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The cornea supplies much of the eye's converging optical power; the crystalline lens supplies additional, adjustable power through ocular accommodation. The transparent aqueous and vitreous media transmit the light. The iris controls the pupil, acting as an aperture rather than as the focusing element, and the retina is the receiving surface. The posterior optic nerve conveys the resulting neural signals; it does not carry an optical picture out of the eye.

Each sufficiently small object patch sends a pencil of rays through the pupil. Refraction at the corneal and lenticular surfaces brings that pencil towards a retinal image point. Pencils from different object heights meet at different retinal positions, producing a real inverted image. In a paraxial equivalent model,The several physical refracting surfaces have been replaced here by an equivalent thin lens; this is a model, not a claim that all bending occurs at the crystalline lens. For a distant object, approximately parallel incoming pencils focus near the back focal surface. Ocular accommodation increases power for nearer objects while the retinal position remains nearly fixed.

In regular ocular astigmatism, the two principal meridians are perpendicular but have different refractive powers, commonly because the cornea has different curvatures in those meridians. A point object then gives two line foci at different depths rather than a single sharp point. The difference is not merely an overall spherical focusing error. Refraction with differently oriented cylindrical trial lenses can locate the power and axis; keratometry or corneal topography measures corneal shape. Cylindrical lens or toric lens correction supplies the missing meridional power with the proper orientation. Spectacles and appropriately fitted toric contact lenses can provide such correction. A method for measuring corneal curvature should not be confused with a complete measurement of the eye's total refractive error.^[ref][ref]

Expose the orbit (anatomy) in layers, preserving the eye, extraocular muscles, nerves and blood vessels so that their relations can be demonstrated. This is a general explanation of the practical exercise, using present-day anatomy terminology. It does not assert findings in the individual head supplied in 1867. The essential result is an intelligible dissection, with structures traced to their attachments or continuations, rather than a collection of detached parts.

Begin by orienting the head and choosing a superior approach through the anterior cranial fossa. Useful apparatus consists of a small saw or bone-cutting forceps, a fine chisel, fine scissors, dissecting forceps and a blunt probe. The coarse instruments remove bone; the fine instruments separate connective tissue. Remove the dura mater from the orbital part of the frontal bone, then carefully remove the roof of the orbit (anatomy) while leaving the periorbita intact. Extend the exposure towards the apex without driving the instrument into the optic canal or the superior orbital fissure. Preserve the delicate medial wall and its anterior ethmoidal nerve, posterior ethmoidal nerve and accompanying blood vessels. Open the periorbita under direct vision. This establishes a continuous view from the anterior margin towards the apex.^[ref]

In the superficial plane, identify the frontal nerve above the levator palpebrae superioris, and follow its division into the supraorbital nerve and supratrochlear nerve. On the lateral side identify the lacrimal gland, lacrimal nerve and accompanying lacrimal artery. On the medial side find the superior oblique muscle and the trochlear nerve entering it. Separate small amounts of adipose tissue with a blunt probe instead of stripping out the contents in a single mass. Preserve the superior ophthalmic vein where recognizable. Before reflecting any structure, show its course in place: removal of an overlying structure should answer a particular question about what lies underneath it.^[ref]

Next isolate the levator palpebrae superioris and trace it forward towards the upper eyelid. Its expanded tendon reaches the upper tarsal plate and adjacent eyelid tissues; distinguish this from an attachment to the sclera. Divide the levator palpebrae superioris across its belly and reflect the ends, keeping its oculomotor nerve supply attached where practicable. The superior rectus muscle is now exposed. Isolate and reflect it in turn, preserving the superior division of the oculomotor nerve entering the deep surface. This successive exposure demonstrates why the superficial frontal nerve should be located before either muscle is divided.^[ref][ref]

Trace the four rectus extraocular muscles from the common tendinous ring at the apex to the anterior sclera, behind the margin of the cornea. Demonstrate the medial rectus muscle and lateral rectus muscle along the corresponding sides of the eye, and the inferior rectus muscle below it. Trace the superior oblique muscle forwards to the trochlea of superior oblique; its tendon turns backwards and laterally beneath the superior rectus muscle to reach the sclera behind the equator of the eye. The inferior oblique muscle is the important exception to an apical origin: it begins on the anterior medial orbital floor of the maxilla, lateral to the lacrimal sac, and passes backwards and laterally beneath the inferior rectus muscle to the posterior lateral sclera.^[ref]

The following functional explanation makes the muscle display meaningful. The medial rectus muscle produces adduction of the eye, and the lateral rectus muscle produces abduction of the eye. The superior rectus muscle elevates and the inferior rectus muscle depresses, with additional adduction of the eye; the superior rectus muscle also produces intorsion of the eye, and the inferior rectus muscle produces extorsion of the eye. The superior oblique muscle produces intorsion of the eye, depression and abduction of the eye; the inferior oblique muscle produces extorsion of the eye, elevation and abduction of the eye. Depression by the superior oblique muscle is demonstrated most clearly with the eye adducted. Gentle traction on an isolated tendon, with the eye supported, can illustrate its line of pull in the preparation. This mechanical demonstration does not test living nerve function, and no observed movement in the historical specimen is supplied.^[ref]

In the deeper plane, identify the optic nerve entering the posterior eye and trace it back to the optic canal. Identify the nasociliary nerve crossing above it towards the medial wall; follow the long ciliary nerves towards the eye and the anterior ethmoidal nerve and posterior ethmoidal nerve towards the medial bone. On the lateral side of the optic nerve, between it and the lateral rectus muscle, seek the small ciliary ganglion. Preserve the short ciliary nerves that pass from its anterior aspect to the eye; an indiscriminate sweep through the surrounding adipose tissue would destroy precisely these small connections.^[ref]

Trace the inferior division of the oculomotor nerve towards the medial rectus muscle, inferior rectus muscle and inferior oblique muscle, including its connection to the ciliary ganglion. Trace the abducens nerve to the deep surface of the lateral rectus muscle, and the trochlear nerve to the superior oblique muscle. The lateral rectus muscle receives the abducens nerve, the superior oblique muscle receives the trochlear nerve, and the remaining listed extraocular muscles receive the oculomotor nerve. The ciliary ganglion is a relay for fibres of the parasympathetic nervous system carried with the oculomotor nerve towards the sphincter pupillae muscle and ciliary muscle. Sensory fibres connected with the nasociliary nerve, and already postganglionic fibres of the sympathetic nervous system, traverse the ciliary ganglion without another relay.^[ref]

Trace the ophthalmic artery from the optic canal and its continuity with the internal carotid artery, distinguishing it from the optic nerve. Follow recognizable branches: the central retinal artery towards and into the optic nerve, the posterior ciliary arteries towards the posterior sclera, the lacrimal artery towards the lacrimal gland, and the supraorbital artery, anterior ethmoidal artery and posterior ethmoidal artery towards their exits. The usual ophthalmic artery crosses above the optic nerve to reach the medial side, but an individual course must be established by tracing, not imposed on the preparation. ^[ref] Follow the superior ophthalmic vein towards the superior orbital fissure and cavernous sinus. The inferior ophthalmic vein also has communications towards the pterygoid plexus through the inferior orbital fissure.^[ref]

Finally, show the relations at the apex. The optic nerve and ophthalmic artery pass through the optic canal within the common tendinous ring. The divisions of the oculomotor nerve, nasociliary nerve and abducens nerve enter through the part of the superior orbital fissure enclosed by the common tendinous ring; the frontal nerve, lacrimal nerve and trochlear nerve enter outside it. Keep the eye attached until these relations have been displayed. A final labelled account should distinguish structures actually preserved from structures damaged or too small to demonstrate. That qualification matters in a practical dissection: an expected structure is a guide to search, not an observation.

For regular astigmatism, the two principal meridians of the eye are perpendicular and have different optical powers, commonly because the cornea has unequal curvatures. The crystalline lens can also contribute. A point object consequently does not form one sharp point image: the idealised paraxial optics gives two focal lines at different distances, perpendicular to one another, with an intervening region of blur. An ordinary spherical lens changes the focus in both meridians together and cannot by itself remove their difference. Irregular astigmatism, for example with a scarred cornea, lacks this simple pair of uniform principal powers.^[ref]

Several complementary observations reveal it:

The prescription must specify both the difference in optical power and its orientation. If the required correcting powers in the two principal directions are $R_1$ and $R_2$, choose the cylinder axis along direction 1. In the ideal thin lens model:Here $S$ is the spherical correcting power, $C$ the cylindrical correcting power and $\alpha$ the cylinder axis, all powers measured in dioptres. A cylindrical lens contributes no extra power along its axis and its full power perpendicular to that axis. For example, required corrections of $-1$ and $-3$ dioptres are supplied by a sphere of $-1$ dioptre and a cylinder of $-2$ dioptres, with its axis in the direction requiring the smaller negative correction. These are correcting powers, not the uncorrected eye's intrinsic powers; confusing the two reverses the intended correction.

Spectacles with this sphere-and-cylinder combination are the central historical remedy. Present options also include toric contact lenses, appropriate rigid contact lenses for some irregular cases, and selected refractive surgery. The suitability of these depends on the cause and condition of the cornea; a spectacle cylinder cannot generally cancel all irregularities of an irregular cornea.^[ref]

The opening in the iris through which light enters the eye. Its aperture affects admitted pencils of rays; the cornea and crystalline lens provide focusing power.