# Ray (optics)

In optics a ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow.[1][2] Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray theory (geometrical optics) does not describe phenomena such as interference and diffraction, which require wave theory (involving the relative phase of the rays).

## Definition

A light ray is a line (straight or curved) that is perpendicular to the light's wavefronts; its tangent is collinear with the wave vector. Light rays in homogeneous media are straight. They bend at the interface between two dissimilar media and may be curved in a medium in which the refractive index changes. Geometric optics describes how rays propagate through an optical system. Objects to be imaged are treated as collections of independent point sources, each producing spherical wavefronts and corresponding outward rays. Rays from each object point can be mathematically propagated to locate the corresponding point on the image.

A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.[3]

## Special rays

There are many special rays that are used in optical modelling to analyze an optical system. These are defined and described below, grouped by the type of system they are used to model.

### Interaction with surfaces

Diagram of rays at a surface, where ${\displaystyle \theta _{\mathrm {i} }}$ is the angle of incidence, ${\displaystyle \theta _{\mathrm {r} }}$ is the angle of reflection, and ${\displaystyle \theta _{\mathrm {R} }}$ is the angle of refraction.
• An incident ray is a ray of light that strikes a surface. The angle between this ray and the perpendicular or normal to the surface is the angle of incidence.
• The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. The angle between the surface normal and the reflected ray is known as the angle of reflection. The Law of Reflection says that for a specular (non-scattering) surface, the angle of reflection always equals the angle of incidence.
• The refracted ray or transmitted ray corresponding to a given incident ray represents the light that is transmitted through the surface. The angle between this ray and the normal is known as the angle of refraction, and it is given by Snell's Law. Conservation of energy requires that the power in the incident ray must equal the sum of the power in the refracted ray, the power in the reflected ray, and any power absorbed at the surface.
• If the material is birefringent, the refracted ray may split into ordinary and extraordinary rays, which experience different indexes of refraction when passing through the birefringent material.

### Optical systems

• A meridional ray or tangential ray is a ray that is confined to the plane containing the system's optical axis and the object point from which the ray originated.[4]
• A skew ray is a ray that does not propagate in a plane that contains both the object point and the optical axis. Such rays do not cross the optical axis anywhere, and are not parallel to it.[4]
• The marginal ray (sometimes known as an a ray or a marginal axial ray) in an optical system is the meridional ray that starts at the point where the object crosses the optical axis, and touches the edge of the aperture stop of the system.[5][6] This ray is useful, because it crosses the optical axis again at the locations where an image will be formed. The distance of the marginal ray from the optical axis at the locations of the entrance pupil and exit pupil defines the sizes of each pupil (since the pupils are images of the aperture stop).
• The principal ray or chief ray (sometimes known as the b ray) in an optical system is the meridional ray that starts at the edge of the object, and passes through the center of the aperture stop.[5][7] This ray crosses the optical axis at the locations of the pupils. As such chief rays are equivalent to the rays in a pinhole camera. The distance between the chief ray and the optical axis at an image location defines the size of the image. The marginal and chief rays together define the Lagrange invariant, which characterizes the throughput or etendue of the optical system.[8] Some authors define a "principal ray" for each object point. The principal ray starting at a point on the edge of the object may then be called the marginal principal ray.[6]
• A sagittal ray or transverse ray from an off-axis object point is a ray that propagates in the plane that is perpendicular to the meridional plane and contains the principal ray.[4] Sagittal rays intersect the pupil along a line that is perpendicular to the meridional plane for the ray's object point and passes through the optical axis. If the axis direction is defined to be the z axis, and the meridional plane is the y-z plane, sagittal rays intersect the pupil at yp=0. The principal ray is both sagittal and meridional.[4] All other sagittal rays are skew rays.
• A paraxial ray is a ray that makes a small angle to the optical axis of the system, and lies close to the axis throughout the system.[9] Such rays can be modeled reasonably well by using the paraxial approximation. When discussing ray tracing this definition is often reversed: a "paraxial ray" is then a ray that is modeled using the paraxial approximation, not necessarily a ray that remains close to the axis.[10][11]
• A finite ray or real ray is a ray that is traced without making the paraxial approximation.[11][12]
• A parabasal ray is a ray that propagates close to some defined "base ray" rather than the optical axis.[13] This is more appropriate than the paraxial model in systems that lack symmetry about the optical axis. In computer modeling, parabasal rays are "real rays", that is rays that are treated without making the paraxial approximation. Parabasal rays about the optical axis are sometimes used to calculate first-order properties of optical systems.[14]

### Fiber optics

• A meridional ray is a ray that passes through the axis of an optical fiber.
• A skew ray is a ray that travels in a non-planar zig-zag path and never crosses the axis of an optical fiber.
• A guided ray, bound ray, or trapped ray is a ray in a multi-mode optical fiber, which is confined by the core. For step index fiber, light entering the fiber will be guided if it makes an angle with the fiber axis that is less than the fiber's acceptance angle.
• A leaky ray or tunneling ray is a ray in an optical fiber that geometric optics predicts would totally reflect at the boundary between the core and the cladding, but which suffers loss due to the curved core boundary.

## References

1. ^ Moore, Ken (25 July 2005). "What is a ray?". ZEMAX Users' Knowledge Base. Retrieved 30 May 2008.
2. ^ Greivenkamp, John E. (2004). Field Guide to Geometric Optics. SPIE Field Guides. p. 2. ISBN 0819452947.
3. ^ Arthur Schuster, An Introduction to the Theory of Optics, London: Edward Arnold, 1904 online.
4. ^ a b c d Stewart, James E. (1996). Optical Principles and Technology for Engineers. CRC. p. 57. ISBN 978-0-8247-9705-8.
5. ^ a b Greivenkamp, John E. (2004). Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. SPIE. ISBN 0-8194-5294-7., p. 25 [1].
6. ^ a b Riedl, Max J. (2001). Optical Design Fundamentals for Infrared Systems. Tutorial texts in optical engineering. 48. SPIE. p. 1. ISBN 978-0-8194-4051-8.
7. ^ Malacara, Daniel and Zacarias (2003). Handbook of Optical Design (2nd ed.). CRC. p. 25. ISBN 978-0-8247-4613-1.
8. ^ Greivenkamp (2004), p. 28 [2].
9. ^ Greivenkamp (2004), pp. 19–20 [3].
10. ^ Nicholson, Mark (21 July 2005). "Understanding Paraxial Ray-Tracing". ZEMAX Users' Knowledge Base. Retrieved 17 August 2009.
11. ^ a b Atchison, David A.; Smith, George (2000). "A1: Paraxial optics". Optics of the Human Eye. Elsevier Health Sciences. p. 237. ISBN 978-0-7506-3775-6.
12. ^ Welford, W. T. (1986). "4: Finite Raytracing". Aberrations of Optical Systems. Adam Hilger series on optics and optoelectronics. CRC Press. p. 50. ISBN 978-0-85274-564-9.
13. ^ Buchdahl, H. A. (1993). An Introduction to Hamiltonian Optics. Dover. p. 26. ISBN 978-0-486-67597-8.
14. ^ Nicholson, Mark (21 July 2005). "Understanding Paraxial Ray-Tracing". ZEMAX Users' Knowledge Base. p. 2. Retrieved 17 August 2009.
EXOSAT

The European X-ray Observatory Satellite (EXOSAT), originally named HELOS, was an X-ray telescope operational from May 1983 until April 1986 and in that time made 1780 observations in the X-ray band of most classes of astronomical object including active galactic nuclei, stellar coronae, cataclysmic variables, white dwarfs, X-ray binaries, clusters of galaxies, and supernova remnants.

This European Space Agency (ESA) satellite for direct-pointing and lunar-occultation observation of X-ray sources beyond the solar system was launched into a highly eccentric orbit (apogee 200,000 km, perigee 500 km) almost perpendicular to that of the moon on May 26, 1983. The instrumentation includes two low-energy imaging telescopes (LEIT) with Wolter I X-ray optics (for the 0.04-2 keV energy range), a medium-energy experiment using Ar/CO2 and Xe/CO2 detectors (for 1.5-50 keV), a Xe/He gas scintillation spectrometer (GSPC) (covering 2-80 keV), and a reprogrammable onboard data-processing computer. Exosat was capable of observing an object (in the direct-pointing mode) for up to 80 hours and of locating sources to within at least 10 arcsec with the LEIT and about 2 arcsec with GSPC.

Geometrical optics

Geometrical optics, or ray optics, describes light propagation in terms of rays. The ray in geometric optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.

The simplifying assumptions of geometrical optics include that light rays:

propagate in straight-line paths as they travel in a homogeneous medium

bend, and in particular circumstances may split in two, at the interface between two dissimilar media

follow curved paths in a medium in which the refractive index changes

may be absorbed or reflected.Geometrical optics does not account for certain optical effects such as diffraction and interference. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of imaging, including optical aberrations.

Johannes Ullrich

Johannes Ullrich is the founder of DShield. DShield is now part of the SANS Internet Storm Center which he leads since it was created from Incidents.org and DShield back in 2001. In 2005, he was named one of the 50 most powerful people in Networking by Network World Magazine. He is the dean of research, and an instructor for the SANS Institute.Johannes grew up in Germany and moved to the US where he obtained a Ph.D. in physics from the University at Albany. His work on x-ray optics was awarded a number of research grants by NASA and the Department of Energy. He also authored a chapter in the Handbook of Optics.

Keith Nugent

Keith Alexander Nugent (born 28 June 1959) is an Australian physicist. He is Deputy Vice-Chancellor and Vice-President (Research) at La Trobe University and a Professor of Physics at the University of Melbourne, Australia specialising in X-ray optics and near-field optics. He was born in Bath, England. He received a first class honours degree from the University of Adelaide and his postgraduate degree from the Australian National University in Canberra.

In 1989 Professor Nugent in collaboration with Dr. Stephen Wilkins pioneered a form of X-ray optics known as lobster-eye optics. Using the capillary structure found in lobster eyes, Nugent and Wilkins were able to design telescopes with a 360 degree view of the sky. This was initially planned to be used in a LOBSTER satellite which would, indeed, conduct 360 degree surveys of the sky, though never came to fruition. NASA currently have plans to use the technology to view space objects and phenomena from the International Space Station.In 2001 Nugent was made a Federation Fellow by the Australian Government. This position was renewed in 2006. He also chairs the Sciences Advisory Board of IATIA, a company designed to commercialise some of his inventions. Nugent is a fellow of the Australian Academy of Science (FAA). He sits on the Advisory Board of the Australian Synchrotron.

Since 2005 Nugent has been director of the ARC Centre of Excellence for Coherent X-ray Science, based at the University of Melbourne, where he has driven the development of coherent X-ray diffraction methods for imaging biological structures. His other research focusses on the complete recovery of phase from intensity and the applications of this to imaging. This work is currently being used to monitor wear in car engines and has potential for research into the treatment of cancer.In 2011 Nugent was appointed part-time Director of the Australian Synchrotron.

He was appointed as Deputy Vice-Chancellor and Vice-President (Research) at La Trobe University in January 2013.

Light field microscopy

Light field microscopy (LFM) is a scanning-free 3-dimensional (3D) microscopic imaging method based on the theory of light field. This technique allows sub-second (~10 Hz) large volumetric imaging ([~0.1 to 1 mm]3) with ~1 μm spacial resolution in the condition of weak scattering and semi-transparence, which has never been achieved by other methods. Just as in traditional light field rendering, there are two steps for LFM imaging: light field capture and processing. In most setups, a microlens array is used to capture the light field. As for processing, it can be based on two kinds of representations of light propagation: the ray optics picture and the wave optics picture. The Stanford University Computer Graphics Laboratory published their first prototype LFM in 2006 and has been working on the cutting edge since then.

Mauritius Renninger

Mauritius Renninger (8 June 1905 – 22 December 1987) was a German theoretical physicist noted for his work on crystallography and x-ray optics. He's known for the Renninger effect and for the Renninger negative-result experiment.

Micro-X-ray fluorescence

Micro x-ray fluorescence (µXRF) is an elemental analysis technique that relies on the same principles as x-ray fluorescence (XRF). The difference is that micro x-ray fluorescence has a spatial resolution with a diameter many orders of magnitude smaller than conventional XRF. While a smaller excitation spot can be achieved by restricting x-ray beam using a pinhole aperture, this method blocks much of the x-ray flux which has an adverse effect on the sensitivity of trace elemental analysis. Two types of x-ray optics, polycapillary and doubly curved crystal focusing optics, are able to create small focal spots of just a few micrometers in diameter. By using x-ray optics, the irradiation of the focal spot is much more intense and allows for enhanced trace element analysis and better resolution of small features. Micro x-ray fluorescence using x-ray optics has been used in applications such as forensics, small feature evaluations, elemental mapping, mineralogy, electronics, multi-layered coating analysis, micro-contamination detection, film and plating thickness, biology and environment.

Modal dispersion

Modal dispersion is a distortion mechanism occurring in multimode fibers and other waveguides, in which the signal is spread in time because the propagation velocity of the optical signal is not the same for all modes. Other names for this phenomenon include multimode distortion, multimode dispersion, modal distortion, intermodal distortion, intermodal dispersion, and intermodal delay distortion.In the ray optics analogy, modal dispersion in a step-index optical fiber may be compared to multipath propagation of a radio signal. Rays of light enter the fiber with different angles to the fiber axis, up to the fiber's acceptance angle. Rays that enter with a shallower angle travel by a more direct path, and arrive sooner than rays that enter at a steeper angle (which reflect many more times off the boundaries of the core as they travel the length of the fiber). The arrival of different components of the signal at different times distorts the shape.Modal dispersion limits the bandwidth of multimode fibers. For example, a typical step-index fiber with a 50 µm core would be limited to approximately 20 MHz for a one kilometer length, in other words, a bandwidth of 20 MHz·km. Modal dispersion may be considerably reduced, but never completely eliminated, by the use of a core having a graded refractive index profile. However, multimode graded-index fibers having bandwidths exceeding 3.5 GHz·km at 850 nm are now commonly manufactured for use in 10 Gbit/s data links.

Modal dispersion should not be confused with chromatic dispersion, a distortion that results due to the differences in propagation velocity of different wavelengths of light. Modal dispersion occurs even with an ideal, monochromatic light source.

A special case of modal dispersion is polarization mode dispersion (PMD), a fiber dispersion phenomenon usually associated with single-mode fibers. PMD results when two modes that normally travel at the same speed due to fiber core geometric and stress symmetry (for example, two orthogonal polarizations in a waveguide of circular or square cross-section), travel at different speeds due to random imperfections that break the symmetry.

Optical tweezers

Optical tweezers (originally called single-beam gradient force trap) are scientific instruments that use a highly focused laser beam to provide an attractive or repulsive force (typically on the order of piconewtons), depending on the relative refractive index between particle and surrounding medium, to physically hold and move microscopic objects similar to tweezers. They are able to trap and manipulate small particles, typically order of micron in size, including dielectric and absorbing particles. Optical tweezers have been particularly successful in studying a variety of biological systems in recent years.

Physical optics

In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory.

Rigaku

Rigaku Corporation is an international manufacturer and distributor of scientific, analytical and industrial instrumentation specializing in X-ray related technologies, including X-ray crystallography, X-ray diffraction (XRD), X-ray reflectivity, X-ray fluorescence (XRF), automation, cryogenics and X-ray optics.

Schlieren imaging

Schlieren imaging is a method to visualize density variations in transparent media.

The term "schlieren imaging" is commonly used as a synonym for schlieren photography, though this article particularly treats visualization of the pressure field produced by ultrasonic transducers, generally in water or tissue-mimicking media. The method provides a two-dimensional (2D) projection image of the acoustic beam in real-time ("live video").

The unique properties of the method enable the investigation of specific features of the acoustic field (e.g. focal point in HIFU transducers), detection of acoustic beam-profile irregularities (e.g. due to defects in transducer) and on-line identification of time-dependent phenomena

(e.g. in phased array transducers). Some researchers say that schlieren imaging is equivalent to an X-ray radiograph of the acoustic field.

Spherical aberration

Spherical aberration is a type of aberration found in optical systems that use elements with spherical surfaces. Lenses and curved mirrors are most often made with surfaces that are spherical, because this shape is easier to form than non-spherical curved surfaces. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems.

Traveling microscope

A travelling microscope is an instrument for measuring length with a resolution typically in the order of 0.01mm. The precision is such that better-quality instruments have measuring scales made from Invar to avoid misreadings due to thermal effects. The instrument comprises a microscope mounted on two rails fixed to, or part of a very rigid bed. The position of the microscope can be varied coarsely by sliding along the rails, or finely by turning a screw. The eyepiece is fitted with fine cross-hairs to fix a precise position, which is then read off the vernier scale. Some instruments, such as that produced in the 1960s by the Precision Tool and Instrument Company of Thornton Heath, Surrey, England, also measure vertically. The purpose of the microscope is to aim at reference marks with much higher accuracy than is possible using the naked eye. It is used in laboratories to measure the refractive index of liquids using the geometrical concepts of ray optics. It is also used to measure very short distances precisely, for example the diameter of a capillary tube. This mechanical instrument has now largely been superseded by electronic- and optically-based measuring devices that are both very much more accurate and considerably cheaper to produce.

Travelling microscope consists of a cast iron base with machined-Vee-top surface and is fitted with three levelling screws. A metallic carriage, clamped to a spring-loaded bar slides with its attached vernier and reading lens along an inlaid strip of metal scale. The scale is divided in half millimeters. Fine adjustments are made by means of a micrometer screw for taking accurate reading. Both vernier reading to 0.01mm or 0.02mm. Microscope tube consists of 10x Eyepice and 15mm or 50mm or 75mm objectives. The Microscope, with its rack and pinion attachment is mounted on a vertical slide, which too, runs with an attached vernier along the vertical scale. The microscope is free to rotate n vertical plane. The vertical guide bar is coupled to the horizontal carriage of the microscope. for holding objects a horizontal stage made of a milki conolite sheet is provided in the base.

X-ray optics

X-ray optics is the branch of optics that manipulates X-rays instead of visible light. It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, X-ray astronomy etc.

Since X-rays and visible light are both electromagnetic waves they propagate in space in the same way, but because of the much higher frequency and photon energy of X-rays they interact with matter very differently. Visible light is easily redirected using lenses and mirrors, but because the refractive index of all materials is very close to 1 for X-rays, they instead tend to initially penetrate and eventually get absorbed in most materials without changing direction much.

X-ray telescope

An X-ray telescope (XRT) is a telescope that is designed to observe remote objects in the X-ray spectrum. In order to get above the Earth's atmosphere, which is opaque to X-rays, X-ray telescopes must be mounted on high altitude rockets, balloons or artificial satellites.

The basic elements of the telescope are the optics (focusing or collimating), that collects the radiation entering the telescope, and the detector, on which the radiation is collected and measured. A variety of different designs and technologies have been used for these elements.

Many of the existing telescopes on satellites are compounded of multiple copies or variations of a detector-telescope system, whose capabilities add or complement each other and additional fixed or removable elements (filters, spectrometers) that add functionalities to the instrument.

Yvette Cauchois

Yvette Cauchois (French pronunciation: [ivɛt koʃwa] (listen); 19 December 1908 – 19 November 1999) was a French physicist known for her contributions to x-ray spectroscopy and x-ray optics, and for pioneering European synchrotron research.

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