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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]

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]