Irregular astigmatism is quantified by a vector calculation called topographic disparity. Focus of the principal meridian
With accommodation relaxed:

Simple astigmatism
Simple hyperopic astigmatism – first focal line is on the retina, while the second is located behind the retina. Simple myopic astigmatism – first focal line is in front of the retina, while the second is on the retina. Compound astigmatism
Compound hyperopic astigmatism – both focal lines are located behind the retina. Compound myopic astigmatism – both focal lines are located in front of the retina. Mixed astigmatism – focal lines are on both sides of the retina (straddling the retina). Throughout the eye
Astigmatism, whether it is regular or irregular, is caused by some combination of external (corneal surface) and internal (posterior corneal surface, human lens, fluids, retina, and eye-brain interface) optical properties. In some people, the external optics may have the greater influence, and in other people, the internal optics may predominate. Importantly, the axes and magnitudes of external and internal astigmatism do not necessarily coincide, but it is the combination of the two that by definition determines the overall optics of the eye. The overall optics of the eye are typically expressed by a persons refraction; the contribution of the external (anterior corneal) astigmatism is measured through the use of techniques such as keratometry and corneal topography. One method analyzes vectors for planning refractive surgery such that the surgery is apportioned optimally between both the refractive and topographic components.
Classification
There are three primary types of astigmatism: myopic astigmatism, hyperopic astigmatism, and mixed astigmatism. Cases can be classified further, such as regular or irregular and lenticular or corneal. Treatment
Astigmatism may be corrected with eyeglasses, contact lenses, or refractive surgery. Glasses are the simplest and safest, although contact lenses can provide a wider field of vision. Refractive surgery can eliminate the need to wear corrective lenses altogether by permanently changing the shape of the eye but, like all elective surgery, comes with both greater risk and expense than the non-invasive options. Various considerations involving eye health, refractive status, and lifestyle determine whether one option may be better than another. In those with keratoconus, certain contact lenses often enable patients to achieve better visual acuity than eyeglasses. Once only available in a rigid, gas-permeable form, toric lenses are now also available as soft lenses. In older people, astigmatism can also be corrected during cataract surgery. This can either be done by inserting a toric intraocular lens or by performing special incisions (limbal relaxing incisions). Toric intraocular lenses probably provide a better outcome with respect to astigmatism in these cases than limbal relaxing incisions.Toric intraocular lenses can additionally be used in patients with complex ophthalmic history, such as previous ophthalmic surgery. In such complex cases, toric intraocular lenses seems to be as effective as in non-complex cases for correction of concurrent corneal astigmatism. Epidemiology
According to an American study, nearly three in ten children (28.4%) between the ages of five and seventeen have astigmatism.