<p>There are two distinct forms of astigmatism. The first is a third-order aberration, which occurs for objects (or parts of objects) away from the optical axis. This form of aberration occurs even when the optical system is perfectly symmetrical. This is often referred to as a &quot;monochromatic aberration&quot;, because it occurs even for light of a single wavelength. This terminology may be misleading, however, as the <em>amount</em> of aberration can vary strongly with wavelength in an optical system.</p>

<p>The second form of astigmatism occurs when the optical system is not symmetric about the optical axis. This may be by design (as in the case of a cylindrical lens), or due to manufacturing error in the surfaces of the components or misalignment of the components. In this case, astigmatism is observed even for rays from on-axis object points. This form of astigmatism is extremely important in ophthalmology, since the human eye often exhibits this aberration due to imperfections in the shape of the cornea or the lens.</p>

<h3><span class="mw-headline">Third-order astigmatism</span></h3>

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<h4><span class="mw-headline">Ophthalmic astigmatism</span></h4>

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<p>In ophthalmology, the vertical and horizontal planes are identified as <em>tangential</em> and <em>sagittal</em> meridians, respectively. Ophthalmic astigmatism is a refraction error of the eye in which there is a difference in degree of refraction in different meridians. It is typically characterized by an aspherical, non-figure of revolution cornea in which the corneal profile slope and refractive power in one meridian is greater than that of the perpendicular axis.</p>

<p>Grinding and polishing of precision optical parts, either by hand or machine, typically employs significant downward pressure, which in turn creates significant frictional side pressures during polishing strokes that can combine to locally flex and distort the parts. These distortions generally do not possess figure-of-revolution symmetry and are thus astigmatic, and slowly become permanently polished into the surface if the problems causing the distortion are not corrected. Astigmatic, distorted surfaces potentially introduce serious degradations in optical system performance.</p>

<p>Surface distortion due to grinding or polishing increases with the aspect ratio of the part (diameter to thickness ratio). To a first order, glass strength increases as the cube of the thickness. Thick lenses at 4:1 to 6:1 aspect ratios will flex much less than high aspect ratio parts, such as optical windows, which can have aspect ratios of 15:1 or higher. The combination of surface or wavefront error precision requirements and part aspect ratio drives the degree of back support uniformity required, especially during the higher down pressures and side forces during polishing. Optical working typically involves a degree of randomness that helps greatly in preserving figure-of-revolution surfaces, provided the part is not flexing during the grind/polish process.</p>

<h4><span class="mw-headline">Deliberate astigmatism in optical systems</span></h4>

<p>Compact disc players use an astigmatic lens for focusing. When one axis is more in focus than the other, dot-like features on the disc project to oval shapes. The orientation of the oval indicates which axis is more in focus, and thus which direction the lens needs to move. A square arrangement of only four sensors can observe this bias and use it to bring the read lens to best focus, without being fooled by oblong pits or other features on the disc surface.</p>