Aberration Of Light Research Articles

The Lorentz transformation: Simplification through complexification

The general Lorentz transformation, the relation between observations made in different frames, involves the three components of the relative velocity of the two frames and three parameters describing the relative orientation of the frames. A simpler description is known in which the six parameters are encoded in four complex numbers subject to a single algebraic constraint. This description is tied to the transformation of the directions of light propagation and underscores how closely related special relativity is to light propagation. This form of the transformation, which is particularly useful for dealing with the aberration of light is usually introduced through advanced mathematical formulations. We show that the basic idea, in addition to being useful, is quite simple.

Applications of complex analysis to precession, nutation and aberration

Points on the surface of a sphere can be mapped by stereographic projection to points on the plane of complex numbers. If the points on the sphere are identified with the directions of incoming light rays, then the effect of a Lorentz transformation, a rotation plus a boost, is represented by a bilinear or Mobius transformation applied to points on the complex plane. This procedure allows the effects of the aberration of light, precession and nutation, required for computing the mean and apparent positions of celestial objects, to be accounted for in a common framework and yields expressions that are readily evaluated in practice. The general form of the bilinear transformation representing a pure Lorentz boost is derived. Explicit expressions are given for the bilinear transformations representing aberration, precession and nutation as well as frame bias and transformations to the Celestial Intermediate Reference System. The approach described simplifies, and is an alternative to, the standard matrix methods commonly used to perform coordinate system rotations.

Conjectures and reputations: The composition and reception of James Bradley's paper on the aberration of light with some reference to a third unpublished version.

In January 1729 a paper written by James Bradley was read at two meetings of the Royal Society. On a newly discovered motion of the fixed stars, later described as the theory of the aberration of light, it was to transform the science of astrometry. The paper appeared as a narrative of a programme of observation first begun at Kew and finalized at Wanstead, but it was, in reality, a careful reconstruction devised to enhance his reputation in response to a recognition that the programme was initially conducted in terms that were inimical to what he conceived to be his interest. The planned attempt to repeat Robert Hooke's celebrated experiment by James Pound, Samuel Molyneux and George Graham was set up at Molyneux's residence in Kew with James Bradley replacing Pound after his untimely and sudden demise. The unexpected and counterintuitive behaviour of the object star γ Draconis and the eradication of any suspicion of instrumental or systemic error led to the abandonment of the attempt to measure annual parallax and the initiation of new conjectures. An annual nutation was proposed but after the observation of a control star, 35 Camelopardalis, this conjecture was abandoned. Unknown to Bradley and Graham a premature approach was made by Molyneux to Newton claiming that the 'nutation' negated the whole of Newton's system. In the abandonment of the nutation yet another conjecture opposed to Newtonian theory was proposed and abandoned. Bradley determined to use his own instrument designed on different principles by Graham to observe the phenomenon in Wanstead. At Wanstead Bradley observed many stars to determine the parameters of the phenomenon. With the law of the motion described, Bradley proposed a hypothesis to explain it. Drawn from his earlier work on the ephemerides of Jupiter's satellites his hypothesis of the 'new-discovered motion' was quickly presented to the Royal Society as Bradley was working on a later and more definitive version of his paper. It is this later, third, unpublished version that is commonly referred to throughout this essay. It issued a challenge to 'anti-Copernicans' to offer an explanation of the observed phenomenon in geostatic terms. One such astronomer, Eustachio Manfredi, had examined the phenomenon of 'aberrations' in detail, the term being his. It was Bradley who first applied the term to the 'new-discovered motion' and within a short time 'aberration' was being applied by astronomers in the reduction of their observations. Annual aberration was widely accepted as evidence of the motion of the Earth. The paper enhanced Bradley's reputation and projected him into the forefront of European astronomers.

The Search for Stellar Parallaxes and the Discovery of the Aberration of Light: The Observational Proofs of the Earth's Revolution, Eustachio Manfredi, and the ‘Bologna Case’

The Search for Stellar Parallaxes and the Discovery of the Aberration of Light: The Observational Proofs of the Earth's Revolution, Eustachio Manfredi, and the ‘Bologna Case’

Preparation of wholemount mouse intestine for high‐resolution three‐dimensional imaging using two‐photon microscopy

Visualizing overall tissue architecture in three dimensions is fundamental for validating and integrating biochemical, cell biological and visual data from less complex systems such as cultured cells. Here, we describe a method to generate high-resolution three-dimensional image data of intact mouse gut tissue. Regions of highest interest lie between 50 and 200 mum within this tissue. The quality and usefulness of three-dimensional image data of tissue with such depth is limited owing to problems associated with scattered light, photobleaching and spherical aberration. Furthermore, the highest-quality oil-immersion lenses are designed to work at a maximum distance of </=10-15 mum into the sample, further compounding the ability to image at high-resolution deep within tissue. We show that manipulating the refractive index of the mounting media and decreasing sample opacity greatly improves image quality such that the limiting factor for a standard, inverted multi-photon microscope is determined by the working distance of the objective as opposed to detectable fluorescence. This method negates the need for mechanical sectioning of tissue and enables the routine generation of high-quality, quantitative image data that can significantly advance our understanding of tissue architecture and physiology.

Toward inertial reference frames with the SIM observatory

AbstractThe SIM Lite Observatory is expected to provide a global astrometric reference frame surpassing the 1-μas accuracy threshold in some spherical harmonics. A range of time-varying physical distortions of the reference frame will become observable as large-scale perturbations of the proper motion field. I consider the main sources of the apparent and physical motion of reference objects, such as the aberration of light caused by the acceleration of SIM, long gravitational waves and hypothetical rotation of the Universe, and present some estimates of the astrometric sensitivity to these effects. I argue that a global solution and covariance analysis is of crucial importance for the SIM mission to differentiate the inevitable accidental and systematic zonal errors from real physical phenomena.

Confocal microscopy of thick specimens

Confocal microscopy is an excellent tool to gain structural information from deep within a biological sample. The depth from which information can be extracted as well as the resolution of the detection system are limited by spherical aberrations in the laser pathway. These spherical aberrations of the visible light can be efficiently canceled by optimizing the refractive index of the immersion media. Another way of cancelling spherical aberrations is by changing tube length, or alternatively, by changing the objective from infinite correction to finite correction, or vice versa, depending on which microscope is used. A combination of these two methods allows for confocal imaging at continuous depths. Presently, confocal microscopes typically operate at a maximum depth of 40 microm in the sample, but with the methods presented here, we show that information can easily be gained from depths up to 100 microm. Additionally, the precision of localization of a single fluorophore in the axial direction, limited by spherical aberrations, can be significantly improved, even if the fluorophore is located deep within the sample. In principle, this method can improve the efficiency of any kind of microscopy based on visible light.

Relativistic aberration for accelerating observers

We investigate the effects of the aberration of light for a uniformly accelerating observer. The observer is initially at rest with respect to a luminous spherical object and then starts to move away with constant acceleration. Our main results are the following: (i) The observer sees an initial increase of the apparent size of the object, (ii) the apparent size of the object approaches a nonzero value as the proper time of the observer goes to infinity, and (iii) there exists a critical value of the acceleration such that the apparent size of the object is monotonically increasing when the acceleration is supercritical. Although the first effect is purely nonrelativistic, the others are the result of the relativistic aberration of light and are intimately connected with the Lorentzian geometry of Minkowksi spacetime. The examples we present illustrate that the three effects are more or less negligible in everyday life, but significant in the context of space flight.

Evaluation of retinal image degradation by higher-order aberrations and light scatter in chick eyes after photorefractive keratectomy (PRK)

Intraocular light scatter can severely degrade retinal image quality, a key determinant of visual performance and eye growth regulation, yet it is often ignored in analyses of retinal image quality. A method for characterizing ocular light scatter using Shack–Hartmann images is described here. A local light scatter map is derived by de-convolving the dots in the Shack–Hartmann image recorded from a real eye with those from a model eye, and used to estimate overall ocular light scatter. As an index of retinal image quality, the modulation transfer function (MTF) of the eye is derived as the product of MTFs for light scatter and aberrations alone and for comparative purposes, an MTF volume ratio, equivalent to the Strehl ratio computed in the frequency domain, is computed. These analyses were applied to Shack–Hartmann images collected from three chick eyes, one day before and four days after photorefractive keratectomy (PRK) surgery. PRK was performed on one eye of each of three 4-week-old chicks; ablation parameters for a clinical argon fluorine excimer laser system from Visx® were adjusted based on the results of ablations performed on enucleated chick eyes of the same age. While all three eyes showed increased higher order aberrations after PRK, only two eyes showed significantly increased light scatter. The proposed method for characterizing retinal image quality was able to capture these interocular differences.

The effects of hydrogel contact lens wear on low contrast acuity

There is evidence to suggest that hydrogel contact lenses may cause a reduction in the contrast sensitivity function of the eye. Lens surface deposits along with lens-induced changes to the corneal tissue have been implicated. The light scattering properties of lens materials may also differ. This double-masked study was designed to investigate whether low contrast acuity varies between different contact lenses. Low contrast acuity thresholds, intraocular light scatter and aberrations were assessed for six subjects while wearing each of six different hydrogel contact lenses and also no lens. Low contrast acuity thresholds were significantly higher for lens 4 but did not differ significantly between five of the lenses and the no lens condition. Neither higher order aberrations nor intraocular light scatter differed between the six lens types but we cannot rule out the possibility of small angle scatter associated with lens 4.

Tunable blue laser compensates for thermal expansion of the medium in holographic data storage

A tunable laser optical source equipped with wavelength and mode-hop monitors was developed to compensate for thermal expansion of the medium in holographic data storage. The laser's tunable range is 402-409 nm, and supplying 90 mA of laser diode current provides an output power greater than 40 mW. The aberration of output light is less than 0.05 lambdarms. The temperature range within which the laser can compensate for thermal expansion of the medium is estimated based on the tunable range, which is +/-13.5 degrees C for glass substrates and +/-17.5 degrees C for amorphous polyolefin substrates.

A photoelastic deflector based on the spatial gradient of the refractive index in a TeO2 crystal

A new light deflector is proposed in which different polarizations are deflected in opposite directions by equal angles in the presence of nonuniform transverse mechanical pressure. The characteristics of the deflector are calculated. Light deflection is experimentally studied in a deflector based on TeO2. The experimental deflection angles are in good agreement with the calculated results. On the basis of measurements of light aberrations in crystals of various shapes, the configuration of the deflector that is optimal in terms of sensitivity and the smallness of aberrations is determined. Upon a single pass through the crystal, the deflection angles can be as high as tens of milliradians in the case when mechanical deformations are acceptable and the beam is of relatively high quality.

How to Measure Gravitational Aberration?

AbstractIn 1905, Henri Poincaré predicted the existence of gravitational waves and assumed their speed equal to the speed of light. If additionally the gravitational aberration would have the same magnitude as the aberration of light, we would observe several paradoxical phenomena. For instance, the orbit of two bodies would be unstable, since two attractive forces arise that are not in line and hence form a couple. This will be modelled by a nonautonomous system of ordinary differential equations with delay. In fact, any positive value of the gravitational aberration increases the angular momentum of such a system and this may contribute to the expansion of the universe. We found a remarkable coincidence between the Hubble constant and the increasing distance of the Moon from the Earth.In 2000, Carlip showed that in general relativity gravitational aberration is almost cancelled out by velocity–dependent interactions. We show how the actual value of the gravitational aberration can be obtained by measurement of a single angle at a suitable time t* corresponding to the perihelion of an elliptic orbit. We also derive an a priori error estimate that expresses how accurately t* has to be determined to obtain the gravitational aberration to a prescribed tolerance.

Remarks on a New Autograph Letter from Augustin Fresnel: Light Aberration and Wave Theory

ArgumentNew letters from Augustin Fresnel have been uncommon in the literature. This letter was discovered in 2003. It was written to his uncle early in the year 1815 and it gives us a glimpse of Fresnel's state of mind before he emerged on the scientific stage later that same year with a striking essay on light diffraction. In it he tells his uncle of his feelings of agitation at that time. While he believed that he had found something innovative, an explanation of starlight aberration using wave theory instead of corpuscular theory, he felt insecure about how he might deserve the attention of the scientific community, especially given the success of Newton's light theory. The subjects of aether and star aberration were decisive in leading Fresnel to develop his theory.

Relativistic aberration of light as a corollary of the relativity of simultaneity

A new derivation of the relativistic aberration formula for a plane-polarized lightwave is presented that does not require any use of the Lorentz transformation. The method is based on a modification of the Huygens–Fresnel principle to include the relativistic effects introduced by the relative motion between the observer and the emitter. The derivation clearly shows that the aberration formula is a direct consequence of the relative simultaneity.

Detecting the Aberration of the Cosmic Microwave Background

The motion of the solar system barycenter with respect to the cosmic microwave background (CMB) induces a very large apparent dipole component into the CMB brightness map at the 3 mK level. In this Letter, we discuss another kinematic effect of our motion through the CMB: the small shift in apparent angular positions due to the aberration of light. The aberration angles are only of order β 0.001, but this leads to a potentially measurable compression (expansion) of the spatial scale in the hemisphere toward (away from) our motion through the CMB. In turn, this will shift the peaks in the acoustic power spectrum of the CMB by a factor of order 1 ± β. For current CMB missions, and even those in the foreseeable future, this effect is small but should be taken into account. In principle, if the acoustic peak locations were not limited by sampling noise (i.e., the cosmic variance), this effect could be used to determine the cosmic contribution to the dipole term.

Lightlike simultaneity, comoving observers and distances in general relativity

We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, called lightlike distance, obtaining geometrical properties. We show that lightlike distance is a particular case of radar distance in the Minkowski space-time and generalizes the proper radial distance in the Schwarzschild space-time. Finally, we show that lightlike distance gives us a new concept of distance in Robertson–Walker space-times, according to Hubble law.

Chromatic assimilation: spread light or neural mechanism?

Chromatic assimilation is the shift in color appearance of a test field toward the appearance of nearby light. Possible explanations of chromatic assimilation include wavelength independent spread light, wavelength-dependent chromatic aberration and neural summation. This study evaluated these explanations by measuring chromatic assimilation from a concentric-ring pattern into an equal-energy-white background, as a function of the inducing rings’ width, separation, chromaticity and luminance. The measurements showed, in the s direction, that assimilation was observed with different inducing-ring widths and separations when the inducing luminance was lower or higher than the test luminance. In general, the thinner the inducing rings and the smaller their separation, the stronger the assimilation in s. In the l direction, either assimilation or contrast was observed, depending on the ring width, separation and luminance. Overall, the measured assimilation could not be accounted for by the joint contributions from wavelength-independent spread light and wavelength-dependent chromatic aberration. Spatial averaging of neural signals explained the assimilation in s reasonably well, but there were clear deviations from neural spatial averaging for the l direction.

SPEED OF GRAVITY AND GRAVITOMAGNETISM

A vJ/c correction to the Shapiro time delay seems verified by a 2002 Jovian observation by VLBI. In this Essay, this correction is interpreted as an effect of the aberration of light in an optically refractive medium which supplies an analog of Jupiter's gravity field rather than as a measurement of the speed of gravity, as it was first proposed by other authors. The variation of the index of refraction is induced by the Lorentz invariance of the weak gravitational field equations for Jupiter in a uniform translational slow motion with velocity vJ=13.5 km / s . The correction on time delay and deflection is due not to the Kerr (or Lense-Thirring) stationary gravitomagnetic field of Jupiter, but to its Schwarzschild gravitostatic field when measured from the barycenter of the solar system.

Aberration of light in a uniformly moving optical medium

The transverse Fresnel–Fizeau light drag in the presence of a nondispersive homogeneous optical medium in uniform rectilinear motion is explained by using a simple Huygens’ construction. As a consequence of the motion of the medium, the wavefront of every individual secondary wavelet is an ellipse partially dragged by the moving medium. The resulting formula agrees with the experiment by Jones in the early 1970s and with Fresnel’s formula for transverse light drag.