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Nonimaging optics (also called anidolic optics)Roland Winston et al., ''Nonimaging Optics'', Academic Press, 2004 R. John Koshel (Editor), ''Illumination Engineering: Design with Nonimaging Optics'', Wiley, 2013 is the branch of
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
concerned with the optimal transfer of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
radiation between a source and a target. Unlike traditional imaging optics, the techniques involved do not attempt to form an
image An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensio ...
of the source; instead an optimized optical system for optimal
radiative transfer Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative trans ...
from a source to a target is desired.


Applications

The two design problems that nonimaging optics solves better than imaging optics are: * solar energy concentration: maximizing the amount of energy applied to a receiver, typically a solar cell or a thermal receiver * illumination: controlling the distribution of light, typically so it is "evenly" spread over some areas and completely blocked from other areas Typical variables to be optimized at the target include the total
radiant flux In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spe ...
, the angular distribution of optical radiation, and the spatial distribution of optical radiation. These variables on the target side of the optical system often must be optimized while simultaneously considering the collection efficiency of the optical system at the source.


Solar energy concentration

For a given concentration, nonimaging optics provide the widest possible acceptance angles and, therefore, are the most appropriate for use in solar concentration as, for example, in concentrated photovoltaics. When compared to "traditional" imaging optics (such as
parabolic reflector A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface genera ...
s or
fresnel lens A Fresnel lens ( ; ; or ) is a type of composite compact lens developed by the French physicist Augustin-Jean Fresnel (1788–1827) for use in lighthouses. It has been called "the invention that saved a million ships." The design allows the c ...
es), the main advantages of nonimaging optics for concentrating solar energy are: *wider acceptance angles resulting in higher tolerances (and therefore higher efficiencies) for: **less precise tracking **imperfectly manufactured optics **imperfectly assembled components **movements of the system due to wind **finite stiffness of the supporting structure **deformation due to aging **capture of circumsolar radiation **other imperfections in the system *higher solar concentrations **smaller solar cells (in concentrated photovoltaics) **higher temperatures (in concentrated solar thermal) **lower thermal losses (in concentrated solar thermal) **widen the applications of concentrated solar power, for example to solar lasers *possibility of a uniform illumination of the receiver **improve reliability and efficiency of the solar cells (in concentrated photovoltaics) **improve heat transfer (in concentrated solar thermal) *design flexibility: different kinds of optics with different geometries can be tailored for different applications Also, for low concentrations, the very wide acceptance angles of nonimaging optics can avoid
solar tracking A solar tracker is a device that orients a payload toward the Sun. Payloads are usually solar panels, parabolic troughs, fresnel reflectors, lenses or the mirrors of a heliostat. For flat-panel photovoltaic systems, trackers are used to m ...
altogether or limit it to a few positions a year. The main disadvantage of nonimaging optics when compared to
parabolic reflector A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface genera ...
s or
Fresnel lens A Fresnel lens ( ; ; or ) is a type of composite compact lens developed by the French physicist Augustin-Jean Fresnel (1788–1827) for use in lighthouses. It has been called "the invention that saved a million ships." The design allows the c ...
es is that, for high concentrations, they typically have one more optical surface, slightly decreasing efficiency. That, however, is only noticeable when the optics are aiming perfectly towards the sun, which is typically not the case because of imperfections in practical systems.


Illumination optics

Examples of nonimaging optical devices include optical light guides, nonimaging
reflector Reflector may refer to: Science * Reflector, a device that causes reflection (for example, a mirror or a retroreflector) * Reflector (photography), used to control lighting contrast * Reflecting telescope * Reflector (antenna), the part of an ...
s, nonimaging lenses or a combination of these devices. Common applications of nonimaging optics include many areas of illumination engineering (
lighting Lighting or illumination is the deliberate use of light to achieve practical or aesthetic effects. Lighting includes the use of both artificial light sources like lamps and light fixtures, as well as natural illumination by capturing dayl ...
). Examples of modern implementations of nonimaging optical designs include automotive headlamps, LCD backlights, illuminated instrument panel displays, fiber optic illumination devices,
LED light An LED lamp or LED light bulb is an electric light that produces light using light-emitting diodes (LEDs). LED lamps are significantly more energy-efficient than equivalent incandescent lamps and can be significantly more efficient than mo ...
s, projection display systems and
luminaire A light fixture (US English), light fitting (UK English), or luminaire is an electrical device containing an Lamp (electrical component), electric lamp that provides Lighting, illumination. All light fixtures have a fixture body and one or more ...
s. When compared to "traditional" design techniques, nonimaging optics has the following advantages for illumination: *better handling of extended sources *more compact optics *color mixing capabilities *combination of light sources and light distribution to different places *well suited to be used with increasingly popular LED light sources *tolerance to variations in the relative position of light source and optic Examples of nonimaging illumination optics using solar energy are
anidolic lighting Anidolic lighting systems use anidolic optical components to light rooms. Light redirected by these systems does not converge to a focal point or form an image, hence the name (from ''an'', without, and ''eidolon'', image). Anidolic lighting use ...
or solar pipes.


Other applications

Modern portable and wearable optical devices, and systems of small sizes and low weights may require nanotechnology. This issue may be addressed by nonimaging metaoptics, which uses metalenses and metamirrors to deal with the optimal transfer of light energy. Collecting radiation emitted by high-energy particle collisions using the fewest
photomultiplier A photomultiplier is a device that converts incident photons into an electrical signal. Kinds of photomultiplier include: * Photomultiplier tube, a vacuum tube converting incident photons into an electric signal. Photomultiplier tubes (PMTs for sh ...
tubes. Collecting luminescent radiation in
photon upconversion A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
devices with the compound parabolic concentrator being to-date the most promising geometrical optics collector. Some of the design methods for nonimaging optics are also finding application in imaging devices, for example some with ultra-high numerical aperture.


Theory

Early academic research in nonimaging optical mathematics seeking closed form solutions was first published in textbook form in a 1978 book. A modern textbook illustrating the depth and breadth of research and engineering in this area was published in 2004. A thorough introduction to this field was published in 2008. Special applications of nonimaging optics such as Fresnel lenses for solar concentration or solar concentration in general have also been published, although this last reference by O'Gallagher describes mostly the work developed some decades ago. Other publications include book chapters. Imaging optics can concentrate sunlight to, at most, the same flux found at the surface of the sun. Nonimaging optics have been demonstrated to concentrate sunlight to 84,000 times the ambient intensity of sunlight, exceeding the flux found at the surface of the sun, and approaching the theoretical (
2nd law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
) limit of heating objects to the temperature of the sun's surface. The simplest way to design nonimaging optics is called "the method of strings", based on the edge ray principle. Other more advanced methods were developed starting in the early 1990s that can better handle extended light sources than the edge-ray method. These were developed primarily to solve the design problems related to solid state automobile headlamps and complex illumination systems. One of these advanced design methods is the ''simultaneous multiple surface'' design method (SMS). The 2D SMS design method () is described in detail in the aforementioned textbooks. The 3D SMS design method () was developed in 2003 by a team of optical scientists at Light Prescriptions Innovators.


Edge ray principle

In simple terms, the edge ray principle states that if the light rays coming from the edges of the source are redirected towards the edges of the receiver, this will ensure that all light rays coming from the inner points in the source will end up on the receiver. There is no condition on image formation, the only goal is to transfer the light from the source to the target. Figure ''Edge ray principle'' on the right illustrates this principle. A lens collects light from a source S1S2 and redirects it towards a receiver R1R2. The lens has two optical surfaces and, therefore, it is possible to design it (using the SMS design method) so that the light rays coming from the edge S1 of the source are redirected towards edge R1 of the receiver, as indicated by the blue rays. By symmetry, the rays coming from edge S2 of the source are redirected towards edge R2 of the receiver, as indicated by the red rays. The rays coming from an inner point S in the source are redirected towards the target, but they are not concentrated onto a point and, therefore, no image is formed. Actually, if we consider a point P on the top surface of the lens, a ray coming from S1 through P will be redirected towards R1. Also a ray coming from S2 through P will be redirected towards R2. A ray coming through P from an inner point S in the source will be redirected towards an inner point of the receiver. This lens then guarantees that all light from the source crossing it will be redirected towards the receiver. However, no image of the source is formed on the target. Imposing the condition of image formation on the receiver would imply using more optical surfaces, making the optic more complicated, but would not improve light transfer between source and target (since all light is already transferred). For that reason nonimaging optics are simpler and more efficient than imaging optics in transferring radiation from a source to a target.


Design methods

Nonimaging optics devices are obtained using different methods. The most important are: the flow-line or Winston- Welford design method, the
SMS Short Message/Messaging Service, commonly abbreviated as SMS, is a text messaging service component of most telephone, Internet and mobile device systems. It uses standardized communication protocols that let mobile devices exchange short text ...
or Miñano-Benitez design method and the Miñano design method using Poisson brackets. The first (flow-line) is probably the most used, although the second (SMS) has proven very versatile, resulting in a wide variety of optics. The third has remained in the realm of theoretical optics and has not found real world application to date. Often
optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
is also used. Typically optics have refractive and reflective surfaces and light travels through media of different
refractive indices In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
as it crosses the optic. In those cases a quantity called
optical path length In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the product of the geometric length of the optical path followed by light and the refractive index of homogeneous medium throu ...
(OPL) may be defined as S = \sum_i n_i d_i where index ''i'' indicates different
ray Ray may refer to: Fish * Ray (fish), any cartilaginous fish of the superorder Batoidea * Ray (fish fin anatomy), a bony or horny spine on a fin Science and mathematics * Ray (geometry), half of a line proceeding from an initial point * Ray (gr ...
sections between successive deflections (refractions or reflections), ''n''i is the refractive index and ''d''''i'' the distance in each section ''i'' of the ray path. The OPL is constant between
wavefront In physics, the wavefront of a time-varying '' wave field'' is the set ( locus) of all points having the same '' phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal fr ...
s. This can be seen for refraction in the figure "constant OPL" to the right. It shows a separation ''c''(''τ'') between two media of refractive indices ''n''1 and ''n''2, where ''c''(''τ'') is described by a
parametric equation In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric obj ...
with parameter ''τ''. Also shown are a set of rays perpendicular to wavefront ''w''1 and traveling in the medium of refractive index ''n''1. These rays refract at ''c''(''τ'') into the medium of refractive index ''n''2 in directions perpendicular to wavefront ''w''2. Ray ''r''A crosses ''c'' at point ''c''(''τ''A) and, therefore, ray ''r''A is identified by parameter ''τ''A on ''c''. Likewise, ray ''r''B is identified by parameter ''τ''B on ''c''. Ray ''r''A has optical path length . Also, ray ''r''B has optical path length . The difference in optical path length for rays ''r''A and ''r''B is given by: : S(\tau_\text) - S(\tau_\text) = \int_\text^B dS = \int_^ \fracd\tau = \int_^ \fracd\tau In order to calculate the value of this integral, we evaluate , again with the help of the same figure. We have and . These expressions can be rewritten as and . From the law of
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...
and therefore , leading to . Since these may be arbitrary rays crossing ''c'', it may be concluded that the optical path length between ''w''1 and ''w''2 is the same for all rays perpendicular to incoming wavefront ''w''1 and outgoing wavefront ''w''2. Similar conclusions may be drawn for the case of reflection, only in this case . This relationship between rays and wavefronts is valid in general.


Flow-line design method

The flow-line (or Winston-Welford) design method typically leads to optics which guide the light confining it between two reflective surfaces. The best known of these devices is the CPC ( Compound Parabolic Concentrator). These types of optics may be obtained, for example, by applying the edge ray of nonimaging optics to the design of mirrored optics, as shown in figure "CEC" on the right. It is composed of two elliptical mirrors ''e''1 with foci S1 and R1 and its symmetrical ''e''2 with foci S2 and R2. Mirror ''e''1 redirects the rays coming from the edge S1 of the source towards the edge R1 of the receiver and, by symmetry, mirror ''e''2 redirects the rays coming from the edge S2 of the source towards the edge R2 of the receiver. This device does not form an image of the source S1S2 on the receiver R1R2 as indicated by the green rays coming from a point S in the source that end up on the receiver but are not focused onto an image point. Mirror ''e''2 starts at the edge R1 of the receiver since leaving a gap between mirror and receiver would allow light to escape between the two. Also, mirror ''e''2 ends at ray r connecting S1 and R2 since cutting it short would prevent it from capturing as much light as possible, but extending it above r would shade light coming from S1 and its neighboring points of the source. The resulting device is called a CEC (Compound Elliptical Concentrator). A particular case of this design happens when the source S1S2 becomes infinitely large and moves to an infinite distance. Then the rays coming from S1 become parallel rays and the same for those coming from S2 and the elliptical mirrors ''e''1 and ''e''2 converge to parabolic mirrors ''p''1 and ''p''2. The resulting device is called a CPC ( Compound Parabolic Concentrator), and shown in the "CPC" figure on the left. CPCs are the most common seen nonimaging optics. They are often used to demonstrate the difference between Imaging optics and nonimaging optics. When seen from the CPC, the incoming radiation (emitted from the infinite source at an infinite distance) subtends an angle ±''θ'' (total angle 2''θ''). This is called the acceptance angle of the CPC. The reason for this name can be appreciated in the figure "rays showing the acceptance angle" on the right. An incoming ray ''r''1 at an angle ''θ'' to the vertical (coming from the edge of the infinite source) is redirected by the CPC towards the edge R1 of the receiver. Another ray ''r''2 at an angle ''α''<''θ'' to the vertical (coming from an inner point of the infinite source) is redirected towards an inner point of the receiver. However, a ray ''r''3 at an angle ''β''>''θ'' to the vertical (coming from a point outside the infinite source) bounces around inside the CPC until it is rejected by it. Therefore, only the light inside the acceptance angle ±''θ'' is captured by the optic; light outside it is rejected. The ellipses of a CEC can be obtained by the (pins and) string method, as shown in the figure "string method" on the left. A string of constant length is attached to edge point S1 of the source and edge point R1 of the receiver. The string is kept stretched while moving a pencil up and down, drawing the elliptical mirror ''e''1. We can now consider a
wavefront In physics, the wavefront of a time-varying '' wave field'' is the set ( locus) of all points having the same '' phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal fr ...
''w''1 as a circle centered at S1. This wavefront is perpendicular to all rays coming out of S1 and the distance from S1 to ''w''1 is constant for all its points. The same is valid for wavefront ''w''2 centered at R1. The distance from ''w''1 to ''w''2 is then constant for all light rays reflected at ''e''1 and these light rays are perpendicular to both, incoming wavefront ''w''1 and outgoing wavefront ''w''2.
Optical path length In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the product of the geometric length of the optical path followed by light and the refractive index of homogeneous medium throu ...
(OPL) is constant between wavefronts. When applied to nonimaging optics, this result extends the string method to optics with both refractive and reflective surfaces. Figure "DTIRC" (Dielectric Total Internal Reflection Concentrator) on the left shows one such example. The shape of the top surface ''s'' is prescribed, for example, as a circle. Then the lateral wall ''m''1 is calculated by the condition of constant optical path length ''S''=''d''1+''n d''2+''n d''3 where ''d''1 is the distance between incoming wavefront ''w''1 and point P on the top surface ''s'', ''d''2 is the
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
between P and Q and ''d''3 the distance between Q and outgoing wavefront ''w''2, which is circular and centered at R1. Lateral wall ''m''2 is symmetrical to ''m''1. The acceptance angle of the device is 2''θ''. These optics are called flow-line optics and the reason for that is illustrated in figure "CPC flow-lines" on the right. It shows a CPC with an acceptance angle 2''θ'', highlighting one of its inner points P. The light crossing this point is confined to a cone of angular aperture 2''α''. A line ''f'' is also shown whose
tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...
at point P bisects this cone of light and, therefore, points in the direction of the "light flow" at P. Several other such lines are also shown in the figure. They all bisect the edge rays at each point inside the CPC and, for that reason, their tangent at each point points in the direction of the flow of light. These are called flow-lines and the CPC itself is just a combination of flow line ''p''1 starting at R2 and ''p''2 starting at R1.


=Variations to the flow-line design method

= There are some variations to the flow-line design method. A variation are the multichannel or stepped flow-line optics in which light is split into several "channels" and then recombined again into a single output. Aplanatic (a particular case of
SMS Short Message/Messaging Service, commonly abbreviated as SMS, is a text messaging service component of most telephone, Internet and mobile device systems. It uses standardized communication protocols that let mobile devices exchange short text ...
) versions of these designs have also been developed. The main application of this method is in the design of ultra-compact optics. Another variation is the confinement of light by caustics. Instead of light being confined by two reflective surfaces, it is confined by a reflective surface and a caustic of the edge rays. This provides the possibility to add lossless non-optical surfaces to the optics.


Simultaneous multiple surface (SMS) design method

This section describes The design procedure The SMS (or Miñano-Benitez) design method is very versatile and many different types of optics have been designed using it. The 2D version allows the design of two (although more are also possible) aspheric surfaces simultaneously. The 3D version allows the design of optics with freeform surfaces (also called anamorphic) surfaces which may not have any kind of symmetry. SMS optics are also calculated by applying a constant optical path length between wavefronts. Figure "SMS chain" on the right illustrates how these optics are calculated. In general, the rays perpendicular to incoming wavefront ''w''1 will be coupled to outgoing wavefront ''w''4 and the rays perpendicular to incoming wavefront ''w''2 will be coupled to outgoing wavefront ''w''3 and these wavefronts may be any shape. However, for the sake of simplicity, this figure shows a particular case or circular wavefronts. This example shows a lens of a given refractive index ''n'' designed for a source S1S2 and a receiver R1R2. The rays emitted from edge S1 of the source are focused onto edge R1 of the receiver and those emitted from edge S2 of the source are focused onto edge R2 of the receiver. We first choose a point T0 and its normal on the top surface of the lens. We can now take a ray ''r''1 coming from S2 and refract it at T0. Choosing now the optical path length ''S''22 between S2 and R2 we have one condition that allows us to calculate point B1 on the bottom surface of the lens. The normal at B1 can also be calculated from the directions of the incoming and outgoing rays at this point and the refractive index of the lens. Now we can repeat the process taking a ray ''r''2 coming from R1 and refracting it at B1. Choosing now the optical path length ''S''11 between R1 and S1 we have one condition that allows us to calculate point T1 on the top surface of the lens. The normal at T1 can also be calculated from the directions of the incoming and outgoing rays at this point and the refractive index of the lens. Now, refracting at T1 a ray ''r''3 coming from S2 we can calculate a new point B3 and corresponding normal on the bottom surface using the same optical path length ''S''22 between S2 and R2. Refracting at B3 a ray ''r''4 coming from R1 we can calculate a new point T3 and corresponding normal on the top surface using the same optical path length ''S''11 between R1 and S1. The process continues by calculating another point B5 on the bottom surface using another edge ray ''r''5, and so on. The sequence of points T0 B1 T1 B3 T3 B5 is called an SMS chain. Another SMS chain can be constructed towards the right starting at point T0. A ray from S1 refracted at T0 defines a point and normal B2 on the bottom surface, by using constant optical path length ''S''11 between S1 and R1. Now a ray from R2 refracted at B2 defines a new point and normal T2 on the top surface, by using constant optical path length ''S''22 between S2 and R2. The process continues as more points are added to the SMS chain. In this example shown in the figure, the optic has a left-right symmetry and, therefore, points B2 T2 B4 T4 B6 can also be obtained by symmetry about the vertical axis of the lens. Now we have a sequence of spaced points on the plane. Figure "SMS skinning" on the left illustrates the process used to fill the gaps between points, completely defining both optical surfaces. We pick two points, say B1 and B2, with their corresponding normals and interpolate a curve ''c'' between them. Now we pick a point B12 and its normal on ''c''. A ray ''r''1 coming from R1 and refracted at B12 defines a new point T01 and its normal between T0 and T1 on the top surface, by applying the same constant optical path length ''S''11 between S1 and R1. Now a ray ''r''2 coming from S2 and refracted at T01 defines a new point and normal on the bottom surface, by applying the same constant optical path length ''S''22 between S2 and R2. The process continues with rays ''r''3 and ''r''4 building a new SMS chain filling the gaps between points. Picking other points and corresponding normals on curve ''c'' gives us more points in between the other SMS points calculated originally. In general, the two SMS optical surfaces do not need to be refractive. Refractive surfaces are noted R (from Refraction) while reflective surfaces are noted X (from the Spanish word refleXión).
Total Internal Reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflect ...
(TIR) is noted I. Therefore, a lens with two refractive surfaces is an RR optic, while another configuration with a reflective and a refractive surface is an XR optic. Configurations with more optical surfaces are also possible and, for example, if light is first refracted (R), then reflected (X) then reflected again by TIR (I), the optic is called an RXI. The SMS 3D is similar to the SMS 2D, only now all calculations are done in 3D space. Figure "SMS 3D chain" on the right illustrates the algorithm of an SMS 3D calculation. The first step is to choose the incoming wavefronts ''w''1 and ''w''2 and outgoing wavefronts ''w''3 and ''w''4 and the optical path length ''S''14 between ''w''1 and ''w''4 and the optical path length ''S''23 between ''w''2 and ''w''3. In this example the optic is a lens (an RR optic) with two refractive surfaces, so its refractive index must also be specified. One difference between the SMS 2D and the SMS 3D is on how to choose initial point T0, which is now on a chosen 3D curve ''a''. The normal chosen for point T0 must be perpendicular to curve ''a''. The process now evolves similarly to the SMS 2D. A ray ''r''1 coming from ''w''1 is refracted at T0 and, with the optical path length ''S''14, a new point B2 and its normal is obtained on the bottom surface. Now ray ''r''2 coming from ''w''3 is refracted at B2 and, with the optical path length ''S ''23, a new point T2 and its normal is obtained on the top surface. With ray ''r''3 a new point B2 and its normal are obtained, with ray ''r''4 a new point T4 and its normal are obtained, and so on. This process is performed in 3D space and the result is a 3D SMS chain. As with the SMS 2D, a set of points and normals to the left of T0 can also be obtained using the same method. Now, choosing another point T0 on curve ''a'' the process can be repeated and more points obtained on the top and bottom surfaces of the lens. The power of the SMS method lies in the fact that the incoming and outgoing wavefronts can themselves be free-form, giving the method great flexibility. Also, by designing optics with reflective surfaces or combinations of reflective and refractive surfaces, different configurations are possible.


Miñano design method using Poisson brackets

This design method was developed by Miñano and is based on Hamiltonian optics, the Hamiltonian formulation of geometrical optics which shares much of the mathematical formulation with
Hamiltonian mechanics Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
. It allows the design of optics with variable refractive index, and therefore solves some nonimaging problems that are not solvable using other methods. However, manufacturing of variable refractive index optics is still not possible and this method, although potentially powerful, did not yet find a practical application.


Conservation of etendue

Conservation of
etendue Etendue or étendue (; ) is a property of light in an optics, optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue i ...
is a central concept in nonimaging optics. In concentration optics, it relates the acceptance angle with the maximum concentration possible. Conservation of etendue may be seen as constant a volume moving in
phase space In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usuall ...
.


Köhler integration

In some applications it is important to achieve a given
irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
(or illuminance) pattern on a target, while allowing for movements or inhomogeneities of the source. Figure "Köhler integrator" on the right illustrates this for the particular case of solar concentration. Here the light source is the sun moving in the sky. On the left this figure shows a lens L1 L2 capturing sunlight incident at an angle ''α'' to the
optical axis An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens, microscope or telescopic sight. The optical axis is an imaginary line that defines the path along which light pro ...
and concentrating it onto a receiver L3 L4. As seen, this light is concentrated onto a hotspot on the receiver. This may be a problem in some applications. One way around this is to add a new lens extending from L3 to L4 that captures the light from L1 L2 and redirects it onto a receiver R1 R2, as shown in the middle of the figure. The situation in the middle of the figure shows a nonimaging lens L1 L2 is designed in such a way that sunlight (here considered as a set of parallel rays) incident at an angle ''θ'' to the
optical axis An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens, microscope or telescopic sight. The optical axis is an imaginary line that defines the path along which light pro ...
will be concentrated to point L3. On the other hand, nonimaging lens L3 L4 is designed in such a way that light rays coming from L1 are focused on R2 and light rays coming from L2 are focused on R1. Therefore, ray ''r''1 incident on the first lens at an angle ''θ'' will be redirected towards L3. When it hits the second lens, it is coming from point L1 and it is redirected by the second lens to R2. On the other hand, ray ''r''2 also incident on the first lens at an angle ''θ'' will also be redirected towards L3. However, when it hits the second lens, it is coming from point L2 and it is redirected by the second lens to R1. Intermediate rays incident on the first lens at an angle ''θ'' will be redirected to points between R1 and R2, fully illuminating the receiver. Something similar happens in the situation shown in the same figure, on the right. Ray ''r''3 incident on the first lens at an angle ''α''<''θ'' will be redirected towards a point between L3 and L4. When it hits the second lens, it is coming from point L1 and it is redirected by the second lens to R2. Also, Ray ''r''4 incident on the first lens at an angle ''α''<''θ'' will be redirected towards a point between L3 and L4. When it hits the second lens, it is coming from point L2 and it is redirected by the second lens to R1. Intermediate rays incident on the first lens at an angle ''α''<''θ'' will be redirected to points between R1 and R2, also fully illuminating the receiver. This combination of optical elements is called
Köhler illumination Köhler illumination is a method of specimen illumination used for transmitted and reflected light (trans- and epi-illuminated) optical microscopy. Köhler illumination acts to generate an even illumination of the sample and ensures that an image o ...
. Although the example given here was for solar energy concentration, the same principles apply for illumination in general. In practice, Köhler optics are typically not designed as a combination of nonimaging optics, but they are simplified versions with a lower number of active optical surfaces. This decreases the effectiveness of the method, but allows for simpler optics. Also, Köhler optics are often divided into several sectors, each one of them channeling light separately and then combining all the light on the target. An example of one of these optics used for solar concentration is the Fresnel-R Köhler.


Compound parabolic concentrator

In the drawing opposite there are two parabolic mirrors CC' (red) and DD' (blue). Both parabolas are cut at B and A respectively. A is the focal point of parabola CC' and B is the focal point of the parabola DD' The area DC is the entrance aperture and the flat absorber is AB. This CPC has an acceptance angle of ''θ''. The parabolic concentrator has an entrance aperture of DC and a focal point F. The parabolic concentrator only accepts rays of light that are perpendicular to the entrance aperture DC. The tracking of this type of concentrator must be more exact and requires expensive equipment. The compound parabolic concentrator accepts a greater amount of light and needs less accurate tracking. For a 3-dimensional "nonimaging compound parabolic concentrator", the maximum concentration possible in air or in vacuum (equal to the ratio of input and output aperture areas), is: C = \frac, where \theta is the half-angle of the acceptance angle (of the larger aperture).


History

The development started in the mid-1960s at three different locations by V. K. Baranov (
USSR The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nati ...
) with the study of the focons (focusing cones) Martin Ploke (Germany), and
Roland Winston Roland Winston (born March 12, 1936) is a leading figure in the field of nonimaging optics and its applications to solar energy, and is sometimes termed the "father of non-imaging optics". He is the inventor of the Nonimaging optics#Compound parabol ...
(United States), and led to the independent origin of the first nonimaging concentrators, later applied to solar energy concentration.R. Winston, ''Principles of solar concentrators of a novel design'', Solar Energy, Volume 16, Issue 2, p. 89–95,1974 Among these three earliest works, the one most developed was the American one, resulting in what nonimaging optics is today. A good introduction was published by - Winston, Roland. “Nonimaging Optics.” Scientific American, vol. 264, no. 3, 1991, pp. 76–81. JSTOR

There are different commercial companies and universities working on nonimaging optics. Currently the largest research group in this subject is the Advanced Optics group at th
CeDInt
part of the Technical University of Madrid#Research, Technical University of Madrid (UPM).


See also

*
Etendue Etendue or étendue (; ) is a property of light in an optics, optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue i ...
* Acceptance angle * Concentrated photovoltaics *
Concentrated solar power Concentrated solar power (CSP, also known as concentrating solar power, concentrated solar thermal) systems generate solar power by using mirrors or lenses to concentrate a large area of sunlight into a receiver. Electricity is generated when ...
*
Solid-state lighting Solid-state lighting (SSL) is a type of lighting that uses semiconductor light-emitting diodes (LEDs), organic light-emitting diodes (OLED), or polymer light-emitting diodes (PLED) as sources of illumination rather than electrical filaments, pl ...
*
Lighting Lighting or illumination is the deliberate use of light to achieve practical or aesthetic effects. Lighting includes the use of both artificial light sources like lamps and light fixtures, as well as natural illumination by capturing dayl ...
*
Anidolic lighting Anidolic lighting systems use anidolic optical components to light rooms. Light redirected by these systems does not converge to a focal point or form an image, hence the name (from ''an'', without, and ''eidolon'', image). Anidolic lighting use ...
* Hamiltonian optics *
Winston cone A Winston cone is a non-imaging light collector in the shape of an off-axis parabola of revolution with a reflective inner surface. It concentrates the light passing through a relatively large entrance aperture through a smaller exit aperture. The ...


References


External links

* Oliver Dross et al.
Review of SMS design methods and real-world applications
SPIE Proceedings Vol. 5529, pp. 35–47, 2004
Compound Parabolic Concentrator for Passive Radiative Cooling

Photovoltaic applications of Compound Parabolic Concentrator (CPC)
{{DEFAULTSORT:Nonimaging Optics Optics