual axis and optical axis.  The optical axis is defined as a line passing through the nodal point that is normal to the surface of the cornea.  Angle gamma is another one which is defined as the angle formed between the fixation axis and optical axis. The fixation axis is a line connecting the point of fixation to the center of rotation of the eye.

Table 4.1 Angles formed between various ocular axes


Visual axis

Line of sight

Fixation axis

Pupillary axis




Optical axis





Fig 4.3  Angle kappa for infant and adult.

A normal nasalward displacement of the corneal light reflex from the center of the pupil is called a positive angle kappa.  A temporalward displacement is negative.   The positive angle is the result of the temporalward projection of the pupillary axis into space relative to the visual axis.  This angle is normally about 10 prism diopters in an adult and 20 prism diopters in a newborn infant.  The reflex displacements are normally symmetrical in the two eyes, i.e. they are both nasalward (positive) when either eye fixates monocularly.

If you observe unequal angles in the two eyes this can mean that one eye is not fixating foveally.  This condition is called eccentric fixation and it accompanies a condition called amblyopia.  Amblyopia is a developmental anomaly that results in reduced visual acuity.  Acuity is reduced in part because the patient uses a nasal retinal point to fixate with rather than the fovea of the amblyopic eye.  This nasal eccentric fixation causes a temporalward displacement of the corneal light reflex and a negative angle Kappa.  The acuity of the amblyopic eye can be approximated from the amount of eccentric fixation.  The minimum angle of resolution in minutes of arc is approximately equal the eccentric fixation in prism diopters when it exceeds 1 prism diopter. 
A slight variation of the angle Kappa test is the Hirschberg test.  In this test you have the subject fixate the penlight binocularly rather than monocularly and observe the symmetry of the corneal light reflections. 

If there is strabismus or eye turn in which only one eye foveates the target and the other eye deviates nasalward or temporalward, you will see the corneal light reflex of the turned eye displaced from the pupil center.  If the eye deviates nasalward (esotropia) the reflex is displaced temporalward.  You can estimate the magnitude of the eye turn by taking the differences in each eye's angle Kappa.  If the eyes fixate binocularly and there is no deviation, then the angle Kappas should both be nasalward and equal.  If one eye turns in (resulting in a temporalward displacement of the corneal light reflex), its angle Kappa will be less positive or more negative than the angle Kappa in the other eye by the amount of the eye turn.  This is a very crude measure that only senses large eye turns that are greater than 10 prism diopters or 5 degrees (corresponding to 0.5 mm).  There are approximately 20 prism diopters per millimeter displacement.  The penlight can also increase your sensitivity to observing nystagmus.  You can also enhance your view by holding up a 5D lens or magnifier before the eye.


Fig 4.4 
Method of measurement of angle lambda.


Another way to detect and measure an eye turn is to conduct a cover test.  In this test the patient starts out fixating a target with both eyes open.  In the unilateral cover test, you cover one eye with a paddle, and if the remaining eye moves to pick up fixation, you assume that eye was turned away from the target during binocular fixation.   This test is used to detect the presence of a strabismus (an eye turn). 

Fig 4.5 Strabismus (right esotropia)

The magnitude of the eye turn can be estimated with the alternate cover test.  Here you alternately occlude one eye and then the other and watch the eyes move as they alternate fixation.  You can put prisms up before one eye until the movement stops.  The neutralizing prism quantifies the magnitude of the eye turn.  Most patients show some movement on the alternate cover test even if they do not have an eye turn.  This movement is caused by a difference between the resting position of the eyes and the direction of the binocular fixation stimulus.  Normally, convergence and divergence overcome this resting position and we do not have a strabismus.  This relaxed deviation of the eyes under monocular viewing conditions is called the phoria.  However, if the patient fails the unilateral cover test it is called a strabismus.

Projection Tests and Diplopia
There are also subjective techniques that utilize filters and distorting lenses for quantifying eye turns and phorias.  You can put a distorting filter like a Maddox rod over one eye and ask the patient to align the image of the distorted line with another image seen only by the other eye.  If the eyes are aligned, the targets appear superimposed.  If they are misaligned, there is a phoria or tropia.  The targets appear displaced in a direction opposite to the ocular deviation.  Thus eso deviations cause the target to appear temporalward, and exo deviations cause it to appear nasalward.  In effect, each eye has its own target and the patient moves the targets until they are both on the foveas.  When this is done, you assume that the directions that the visual axes point in space as measured by any separation of these images indicates either a phoria or a strabismus (also known as a tropia).

Fig 4.6 Maddox rod. Clinical use of Maddox rod. Patient is asked to align the distorted (line) image of the right eye with the undistorted image of the left eye

Entoptic Phenomenon
It is also possible to use entoptic phenomenon to measure eye position (See chapter 15 in Adler's Physiology of the Eye).  An entoptic phenomenon is a perception resulting from some structure within the eye. For example Maxwell's spot is the perception of a pinkish spot seen while viewing a uniform purple background at the point of fixation.  The spot  results from the filtering properties of the yellow macular pigment.  This pigment absorbs short "blue" wave lengths and passes long "red" wave lengths.  The surrounding retina gets both long and short wavelength that are perceived as purple.  Patients are asked to fixate a point in the purple field and indicate the location of the pink spot relative to the fixation point.  If it is displaced, eccentric non-foveal fixation is suggested. 

Another entoptic phenomenon is Haidinger's brushes.  When you view an illuminated field through a rotating Polaroid filter you will see a small rotating brush at the point of fixation.  The brush is produced by the arrangement of optic nerve fibers near the fovea in Henley's layer of the retina.  The orderly arrangement of fibers acts like a polarizer so that if light entering the eye is polarized it is mainly transmitted by fibers lying in the plane of polarization.  When the Polaroid filter rotates the transmitted orientation appears to rotate in space about the point the fovea is directed.  Eccentric fixation can be measured in the same way as done with the Maxwell spot.   You can buy these cobalt color filters and rotating Polaroid filters from Bernell corporation for use in clinical practice.

Objective eye measurement techniques
There are many clinical instruments that allow you to take objective records of eye position and store them on a computer disk for future record.  In the past these were used for reading analysis and visual training of binocular disorders, however, in the future it may serve the diagnosis of neurological disorders.

Clinical techniques
EOG (Electro Oculography):  EOG is based upon the dipole properties of the eye. The cornea has a positive 10 to 30 millivolt charge compared to the back of the sclera.  This is because the retina has a positive charge and the pigment epithelium acts an insulator and produces a negative charge on the other side of Bruch's membrane.  Silver chloride electrodes are placed on the nasal and temporal canthi and they are used to sense the proximity of the positive apex of the cornea.

Fig 4.7 (far left)  EOG (Electro Oculography) Silver chloride electrodes are used to sense the proximity of the corneal apex. Principal of EOG.  Charge on electrodes varies as proximity of cornea changes during secondary gaze.



EOG is probably the most widely used clinical objective eye movement recording device.  It is sensitive to one degree eye movement and it works on non-communicative patients like infants.  Its disadvantage is that it is also sensitive to muscle action potentials coming from the orbicularis oculus when the child cries and from the temporal lobe muscles when the child sucks from a pacifier or bottle.  You can get around these problems by recording as soon as the child wakes, and has been fed and changed.  You have about 20 more minutes before it becomes tired and cranky again.  You will need some kind of record or data storage apparatus like a strip chart or computer that digitizes the voltage analogs of eye movements.  Typically you will measure OKN and fixational eye movements in the infants under 4 months of age.

Infrared Reflection (limbal trackers):  This technique is much more sensitive than EOG.  It senses 1/4 of a degree of horizontal movement by sensing infrared light reflected from the limbal region of the eye.  Light reflected from the limbus moves with the eye because the center of curvature of the cornea is anterior to the center of rotation of the eye.  Thus as the eye rotates, the cornea is translated.  (If the center of the cornea was coincident with the center of rotation of the eye, the eye would be a perfect sphere and the reflection of an external light source would not move when the eye rotated.)  The reflected light is sensed by a light sensitive diode that varies its resistance as it receives light.  This variation in resistance shunts various amounts of voltage and it is possible to get a voltage analog of eye position.

Fig 4.8  (far left) Spectacle-mounted infrared limbal sensors.




Fig 4.9 Record of eye movements using a limbal sensor.

Infrared limbal tracker devices are used mostly in adults because the infrared sensors must be attached near the eyes with spectacle frames.  The "Ober 2-"device works similarly to this, but it is mounted in swim goggles and may be attached to a child's face.  The main disadvantage of this type is system is it can't measure vertical eye position well because the limbus is occluded by the eye lids. 


Fig 4.10  Principal of operation of a limbal tracking system, illustrating the illumination of the limbus and detection of the reflected infrared light.


Video based systems (pupil trackers):  These devices are analyzing the image of the corneal light reflex and pupil center.  They track the change in shape of the pupil and the displacement of the center of the pupil or position of the corneal light reflex.  They are more remote than the infrared systems and they also are equally good at measuring horizontal and vertical eye movements because they analyze the pupil center rather than the eye limbus.

Fig 4.11 Head-mounted video-based pupil tracker.

Video cameras can be mounted in a helmet and move with the head.  They can also combine the position of the eye with the scene viewed by the subject to indicate where in the scene someone is fixating.  This type of analysis is useful in analyzing information used in heading perception such as with pilots or drivers.  It is also useful in virtual reality machines that need to know where the user is directing his/her interest.

Laboratory eye measurement techniques

Search Coil:  It is also possible to get extremely precise measures of eye position of 1 arc min using a coil of copper wire mounted in a contact lens, much like an erg electrode.  A subject sits in a magnetic field and as the coil on the eye rotates with the eye a small voltage is generated in the coil, much like it was in your elementary physics class.  The voltage can be calibrated to indicate eye position.  Such a device is used to measure saccadic eye movements with a high degree of spatial and temporal resolution.  The disadvantage of this device is that the contact lens can only be worn for 20 minutes before corneal swelling occurs.  It fits tightly to prevent slippage when the eye rotates.  A related corneal contact lens device attaches a small mirror to the eye on a contact lens.  This technique has been used primarily to stabilize the retinal image.  An image is reflected off the mirror and back into the eye through an optical system that moves the image with the eye.  The stabilized image is unaffected by eye movements and researchers are able to measure visual perception without retinal image smear.

Fig 4.12 Search coil. (copper wire mounted in a contact lens)

SRI Eye tracker:  It is possible to get very good position accuracy without the contact lens with an infrared reflection sensor that measures the position of both the first and fourth Purkinje images.  The first image is influenced by both rotation and translation of the eye, and the fourth image is mainly influenced by translation.  The difference between the motion of the two is a good measure of pure eye rotation.  This device is excellent for long term non-invasive measures of small eye movements.  Its main disadvantage is that it has a whiplash artifact of ocular lens motion during saccades.  In addition, the tracker itself is very large, and the head must remain fixed inside the apparatus.  However, it is excellent for laboratory measurements of slow eye movements (like pursuits and vergence) and for steady eye position.

Review Questions:
1.  List two entoptic measures of eye position.
2.  Define angles Kappa, Lambda (classical definition).
3.  Which objective measure of eye position utilizes the dipole characteristic of the eye?
4.  Define the 4 Purkinje images, describe their relative size and orientation.
5.  Explain the difference between the unilateral and alternate cover tests.

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