Physics
Atmospheric Aberration
Atmospheric aberration is a phenomenon that occurs when light passes through the Earth's atmosphere, causing it to bend and scatter. This can result in distorted images of celestial objects, particularly when viewed through telescopes. The effect is most pronounced at low altitudes and can be corrected for by adjusting the telescope's optics.
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11 Key excerpts on "Atmospheric Aberration"
eBook - PDFAstrometry for Astrophysics
Methods, Models, and Applications
- William F. van Altena(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
Finally, since the effects of atmospheric refraction are calculable, they should be analyt- ically removed from the observations so that the final relative positions can be analyzed and understood in terms of the instrumental characteristics without the interference of the atmosphere. Up to this point, the deviation in the light path has been calculable in an exact manner dependent only on the zenith angle of the object, its spectral-energy distribution, the atmospheric parameters, and their variation with height. In the next section we will explore the effects of turbulence in the atmosphere that introduce statistical fluctuations in the light-path direction. 9.3 Turbulence in the atmosphere If we rewrite Eq. (9.3) and look only at the incremental change in the refraction when a light ray passes from one level to the next in the atmosphere and assume z is small, we have Ξ΄z β βz(Ξ΄n/n) (9.18) We can now utilize Eq. (9.18) in a slightly different way. Turbulence in the atmosphere results from the largely chaotic temperature and pressure changes that occur from one element of the atmosphere to another. Temperature, as well as pressure and humidity, variations, produce corresponding changes in the index of refraction (Ξ΄n), which, according to Eq. (9.18), result in a refraction change Ξ΄z that we interpret as astronomical βseeing.β As noted by Schroeder (2000), integrating Eq. (9.18) from the top of the atmosphere down to the surface yields a ray that random walks with an angular scale on the order of one arcsecond around the refracted position for a stable atmosphere. Depending on the duration of the exposure, the time average of the deviations will be the same as that for a stable atmosphere, while the time average of the squared deviation will yield a blur circle that we refer to as the seeing disk. Fortunately, for much of astronomical data analysis, the shape of that seeing disk is very close to Gaussian (see for example Fig. 16.6 in Schroeder 1987).
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 , GΓΆttingen, 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.
eBook - PDF- Robert Tyson(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Chapter 2 Sources of Aberrations Unwanted variations of intensity in an image or during beam propagation create the need for adaptive optics. As shown in the first chapter, it is the deviation of the phase from the reference sphere, the wavefront, that is the principal cause of the intensity variations that can be treated by adaptive optics. There are many sources of wavefront error. Astronomers are mostly concerned about the turbulence in the atmo-sphere that degrades an image. Engineers working to propagate a beam and maximize its useful energy at a receiver must be concerned with er-rors introduced by lasers themselves, the optics that direct them, and the propagation medium they encounter. This chapter will discuss the many sources of phase aberrations addressed by adaptive optics systems. They include linear effects due to turbulence, optical manufacturing, and mis-alignments, as well as errors that result from nonlinear thermal effects and fluid properties. The minimization of these effects is always a considera-tion in developing any optical system from the ground up. The real-time compensation for the effects of these disturbances is the realm of adaptive optics. 2.1 Atmospheric Turbulence Naturally occurring small variations in temperature (< 1Β°C) cause random changes in wind velocity (eddies), which we view as turbulent motion in the atmosphere. The changes in temperature give rise to small changes in the atmospheric density and, hence, to the index of refraction. These 25 26 CHAPTER 2. SOURCES OF ABERRATIONS changes, on the order of 10~ 6 , can accumulate. The cumulative effect can cause significant inhomogeneities in the index profile of the atmosphere. The wavefront of a beam will change in the course of propagation. This can lead to beam wander, intensity fluctuations (scintillations), and beam spreading. These small changes in the index of refraction act like small lenses in the atmosphere.
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 β’ Piston β’ Tilt β’ Defocus β’ Spherical aberration β’ Coma β’ Astigmatism β’ Field curvature β’ 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 β’ Axial, or longitudinal, chromatic aberration β’ 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 β’ Piston β’ Tilt β’ Defocus β’ Spherical aberration β’ Coma β’ Astigmatism β’ Field curvature β’ 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 β’ Axial, or longitudinal, chromatic aberration ________________________ WORLD TECHNOLOGIES ________________________ β’ 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 β’ Piston β’ Tilt β’ Defocus β’ Spherical aberration β’ Coma β’ Astigmatism β’ Field curvature β’ 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 β’ Axial, or longitudinal, chromatic aberration β’ 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)
- 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 β’ Piston β’ Tilt β’ Defocus β’ Spherical aberration β’ Coma β’ Astigmatism β’ Field curvature β’ 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 β’ Axial, or longitudinal, chromatic aberration β’ 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- Cesare Barbieri, Ivano Bertini, Elena Fantino(Authors)
- 2020(Publication Date)
- CRC Press(Publisher)
7 Aberration of LightAs seen in the previous chapters, precession and nutation are phenomena due to the variable orientation of the observerβs system with respect to the fixed stars. The aberration, instead, is an effect due to the finite velocity of light and to the motions of the observer with respect to the celestial sources. As a consequence, the apparent direction of a celestial source, be it a distant star or a body of the Solar System, is not the same as the geometric direction at the instant of the observation. Following the traditional treatment, we shall call stellar aberration that part of the displacement that depends on the motion of the observer around the Sun, namely, the annual revolution and the diurnal rotation. Planetary aberration is the sum of the stellar aberration and the part of displacement due to the light time from the planet, comet or asteroid to the observer. The part of displacement due to the motion of the Solar System in the inertial space, a sort of secular aberration, is absorbed in the proper motions of the stars, to be discussed in Chapter 9 .Many philosophers and physicists of the past suspected the finiteness of the velocity of light, indicated as usual by c , long ago. Galileo Galilei suggested a method to measure it by means of the ephemerides of the Medicean moons of Jupiter he had discovered in Padova in January 1610. The credit for obtaining the first reliable value of c by purely astronomical means goes to Γleg RΓΆmer, at the end of the 17th century. In Paris, RΓΆmer had taken up the task of comparing the observed times of the eclipses of the Medicean moons of Jupiter with the tables compiled by Cassini. Those times could have great practical importance for the determination of the longitude of ships, as suggested by Galileo. The observations proved that Cassiniβs ephemerides for the innermost moon, Io, were quite accurate at the quadratures of Jupiter with the Sun. However, the observed positions retarded or anticipated by approximately 11 (subsequently corrected in 8) min near opposition or conjunction (see Figure 7.1
eBook - PDF- Jean Kovalevsky, P. Kenneth Seidelmann(Authors)
- 2004(Publication Date)
- Cambridge University Press(Publisher)
These are the parallactic corrections. Sometimes, particularly for objects in the Solar System, one wishes to know the position of an object at the time of the observation, or the exact time at which the observed light was emitted. This is called the light-time correction. All these effects are discussed in this chapter. 6.1 Atmospheric refraction When light crosses a surface which separates two gas layers with refractive indices n and n + dn, it is deviated β refracted β in a manner described by Snellβs law. Let ΞΎ be the angle of incidence (angle of the ray with the normal of the separation surface) 121 122 Apparent displacements of celestial objects in the medium characterized by the refractive index n. The angle of refraction in the medium of refractive index n + dn is ΞΎ + dΞΎ and obeys the relation (n + dn) sin(ΞΎ + dΞΎ ) = n sin ΞΎ. (6.1) The total bending of the light is the quantity R = z β z 0 , where z 0 is the observed zenith distance of the object, and z is the zenith distance it would have had without the atmosphere and is referred to the vertical direction (zenith) O Ξ© of the observer, z = z 0 + R . (6.2) In theory, the determination of R should imply the knowledge of n at all points of the atmosphere crossed by the ray, and the angle of the local normals to iso-index layers with the vertical V at the origin. It would be obtained by integrating (6.1) from the ground with a measured refractive index n 0 to space β at a height of the order of 50 km β from which one may consider that the vacuum is sufficient to assume n = 1. The theory was made by Garfinkel (1944) and applied using lidar measurements at various altitudes. For practical applications in astrometry, no lidar observations are available, and one is led to represent the atmosphere by a model that allows computation of R as a function only of conditions (temperature, pressure, etc.) at the observatory.
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 ΞΈ to the normal of this point on the surface. The reflected ray also has an angle of ΞΈ to the normal according to the reflection law. From Figure 2.1a, we have sin( ) ΞΈ = h R (2.1) cos( ) ΞΈ = 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 β R/2, we obtain SA x R R h R = - = - ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ - ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ 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 β 0, SA β 0 and x β R/2. So,Β R/2 is the paraxial focal length of the mirror. We usually omit the term βpar- axialβ and simply use the term βfocal length.β 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.
eBook - PDFNineteenth-Century Aether Theories
The Commonwealth and International Library: Selected Readings in Physics
- Kenneth F. Schaffner, D. Ter Haar(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
One only need assume that the corpuscles are not affected by the Earth's gravitational attraction. On the basis of the wave theory, the true path of the light is more difficult to explain, for the explanation apparently has to involve the assumption that the ABERRATION FROM BRADLEY 23 Earth's motion through the aether medium does not affect the motion of the medium. Thomas Young (1804) actually made this suggestion in connection with an explanation of aberration when Direction of earth's motion FIG. III. 1. Stellar aberration. he wrote : Upon considering the phenomenon of the aberration of the stars I am disposed to believe that the luminiferous aether pervades the substance of all material bodies with little or no resist-ance, as freely perhaps as the wind passes through a grove of trees. 2. Fresnel In the beginning of the nineteenth century the French physicist François Arago reasoned, on the basis of the corpuscular theory of light, that the aberration of light in an optically dense medium, such as in a glass prism, would be different if the incident starlight S-N.C.A.T. 3 24 NINETEENTH-CENTURY AETHER THEORIES were passed through the prism in the same direction as the Earth's motion than if it were passed in an opposite direction. Arago's experiments to test this hypothesis were performed in 1808-9 but gave a null result. Though their accuracy has since been ques-tioned, it appeared at the time that a most peculiar phenomenon was occurring. Though it was clear that the motion of the Earth affected the direction of apparent propagation of incoming light from a star, when the same light was sent through a refracting medium, the medium exerted no additional aberrational effect on it. This seemed to imply that aberration was and yet was not operative.
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