Physics
Coma Aberration
Coma aberration is an optical distortion that occurs in imaging systems, such as telescopes and microscopes. It causes off-axis light rays to focus at different points, resulting in a comet-like or tail-shaped blur in the image. Coma aberration can degrade the quality of images and is often corrected using specialized optical designs or software algorithms.
Written by Perlego with AI-assistance
Related key terms
1 of 5
10 Key excerpts on "Coma Aberration"
eBook - PDFLens Design
A Practical Guide
- Haiyin Sun(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
The origin of Coma Aberration is that the ray pairs symmetric to the chief rays have different incident and exit angles that results in different refractions. The mag- nitude of Coma Aberration increases as the ray incident angle and/or the lens aper- ture increase. Coma Aberration will reduce the sharpness of the image and can often be significantly reduced by using properly designed aspheric lens or combining sev- eral spherical lens elements with properly selected surface curvatures and glasses. 2.4 FIELD CURVATURE 2.4.1 PETZVAL SURFACE Every lens has a basic curved image surface, called Petzval surface, as shown in Figure 2.7. For a simple thin lens, the longitudinal distance between the Petzval sur- face and the ideal planar image surface is given by h 2 /(2nf ) [4], where h is the image Image plane Coma Spot diagram (b) (a) Chief ray FIGURE 2.6 (a) Zemax generated ray tracing diagram to illustrate Coma Aberration. Coma appears when parallel rays with an angle to the optical axis are focused. (b) Spot diagram shows the coma-like intensity pattern of the focused spot of the 20° incident rays. 61 Optical Aberrations height, n is the refractive index of the lens material, and f is the lens focal length. The image surface of a lens may be more severely curved than the Petzval surface because of aberrations. 2.4.2 FIELD CURVATURE In Figure 2.7, we reproduce the raytracing diagram shown in Figure 2.6a, but the incident rays have five angles of 0°, 5°, 10°, 15°, and 20°, to the optical axis. To sim- plify the situation, we only plot two meridional rays, and not the chief rays. The five focused spots for the five fields are marked by black dots. We can see that the longitu- dinal position of the focused spots moves toward the lens as the field angle increases, and the image plane marked by the dash line is curved.
eBook - ePub- Jeremy Sanderson(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Figure 6.7 ) and is thus an off-axis aberration. It is similar to spherical aberration, because the refraction of an off-axis image point is different for different parts of the curvature (or ‘figure’) of the lens surface. The presence of coma in an image generally indicates that lens elements within the objective have been – or have become – misaligned. The image streak is usually therefore blurred very much like a comet-shaped flare: lying with a wide, blurred tail away from the optical axis. Manufacturers take a great deal of trouble to design out this aberration by selecting optimum combinations of lens configurations. Coma is very rarely encountered in an objective unless, of course, it has been dropped at some point. An aplanatic lens (see Boxes 6.1 & 6.2) is one that is effectively free from both spherical aberration and coma. Good-quality condensers will be aplanats.Source: Goodwin 2007. Reproduced with permission from Elsevier.Figure 6.7The ray path of coma The ray path of an image point suffering from coma.6.6 Astigmatism
Axial astigmatism occurs where rays that propagate in two perpendicular planes are refracted to differing extents and thus have different foci (Figure 6.8 and Figure 6.9 ). The image is smeared longitudinally at different focal points; the visual effect (Figure 1.13 ) being a blurring along one axis in the image. Axial astigmatism does not occur with a perfectly spherical lens. It is this form of astigmatism that can occur in the eye. It may also occur because lens elements in the objective are not in perfect alignment with respect to one another. This can happen if the objective is dropped, for example.Source: Goodwin, 2007. Reproduced with permission from Elsevier.Figure 6.8The ray path of astigmatism The ray path and effect of imaging a point through an astigmatic lens. The overall effect is a smeared and elongated point spread function that rotates through 90° as the ray propagates from the point of focus of the sagittal plane to that of the tangential plane.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
____________________ WORLD TECHNOLOGIES ____________________ Chapter 4 Optical Aberration Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge into (or does not diverge from) a single point. Instrument-makers need to correct optical systems to compensate for aberration. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays. Overview Aberrations fall into two classes: monochromatic and chromatic . Monochromatic aberrations are caused by the geometry of the lens and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name. Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. They do not appear when monochromatic light is used. Monochromatic aberrations • Piston • Tilt • Defocus • Spherical aberration • Coma • Astigmatism • Field curvature • Image distortion Piston and tilt are not actually true optical aberrations, as they do not represent or model curvature in the wavefront. If an otherwise perfect wavefront is aberrated by piston and ____________________ WORLD TECHNOLOGIES ____________________ tilt, it will still form a perfect, aberration-free image, only shifted to a different position. Defocus is the lowest-order true optical aberration. Chromatic aberrations • Axial, or longitudinal, chromatic aberration • Lateral, or transverse, chromatic aberration Monochromatic aberration The elementary theory of optical systems leads to the theorem: Rays of light proceeding from any object point unite in an image point ; and therefore an object space is reproduced in an image space. The introduction of simple auxiliary terms, due to C.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 8 Optical Aberration Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after trans-mission through the system does not converge into (or does not diverge from) a single point. Instrument-makers need to correct optical systems to compensate for aberration. Overview Aberrations fall into two classes: monochromatic and chromatic . Monochromatic aberr-ations are caused by the geometry of the lens and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name. Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. They do not appear when monochromatic light is used. Monochromatic aberrations • Piston • Tilt • Defocus • Spherical aberration • Coma • Astigmatism • Field curvature • Image distortion Piston and tilt are not actually true optical aberrations, as they do not represent or model curvature in the wavefront. If an otherwise perfect wavefront is aberrated by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position. Defocus is the lowest-order true optical aberration. Chromatic aberrations • Axial, or longitudinal, chromatic aberration ________________________ WORLD TECHNOLOGIES ________________________ • Lateral, or transverse, chromatic aberration Monochromatic aberration The elementary theory of optical systems leads to the theorem: Rays of light proceeding from any object point unite in an image point ; and therefore an object space is reproduced in an image space. The introduction of simple auxiliary terms, due to C.
eBook - PDFOptical Imaging and Photography
Introduction to Science and Technology of Optics, Sensors and Systems
- Ulrich Teubner, Hans Josef Brückner(Authors)
- 2019(Publication Date)
- De Gruyter(Publisher)
3.41: Coma. (a) Front view of lens with circular zones; (b) image formation in a meridional plane; (c) comatic image consisting of circles each characteristic for one lens zone. distance y e from the axis. Rays traversing the upper respectively lower part of a differ-ent zone in the meridional plane are imaged to points with distances between y e and y c . In the case of paraxial imaging, both points would be identical with y e = y c . In a comatic image, however, we have with y e > y c a positive coma or a negative coma with y e < y c . If we follow the path of rays through the lens zones in a horizontal cut, for instance rays from points o 2 in the extreme zone in Figure 3.41a, then the left and right extreme rays are also imaged to one point i 2 (Figure 3.41c). This point, however, is not identical with i 1 at a distance y e from the axis but lies on a circle in the image plane, which is constituted by the image points of all parallel rays traversing the same zone. Likewise, all rays passing the same zone produce a circular image in the image plane. The radius of these circles increases the larger the distance of their image point in the meridional plane from the image point i c of the center ray is. The superposition of all these image circles yields the overall comatic flare. It becomes evident that by reducing the aperture the comatic aberration decreases. The principal cause for the comatic image is that the magnification varies locally due to the curved principal planes. In the absence of spherical aberration, points on the optical axis are imaged perfectly. However, small area elements perpendicular to the optical axis must also be imaged without distortion in order to prevent coma. This means that the magnification for any ray in the imaging process must be constant and independent from the elevation or aperture angle.
- Bernd Jahne(Author)
- 2004(Publication Date)
- CRC Press(Publisher)
All these aberrations have their common cause in the refraction and reflection law. First-order optics, which is the basis of the simple image equation, requires paraxial rays which have a low inclination α and offset to the optical axis so that tan α ≈ sin α ≈ α. (4.30) Only in this limit, mirrors and lenses with spherical shape focus a parallel light beam onto a single point. Additionally, so-called chromatic aberrations are caused by the wavelength dependency of the index of refraction (Section 3.3.1a). For larger angles α and object height h , we can expect aberrations. Seven primary aberrations can be distinguished which are summarized in Table 4.1 and Fig. 4.13. Spherical aberration is related to the focusing of an axial parallel bundle of monochro-matic light. Each radial zone of the lens aperture has a slightly different focal length. For a simple planoconvex lens, the focal length decreases with the distance of the ray from the optical axis. The lack of a common focus results in a certain spot size onto which a parallel light bundle is focused. Due to the larger area of the off-axis rays, the minimum blur circle is found slightly short off the focus for paraxial rays. 4.3 Concepts 135 astigmatism field curvature spherical aberration coma & distortion Figure 4.13: Schematic illustration of the five primary monochromatic aberrations: spherical aberration, coma, astigmatism, field curvature, and distortion. Coma is an aberration that affects only off-axis light bundles. For such a light bundle, even rays piercing the lens aperture at a radial zone are not focused onto a point but — because of the lack of symmetry — onto a blur circle with a spot size increasing with the radius of the zone. Also, in contrast to spherical aberration, each radial zone focuses onto the image plane at a slightly different height. The result is a spot of comatic shape with a bright central core and a triangular shaped flare extending toward the optical axis.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Research World(Publisher)
____________________ WORLD TECHNOLOGIES ____________________ Chapter 4 Optical Aberration Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge into (or does not diverge from) a single point. Instrument-makers need to correct optical systems to compensate for aberration. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays. Overview Aberrations fall into two classes: monochromatic and chromatic . Monochromatic aberrations are caused by the geometry of the lens and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name. Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. They do not appear when monochromatic light is used. Monochromatic aberrations • Piston • Tilt • Defocus • Spherical aberration • Coma • Astigmatism • Field curvature • Image distortion ____________________ WORLD TECHNOLOGIES ____________________ Piston and tilt are not actually true optical aberrations, as they do not represent or model curvature in the wavefront. If an otherwise perfect wavefront is aberrated by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position. Defocus is the lowest-order true optical aberration. Chromatic aberrations • Axial, or longitudinal, chromatic aberration • Lateral, or transverse, chromatic aberration Monochromatic aberration The elementary theory of optical systems leads to the theorem: Rays of light proceeding from any object point unite in an image point ; and therefore an object space is reproduced in an image space. The introduction of simple auxiliary terms, due to C.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 1 Optical Aberration Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after trans-mission through the system does not converge into (or does not diverge from) a single point. Instrument-makers need to correct optical systems to compensate for aberration. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays. Overview Aberrations fall into two classes: monochromatic and chromatic . Monochromatic aber-rations are caused by the geometry of the lens and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name. Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. They do not appear when monochromatic light is used. Monochromatic aberration The elementary theory of optical systems leads to the theorem: Rays of light proceeding from any object point unite in an image point ; and therefore an object space is reproduced in an image space. The introduction of simple auxiliary terms, due to C. F. Gauss ( Dioptrische Untersuchungen , Göttingen, 1841), named the focal lengths and focal planes, permits the determination of the image of any object for any system. The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis (the symmetrical axis of the system) are infinitely small, i.e. with infinitesimal objects, images and lenses; in practice these conditions are not realized, and the images projected by uncorrected systems are, in general, ill defined and often completely blurred, if the aperture or field of view exceeds certain limits.
No longer available |Learn moreOptics
An Introduction
- Sarhan M. Musa(Author)
- 2020(Publication Date)
- Mercury Learning and Information(Publisher)
CHAPTER 4ABERRATIONS OF OPTICAL IMAGESChapter Outline4.0Introduction4.1Spherical Aberration of a Lens4.2Coma4.3Astigmatism4.4Curvature of Field4.5Distortion4.6Chromatic Aberration4.7Axial Chromatic Aberration for an Object at Infinity4.8Achromatism4.9Condition of Achromatism for Two Lenses in Contact4.10Condition of Achromatism of a Separated Doublet4.11The Balancing of Aberrations4.12Exercises4.0 INTRODUCTIONThe theory of image formation by mirrors and lenses, developed in the previous chapters, was based on two fundamental assumptions: (a) the object and the image points were considered as if they were situated on or very close to the principal axis, and (b) the rays of light diverging from the object point were assumed to be confined to a narrow cone of a small angular opening so as to allow us to replace the sine of the slope angle θ of the ray by the angle θ. These paraxial conditions lead to a point image of a point object in the first order theory, so called because of the inclusion of the first order of the slope angle only.In reality objects have finite dimensions and, moreover, considerations of the brightness of the image demand the use of reflecting and refracting systems having large apertures. In actual practice, therefore, the rays from object points are confined not simply to a region close to the principal axis, termed the paraxial region, but they form a cone of such a wide angular opening that in the expansion of the sine of the slope angle θ into a series,and it becomes essential to take into account, in our discussions of the image formation, at least the first two terms of this series. This theory, called the third order theory due to the inclusion of the third order term in θ, was developed by Ludwig Von Seidal in 1855 and gives various departures of the actual image from the one predicted by the first order theory. These departures, the so-called Seidal aberrations, may be classified as (a) spherical aberration, (b) coma, (c) astigmatism, (d) curvature, and (e) distortion. These aberrations are present in the images formed by ordinary lenses, even when the light of only one wavelength is employed. They are, therefore, also known as monochromatic aberrations
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 8 Optical Aberration Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system. It occurs when light from one point of an object after transmission through the system does not converge into (or does not diverge from) a single point. Instrument-makers need to correct optical systems to compensate for aberration. Overview Aberrations fall into two classes: monochromatic and chromatic . Monochromatic aberrations are caused by the geometry of the lens and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name. Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. They do not appear when monochromatic light is used. Monochromatic aberrations • Piston • Tilt • Defocus • Spherical aberration • Coma • Astigmatism • Field curvature • Image distortion ________________________ WORLD TECHNOLOGIES ________________________ Piston and tilt are not actually true optical aberrations, as they do not represent or model curvature in the wavefront. If an otherwise perfect wavefront is aberrated by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position. Defocus is the lowest-order true optical aberration. Chromatic aberrations • Axial, or longitudinal, chromatic aberration • Lateral, or transverse, chromatic aberration Monochromatic aberration The elementary theory of optical systems leads to the theorem: Rays of light proceeding from any object point unite in an image point ; and therefore an object space is reproduced in an image space. The introduction of simple auxiliary terms, due to C.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
