Think of the eye as having two important directions that may need different amounts of lens power. Your job is to find those two numbers.
Sphere = the shared starting power. Cylinder = the extra difference one direction needs.
Just the unit for lens power. Think “how strong is this lens?”
Just a direction through the eye, like a spoke through the centre of a wheel.
The eye's two main directions in regular astigmatism. They are 90° apart.
The shared baseline. It changes every direction by the same amount.
The extra top-up. It supplies the difference between the two main directions.
The cylinder's do-nothing line: plus cylinder adds 0 D along the axis and its full power 90° away.
The thin line of light you project from the retinoscope.
The direction you test is 90° from the visible streak. A vertical 90° streak sweeps horizontally and tests the 180° meridian.
The broader glow coming back through the pupil. This is the light you judge.
The reflex moves the same way as your sweep. That direction still needs more plus.
The reflex moves the opposite way. That direction has too much plus.
The reflex barely moves relative to your sweep, after the streak and reflex are lined up.
Your gross reading includes extra plus because you are standing close to the eye. Subtract that amount from sphere only at the end.
The power you measure during retinoscopy before subtracting working distance.
The prescription left after working-distance power is removed from sphere.
Each row answers one question: “In this direction, what lens power made the reflex neutral?” We call this the gross reading because working distance has not been subtracted yet. Two perpendicular readings are enough to build the final plus-cylinder prescription.
You only need four decisions. Use the tested meridian, not the visible streak angle.
Worked Example (fixed numbers; your own readings are worked through at the bottom)
Lower number = +3.00 D. That is the gross sphere baseline.
+4.00 − +3.00 = +1.00 D cylinder.
The lower reading was in the 45° meridian, so the plus-cylinder axis is 45°.
At 67 cm, subtract +1.50 D: +3.00 − 1.50 = +1.50 D sphere. Cylinder and axis do not change.
The compact single-screen interaction model and staged teaching workflow were inspired by the American Academy of Ophthalmology Retinoscopy Simulator.
OpenOphthoSim is an independently written open-source implementation. It does not copy AAO source code or artwork. Independent implementation; not affiliated with or endorsed by the AAO.
Retinoscopy clinical sequence references also include University of Iowa EyeRounds and Moran CORE plus-cylinder retinoscopy teaching resources.
The Strabismus module interaction model and teaching flow were inspired by the AAO Strabismus Simulator and Complex Strabismus Simulator. The complex simulator credits Faruk H. Örge, MD and K. David Epley, MD. OpenOphthoSim is independently written and does not copy AAO source code or artwork. Clinical references include AAO EyeWiki, Moran CORE, and AAPOS.
Clinical scope: retinoscopy models static plane-mirror streak retinoscopy for regular spherocylindrical refractive error. The Strabismus module includes a teaching model of comitant and selected incomitant deviations, nine diagnostic gaze positions, A/V patterns, Brown Syndrome, sixth-nerve palsy, DVD/DHD, and customizable gaze-position values. It is an educational model, not a diagnostic device.
Strabismus means the two eyes are not pointed at the same thing. The exam that looks for it is the ocular motility (or sensorimotor) exam, and it asks three questions in order: Is an eye turned right now? How big is the turn? Does it change with gaze?
No term matches that search.
Normally both eyes point at the same thing. In strabismus one eye points somewhere else. It matters because a child's brain may switch off the turned eye (amblyopia, loss of depth perception), and an adult with a new turn sees double.
OD = the patient's right eye. OS = the patient's left eye. OU = both. You face the patient, so their right eye is on your left. The simulator labels each eye in the corners.
Is an eye turned right now? → cover–uncover test.
How big is it? → alternate cover, then prisms (PACT, SPCT).
Does it change with gaze or distance? → repeat in other directions and at near.
A tropia is a turn you can catch with both eyes open. A phoria is a hidden drift: the brain keeps the eyes straight, and it only shows when one eye is covered. Many patients have both.
Turns are measured with prisms, in prism diopters (Δ). Under 10Δ is small and easy to miss; 20Δ or more is obvious. You cannot read an exact number by eye: you estimate small, moderate or large, then measure with prisms. That is why the simulator describes movements in words, with the measured size alongside.
Learn guides you step by step, explains every movement in What You Just Saw, and ends with a quiz. Explore lets you change the patient freely and watch what happens. Test gives you unknown patients to examine and diagnose. Underlined words link to their definition here.
Each eye has four straight muscles (recti) and two slanted ones (obliques). Every muscle has a main job, and some have smaller extra jobs.
| Muscle | Main Job | Extra Jobs | Nerve |
|---|---|---|---|
| Medial Rectus (MR) | Turns the eye in (adduction) | None | CN III |
| Lateral Rectus (LR) | Turns the eye out (abduction) | None | CN VI |
| Superior Rectus (SR) | Lifts the eye (elevation) | Rolls it in (intorsion); turns it in | CN III |
| Inferior Rectus (IR) | Lowers the eye (depression) | Rolls it out (extorsion); turns it in | CN III |
| Superior Oblique (SO) | Rolls the eye in (intorsion) | Lowers it; turns it out | CN IV |
| Inferior Oblique (IO) | Rolls the eye out (extorsion) | Lifts it; turns it out | CN III |
Memory aids: LR6 SO4, the rest 3 (lateral rectus = CN VI, superior oblique = CN IV, all others = CN III). RAD SIN: the Recti (vertical ones) ADduct; the Superior muscles INtort.
The obliques lift or lower the eye best when it is turned in toward the nose; the vertical recti work best when it is turned out. So each corner of gaze tests one muscle of each eye (see Diagnostic Positions in Grading & Notation). This is why Brown syndrome shows up looking up and in, and a CN IV palsy looking down and in.
CN VI: the eye cannot turn out; esotropia. CN IV: the eye rides high, worse looking down and in; head tilt away. CN III: the eye sits down and out, with a droopy lid and sometimes a big pupil, because CN III also runs the lid and pupil.
The eyes are not both aimed at the same target. It is the umbrella word; tropias and phorias are the two kinds.
Orthotropia: both eyes straight with both open (no tropia). Orthophoria: still straight even when fusion is broken by alternate cover (no phoria either). True orthophoria is uncommon; a small phoria is normal.
A manifest turn: one eye is off target even with both eyes open. Found with the cover–uncover test.
A latent turn. Fusion holds the eyes straight while both can see; the eye drifts only when covered. Seen as a recovery movement when the cover comes off, and measured with alternate cover.
All three are the same kind of misalignment; what differs is whether fusion holds it straight.
| Both Eyes Open | Cover–Uncover | Write | |
|---|---|---|---|
| Phoria | Always straight | No refixation; covered eye drifts and swings back | X |
| Intermittent Tropia | Straight some of the time, turns when tired, ill or daydreaming | Sometimes a phoria response, sometimes a tropia | X(T) |
| Tropia | Always turned | The other eye refixates every time | XT |
Intermittent exotropia is the classic example: parents notice one eye drifting out in bright sun or when tired. Clinicians also grade control: how easily it breaks down and how quickly it recovers after a blink (see the X(T) lesson). An intermittent esotropia, E(T), also exists, for example a partly controlled accommodative esotropia or a decompensating esophoria, but X(T) is far more common, so it is the one taught here.
Eso = turned in toward the nose. Exo = turned out toward the ear. Add “-tropia” or “-phoria”: esotropia, exophoria.
Hyper = turned up. Hypo = turned down. By convention a vertical turn is named after the higher eye: a right hypertropia (RHT) is the same alignment as a left hypotropia.
The fixing eye is looking at the target. The deviating eye is the one that is turned. Cover the fixing eye and the deviating eye must move to take up fixation.
The brain's drive to merge the two eyes' images into one. It keeps a phoria hidden. Any cover breaks fusion; alternate cover keeps it broken.
The unit for the size of a turn: 1Δ bends light 1 cm at 1 m. About 1.75Δ ≈ 1°. On the cornea, 1 mm of light-reflex shift ≈ 15Δ.
The turn is about the same size (within roughly 5Δ) in every gaze direction and whichever eye fixes. Typical of childhood esotropia and exotropia.
The size of the turn changes with gaze direction, or with which eye is fixing. It points to a weak muscle (e.g. CN VI palsy), a mechanical restriction (e.g. Brown syndrome) or a pattern (A / V). Always measure the nine gaze positions when you find one.
In a nerve palsy, the turn measured with the normal eye fixing is the primary deviation. With the affected eye fixing it is the secondary deviation, and it is larger, because the weak muscle needs extra drive and its yoke muscle gets the same extra drive (Hering's law).
Paired “yoke” muscles of the two eyes receive equal nerve drive. It explains secondary deviation, and why DVD is unusual: DVD breaks this law.
Within one eye, when a muscle contracts its opposing muscle relaxes by the same amount (reciprocal innervation). Looking right, the right lateral rectus contracts and the right medial rectus relaxes. Hering's law is about the two eyes working as a pair; Sherrington's is about the pair of opposing muscles inside each eye.
Duction: one eye moving on its own (the other covered). Version: both eyes moving together. Ab-duction = out, ad-duction = in, elevation = up, depression = down.
In a normal eye the light reflex sits slightly nasal to the pupil centre (about 0.5 mm), because the line of sight does not pass exactly through the pupil centre. Compare the two eyes with each other, not with the exact pupil centre.
The movement an eye makes to pick up the target. Its direction is opposite to the turn: an eye that moves out to fixate was turned in (eso).
The angle between where the turned eye points and where it should point (the target). It is measured in prism diopters (Δ): the prism power that would bend the light by exactly that much, so the eye no longer has to move.
| Size | What It Looks Like |
|---|---|
| Under 10Δ | Small; usually not visible, found only on cover testing |
| 10–20Δ | Moderate; often visible to a careful observer |
| 20–40Δ | Obvious turn |
| Over 40Δ | Large; light reflex near mid-iris or beyond |
These bands are rough teaching guides, not diagnostic cut-offs.
A patient can have both at once. The tropia is the part you see with both eyes open. The phoria is the extra drift fusion normally hides. Break fusion completely (alternate cover) and the eye shows the total.
| Example | Tropia | Phoria | Total |
|---|---|---|---|
| Pure Phoria | 0 | 10Δ | 10Δ |
| Pure Tropia | 20Δ | 0 | 20Δ |
| Both | 20Δ | 10Δ | 30Δ |
| Test | Gives You | Why You Want It |
|---|---|---|
| Light Reflex | A rough estimate (1 mm ≈ 15Δ) | Quick screen; works when cover testing cannot |
| Cover–Uncover | Yes / no, which eye, which way | Separates a tropia from a phoria |
| Alternate Cover | Direction of the total, no number | Shows everything fusion hides |
| PACT | The total, in Δ | The size used to plan most surgery |
| SPCT | The tropia, in Δ | How much is constantly manifest; PACT − SPCT = phoria |
An entry is built from up to five parts, always in this order:
| Part | Choices | Rule |
|---|---|---|
| Size | A number of prism diopters | Typed as 30Δ, 30 PD or just 30 (see Typing It, below) |
| Eye | R or L | Only for a tropia with a clear turned eye. Leave it out for a phoria (neither eye is turned with both open) and when fixation alternates (either eye can be the turned one). |
| Direction | E (in) · X (out) · H (up) · Ho (down) | E and X always describe the pair. For vertical, see below. |
| Type | T · (T) · nothing | T = tropia. (T) = intermittent tropia. No T = phoria. |
| Near | ′ (prime) | Measured at near (33 cm). No prime = distance (6 m). |
Vertical turns (hyper vs hypo). One eye higher always means the other is lower: a right hypertropia and a left hypotropia describe the same alignment. By convention you name the higher eye: RHT or LHT. Write it as a hypotropia (RHoT, LHoT) when the lower eye is the one at fault, for example an eye that cannot elevate. Phorias drop the T: RH, LH.
| You Found | Write |
|---|---|
| Exophoria of 10Δ | 10Δ X |
| Right eye turned out 20Δ, constantly | 20Δ RXT |
| Esotropia 30Δ, either eye fixes | 30Δ ET (alternating) |
| Left eye turned out some of the time | 25Δ X(T) |
| Right eye 6Δ higher, constantly | 6Δ RHT |
| Left eye 8Δ lower and cannot look up | 8Δ LHoT |
| Left hyperphoria of 4Δ | 4Δ LH |
| Left eye in 20Δ and higher 5Δ | 20Δ LET + 5Δ LHT |
| Esotropia 25Δ at near only | 25Δ ET′ |
| No deviation on any test | Ortho |
Tropia and phoria together. Label the test: SPCT 20Δ LET · PACT 30Δ ET means the tropia is 20Δ (left eye) and the total is 30Δ, so 10Δ of it is phoria.
Typing it. Most keyboards have no Δ key. Write PD (prism diopters) or leave the unit out: 20 PD LET or 20 LET. Some clinics put the letters first (LET 20); both are understood. This simulator's practice accepts all of these.
SPCT 20Δ LET · PACT 30Δ ET says: with both eyes open the left eye turns in 20Δ (the tropia); with fusion fully broken the eyes deviate 30Δ in total, so a 10Δ esophoria sits on top.
In clinic you also record where (distance 6 m, near 33 cm; near gets a prime, ET′) and how (cc = with glasses, sc = without), e.g. Dist cc: 20Δ ET · Near cc: 25Δ ET′. This simulator models one distance.
Why it matters: a phoria is usually harmless unless it breaks down (eye strain, intermittent double vision). A tropia means the eyes are not working together: in children it risks amblyopia and lost depth perception; in adults it often causes double vision. The numbers guide glasses, prisms and surgery.
When you uncover the fixing eye, a patient with a strong preference immediately switches back to their favourite eye, and the other eye turns again. That hints the non-preferred eye may see less well (amblyopia). An alternator keeps fixing with whichever eye was last uncovered, which suggests similar vision in both eyes. Chart it as “alternating” rather than naming one eye.
Is there a tropia? Cover one eye and watch the other. If it moves to pick up the target, it was turned: moves out = was eso, moves in = was exo, moves down = was hyper. No movement: that eye was straight; now test the other eye. As the cover comes off, watch the uncovered eye: a recovery movement back to straight means a phoria.
How big is everything? Move the cover straight from eye to eye, pausing a second or two on each, so the eyes never see together. Fusion stays broken, so the movement shows tropia + phoria: the total deviation. It cannot tell a tropia from a phoria on its own.
Alternate the cover with a prism in front of one eye, increasing it until the eyes stop moving. That prism is the total deviation. If the movement reverses direction you have gone past it; step back down.
Place the prism over the deviating eye and cover the fixing eye at the same moment, then uncover to let fusion return before each try. The phoria has no time to appear, so it measures the tropia only. SPCT ≤ PACT; the difference is the phoria.
Shine a penlight from where the patient is looking and compare the reflection on each cornea. In a turned eye the reflex shifts opposite to the turn: temporal = eso, nasal = exo, below centre = hyper, above = hypo. Each 1 mm ≈ 15Δ (see Grading & Notation). Quick, but only an estimate.
A light-reflex test with prisms: add prism over the deviating eye until its reflex matches the fixing eye. Used when the cover test is not possible (poor vision in one eye, poor cooperation). Not simulated here.
A red ridged lens over one eye turns a spotlight into a red line, so the two eyes cannot fuse. The patient reports where the line sits relative to the light: line on the same side as the rod eye (uncrossed) = eso; opposite side (crossed) = exo. Turned 90°, it measures vertical deviations. It shows the total deviation; prisms that bring the line onto the light measure it.
A red and a white rod, one before each eye, both set to give horizontal lines. If an eye is torted, its line looks tilted; the patient rotates the rod until the lines are parallel, and the angle is the torsion. Excyclotorsion over about 10° suggests a bilateral CN IV palsy.
Red goggle over the right eye, green over the left, looking at 1 red, 2 green and 1 white light. 4 lights: fusion. 2 red: left eye suppressed. 3 green: right eye suppressed. 5 lights: double vision (red on the right = uncrossed = eso; on the left = crossed = exo). Children usually suppress; adults with a new turn see double.
How fine a depth difference the patient can see, in seconds of arc (″). About 40–60″ is normal and needs both eyes aligned and working together. A small-angle tropia with peripheral fusion (monofixation) gives reduced stereo (a few hundred ″); a larger tropia or suppression gives none.
For a vertical deviation: (1) which eye is higher, (2) is it worse looking right or left, (3) is it worse with the head tilted right or left. Each step halves the list of eight vertical muscles. Worse on the opposite gaze and same-side tilt = superior oblique palsy of the higher eye.
Under anaesthetic drops, the eye is moved with forceps. If it moves freely, the limit is from a weak muscle (palsy). If it resists, something is holding it: a restriction (Brown syndrome, thyroid eye disease, a trapped muscle after a fracture).
Point the prism base opposite to the turn (the apex points the way the eye is turned): eso → Base Out (BO), exo → Base In (BI), hyper → Base Down (BD), hypo → Base Up (BU).
Horizontal + vertical together: hold one horizontal and one vertical prism at once (stacked), then adjust each until nothing moves. Never stack two prisms in the same direction: their powers do not simply add.
Straight ahead (primary) plus eight directions: up, down, right, left and the four corners. Measuring the turn in each shows whether it is comitant, and which muscle is responsible when it is not (see Grading & Notation for the muscles).
Maps and the gaze pad here are drawn as you face the patient: the patient's right is on your left. That is why “Up-Right” sits in the top-left box.
In clinic every measurement is taken at distance (6 m) and near (33 cm), because some turns differ (e.g. CN VI palsy is often worse at distance). This simulator models a single distance.
1) Light reflex. 2) Cover–uncover each eye. 3) Alternate cover. 4) Measure with prisms (PACT, and SPCT if a tropia + phoria). 5) Repeat in other gaze positions. 6) Check ductions and versions.
An eye turned in or out by roughly the same amount in every direction. Cover–uncover finds which eye; PACT measures the size.
The horizontal turn changes between up and down gaze (measured about 25° up and 25° down). V pattern: more exo (or less eso) looking up; counts at ≥ 15Δ difference. A pattern: more exo (or less eso) looking down; counts at ≥ 10Δ. V often goes with inferior oblique overaction, A with superior oblique overaction.
A tight superior oblique tendon mechanically tethers the eye, so it cannot elevate when turned in (up and in). Elevation straight up is mildly limited and up-and-out is nearly normal. Severe cases sit slightly low in primary gaze and may use a chin-up posture. Forced ductions are positive (the eye is stuck, not weak). Differs from inferior oblique palsy, where forced ductions are free and an A pattern is common.
The lateral rectus is weak, so the eye cannot turn out (limited abduction). The esotropia is largest looking toward the affected side and smallest looking away. Patients often turn their face toward the affected side to stay single. The deviation is larger when the affected eye fixes (secondary deviation). Bilateral palsy (both eyes, e.g. after head injury or raised intracranial pressure) gives a larger esotropia that grows looking to either side, with each eye limited toward its own side.
Whenever an eye is covered it slowly floats up (often with a little outward roll), then comes back down when uncovered. Unlike a true hypertropia, the other eye does not move down when the drifting eye refixates: it breaks Hering's law. Often in both eyes, unequally, and common after infantile esotropia. Measured one eye at a time: base-down prism over the drifting eye, cover and uncover that eye, and increase the prism until it no longer comes down.
The horizontal cousin of DVD: the covered eye drifts sideways (usually outward) without the matching movement of the fellow eye that a true tropia would produce.
Eyes that look turned but are straight, usually because wide epicanthal folds hide the nasal white of the eye. The light reflexes are symmetric and the cover test shows no movement. Not simulated here, but a common real-world question.
Focusing up close also pulls the eyes in (accommodative convergence), so deviations are measured at 6 m and 33 cm. Convergence insufficiency: fine at distance, exo at near; tired eyes and blur when reading. Convergence excess: eso much bigger at near (high AC/A ratio); often helped by bifocals. Accommodative esotropia: a child's eso driven by focusing through uncorrected long-sightedness; glasses straighten it (fully or partly). Chart cc (with glasses) and sc (without), and mark near with a prime: E 4Δ · ET′ 20Δ cc.
The superior oblique depresses the eye in adduction and intorts it. When weak, the eye rides high: a hypertropia that is worse looking to the opposite side (especially down and in) and with the head tilted toward the affected side. There is excyclotorsion, and patients often tilt their head away from the affected side. The commonest acquired cause is head injury; congenital cases are common too. Found with the Parks three-step test.
The eye is down and out, with ptosis and limited adduction, elevation and depression; the pupil may be dilated. A new pupil-involving palsy is an emergency until an aneurysm is excluded. Pupil-sparing palsies are more often microvascular (diabetes, hypertension) but still need urgent assessment.
A congenital miswiring: the lateral rectus is supplied by a branch of the third nerve. Type 1 (most common): limited abduction, but only a small esotropia straight ahead; the globe retracts and the lids narrow on adduction. Diplopia is rare; a face turn toward the affected side keeps the eyes straight. Types 2 and 3 limit adduction, or both.
Thyroid eye disease: swollen, scarred muscles, most often a tight inferior rectus, so the eye sits low and cannot elevate (a restriction, not a weakness). Often lid retraction and proptosis. Orbital floor (blowout) fracture: after trauma the inferior rectus is trapped, limiting up and down gaze, often with numbness of the cheek. Both show positive forced ductions.
How far an eye can move in a direction compared with normal. Used for ductions and versions, and shown in the Motility map.
| Grade | Meaning | How Far the Eye Still Moves |
|---|---|---|
| 0 | Full, Normal Movement | All the way (100%) |
| −1 | Mild Limitation | About 75% |
| −2 | Moderate Limitation | About 50% |
| −3 | Marked Limitation | About 25% |
| −4 | Cannot Move Past the Midline | Not past straight ahead (0%) |
Overaction is graded the same way with plus signs (+1 to +4). This simulator models limitations only.
Where the reflex sits in the turned eye, measured from where it sits in the straight eye.
| Reflex Position | Shift | About |
|---|---|---|
| Shifted 1 mm | 1 mm | 15Δ (7°) |
| Pupil Margin | ~2 mm | 30Δ (15°) |
| Mid-Iris | ~4 mm | 60Δ (30°) |
| Limbus | ~6 mm | 90Δ (45°) |
Temporal shift = eso · nasal shift = exo · below = hyper · above = hypo.
In each position one muscle of each eye does most of the work. A limit or a bigger turn there points to that muscle.
| Patient Looks | Right Eye (OD) | Left Eye (OS) |
|---|---|---|
| Right | Lateral Rectus | Medial Rectus |
| Left | Medial Rectus | Lateral Rectus |
| Up-Right | Superior Rectus | Inferior Oblique |
| Up-Left | Inferior Oblique | Superior Rectus |
| Down-Right | Inferior Rectus | Superior Oblique |
| Down-Left | Superior Oblique | Inferior Rectus |
| Write | Means |
|---|---|
| ET · XT | Esotropia · Exotropia |
| E · X | Esophoria · Exophoria |
| E(T) · X(T) | Intermittent Esotropia · Exotropia |
| RHT · LHT | Right · Left Hypertropia |
| LET · RXT | Left Esotropia · Right Exotropia (Names the Deviating Eye) |
| ET′ (with prime) | Measured at Near |
| OD · OS · OU | Right Eye · Left Eye · Both Eyes |
| BO · BI · BU · BD | Base Out · In · Up · Down |
Example: a 20Δ left esotropia plus a 10Δ esophoria is written SPCT 20Δ LET · PACT 30Δ ET.
| V Pattern | ≥ 15Δ more exo in up gaze than down gaze |
| A Pattern | ≥ 10Δ more exo in down gaze than up gaze |
| Comitant | Varies by less than about 5Δ across gazes |
| Normal Kappa | Reflex ~0.5 mm nasal to pupil centre |
| 1° | ≈ 1.75Δ |