Introduction to Nonimaging Optics (Optical Science and Engineering)

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The amount of material covered by Chaves is enormous, ranging from the Winston-Welford design method to Kohler optics and to luminaries. This book is aimed at optical engineers and designers of all levels; however, it is not meant to serve as an introduction to geometrical optics.

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It could be through conference attendance, group discussion or directed reading to name just a few examples. We provide a free online form to document your learning and a certificate for your records. Already read this title? Please accept our apologies for any inconvenience this may cause. Exclusive web offer for individuals. Add to Wish List. Toggle navigation Additional Book Information. Tailored edge-ray concentrators as ideal second stages for Fresnel reflectors J.

Complementary construction of ideal nonimaging concentrators and its applications J. Integral design method for nonimaging concentrators D. New method of design of nonimaging concentrators Juan C. Geometrical vector flux and some new nonimaging concentrators R.

Modest, Radiative Heat Transfer Academic, Goldstein, Classical Mechanics Addison-Wesley, Figure 1 Comparison between imaging left and nonimaging right optics. Figure 2 Elliptical paradox where the imaging optics fails. Figure 3 Typical setup of a concentrator. Figure 5 Radiative heat transfer between areas 1 and 2.

Figure 6 Discrete representation of the phase space. Figure 7 Dense representation of the phase space. Figure 11 Setup of edge rays or wavefronts.

Illumination Engineering: Design with Nonimaging Optics

Figure 12 Using simple straight line reflectors to form the concentrator. Figure 13 Mapping points to edge rays. Figure 14 Phase space of a CPC. Figure 15 Difference between nonimaging and imaging optics. Figure 16 Ray 1 cannot red square interchange its position with a ray blue square that is not originally inside the boundary. Figure 17 In order for the ray 1 to interchange its phase space position, it will have to merge with a small phase space that was originally not on the boundary.

Figure 18 Merging of the edge ray with an internal ray in their phase space representations. Figure 19 CPC design for a tubular absorber. For a thin lens in air, the location of the image is given by the simple equation. In the sign convention used here, the object and image distances are positive if the object and image are on opposite sides of the lens. Incoming parallel rays are focused by a converging lens onto a spot one focal length from the lens, on the far side of the lens.

This is called the rear focal point of the lens. Rays from an object at finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. With diverging lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at a spot one focal length in front of the lens. This is the lens's front focal point. Rays from an object at finite distance are associated with a virtual image that is closer to the lens than the focal point, and on the same side of the lens as the object.

The closer the object is to the lens, the closer the virtual image is to the lens. As with mirrors, upright images produced by a single lens are virtual, while inverted images are real. Lenses suffer from aberrations that distort images. Monochromatic aberrations occur because the geometry of the lens does not perfectly direct rays from each object point to a single point on the image, while chromatic aberration occurs because the index of refraction of the lens varies with the wavelength of the light. In physical optics, light is considered to propagate as a wave.

This model predicts phenomena such as interference and diffraction , which are not explained by geometric optics. The speed of light waves in air is approximately 3. The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated.

These waves propagate at the speed of light and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves. Many simplified approximations are available for analysing and designing optical systems. Most of these use a single scalar quantity to represent the electric field of the light wave, rather than using a vector model with orthogonal electric and magnetic vectors.

This was derived empirically by Fresnel in , based on Huygens' hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition of waves. The Kirchhoff diffraction equation , which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens—Fresnel principle can be found in the sections on diffraction and Fraunhofer diffraction.

More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with the detailed interaction of light with materials where the interaction depends on their electric and magnetic properties. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarised light. Numerical modeling techniques such as the finite element method , the boundary element method and the transmission-line matrix method can be used to model the propagation of light in systems which cannot be solved analytically.

Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions. All of the results from geometrical optics can be recovered using the techniques of Fourier optics which apply many of the same mathematical and analytical techniques used in acoustic engineering and signal processing. Gaussian beam propagation is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused.

Gaussian beam propagation thus bridges the gap between geometric and physical optics. In the absence of nonlinear effects, the superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances. If two waves of the same wavelength and frequency are in phase , both the wave crests and wave troughs align. This results in constructive interference and an increase in the amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice versa.

This results in destructive interference and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect. Since the Huygens—Fresnel principle states that every point of a wavefront is associated with the production of a new disturbance, it is possible for a wavefront to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns. The appearance of thin films and coatings is directly affected by interference effects.

Antireflective coatings use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimise glare and unwanted reflections. The simplest case is a single layer with thickness one-fourth the wavelength of incident light. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength.

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Constructive interference in thin films can create strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make dielectric mirrors , interference filters , heat reflectors , and filters for colour separation in colour television cameras. This interference effect is also what causes the colourful rainbow patterns seen in oil slicks. Diffraction is the process by which light interference is most commonly observed. The effect was first described in by Francesco Maria Grimaldi , who also coined the term from the Latin diffringere , 'to break into pieces'.

The first physical optics model of diffraction that relied on the Huygens—Fresnel principle was developed in by Thomas Young in his interference experiments with the interference patterns of two closely spaced slits.

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Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles. In general, the equation takes the form. This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a diffraction grating that contains a large number of slits at equal spacing. X-ray diffraction makes use of the fact that atoms in a crystal have regular spacing at distances that are on the order of one angstrom.

To see diffraction patterns, x-rays with similar wavelengths to that spacing are passed through the crystal. Diffraction effects limit the ability for an optical detector to optically resolve separate light sources. In general, light that is passing through an aperture will experience diffraction and the best images that can be created as described in diffraction-limited optics appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern , and the central bright lobe as an Airy disk.

If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. Rayleigh defined the somewhat arbitrary " Rayleigh criterion " that two points whose angular separation is equal to the Airy disk radius measured to first null, that is, to the first place where no light is seen can be considered to be resolved.

It can be seen that the greater the diameter of the lens or its aperture, the finer the resolution. For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric scattering and dispersion which cause stars to twinkle. Astronomers refer to this effect as the quality of astronomical seeing. Techniques known as adaptive optics have been used to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit.

Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is Thomson scattering which occurs when electromagnetic waves are deflected by single particles. In the limit of Thomson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to Compton scattering which is frequency-dependent and strictly a quantum mechanical process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as Rayleigh scattering while the similar process for scattering by particles that are similar or larger in wavelength is known as Mie scattering with the Tyndall effect being a commonly observed result.

A small proportion of light scattering from atoms or molecules may undergo Raman scattering , wherein the frequency changes due to excitation of the atoms and molecules.

Brillouin scattering occurs when the frequency of light changes due to local changes with time and movements of a dense material. Dispersion occurs when different frequencies of light have different phase velocities , due either to material properties material dispersion or to the geometry of an optical waveguide waveguide dispersion.

The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called "normal dispersion". It occurs in all dielectric materials , in wavelength ranges where the material does not absorb light.

This is called "anomalous dispersion". The separation of colours by a prism is an example of normal dispersion. Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known rainbow pattern. Material dispersion is often characterised by the Abbe number , which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the propagation constant. If D is less than zero, the medium is said to have positive dispersion or normal dispersion.

If D is greater than zero, the medium has negative dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more than the lower frequency components. The pulse therefore becomes positively chirped , or up-chirped , increasing in frequency with time.

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Conversely, if a pulse travels through an anomalously negatively dispersive medium, high frequency components travel faster than the lower ones, and the pulse becomes negatively chirped , or down-chirped , decreasing in frequency with time. The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fibres , since if dispersion is too high, a group of pulses representing information will each spread in time and merge, making it impossible to extract the signal.

Polarization is a general property of waves that describes the orientation of their oscillations. For transverse waves such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction linear polarization , or the oscillation direction may rotate as the wave travels circular or elliptical polarization.

Circularly polarised waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's chirality. The typical way to consider polarization is to keep track of the orientation of the electric field vector as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y with z indicating the direction of travel.

The shape traced out in the x-y plane by the electric field vector is a Lissajous figure that describes the polarization state. The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation. In the leftmost figure above, the x and y components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector the vector sum of these two components is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarization.

The direction of this line depends on the relative amplitudes of the two components. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: In this special case, the electric vector traces out a circle in the plane, so this polarization is called circular polarization.

The rotation direction in the circle depends on which of the two phase relationships exists and corresponds to right-hand circular polarization and left-hand circular polarization. This is shown in the above figure on the right. Detailed mathematics of polarization is done using Jones calculus and is characterised by the Stokes parameters. Media that have different indexes of refraction for different polarization modes are called birefringent. For example, this is the case with macroscopic crystals of calcite , which present the viewer with two offset, orthogonally polarised images of whatever is viewed through them.

It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in In addition, the phase shift, and thus the change in polarization state, is usually frequency dependent, which, in combination with dichroism , often gives rise to bright colours and rainbow-like effects. In mineralogy , such properties, known as pleochroism , are frequently exploited for the purpose of identifying minerals using polarization microscopes. Additionally, many plastics that are not normally birefringent will become so when subject to mechanical stress , a phenomenon which is the basis of photoelasticity.

Media that reduce the amplitude of certain polarization modes are called dichroic , with devices that block nearly all of the radiation in one mode known as polarizing filters or simply " polarisers ". A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. In addition to birefringence and dichroism in extended media, polarization effects can also occur at the reflective interface between two materials of different refractive index.

These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected, with the ratio depending on angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle. Most sources of electromagnetic radiation contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be correlated , in which case the light is said to be unpolarised.

If there is partial correlation between the emitters, the light is partially polarised. If the polarization is consistent across the spectrum of the source, partially polarised light can be described as a superposition of a completely unpolarised component, and a completely polarised one.

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One may then describe the light in terms of the degree of polarization , and the parameters of the polarization ellipse. Light reflected by shiny transparent materials is partly or fully polarised, except when the light is normal perpendicular to the surface. Polarization occurs when light is scattered in the atmosphere. The scattered light produces the brightness and colour in clear skies. This partial polarization of scattered light can be taken advantage of using polarizing filters to darken the sky in photographs. Optical polarization is principally of importance in chemistry due to circular dichroism and optical rotation " circular birefringence " exhibited by optically active chiral molecules.

Modern optics encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics.

A major subfield of modern optics, quantum optics , deals with specifically quantum mechanical properties of light. Quantum optics is not just theoretical; some modern devices, such as lasers, have principles of operation that depend on quantum mechanics. Light detectors, such as photomultipliers and channeltrons , respond to individual photons.

Electronic image sensors , such as CCDs , exhibit shot noise corresponding to the statistics of individual photon events. Light-emitting diodes and photovoltaic cells , too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with quantum electronics. Specialty areas of optics research include the study of how light interacts with specific materials as in crystal optics and metamaterials. Other research focuses on the phenomenology of electromagnetic waves as in singular optics , non-imaging optics , non-linear optics , statistical optics , and radiometry.

Additionally, computer engineers have taken an interest in integrated optics , machine vision , and photonic computing as possible components of the "next generation" of computers. Today, the pure science of optics is called optical science or optical physics to distinguish it from applied optical sciences, which are referred to as optical engineering.

Prominent subfields of optical engineering include illumination engineering , photonics , and optoelectronics with practical applications like lens design , fabrication and testing of optical components , and image processing. Some of these fields overlap, with nebulous boundaries between the subjects terms that mean slightly different things in different parts of the world and in different areas of industry. A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in laser technology.

OSA | Nonimaging optics: a tutorial

A laser is a device that emits light electromagnetic radiation through a process called stimulated emission. Because the microwave equivalent of the laser, the maser , was developed first, devices that emit microwave and radio frequencies are usually called masers. The first application of lasers visible in the daily lives of the general population was the supermarket barcode scanner, introduced in Fibre-optic communication relies on lasers to transmit large amounts of information at the speed of light.

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