Physics
Chromatic Aberration
Chromatic aberration refers to the phenomenon in which different colors of light are refracted by different amounts when passing through a lens, resulting in a blurred or distorted image. This occurs because the refractive index of a lens material varies with the wavelength of light, causing colors to focus at different points.
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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 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.
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)
- 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.
eBook - ePub- Jeremy Sanderson(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Classical Optics and its Applications, 2nd ed. Cambridge: CUP, pp. 9–22.With an uncorrected condenser, spherical aberration is very evident with a small light source, because the lens elements are not corrected to the same degree as for objectives. Since Köhler illumination effectively uses a large light source, this reduces the effect of spherical aberration. If annular illumination is used (e.g. as for dark-field or phase contrast microscopy), the degree of spherical aberration present is further reduced.6.4 Chromatic Aberration
Chromatic Aberration arises because all materials from which lenses can be made have a different refractive index for each colour. In other words, Chromatic Aberration occurs because the refractive index of a transparent solid (or liquid) medium varies with wavelength4 . This is why white light refracted by a prism is dispersed into a coloured spectrum. The refractive index is5 generally higher for shorter (RIblue = 1.522; ‘blue bends best’) than for longer (RIred = 1.513) wavelengths. The effect of Chromatic Aberration is to focus different wavelengths of light at different focal points along the optical axis (Figure 6.1c ; Figure 6.6 ). For this reason this particular form of aberration is also known as longitudinal, or axial, Chromatic Aberration to distinguish it from Chromatic Aberration occurring transversely to the optical axis, which is called lateral Chromatic Aberration. This second type of Chromatic Aberration is considered later (Section 6.9 ); for the time being, we shall discuss only longitudinal Chromatic Aberration.As Figure 6.6 shows, an image suffering from longitudinal Chromatic Aberration can exhibit a colour tint throughout and not just at the edges of the object. It is well known that Newton discovered prismatic dispersion in 1666. Regrettably, on the basis of some rather unfortunate experiments, he concluded that dispersion is directly proportional to refraction, and it was thus impossible to correct Chromatic Aberration using lenses. We now know that this is not true. Dispersion varies with different types of glass, and it is possible to minimise Chromatic Aberration due to dispersion simply by combining lenses of different types of glass into doublets6 . There are two principal types of glass: crown glass, with a lower refractive index and less dispersion (see Table 2.3 & Table 2.4 ), and flint glass, with a high refractive index and dispersion. By combining a positive convex crown glass lens with a negative concave flint glass lens (Figure 6.1d
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.
eBook - PDF- W.T Welford(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
10 Chromatic Aberration 10.1 I n t r o d u c t i o n : H i s t o r i c a l a s p e c t s The refractive index of any medium other than vacuum varies with wave-length. Thus the Gaussian and aberrational properties of any refracting optical system are functions of wavelength, i.e. Chromatic Aberrations exist. It is traditional to consider chromatic variations of Gaussian properties as aberra-tions as well as chromatic variations of true aberrations. This usage, although perhaps inaesthetic, has ample practical justification; in fact, many modern refracting systems intended for use over an appreciable range of wavelengths are ultimately limited in performance by chromatic effects, both Gaussian and higher order, rather than by the monoChromatic Aberrations which we have so far been considering. The history of astronomical telescope design provides a useful example. Sir Isaac Newton invented the reflecting telescope because he considered that it was impossible to correct the chromatic effects in singlet lenses by combining two to form what we now call an achromatic doublet; in effect he thought that the Chromatic Aberrations of all lenses were proportional to their powers, with the same constant of proportionality even for different glasses. Then, in the middle of the eighteenth century, John Dollond and Chester Moore Hall showed that Newton had been wrong and they made achromatic doublets. From this point larger and larger astronomical telescope doublet objectives were made, the largest ever being the famous Yerkes objective of 1 m diameter. However, as the objectives became larger and the design techniques became subtler it was found that an achromatic doublet was not quite free from Chromatic Aberration and a residual error, known as secondary spectrum, appeared. This led to the re-introduction of Chromatic Aberration AND THE ACHROMATIC DOUBLET 193 reflecting objectives and these are now universally used for apertures exceed-ing 1 m.
eBook - PDF- Troy E. Fannin, Theodore Grosvenor(Authors)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Expressed in prism diopters, the lateral Chromatic Aberration is therefore equal to dF v -dF i: = d(F v - F c ). b. Prisms. Since a prism does not change the ver-gence of light, it does not manifest axial Chromatic Aberration. It does, however, manifest angular dis-persion (lateral Chromatic Aberration), as shown in Figure 6-4. The angular dispersion is defined as the difference in prismatic effects for blue and red light, that is, e F — 8 ( > Chromatic Aberration will be discussed further in Section 6.4 (for prisms) and in Section 6.6 (for lenses). Due to the presence of Chromatic Aberration, a wearer of high-powered lenses may occasionally see color fringes around objects. The amount of chro-matic aberration is dependent upon the material of FIGURE 6-3. Transverse Chromatic Aberration (C.A.) expressed as the difference in prismatic effects created by red and blue light. which the lens is made: For example, it is relatively high for flint glass, used for the manufacture of some bifocal segments. Since Chromatic Aberration requires light contain-ing a range of wavelengths it does not occur with monochromatic light. However, light falling upon an ophthalmic lens is very seldom monochromatic, with the result that all substances from which lenses and prisms are made are subject to Chromatic Aberration. Since it is due to the material itself, chromatic aberra-tion cannot be reduced or eliminated by changing the form (the amount oí bend) of the lens. However, it can be controlled by the use of a doublet, which is a lens made of two kinds of glass. Chromatic Aberration does not occur in reflection, because the angle of reflection is the same for all wavelengths of light; nor does it occur when light is refracted by parallel plates of glass. 6.3. Chromatic Dispersion When we specify the index of refraction of a sub-stance, we normally specify the index for the sodium D line. This is the Fraunhofer line having a wavelength of 589 nm.
eBook - ePub- A. E. Conrady(Author)
- 2014(Publication Date)
- Dover Publications(Publisher)
CHAPTER XVChromatic Aberration AS AN OPD
[101] THE optical-path method leads to a particularly simple treatment of the problem of establishing achromatism at the axial focal point of a lens system.[101]In Fig. 133 , let O represent any lens system which refracts light from an object-point B towards an image-point B ′. Physically considered, point B will be sending out spherical waves of light towards the lens system, and the latter will alter the curvature of these waves so as to direct them towards the image-point B ′. In the ideal case, the refracted waves W ′ would be truly spherical with B ′ as centre. Actually they will be always more or less distorted owing to the inevitable residuals of spherical aberration, and it is important to notice that we make no restriction as to the amount of this distortion of the refracted waves. The formulae which we shall deduce will therefore remain valid however great the spherical aberration of a system may be.Chromatic Aberration, from our present point of view, consists in this: That the refracted waves corresponding to some other colour will have greater or less mean curvature than W ′ when tangent to it at the optical axis. Perfect achromatism would exist if it were possible to cause waves corresponding to other colours to coincide absolutely with W ′ when passing through the same point of the axis. As this perfect coincidence is practically unobtainable, we adopt a compromise, by stipulating that the refracted wave of a wave-length slightly differing from that of W ′ shall, when passing the point where W cuts the optical axis, simultaneously intersect with W ′ at the margin of the segment which the lens system allows to pass.FIG . 133.By way of example, let the full-drawn marginal ray in the upper part of Fig. 133 represent the brightest light and W ′ the emerging wave of that colour. If the lens system were chromatically under-corrected, then red (say C) light would come to a longer focus beyond B ′ and blue (say F ) light to a shorter focus at the left of B ′. The emerging waves of these colours would have respectively less and more mean curvature than the wave of brightest light, as indicated by the thinner curves marked C and F . Our new definition of achromatism is illustrated in the lower part of Fig. 133 . We demand that the waves of other colours shall intersect each other at the margin of the clear aperture.[101] In the absence of the secondary spectrum they would do so on W ′. If the secondary spectrum is appreciable they will intersect a little to the left of the margin of W
eBook - ePub- W.T Welford(Author)
- 2017(Publication Date)
- Routledge(Publisher)
10 Chromatic Aberration10.1 Introduction: Historical aspects
The refractive index of any medium other than vacuum varies with wavelength. Thus the Gaussian and aberrational properties of any refracting optical system are functions of wavelength, i.e. chromatic aberrations exist. It is traditional to consider chromatic variations of Gaussian properties as aberrations as well as chromatic variations of true aberrations. This usage, although perhaps inaesthetic, has ample practical justification; in fact, many modern refracting systems intended for use over an appreciable range of wavelengths are ultimately limited in performance by chromatic effects, both Gaussian and higher order, rather than by the monoChromatic Aberrations which we have so far been considering. The history of astronomical telescope design provides a useful example. Sir Isaac Newton invented the reflecting telescope because he considered that it was impossible to correct the chromatic effects in singlet lenses by combining two to form what we now call an achromatic doublet; in effect he thought that the Chromatic Aberrations of all lenses were proportional to their powers, with the same constant of proportionality even for different glasses. Then, in the middle of the eighteenth century, John Dollond and Chester Moore Hall showed that Newton had been wrong and they made achromatic doublets. From this point larger and larger astronomical telescope doublet objectives were made, the largest ever being the famous Yerkes objective of 1 m diameter. However, as the objectives became larger and the design techniques became subtler it was found that an “achromatic” doublet was not quite free from Chromatic Aberration and a residual error, known as “secondary spectrum”, appeared. This led to the re-introduction of reflecting objectives and these are now universally used for apertures exceeding 1 m. There are in fact other reasons why reflecting objectives are used exclusively for large telescopes but the secondary spectrum would be a sufficient reason if the others did not exist.†
eBook - PDF- Hugh Davson(Author)
- 2013(Publication Date)
- Academic Press(Publisher)
This effect is known as transverse Chromatic Aberration or chromatic difference of magnification. It is occasionally notice-able when the edge of a white object is viewed obliquely through a spectacle lens. As shown in Fig. 8, the action of a lens on an oblique pencil is akin to FIG. 8. Transverse Chromatic Aberration of a spectacle lens. that of a prism. Dispersion takes place and the refracted rays corresponding to different colours enter the eye in slightly different directions. In the cir-cumstances shown in the diagram, the image might be seen with a blue fringe, the blue ray denoted by B making a greater angle with the optical axis than the red ray denoted by R. F. ACHROMATIC LENSES AND PRISMS The fact that dispersive power (or its reciprocal, constringence) is not the same for all transparent substances makes possible the construction of achro-matic lenses. Two components of different materials are needed, one of posi-tive and the other of negative power. One material is generally selected from the crown and the other from the flint family of optical glasses. To achroma-tize the combination, the axial Chromatic Aberration of one component must neutralize that of the other. This can be done while still leaving a balance of positive or negative power, as required, by making the powers of the com-ponents numerically proportional to their respective constringences. Let the powers of the two components (assumed thin and in contact) be denoted by F x and F 2 , and the constringences of the two materials by 7. ABERRATION OF OPTICAL IMAGES 99 v± and v 2 respectively. Then, if F is the desired power of the combination, F x and F 2 must be chosen such that F 1 + F 2 = F Equation (7.11) shows that the combination will be achromatic if The simultaneous solution of these last two equations yields F x = -^— (7.13) v i -^2 and F 2 = ^ ^ -(7.14) v x - v 2 The requisite powers of the two components are hence determined.
eBook - PDFLens Design
A Practical Guide
- Haiyin Sun(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
55 2 Optical Aberrations Any real optical system contains various aberrations. The main task of optical design is to minimize these aberrations. In this chapter, we briefly describe the five important aberrations: spherical aberration, coma, astigmatism, field curvature, and image distortion. These five aberrations are monochromatic. We will also describe two Chromatic Aberrations: longitudinal color and lateral color. 2.1 SPHERICAL ABERRATION 2.1.1 REFLECTION SPHERICAL ABERRATION The most commonly seen aberration is the spherical aberration. Figure 2.1a shows a spherical mirror focusing a ray parallel to its optical axis. The mirror surface has a radius of curvature R, the incident ray has a height of h to the optical axis, and the focused spot is a distance of x away from the center of surface curvature. The incident ray hits one point on the mirror surface and has an angle of θ to the normal of this point on the surface. The reflected ray also has an angle of θ to the normal according to the reflection law. From Figure 2.1a, we have sin( ) θ = h R (2.1) cos( ) θ = R x /2 (2.2) Equation 2.2 holds because the distance between the focused spot and the point where the ray hits the mirror surface also equals to x. Combining Equations 2.1 and 2.2 to solve for the spherical aberration SA = x − R/2, we obtain SA x R R h R = - = - - 2 2 1 1 1 2 0 5 . (2.3) From Equation 2.3, we can see that for a given mirror, the spherical aberration varies as the height of the incident ray varies. When h → 0, SA → 0 and x → R/2. So, R/2 is the paraxial focal length of the mirror. We usually omit the term “par- axial” and simply use the term “focal length.” For h > 0, SA > 0. 56 Lens Design Plotted in Figure 2.1b is a raytracing diagram generated by Zemax showing the spherical aberration of a spherical mirror. Spherical aberration prevents a group of parallel rays being focused at the same spot and is an undesired property.
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