5 lens aberrations that occur with monochromatic light

In 1856, a German by the name of Seidl, as a result of analysis, established five lens aberrations that occur with monochromatic light (with light of one wave). These aberrations, described below, are called the five Seidl aberrations.

Spherical aberration

To a certain extent, this aberration is present in all lenses built entirely from spherical elements. Spherical aberration causes parallel light rays passing through the edge of a lens to merge at a focal point closer to the lens than light rays passing through the center of the lens. (The amount of displacement of the focal point along the optical axis is called longitudinal spherical aberration.) The degree of spherical aberration tends to increase with large aperture lenses. A dot image affected by spherical aberration sharply forms rays of light near the optical axis, however, it is affected by flare from peripheral light rays (this flare is also called halo, and its radius is called transverse spherical aberration). As a result, spherical aberration affects the entire image area,

It is very difficult to correct spherical aberration in spherical lenses. Although this correction is usually made by combining two lenses - one convex and one concave - based on light rays with a certain height of incidence (distance from the optical axis), there is a limit to the degree of correction using spherical lenses, so some amount of aberration is always preserved. This residual aberration can be largely eliminated by stopping the lens to reduce the amount of peripheral light. With a large aperture lens at full aperture, the only effective way to substantially compensate for spherical aberration is to use an aspherical lens.

Coma (comatic aberration)

Coma, or coma aberration, is a phenomenon seen at the periphery of an image that is created by a lens corrected for spherical aberration and causes light rays entering the edge of the lens at some angle to converge into a comet rather than the desired point. Hence its name. The shape of the comet is oriented radially, with its tail pointing either toward or away from the center of the image. The resulting blurring at the edges of an image is called coma flare. Coma, which can occur even in lenses that accurately reproduce the point as a point on the optical axis, is caused by the difference in refraction between light rays from a point located outside the optical axis and passing through the edges of the lens, and the main light ray from the same point passing through center of the lens. The coma increases as the angle of the main beam increases and leads to a decrease in contrast at the edges of the image. A certain degree of improvement can be achieved by stopping the lens. Coma can also cause blurry areas of the image to blow out, creating an unpleasant effect. The elimination of both spherical aberration and coma for an object located at a certain shooting distance is called aplanatism, and a lens corrected in this way is called aplanatism.

Astigmatism

With a lens corrected for spherical and comatic aberration, an object point on the optical axis will be accurately reproduced as a point in the image, but an object point off the optical axis will not appear as a point in the image, but rather as a shadow or line. This type of aberration is called astigmatism. You can observe this phenomenon at the edges of the image if you slightly shift the focus of the lens to a position in which the object point is sharply depicted as a line oriented in a radial direction from the center of the image, and again shift the focus to another position in which the object point is sharply depicted as a line oriented in the direction of the concentric circle. (The distance between these two focus positions is called the astigmatic difference.) In other words, the light rays in the meridional plane and the light rays in the sagittal plane are in different positions, so these two groups of rays do not merge at one point. When the lens is set to the optimal focal position for the meridional plane, the light rays in the sagittal plane are aligned in the direction of the concentric circle (this position is called the meridional focus). Similarly, when the lens is set to the optimal focal position for the sagittal plane, the light rays in the meridional plane form a line oriented in the radial direction (this position is called the sagittal focus). light rays in the sagittal plane are aligned in the direction of a concentric circle (this position is called the meridional focus). Similarly, when the lens is set to the optimal focal position for the sagittal plane, the light rays in the meridional plane form a line oriented in the radial direction (this position is called the sagittal focus). light rays in the sagittal plane are aligned in the direction of a concentric circle (this position is called the meridional focus). Similarly, when the lens is set to the optimal focal position for the sagittal plane, the light rays in the meridional plane form a line oriented in the radial direction (this position is called the sagittal focus).

Image field curvature

Image field curvature is a phenomenon that causes the imaging plane to become curved like the inside of a shallow bowl, preventing the lens from forming a flat image of a flat object. When the center of an image is in focus, the edges are out of focus, and when the edges are in focus, the center is out of focus. The degree of curvature of the image field is greatly affected by the method used to correct astigmatism. Because the image plane falls between the sagittal and meridional image planes, good astigmatism correction results in little distortion of the image field.

Since field curvature cannot be reduced by stopping the lens, lens designers reduce it as much as possible by optical sorting to various methods such as changing the shape of individual lens elements, lens assembly, and changing the position of the aperture. In this case, one indispensable condition for the simultaneous correction of astigmatism and curvature of the image field must be observed - the Petsval condition (1843). The Petsval condition states that a lens element is good if a zero result is obtained when the reciprocal of the product of the refractive index and the focal length of that lens element is added to the total number of elements from which the lens is made. This result is called the Petsval sum.

Distortion

One of the requirements for an ideal lens is that "the image of the object formed by the lens must have the same shape as the object itself." Distortion is a type of aberration that causes straight lines to become curved (distorted) in an image, thus not meeting this ideal condition. A distortion that stretches the (+) shape diagonally is called pincushion (positive) distortion, and one that compresses the (-) shape diagonally is called barrel (negative) distortion. In rare cases, with an ultra wide angle lens, these two types of distortion can coexist, resulting in a shape that is both stretched and compressed.

Distortion is small in lenses that are shaped symmetrically on both sides of the aperture stop, but can occur in lenses with asymmetric configurations.

Zoom lenses tend to create barrel distortion at wide angle and pincushion distortion at telephoto (due to slight changes in distortion characteristics as the focal length changes). However, in zoom lenses incorporating one or more aspherical lenses, this distortion is well corrected due to the compensating effect of the aspherical lenses.

Because this type of aberration is caused by abnormal main light rays passing through the center of the lens, its effects cannot be reduced by stopping the lens.

Meridian plane

The plane in which both the optical axis and the main ray of light from a point of the object that is outside the optical axis are located is called the meridian plane. This position of the image, formed by light rays passing through the lens in this plane, is called the meridional surface of the object. This image surface provides optimal image quality in the form of a concentric circle on the film plane. If we imagine the spherical surface of the lens as part of the earth's surface, and the optical axis as part of the earth's axis, then the meridional plane coincides exactly with the earth's meridian. Hence its name. On MTF diagrams, the curve showing the characteristics of the meriadian surface of the image is usually denoted only by the letter M.

Sagittal plane

The sagittal plane is the plane perpendicular to the meridional plane. The position of the image formed by light rays passing through the lens in this plane is called the sagittal image surface. The image surface provides optimum image quality in a radial direction to the film plane. The word "sagittal" is of Greek origin and means "sagittal". In MTF diagrams, the curve showing the characteristics of the sagittal surface of the image is usually indicated by a single letter S.

How to reduce the effects of aberrations

Today's lenses are designed using large computers to perform mind-bending calculations and high-level simulations to reduce aberrations of all types and achieve the highest level of imaging. Even with this technology, however, it is not possible to completely remove all aberrations, which means that all lenses on the market have at least a minimum of aberration. It is called residual aberration. The type of residual aberration in the lens as a whole determines the characteristics of the image produced by the lens, such as sharpness and blur effect. Because of this, modern lenses are often designed to achieve a pleasing blur effect (image characteristics outside the imaging plane) through the use of computer simulation techniques, so that you can analyze the performance of the lens at the design stage. As mentioned in various descriptions of aberration, the effect of some types of aberrations can be reduced by stopping the lens. Other effects cannot be reduced.

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