Measuring the Eye and Its Lenses

Some instruments look; others measure. This chapter covers the ones that put numbers on the eye and its lenses: the pressure inside the eye, the thickness and endothelium of the cornea, the shape of its surface, the power of a pair of glasses, the refraction and the aberrations of the eye. Each number comes with its own sources of error, and knowing the optics behind the measurement is the way to recognise them.

#Applanation tonometry

The pressure inside a sphere with a thin, flexible wall can be measured by flattening part of it. By the Imbert–Fick law, the pressure is the force needed divided by the area flattened:

The cornea is neither thin nor perfectly flexible: it resists being bent, which adds to the force needed, while the tear film’s surface tension pulls the tonometer toward the cornea, which subtracts from it. Goldmann found that the two roughly cancel for flattened circles about 3 mm across, and chose 3.06 mm, at which each gram of force corresponds to 10 mmHg. Flattening displaces only about half a microlitre of aqueous, so the measurement barely raises the pressure it measures.

The tonometer tip carries a biprism. Under cobalt blue light, the tear meniscus stained with fluorescein outlines the flattened circle, and the biprism splits its image into two semicircles displaced by 3.06 mm. The examiner turns the force dial until the inner edges of the semicircles just touch; the reading in grams, times ten, is the pressure in mmHg. The ocular pulse makes the semicircles oscillate, and the reading is taken at the middle of their swing.

The reading is only as good as the cornea and the technique:

• Corneal thickness: a thick cornea resists flattening and reads high; a thin one reads low, as does the cornea after myopic LASIK or PRK. The effect is roughly 1 to 3 mmHg per 50 µm, but no correction formula is reliable. A swollen, oedematous cornea reads falsely low; a scarred, stiff one may read high. After LASIK, a steroid-induced pressure rise can drive fluid into the flap interface, and the central reading is then falsely low, even normal; it is measured peripherally as well.
• Corneal astigmatism distorts the flattened circle into an ellipse: with-the-rule astigmatism makes the reading low and against-the-rule high, by about 1 mmHg for every 4 D. Above about 3 D the error is worth correcting: the prism is rotated so that the axis of the minus cylinder lies at the red 43° mark on its holder, or two readings 90° apart are averaged.
• Fluorescein: too much makes the mires wide and the reading high; too little makes them thin and the reading low. Well-judged mires are about a tenth as wide as the flattened circle.
• The patient: squeezing the lids, pressing on the globe while holding the lids, a tight collar or breath-holding raise the reading.
• The instrument: its calibration should be checked regularly, and the tip disinfected or a disposable tip used.

Other tonometers trade accuracy for convenience, or work where Goldmann cannot:

• Tono-Pen: a small plunger set in a footplate (the Mackay–Marg principle) senses the force as the cornea flattens over a tiny area; several readings are averaged. It works on scarred, irregular or oedematous corneas and through a bandage contact lens.
• Non-contact (air-puff) tonometers time how long a jet of air takes to flatten the cornea, detected by the change in its reflection of light. No anaesthesia is needed, which suits screening.
• Rebound tonometers fire a light probe at the cornea and measure how quickly it decelerates. They need no anaesthesia, suit children, and are used for home monitoring.
• Dynamic contour tonometry (Pascal) uses a concave tip matched to the cornea’s shape, with a pressure sensor at its centre; it depends less on corneal thickness. The Ocular Response Analyzer records two applanations during an air puff, inward and outward; the difference in pressure between them is the corneal hysteresis, a measure of the cornea’s damping, and a low value is a risk factor for glaucoma progression.
• Schiøtz indentation tonometry measures how far a weighted plunger sinks into the cornea. The result depends on the rigidity of the eye’s walls, so it misleads in high myopia, for example.
• The Perkins tonometer is a hand-held Goldmann applanation tonometer, for patients lying down or under anaesthesia; the pneumatonometer senses the pressure through a small probe floating on a cushion of air.

#The cornea’s thickness and endothelium

Pachymetry measures corneal thickness, by ultrasound (timing the echo, with a sound velocity of about 1640 m/s in the cornea) or optically, by OCT, Scheimpflug imaging or the specular microscope. The normal central cornea is about 540 to 550 µm thick. Thickness matters for interpreting the pressure, for deciding whether refractive surgery is safe (Chapter 17), and as a measure of endothelial function: a thin central cornea is an independent risk factor for glaucoma in ocular hypertension (in the Ocular Hypertension Treatment Study, a cornea of 555 µm or less carried about three times the risk of one over 588 µm), and a thickening cornea signals failing endothelium.

The specular microscope photographs the endothelium by specular reflection from its boundary with the aqueous, through a narrow slit at high magnification, the same principle as specular reflection at the slit lamp (Chapter 21). Software counts the cells and measures their sizes and shapes:

• Cell density: typically 2000 to 3000 cells/mm² in adults, falling slowly with age, by about 0.5% a year. Endothelial cells do not divide; when cells are lost, their neighbours spread to fill the gap. Below about 1000 cells/mm² the risk of decompensation after intraocular surgery rises steeply, and below about 500 the cornea swells.
• Polymegethism: variation in cell size, measured as the coefficient of variation of cell area (normally under about 0.3).
• Pleomorphism: variation in cell shape, measured as the percentage of hexagonal cells (normally about two-thirds).

Both rise with age and with stress on the endothelium: contact lens wear, diabetes, surgery and Fuchs dystrophy. Guttae reflect no light and appear as dark spots among the cells.

Confocal microscopy lights a tiny spot or slit and views it through a matching aperture focused at the same depth, rejecting light from other depths. It gives optical sections of every layer of the living cornea: epithelium, nerves, keratocytes and endothelium, and organisms such as Acanthamoeba cysts and fungal hyphae.

#Keratometry and topography

The keratometer (Chapter 8) measures the radius of the central cornea from the size of the image it reflects, at points about 3 mm apart, and converts it to power with a standard index (337.5 / r, with r in mm). It assumes a regular spherocylindrical surface: it cannot measure the periphery or quantify irregular astigmatism, though distorted, irregular mires reveal it. Its range, about 36 to 52 D, is extended upward by about 9 D with a +1.25 D lens over the aperture, and downward by about 6 D with a −1.00 D lens.

Placido-disc topography extends the idea to the whole cornea. The patient looks into a cone of illuminated concentric rings; the cornea, acting as a convex mirror, reflects them, and a camera records the image. Where the cornea is steeper the rings are reflected smaller and crowd together; where it is flatter they spread apart. The computer reconstructs the slope and curvature at thousands of points and displays them as colour-coded maps:

• Axial (sagittal) curvature: curvature measured relative to the instrument’s axis. It smooths the map and is good for the overall pattern and power, but it blurs a localised steep area such as a cone, understating its peak and misplacing it.
• Tangential (instantaneous) curvature: the local curvature at each point. It shows the true size, shape and position of a cone or the edge of an ablation zone.
• Elevation: the height of the surface above or below a reference, usually a best-fit sphere. Elevation maps of the back surface come from Scheimpflug or OCT imaging, not from Placido reflection.

Maps use either an absolute colour scale, fixed so that maps can be compared from visit to visit, or a normalised scale, fitted to each cornea’s range, which makes small variations look dramatic. Contact lenses warp the cornea, sometimes mimicking keratoconus, so soft lenses are left out for a week or two, and rigid lenses for several weeks, before topography for surgery.

Patterns worth knowing: a round or oval map in a normal cornea; a symmetric bow-tie in regular astigmatism; inferior steepening and an asymmetric bow-tie in keratoconus, suspected by Rabinowitz’s criteria when the central power exceeds about 47.2 D or the inferior–superior (I–S) difference 3 mm from the centre exceeds 1.4 D; the crab claw of pellucid marginal degeneration; central flattening after myopic and central steepening after hyperopic refractive surgery.

Scheimpflug imaging photographs a slit of light across the anterior segment with a camera whose image plane is tilted relative to its lens, so that the whole oblique slice, from the cornea to the lens, is in focus at once (the Scheimpflug principle). Rotating the camera builds a three-dimensional model: front and back corneal elevation, a thickness map, the depth and angle of the anterior chamber, and the density of the lens. Changes in back-surface elevation and a displaced thinnest point reveal keratoconus before the front surface shows it. Anterior segment OCT also maps the epithelium, which thins over a cone and thickens around it, masking the shape of the stroma beneath.

#The lensmeter

The lensmeter (focimeter) measures the back vertex power of a spectacle lens, the power a prescription specifies (Chapter 5). An illuminated target is moved behind a fixed standard lens, and the spectacle lens sits against a stop at the standard lens’s focal point. This is the Badal arrangement (Chapter 10): it makes the target’s movement proportional to the lens’s power, so the scale is linear. A telescope focused at infinity views the target, which is sharp when the light leaving the spectacle lens is parallel.

• Focus the eyepiece first, turning it from the plus end until the reticle just becomes sharp, so that the observer’s own accommodation does not add minus to the reading.
• Sphere and cylinder: an astigmatic lens has two principal powers. At one drum setting the target is drawn out into sharp lines along one meridian, at the other along the perpendicular one; the lines point along the meridian still out of focus, so the meridian in focus is the one at right angles to them. In minus-cylinder form the sphere is the more plus of the two powers, the cylinder is the difference, and the axis is the meridian of the sphere power.
• Prism: with the point being checked (the patient’s pupil position, marked from the pupillary distance) on the stop, the target is displaced from the centre of the reticle, toward the base of the prism, by the number of rings (each 1 Δ). The optical centre of each lens is marked by moving the lens until the target is centred. Prism beyond the rings, about 5 Δ, is measured with an auxiliary prism added to the instrument.
• Adds: the segment of a bifocal is on the front surface, so the add is measured as the difference between the front vertex powers of the near and distance portions, with the front surface of the lens against the stop. For strong plus lenses the back vertex difference overestimates the add.
• Progressive lenses carry faint engraved circles 34 mm apart that mark the horizontal; the add is engraved below the temporal one. The distance power is read in the distance circle above the fitting cross, the near power in the near circle, and prism at the prism reference point midway between the engravings.
• Contact lenses are dried and held concave side against the stop, to read their back vertex power.

Automated lensmeters measure how a lens deflects several beams of light and calculate sphere, cylinder, axis and prism; most have a progressive mode that guides the user to the distance and near zones, while maps of power across the whole lens come from dedicated lens mappers.

#Automated refraction

Autorefractors shine infrared light into the eye, invisible so that the pupil stays large and the patient is not dazzled, and analyse the light returning from the fundus to find where it focuses, meridian by meridian. They work on several principles:

• The Scheiner principle: light entering through two separate small zones of the pupil meets at a single point on the retina only when the eye is focused; otherwise it forms two spots, whose separation measures the error.
• Retinoscopy and knife-edge principles: the movement of a reflex across the pupil, as in retinoscopy (Chapter 12).
• Wavefront sensing, as in the aberrometer below.

Infrared light is reflected from layers behind the photoreceptors, which makes the eye look slightly more myopic, while the eye’s chromatic aberration focuses infrared farther back, which makes it look more hyperopic; the instruments are calibrated against subjective refraction to report the refraction for visible light. Their main error is instrument myopia: knowing the target is close, the patient accommodates, especially if young, and the reading has too much minus. The target is a picture with distance cues, such as a road leading to the horizon, and the instrument fogs it, moving it optically beyond the far point so that accommodation relaxes. This helps, but cycloplegia is needed for an accurate refraction in children. Autorefraction is a starting point for a subjective refraction, not a prescription.

#Wavefront aberrometry

An aberrometer measures all the eye’s aberrations, not just its sphere and cylinder. In the commonest design, the Hartmann–Shack sensor, a narrow beam forms a small spot of light on the retina, which acts as a source. The light returning out through the pupil falls on an array of tiny lenslets, each focusing its part of the wavefront to a spot on a camera. A perfect eye sends out a flat wavefront and the spots form a regular grid; where the wavefront is tilted, the spot shifts, by an amount proportional to the local slope.

The slopes are combined into a map of the wavefront, expressed as Zernike terms (Chapter 17): defocus and astigmatism, the lower-order aberrations a spectacle can correct, and the higher-order aberrations such as coma, trefoil and spherical aberration, summarised by their root-mean-square value. Other aberrometers project a grid onto the retina and analyse its distortion (Tscherning), or trace single rays through the pupil one at a time. Aberrometry guides wavefront-guided ablation and explains poor vision with apparently good acuity, while the cornea’s own aberrations, calculated from topography or tomography, guide the choice of IOL asphericity. Values are always given for a stated pupil: at 6 mm, a normal eye has about 0.3 µm of higher-order aberration, and the average cornea about +0.27 µm of spherical aberration, which some aspheric IOLs are designed to offset. The measurement depends on pupil size, the tear film and accommodation, and very irregular corneas can scatter the spots beyond recognition.

#Recap

• Imbert–Fick: P = F/A. Goldmann flattens 3.06 mm, where rigidity and tear attraction cancel: 1 g = 10 mmHg. Endpoint: the inner edges of the semicircles touch.
• Reads high: thick or scarred cornea, against-the-rule astigmatism, too much fluorescein, squeezing. Reads low: thin cornea or after LASIK, oedema, with-the-rule astigmatism, too little fluorescein. Rotate the prism above 3 D of astigmatism.
• Specular microscopy: density 2000–3000 cells/mm² in adults, risky below 1000, decompensation below about 500. Polymegethism = size, pleomorphism = shape.
• Topography: steep cornea, crowded rings. Axial maps smooth, tangential maps localise, elevation (Scheimpflug, OCT) includes the back surface. Bow-tie = regular astigmatism; inferior steepening = keratoconus; crab claw = pellucid marginal degeneration.
• Lensmeter: back vertex power, by the Badal principle. Lines point along the meridian out of focus. Prism: target displaced toward the base. Add: difference of front vertex powers.
• Autorefractors: infrared, Scheiner or retinoscopic principles; instrument myopia over-minuses the young.
• Hartmann–Shack: spots move inward for a myopic (converging) wavefront, outward for a hyperopic one; displacement = local slope.

#Test yourself

#Further reading

• American Academy of Ophthalmology, Basic and Clinical Science Course, Section 3: Clinical Optics and Vision Rehabilitation, chapter on optical instruments; Section 8: External Disease and Cornea and Section 10: Glaucoma.
• D. Henson, Optometric Instrumentation, 2nd ed. Butterworth-Heinemann (1996).
• R. A. Applegate, L. N. Thibos and G. Hilmantel, Optics of aberroscopy and super vision. Journal of Cataract and Refractive Surgery 27 (2001) 1093–1107.