Nonimaging optics - Knowledge (XXG)

3721: 647: 3662:. 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. 3386: 1972: 428: 1188: 2225: 1906: 2836: 2401: 3017: 901: 2083: 1807: 1674: 1568: 3002:(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. 1183:{\displaystyle {\begin{aligned}S(\tau _{\mathrm {B} })&-S(\tau _{\mathrm {A} })\\&=\int _{\mathrm {A} }^{\mathrm {B} }dS=\int _{\tau _{\mathrm {A} }}^{\tau _{\mathrm {B} }}{\frac {dS}{d\tau }}d\tau \\&=\int _{\tau _{\mathrm {A} }}^{\tau _{\mathrm {B} }}{\frac {S(\tau +d\tau )-S(\tau )}{(\tau +d\tau )-\tau }}d\tau \,.\end{aligned}}} 359:. 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 3252:. 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. 523:

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.

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itself was initially developed in 2-D by Miñano and later also by Benítez. The first generalization to 3-D geometry came from Benítez. It was then much further developed by contributions of Miñano and Benítez. Other people have worked initially with Miñano and later with Miñano and Benítez on programming the method.

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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

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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

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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

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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.

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a nonimaging optics design method known in the field as the simultaneous multiple surface (SMS) or the Miñano-Benitez design method. The abbreviation SMS comes from the fact that it enables the simultaneous design of multiple optical surfaces. The original idea came from Miñano. The design method

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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

2252:. 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 343:

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.

3308:) 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 218:

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.

86:, 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. 2079:(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. 3845:(United States), and led to the independent origin of the first nonimaging concentrators, later applied to solar energy concentration. Among these three earliest works, the one most developed was the American one, resulting in what nonimaging optics is today. 313:

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.

547:. 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 2338:

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

2302:. 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. 3094:. 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 1627:

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

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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)

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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).

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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.

1873:), 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. 2367:

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

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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

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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 (

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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 ±

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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 the

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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

1884:). 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 2499:

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

3342:. 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 3827: 2798:. 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 2213:

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

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Some of the design methods for nonimaging optics are also finding application in imaging devices, for example some with ultra-high numerical aperture.

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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

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A good introduction was published by - Winston, Roland. “Nonimaging Optics.” Scientific American, vol. 264, no. 3, 1991, pp. 76–81. JSTOR,

4352: 4224: 4200: 4180: 4160: 4047: 4013: 3993: 3875: 3271: 200: 115: 95: 3013:, only now all calculations are done in 3D space. Figure "SMS 3D chain" on the right illustrates the algorithm of an SMS 3D calculation. 1928:

to the vertical (coming from an inner point of the infinite source) is redirected towards an inner point of the receiver. However, a ray

3758: 3962: 2295:) versions of these designs have also been developed. The main application of this method is in the design of ultra-compact optics. 1607: 78:: controlling the distribution of light, typically so it is "evenly" spread over some areas and completely blocked from other areas 471:

in the source are redirected towards the target, but they are not concentrated onto a point and, therefore, no image is formed.

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When seen from the CPC, the incoming radiation (emitted from the infinite source at an infinite distance) subtends an angle ±

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or a combination of these devices. Common applications of nonimaging optics include many areas of illumination engineering (

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of the receiver since leaving a gap between mirror and receiver would allow light to escape between the two. Also, mirror

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Geometrical concentration for enhanced up-conversion: A review of recent results in energy and biomedical applications,

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Enhanced energy conversion of up-conversion solar cells by the integration of compound parabolic concentrating optics,

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I. Moreno, M. Avendaño-Alejo, and C. P. Castañeda-Almanza, "Nonimaging metaoptics," Opt. Lett. 45, 2744-2747 (2020).

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and its neighboring points of the source. The resulting device is called a CEC (Compound Elliptical Concentrator).

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When compared to "traditional" design techniques, nonimaging optics has the following advantages for illumination:

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G. E. Arnaoutakis, J. Marques-Hueso, A. Ivaturi, S. Fischer, J. C. Goldschmidt, K. W. Krämer, and B. S. Richards,

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building a new SMS chain filling the gaps between points. Picking other points and corresponding normals on curve

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design flexibility: different kinds of optics with different geometries can be tailored for different applications

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devices with the compound parabolic concentrator being to-date the most promising geometrical optics collector.

3885: 187: 165: 158: 4249: 4393:, Optik, 25, 31, 1967 (English translation of title: A light guiding device with strong concentration action) 3006: 1954:, as shown in the figure "string method" on the left. A string of constant length is attached to edge point 536: 3248:, the Hamiltonian formulation of geometrical optics which shares much of the mathematical formulation with 3659: 3295: 1585: 3746:

The compound parabolic concentrator accepts a greater amount of light and needs less accurate tracking.

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is designed in such a way that sunlight (here considered as a set of parallel rays) incident at an angle

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since cutting it short would prevent it from capturing as much light as possible, but extending it above

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defines a new point and normal on the bottom surface, by applying the same constant optical path length

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to the vertical (coming from the edge of the infinite source) is redirected by the CPC towards the edge

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The parabolic concentrator only accepts rays of light that are perpendicular to the entrance aperture

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Typically optics have refractive and reflective surfaces and light travels through media of different

3890: 287: 72:: maximizing the amount of energy applied to a receiver, typically a solar cell or a thermal receiver 4235: 4028:, SPIE Proceedings Vol. 5185, Nonimaging Optics: Maximum Efficiency Light Transfer VII, pp.1–5, 2004 2224: 1905: 2835: 2400: 2076: 689: 658:. This can be seen for refraction in the figure "constant OPL" to the right. It shows a separation 559: 325: 244: 211: 103: 3743:. The tracking of this type of concentrator must be more exact and requires expensive equipment. 3905: 3283: 3279: 3245: 3232:

the process can be repeated and more points obtained on the top and bottom surfaces of the lens.

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The string is kept stretched while moving a pencil up and down, drawing the elliptical mirror

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J. Opt. Soc. Am. B, JOSAB, vol. 39, no. 1, pp. 239–247, Jan. 2022, doi: 10.1364/JOSAB.437892.

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The simplest way to design nonimaging optics is called "the method of strings", based on the

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Nonimaging optics devices are obtained using different methods. The most important are: the

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and, therefore, are the most appropriate for use in solar concentration as, for example, in

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possible in air or in vacuum (equal to the ratio of input and output aperture areas), is:

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bisects this cone of light and, therefore, points in the direction of the "light flow" at

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in the source that end up on the receiver but are not focused onto an image point. Mirror

318: 4293:, In Progress in Optics (Wolf, E., ed.), Vol. XXV, North Holland, Amsterdam, p. 351, 1988 3724:

Comparison between non-imaging compound parabolic concentrator and parabolic concentrator

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The lens has two optical surfaces and, therefore, it is possible to design it (using the

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The development started in the mid-1960s at three different locations by V. K. Baranov (

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An example of one of these optics used for solar concentration is the Fresnel-R Köhler.

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Single crystal monolithic upconverter solar cell device tandems with integrated optics,

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Something similar happens in the situation shown in the same figure, on the right. Ray

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of the receiver, as indicated by the blue rays. By symmetry, the rays coming from edge

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becomes infinitely large and moves to an infinite distance. Then the rays coming from

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The two design problems that nonimaging optics solves better than imaging optics are:

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is related to the algorithm used by Schulz in the design of aspheric imaging lenses.

372:) is described in detail in the aforementioned textbooks. The 3D SMS design method ( 4439: 4319:, in Nonimaging Optics and Efficient Illumination Systems II, Proc. SPIE 5942, 2005 3910: 3411: 3326: 3270:

is a central concept in nonimaging optics. In concentration optics, it relates the

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of the receiver, as indicated by the red rays. The rays coming from an inner point

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and corresponding normal on the bottom surface using the same optical path length

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Collecting radiation emitted by high-energy particle collisions using the fewest

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Solid-state lighting requires specialized optical design for optimal performance

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V. K. Baranov, Geliotekhnika, 2, 11, 1966 (English translation: V. K. Baranov,

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and corresponding normal on the top surface using the same optical path length

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Similar conclusions may be drawn for the case of reflection, only in this case

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widen the applications of concentrated solar power, for example to solar lasers

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on the right illustrates this principle. A lens collects light from a source

243:). Examples of modern implementations of nonimaging optical designs include 4074: 3954: 3841:) with the study of the focons (focusing cones) Martin Ploke (Germany), and 2995:

gives us more points in between the other SMS points calculated originally.

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Concentration of sunlight to solar-surface levels using non-imaging optics

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tolerance to variations in the relative position of light source and optic

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Another SMS chain can be constructed towards the right starting at point

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surfaces simultaneously. The 3D version allows the design of optics with

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The light crossing this point is confined to a cone of angular aperture 2

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For a given concentration, nonimaging optics provide the widest possible

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Nonimaging Fresnel Lenses: Design and Performance of Solar Concentrators

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can also be obtained using the same method. Now, choosing another point

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resulting in higher tolerances (and therefore higher efficiencies) for:

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Simultaneous multiple surface optical design method in three dimensions

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combination of light sources and light distribution to different places

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Solar Cells: Operating Principles, Technology, and System Applications

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Achromatic and sharp real imaging of a point by a single aspheric lens

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For a 3-dimensional "nonimaging compound parabolic concentrator", the

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on the top surface, by applying the same constant optical path length

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can also be obtained by symmetry about the vertical axis of the lens.

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sections between successive deflections (refractions or reflections),

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and its normal on the top surface of the lens. We can now take a ray

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is the half-angle of the acceptance angle (of the larger aperture).

352:) limit of heating objects to the temperature of the Sun's surface. 4267:, Optical Engineering, July 2004, Volume 43, Issue 7, pp. 1489–1502 2059:

and these light rays are perpendicular to both, incoming wavefront

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Photovoltaic applications of Compound Parabolic Concentrator (CPC)

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Parabolotoroidal mirrors as elements of solar energy concentrators

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The situation in the middle of the figure shows a nonimaging lens

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of the receiver. This device does not form an image of the source

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Examples of nonimaging illumination optics using solar energy are

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Typical variables to be optimized at the target include the total

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is constant for all its points. The same is valid for wavefront

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G. E. Arnaoutakis, E. Favilla, M. Tonelli, and B. S. Richards,

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is calculated by the condition of constant optical path length

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is prescribed, for example, as a circle. Then the lateral wall

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of the source; instead an optimized optical system for optimal

4406:, Review of Scientific Instruments, Vol. 37, p.1094–1095, 1966 4278:

Applications of the SMS method to the design of compact optics

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The Optics of Nonimaging Concentrators: Light and Solar Energy

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In order to calculate the value of this integral, we evaluate

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Compound Parabolic Concentrator for Passive Radiative Cooling

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on the bottom surface, by using constant optical path length

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is the same for all rays perpendicular to incoming wavefront

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Lichtführungseinrichtungen mit starker Konzentrationswirkung

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Solar Energy Materials and Solar Cells 140, 217–223 (2015).

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The main disadvantage of nonimaging optics when compared to

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radiation between a source and a target. Unlike traditional

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This design method was developed by Miñano and is based on

2857:, with their corresponding normals and interpolate a curve 1503:, it may be concluded that the optical path length between 696:. Also shown are a set of rays perpendicular to wavefront 3151:

and its normal is obtained on the bottom surface. Now ray

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on the top surface, by using constant optical path length

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There are some variations to the flow-line design method.

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as it crosses the optic. In those cases a quantity called

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improve reliability and efficiency of the solar cells (in

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optics, the techniques involved do not attempt to form an

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In the drawing opposite there are two parabolic mirrors

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A particular case of this design happens when the source

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Review of SMS design methods and real-world applications

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High performance Fresnel-based photovoltaic concentrator

3619:. When it hits the second lens, it is coming from point 3576:. When it hits the second lens, it is coming from point 3480:. When it hits the second lens, it is coming from point 3300:

In some applications it is important to achieve a given

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and its normal is obtained on the top surface. With ray

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we have one condition that allows us to calculate point

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we have one condition that allows us to calculate point

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is captured by the optic; light outside it is rejected.

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become parallel rays and the same for those coming from

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Efficient light coupler for threshold Čerenkov counters

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Illumination Engineering: Design with Nonimaging Optics

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The parabolic concentrator has an entrance aperture of

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Examples of nonimaging optical devices include optical

4334:, Optics Express, Vol. 18, Issue S1, pp. A25-A40, 2010 3434:

is designed in such a way that light rays coming from

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possibility of a uniform illumination of the receiver

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The first step is to choose the incoming wavefronts

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Principles of solar concentrators of a novel design

1749:as indicated by the green rays coming from a point 4436:, SPIE Proceedings Vol. 5529, pp. 35–47, 2004 3821: 3800:{\displaystyle C={\frac {1}{\sin ^{2}\theta }}\,,} 3799: 3709:is the entrance aperture and the flat absorber is 1215:, again with the help of the same figure. We have 1182: 607: 478:on the top surface of the lens, a ray coming from 207:altogether or limit it to a few positions a year. 4419:, Solar Energy, Volume 16, Issue 2, p. 89–95,1974 4213:Nonimaging Optics: Concentration and Illumination 4140:Ultrahigh-numerical-aperture imaging concentrator 3950:Introduction to Nonimaging Optics, Second Edition 2492:on the bottom surface of the lens. The normal at 2353:and the rays perpendicular to incoming wavefront 2306:Simultaneous multiple surface (SMS) design method 2298:Another variation is the confinement of light by 2052:is then constant for all light rays reflected at 882:. The difference in optical path length for rays 286:well suited to be used with increasingly popular 703:and traveling in the medium of refractive index 3658:This combination of optical elements is called 2321: 2312: 41:that is concerned with the optimal transfer of 2548:on the top surface of the lens. The normal at 439:) so that the light rays coming from the edge 2660:on the bottom surface using another edge ray 1950:The ellipses of a CEC can be obtained by the 1499:. Since these may be arbitrary rays crossing 8: 4280:, Proceedings of the SPIE, Volume 7717, 2010 4127:https://doi.org/10.1016/j.optmat.2018.05.064 4097:https://doi.org/10.1016/j.solmat.2015.04.020 3942: 3940: 3938: 3936: 3934: 3932: 3930: 3928: 3926: 3501:also incident on the first lens at an angle 2422:of the receiver and those emitted from edge 532: 255:displays, fiber optic illumination devices, 199:Also, for low concentrations, the very wide 133:finite stiffness of the supporting structure 4367:, Opt.-Mekh. Prom., 6, 1, 1965 (in Russian) 3626:and it is redirected by the second lens to 3605:will be redirected towards a point between 3583:and it is redirected by the second lens to 3562:will be redirected towards a point between 3519:and it is redirected by the second lens to 3487:and it is redirected by the second lens to 3282:may be seen as constant a volume moving in 3240:Miñano design method using Poisson brackets 2133:is the distance between incoming wavefront 545:Miñano design method using Poisson brackets 4365:Properties of the Parabolico-thoric focons 4142:, J. Opt. Soc. Am. A, Vol. 14, No. 8, 1997 666:) between two media of refractive indices 460:of the source are redirected towards edge 446:of the source are redirected towards edge 3814: 3793: 3778: 3768: 3760: 2436:of the receiver. We first choose a point 2284:Variations to the flow-line design method 2206:. The acceptance angle of the device is 2 1702:of the receiver and, by symmetry, mirror 1608:Learn how and when to remove this message 1172: 1098: 1089: 1088: 1083: 1075: 1074: 1069: 1029: 1020: 1019: 1014: 1006: 1005: 1000: 980: 979: 973: 972: 948: 947: 920: 919: 905: 903: 725:in directions perpendicular to wavefront 599: 589: 579: 567: 3655:, also fully illuminating the receiver. 3382:, as shown in the middle of the figure. 3321:capturing sunlight incident at an angle 1869:. The resulting device is called a CPC ( 1709:redirects the rays coming from the edge 1688:redirects the rays coming from the edge 1584:Relevant discussion may be found on the 1308:. These expressions can be rewritten as 543:or Miñano-Benitez design method and the 4195:, Morgan and Claypool Publishers, 2008 3922: 3597:incident on the first lens at an angle 3554:incident on the first lens at an angle 3469:incident on the first lens at an angle 2520:. Choosing now the optical path length 2464:. Choosing now the optical path length 2217:, highlighting one of its inner points 356: 4121:G. E. Arnaoutakis and B. S. Richards, 3713:. This CPC has an acceptance angle of 3200:and its normal are obtained, with ray 2360:will be coupled to outgoing wavefront 2346:will be coupled to outgoing wavefront 718:) into the medium of refractive index 57:from a source to a target is desired. 3980: 3978: 3976: 3974: 3641:will be redirected to points between 3530:will be redirected to points between 3421:. On the other hand, nonimaging lens 3329:and concentrating it onto a receiver 391:light from the source to the target. 7: 4125:Optical Materials 83, 47–54 (2018). 4026:Taming light using nonimaging optics 3859:Technical University of Madrid (UPM) 3101:, which is now on a chosen 3D curve 2667:, and so on. The sequence of points 2429:of the source are focused onto edge 2415:of the source are focused onto edge 2185:, which is circular and centered at 411:and redirects it towards a receiver 324:Collecting luminescent radiation in 3701:is the focal point of the parabola 3681:(blue). Both parabolas are cut at 3544:, fully illuminating the receiver. 274:better handling of extended sources 130:movements of the system due to wind 4138:Pablo Benítez and Juan C. Miñano, 3172:and, with the optical path length 3137:and, with the optical path length 2977:. The process continues with rays 2861:between them. Now we pick a point 1090: 1076: 1021: 1007: 981: 974: 949: 921: 608:{\textstyle S=\sum _{i}n_{i}d_{i}} 25: 4317:Free-form integrator array optics 4193:Nonimaging Optics in Solar Energy 4151:W.T. Welford and Roland Winston, 4064:https://doi.org/10.1364/OL.391357 3369:and redirects it onto a receiver 1909:Rays showing the acceptance angle 474:Actually, if we consider a point 366:(SMS). The 2D SMS design method ( 142:other imperfections in the system 4402:H. Hinterberger and R. Winston, 4380:, Appl. Sol. Energy, 2, 9, 1966) 4347:, Prentice Hall, 1981 p.205–206 3505:will also be redirected towards 1566: 139:capture of circumsolar radiation 127:imperfectly assembled components 3693:is the focal point of parabola 3669:Compound parabolic concentrator 3112:must be perpendicular to curve 2770:defines a new point and normal 1871:Compound Parabolic Concentrator 1716:of the source towards the edge 1695:of the source towards the edge 1622:Compound Parabolic Concentrator 203:of nonimaging optics can avoid 124:imperfectly manufactured optics 3414:will be concentrated to point 3105:. The normal chosen for point 1855:converge to parabolic mirrors 1796:would shade light coming from 1154: 1139: 1134: 1128: 1119: 1104: 955: 940: 927: 912: 1: 3356:that captures the light from 2625:we can calculate a new point 2576:we can calculate a new point 2090:The shape of the top surface 1961:of the source and edge point 639:the distance in each section 362:simultaneous multiple surface 4306:, Appl. Opt., 22, 3242, 1983 4171:Ralf Leutz and Akio Suzuki, 3073:and the optical path length 3052:and the optical path length 1550:. This relationship between 654:The OPL is constant between 650:Constant optical path length 630:is the refractive index and 147:higher solar concentrations 3473:will be redirected towards 3448:and light rays coming from 2728:defines a point and normal 2408:The rays emitted from edge 1841:and the elliptical mirrors 779:is identified by parameter 761:is identified by parameter 507:will be redirected towards 489:will be redirected towards 4481: 4079:December 22, 2006, at the 3881:Concentrated photovoltaics 3293: 3259: 261:projection display systems 188:concentrated solar thermal 186:improve heat transfer (in 181:concentrated photovoltaics 166:concentrated solar thermal 159:concentrated solar thermal 152:concentrated photovoltaics 100:concentrated photovoltaics 90:Solar energy concentration 70:solar energy concentration 4004:R. John Koshel (Editor), 3494:. On the other hand, ray 3000:Total Internal Reflection 496:. Also a ray coming from 350:2nd law of thermodynamics 280:color mixing capabilities 164:lower thermal losses (in 3886:Concentrated solar power 3038:and outgoing wavefronts 2843:We pick two points, say 2704:is called an SMS chain. 1996:as a circle centered at 1986:. We can now consider a 1952:(pins and) string method 843:has optical path length 797:has optical path length 710:. These rays refract at 562:(OPL) may be defined as 157:higher temperatures (in 150:smaller solar cells (in 136:deformation due to aging 4315:Juan C. Miñano et al., 4276:Juan C. Miñano et al., 4191:Joseph J. O'Gallagher, 4155:, Academic Press, 1978 3988:, Academic Press, 2004 3984:Roland Winston et al., 3822:{\displaystyle \theta } 3280:Conservation of etendue 3256:Conservation of etendue 2900:and its normal between 2178:and outgoing wavefront 2066:and outgoing wavefront 1558:Flow-line design method 1524:and outgoing wavefront 514:. A ray coming through 4328:Pablo Benítez et al., 4263:Pablo Benítez et al., 4038:Norton, Brian (2013). 3947:Chaves, Julio (2015). 3823: 3801: 3725: 3390: 3021: 3009:is similar to the SMS 2840: 2405: 2371:designed for a source 2325: 2317: 2310:This section describes 2229: 2087: 2010:and the distance from 1976: 1910: 1811: 1678: 1184: 754:) and, therefore, ray 651: 609: 432: 4432:Oliver Dross et al., 4040:Harnessing Solar Heat 4024:William J. Cassarly, 3824: 3802: 3751:maximum concentration 3723: 3388: 3276:maximum concentration 3250:Hamiltonian mechanics 3019: 2838: 2513:and refracting it at 2403: 2227: 2174:the distance between 2085: 1974: 1908: 1809: 1676: 1554:is valid in general. 1185: 649: 610: 430: 386:In simple terms, the 375:U.S. patent 7,460,985 369:U.S. patent 6,639,733 121:less precise tracking 3891:Solid-state lighting 3813: 3759: 2893:defines a new point 2319:The design procedure 2240:is also shown whose 2038:. The distance from 1649:and its symmetrical 1577:factual accuracy is 902: 688:) is described by a 619:indicates different 566: 518:from an inner point 245:automotive headlamps 212:parabolic reflectors 104:parabolic reflectors 3660:Köhler illumination 3296:Köhler illumination 2144:on the top surface 2077:Optical path length 1760:starts at the edge 1552:rays and wavefronts 1097: 1028: 986: 690:parametric equation 560:optical path length 539:design method, the 340:published in 2008. 326:photon upconversion 277:more compact optics 223:Illumination optics 4217:Handbook of optics 4211:William Cassarly, 3906:Hamiltonian optics 3819: 3797: 3732:and a focal point 3726: 3391: 3290:Köhler integration 3246:Hamiltonian optics 3022: 2868:and its normal on 2841: 2457:and refract it at 2406: 2230: 2199:is symmetrical to 2088: 1977: 1911: 1812: 1679: 1418:. From the law of 1180: 1178: 1065: 996: 968: 652: 605: 584: 556:refractive indices 433: 431:Edge ray principle 396:Edge ray principle 388:edge ray principle 382:Edge ray principle 357:edge ray principle 309:Other applications 55:radiative transfer 18:Non-imaging optics 4460:Nonimaging optics 4353:978-0-13-822270-3 4291:Aspheric surfaces 4225:978-0-07-149890-6 4215:in Michael Bass, 4201:978-1-59829-330-2 4181:978-3-642-07531-5 4175:, Springer, 2001 4161:978-0-12-745350-7 4049:978-94-007-7275-5 4014:978-0-470-91140-2 3994:978-0-12-759751-5 3986:Nonimaging Optics 3901:Anidolic lighting 3791: 3462:. Therefore, ray 3389:Köhler integrator 2949:and refracted at 2886:and refracted at 2756:. Now a ray from 2333:freeform surfaces 1968:of the receiver. 1902:of the receiver. 1618: 1617: 1610: 1164: 1047: 643:of the ray path. 575: 437:SMS design method 299:anidolic lighting 201:acceptance angles 116:acceptance angles 96:acceptance angles 37:) is a branch of 31:Nonimaging optics 16:(Redirected from 4472: 4420: 4413: 4407: 4400: 4394: 4387: 4381: 4374: 4368: 4361: 4355: 4341: 4335: 4326: 4320: 4313: 4307: 4300: 4294: 4287: 4281: 4274: 4268: 4261: 4255: 4247: 4241: 4233: 4227: 4209: 4203: 4189: 4183: 4169: 4163: 4149: 4143: 4136: 4130: 4119: 4113: 4106: 4100: 4089: 4083: 4072: 4066: 4060: 4054: 4053: 4035: 4029: 4022: 4016: 4002: 3996: 3982: 3969: 3968: 3944: 3876:Acceptance angle 3828: 3826: 3825: 3820: 3806: 3804: 3803: 3798: 3792: 3790: 3783: 3782: 3769: 3272:acceptance angle 3266:Conservation of 3165:is refracted at 3130:is refracted at 2604:. Refracting at 1736:on the receiver 1613: 1606: 1602: 1599: 1593: 1590:reliably sourced 1570: 1569: 1562: 1549: 1498: 1473: 1450: 1417: 1360: 1307: 1259: 1214: 1189: 1187: 1186: 1181: 1179: 1165: 1163: 1137: 1099: 1096: 1095: 1094: 1093: 1082: 1081: 1080: 1079: 1058: 1048: 1046: 1038: 1030: 1027: 1026: 1025: 1024: 1013: 1012: 1011: 1010: 985: 984: 978: 977: 961: 954: 953: 952: 926: 925: 924: 881: 835: 772:. Likewise, ray 614: 612: 611: 606: 604: 603: 594: 593: 583: 377: 371: 253:instrument panel 27:Branch of optics 21: 4480: 4479: 4475: 4474: 4473: 4471: 4470: 4469: 4450: 4449: 4429: 4424: 4423: 4414: 4410: 4401: 4397: 4388: 4384: 4375: 4371: 4363:V. K. Baranov, 4362: 4358: 4342: 4338: 4327: 4323: 4314: 4310: 4301: 4297: 4288: 4284: 4275: 4271: 4262: 4258: 4248: 4244: 4234: 4230: 4210: 4206: 4190: 4186: 4170: 4166: 4150: 4146: 4137: 4133: 4120: 4116: 4107: 4103: 4090: 4086: 4081:Wayback Machine 4073: 4069: 4061: 4057: 4050: 4037: 4036: 4032: 4023: 4019: 4003: 3999: 3983: 3972: 3965: 3946: 3945: 3924: 3919: 3867: 3835: 3811: 3810: 3774: 3773: 3757: 3756: 3671: 3654: 3647: 3632: 3625: 3618: 3611: 3596: 3589: 3582: 3575: 3568: 3553: 3543: 3536: 3525: 3518: 3511: 3500: 3493: 3486: 3479: 3468: 3461: 3455:are focused on 3454: 3447: 3441:are focused on 3440: 3433: 3427: 3420: 3405: 3399: 3381: 3375: 3368: 3362: 3355: 3348: 3341: 3335: 3320: 3314: 3298: 3292: 3264: 3258: 3242: 3227: 3220: 3213: 3206: 3199: 3192: 3185: 3178: 3171: 3164: 3157: 3150: 3143: 3136: 3129: 3122: 3111: 3100: 3093: 3086: 3079: 3072: 3065: 3058: 3051: 3044: 3037: 3030: 2990: 2983: 2976: 2969: 2962: 2955: 2948: 2941: 2934: 2927: 2920: 2913: 2906: 2899: 2892: 2885: 2878: 2867: 2856: 2849: 2828: 2822: 2816: 2810: 2804: 2797: 2790: 2783: 2776: 2769: 2762: 2755: 2748: 2741: 2734: 2727: 2720: 2713: 2703: 2697: 2691: 2685: 2679: 2673: 2666: 2659: 2652: 2645: 2638: 2631: 2624: 2617: 2610: 2603: 2596: 2589: 2582: 2575: 2568: 2561: 2554: 2547: 2540: 2533: 2526: 2519: 2512: 2505: 2498: 2491: 2484: 2477: 2470: 2463: 2456: 2449: 2442: 2435: 2428: 2421: 2414: 2396: 2390: 2384:and a receiver 2383: 2377: 2366: 2359: 2352: 2345: 2308: 2286: 2279: 2272: 2265: 2258: 2205: 2198: 2192:. Lateral wall 2191: 2184: 2173: 2154: 2139: 2132: 2125: 2118: 2111: 2100: 2072: 2065: 2058: 2051: 2044: 2037: 2030: 2023: 2016: 2009: 2002: 1995: 1985: 1967: 1960: 1934: 1919: 1901: 1890: 1868: 1861: 1854: 1847: 1840: 1833: 1826: 1820: 1802: 1791: 1784: 1773: 1766: 1759: 1748: 1742: 1735: 1729: 1722: 1715: 1708: 1701: 1694: 1687: 1669: 1662: 1655: 1648: 1641: 1634: 1614: 1603: 1597: 1594: 1583: 1575:This section's 1571: 1567: 1560: 1548: 1541: 1535: 1530: 1523: 1516: 1509: 1495: 1484: 1475: 1452: 1449: 1442: 1435: 1428: 1422: 1416: 1410: 1403: 1393: 1386: 1380: 1362: 1359: 1353: 1346: 1336: 1329: 1323: 1309: 1306: 1300: 1293: 1286: 1279: 1261: 1257: 1250: 1243: 1236: 1230: 1216: 1193: 1177: 1176: 1138: 1100: 1084: 1070: 1056: 1055: 1039: 1031: 1015: 1001: 959: 958: 943: 930: 915: 900: 899: 895: 888: 880: 874: 867: 861: 854: 844: 842: 834: 828: 821: 815: 808: 798: 796: 785: 778: 767: 760: 753: 738: 731: 724: 709: 702: 692:with parameter 679: 672: 638: 629: 595: 585: 564: 563: 529: 513: 502: 495: 484: 466: 459: 452: 445: 423: 417: 410: 404: 384: 373: 367: 337: 319:photomultiplier 311: 225: 92: 63: 35:anidolic optics 28: 23: 22: 15: 12: 11: 5: 4478: 4476: 4468: 4467: 4462: 4452: 4451: 4448: 4447: 4442: 4437: 4428: 4427:External links 4425: 4422: 4421: 4408: 4395: 4382: 4369: 4356: 4343:Martin Green, 4336: 4321: 4308: 4295: 4282: 4269: 4256: 4242: 4228: 4204: 4184: 4164: 4144: 4131: 4114: 4101: 4084: 4067: 4055: 4048: 4030: 4017: 4008:, Wiley, 2013 3997: 3970: 3964:978-1482206739 3963: 3921: 3920: 3918: 3915: 3914: 3913: 3908: 3903: 3898: 3893: 3888: 3883: 3878: 3873: 3866: 3863: 3857:, part of the 3843:Roland Winston 3834: 3831: 3818: 3796: 3789: 3786: 3781: 3777: 3772: 3767: 3764: 3689:respectively. 3670: 3667: 3652: 3645: 3630: 3623: 3616: 3609: 3594: 3587: 3580: 3573: 3566: 3551: 3541: 3534: 3523: 3516: 3509: 3498: 3491: 3484: 3477: 3466: 3459: 3452: 3445: 3438: 3431: 3425: 3418: 3403: 3397: 3379: 3373: 3366: 3360: 3353: 3346: 3339: 3333: 3318: 3312: 3291: 3288: 3260:Main article: 3257: 3254: 3241: 3238: 3225: 3218: 3211: 3204: 3197: 3190: 3183: 3179:, a new point 3176: 3169: 3162: 3155: 3148: 3144:, a new point 3141: 3134: 3127: 3120: 3109: 3098: 3091: 3084: 3077: 3070: 3063: 3056: 3049: 3042: 3035: 3028: 2988: 2981: 2974: 2967: 2960: 2953: 2946: 2939: 2932: 2925: 2918: 2911: 2904: 2897: 2890: 2883: 2876: 2865: 2854: 2847: 2826: 2820: 2814: 2808: 2802: 2795: 2788: 2781: 2774: 2767: 2760: 2753: 2746: 2739: 2732: 2725: 2718: 2711: 2701: 2695: 2689: 2683: 2677: 2671: 2664: 2657: 2650: 2643: 2636: 2629: 2622: 2615: 2608: 2601: 2594: 2587: 2580: 2573: 2566: 2559: 2552: 2545: 2538: 2531: 2524: 2517: 2510: 2503: 2496: 2489: 2482: 2475: 2468: 2461: 2454: 2447: 2440: 2433: 2426: 2419: 2412: 2394: 2388: 2381: 2375: 2364: 2357: 2350: 2343: 2307: 2304: 2285: 2282: 2277: 2270: 2263: 2256: 2228:CPC flow-lines 2203: 2196: 2189: 2182: 2171: 2152: 2137: 2130: 2123: 2116: 2109: 2098: 2070: 2063: 2056: 2049: 2042: 2035: 2028: 2021: 2014: 2007: 2000: 1993: 1983: 1965: 1958: 1932: 1917: 1899: 1888: 1880:(total angle 2 1866: 1859: 1852: 1845: 1838: 1831: 1824: 1818: 1800: 1789: 1782: 1771: 1764: 1757: 1746: 1740: 1733: 1727: 1720: 1713: 1706: 1699: 1692: 1685: 1667: 1660: 1653: 1646: 1639: 1632: 1616: 1615: 1574: 1572: 1565: 1559: 1556: 1546: 1539: 1528: 1521: 1514: 1507: 1493: 1482: 1451:and therefore 1447: 1440: 1433: 1426: 1414: 1408: 1401: 1391: 1384: 1378: 1357: 1351: 1344: 1334: 1327: 1321: 1304: 1298: 1291: 1284: 1277: 1255: 1248: 1241: 1234: 1228: 1175: 1171: 1168: 1162: 1159: 1156: 1153: 1150: 1147: 1144: 1141: 1136: 1133: 1130: 1127: 1124: 1121: 1118: 1115: 1112: 1109: 1106: 1103: 1092: 1087: 1078: 1073: 1068: 1064: 1061: 1059: 1057: 1054: 1051: 1045: 1042: 1037: 1034: 1023: 1018: 1009: 1004: 999: 995: 992: 989: 983: 976: 971: 967: 964: 962: 960: 957: 951: 946: 942: 939: 936: 933: 931: 929: 923: 918: 914: 911: 908: 907: 893: 886: 878: 872: 865: 859: 852: 840: 832: 826: 819: 813: 806: 794: 783: 776: 765: 758: 751: 736: 729: 722: 707: 700: 677: 670: 634: 627: 602: 598: 592: 588: 582: 578: 574: 571: 551:is also used. 528: 527:Design methods 525: 511: 500: 493: 482: 464: 457: 450: 443: 421: 415: 408: 402: 383: 380: 336: 333: 310: 307: 295: 294: 291: 284: 281: 278: 275: 251:, illuminated 249:LCD backlights 224: 221: 216:Fresnel lenses 205:solar tracking 197: 196: 193: 192: 191: 184: 174: 173: 172: 169: 162: 155: 145: 144: 143: 140: 137: 134: 131: 128: 125: 122: 108:fresnel lenses 91: 88: 80: 79: 73: 62: 59: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 4477: 4466: 4463: 4461: 4458: 4457: 4455: 4446: 4443: 4441: 4438: 4435: 4431: 4430: 4426: 4418: 4412: 4409: 4405: 4399: 4396: 4392: 4386: 4383: 4379: 4373: 4370: 4366: 4360: 4357: 4354: 4350: 4346: 4340: 4337: 4333: 4332: 4325: 4322: 4318: 4312: 4309: 4305: 4299: 4296: 4292: 4286: 4283: 4279: 4273: 4270: 4266: 4260: 4257: 4254: 4251: 4246: 4243: 4240: 4237: 4232: 4229: 4226: 4222: 4218: 4214: 4208: 4205: 4202: 4198: 4194: 4188: 4185: 4182: 4178: 4174: 4168: 4165: 4162: 4158: 4154: 4148: 4145: 4141: 4135: 4132: 4128: 4124: 4118: 4115: 4111: 4105: 4102: 4098: 4094: 4088: 4085: 4082: 4078: 4075: 4071: 4068: 4065: 4059: 4056: 4051: 4045: 4041: 4034: 4031: 4027: 4021: 4018: 4015: 4011: 4007: 4001: 3998: 3995: 3991: 3987: 3981: 3979: 3977: 3975: 3971: 3966: 3960: 3956: 3952: 3951: 3943: 3941: 3939: 3937: 3935: 3933: 3931: 3929: 3927: 3923: 3916: 3912: 3909: 3907: 3904: 3902: 3899: 3897: 3894: 3892: 3889: 3887: 3884: 3882: 3879: 3877: 3874: 3872: 3869: 3868: 3864: 3862: 3860: 3856: 3851: 3850: 3846: 3844: 3840: 3832: 3830: 3816: 3807: 3794: 3787: 3784: 3779: 3775: 3770: 3765: 3762: 3754: 3752: 3747: 3744: 3742: 3737: 3735: 3731: 3722: 3718: 3716: 3712: 3708: 3704: 3700: 3696: 3692: 3688: 3684: 3680: 3676: 3668: 3666: 3663: 3661: 3656: 3651: 3644: 3640: 3636: 3629: 3622: 3615: 3608: 3604: 3600: 3593: 3586: 3579: 3572: 3565: 3561: 3557: 3550: 3545: 3540: 3533: 3529: 3522: 3515: 3508: 3504: 3497: 3490: 3483: 3476: 3472: 3465: 3458: 3451: 3444: 3437: 3430: 3424: 3417: 3413: 3409: 3402: 3396: 3387: 3383: 3378: 3372: 3365: 3359: 3352: 3345: 3338: 3332: 3328: 3324: 3317: 3311: 3307: 3303: 3297: 3289: 3287: 3285: 3281: 3277: 3273: 3269: 3263: 3255: 3253: 3251: 3247: 3239: 3237: 3233: 3231: 3224: 3217: 3210: 3203: 3196: 3189: 3182: 3175: 3168: 3161: 3154: 3147: 3140: 3133: 3126: 3119: 3115: 3108: 3104: 3097: 3090: 3083: 3076: 3069: 3062: 3055: 3048: 3041: 3034: 3027: 3018: 3014: 3012: 3008: 3003: 3001: 2996: 2994: 2987: 2980: 2973: 2966: 2959: 2952: 2945: 2938: 2931: 2924: 2917: 2910: 2903: 2896: 2889: 2882: 2875: 2871: 2864: 2860: 2853: 2846: 2837: 2833: 2830: 2825: 2819: 2813: 2807: 2801: 2794: 2787: 2780: 2773: 2766: 2763:refracted at 2759: 2752: 2745: 2738: 2731: 2724: 2721:refracted at 2717: 2714:. A ray from 2710: 2705: 2700: 2694: 2688: 2682: 2676: 2670: 2663: 2656: 2649: 2642: 2635: 2628: 2621: 2614: 2607: 2600: 2593: 2586: 2579: 2572: 2565: 2558: 2551: 2544: 2537: 2530: 2523: 2516: 2509: 2502: 2495: 2488: 2481: 2474: 2467: 2460: 2453: 2446: 2439: 2432: 2425: 2418: 2411: 2402: 2398: 2393: 2387: 2380: 2374: 2370: 2363: 2356: 2349: 2342: 2336: 2334: 2330: 2324: 2320: 2316: 2311: 2305: 2303: 2301: 2296: 2294: 2289: 2283: 2281: 2276: 2269: 2262: 2255: 2251: 2247: 2243: 2239: 2235: 2226: 2222: 2220: 2216: 2211: 2209: 2202: 2195: 2188: 2181: 2177: 2170: 2166: 2162: 2158: 2151: 2147: 2143: 2136: 2129: 2122: 2115: 2108: 2104: 2097: 2093: 2084: 2080: 2078: 2074: 2069: 2062: 2055: 2048: 2041: 2034: 2027: 2020: 2013: 2006: 1999: 1992: 1989: 1982: 1975:String method 1973: 1969: 1964: 1957: 1953: 1948: 1946: 1942: 1938: 1931: 1927: 1923: 1916: 1907: 1903: 1898: 1894: 1887: 1883: 1879: 1874: 1872: 1865: 1858: 1851: 1844: 1837: 1830: 1823: 1817: 1808: 1804: 1799: 1795: 1788: 1781: 1777: 1770: 1763: 1756: 1752: 1745: 1739: 1732: 1726: 1719: 1712: 1705: 1698: 1691: 1684: 1675: 1671: 1666: 1659: 1652: 1645: 1638: 1631: 1625: 1623: 1612: 1609: 1601: 1591: 1587: 1581: 1580: 1573: 1564: 1563: 1557: 1555: 1553: 1545: 1538: 1532: 1527: 1520: 1513: 1506: 1502: 1496: 1489: 1485: 1478: 1474:, leading to 1471: 1467: 1463: 1459: 1455: 1446: 1439: 1432: 1425: 1421: 1413: 1407: 1400: 1396: 1390: 1383: 1377: 1373: 1369: 1365: 1356: 1350: 1343: 1339: 1333: 1326: 1320: 1316: 1312: 1303: 1297: 1290: 1283: 1276: 1272: 1268: 1264: 1254: 1247: 1240: 1233: 1227: 1223: 1219: 1212: 1208: 1204: 1200: 1196: 1190: 1173: 1169: 1166: 1160: 1157: 1151: 1148: 1145: 1142: 1131: 1125: 1122: 1116: 1113: 1110: 1107: 1101: 1085: 1071: 1066: 1062: 1060: 1052: 1049: 1043: 1040: 1035: 1032: 1016: 1002: 997: 993: 990: 987: 969: 965: 963: 944: 937: 934: 932: 916: 909: 897: 896:is given by: 892: 885: 877: 871: 864: 858: 851: 847: 839: 831: 825: 818: 812: 805: 801: 793: 789: 782: 775: 771: 764: 757: 750: 746: 742: 735: 728: 721: 717: 713: 706: 699: 695: 691: 687: 683: 676: 669: 665: 661: 657: 648: 644: 642: 637: 633: 626: 622: 618: 600: 596: 590: 586: 580: 576: 572: 569: 561: 557: 552: 550: 546: 542: 538: 534: 526: 524: 521: 517: 510: 506: 499: 492: 488: 481: 477: 472: 470: 463: 456: 449: 442: 438: 429: 425: 420: 414: 407: 401: 397: 392: 389: 381: 379: 376: 370: 365: 364:design method 363: 358: 353: 351: 345: 341: 334: 332: 329: 327: 322: 320: 315: 308: 306: 304: 300: 292: 290:light sources 289: 285: 282: 279: 276: 273: 272: 271: 268: 266: 262: 258: 254: 250: 246: 242: 238: 235:, nonimaging 234: 231:, nonimaging 230: 222: 220: 217: 213: 208: 206: 202: 194: 189: 185: 182: 178: 177: 175: 170: 167: 163: 160: 156: 153: 149: 148: 146: 141: 138: 135: 132: 129: 126: 123: 120: 119: 117: 113: 112: 111: 109: 105: 101: 97: 89: 87: 85: 77: 74: 71: 68: 67: 66: 60: 58: 56: 52: 48: 44: 40: 36: 33:(also called 32: 19: 4416: 4415:R. Winston, 4411: 4403: 4398: 4390: 4385: 4377: 4372: 4364: 4359: 4344: 4339: 4330: 4324: 4316: 4311: 4303: 4302:Schulz, G., 4298: 4290: 4289:Schulz, G., 4285: 4277: 4272: 4264: 4259: 4252: 4245: 4238: 4231: 4216: 4212: 4207: 4192: 4187: 4172: 4167: 4152: 4147: 4139: 4134: 4122: 4117: 4109: 4104: 4092: 4087: 4070: 4058: 4042:. Springer. 4039: 4033: 4025: 4020: 4005: 4000: 3985: 3949: 3911:Winston cone 3852: 3847: 3836: 3808: 3755: 3748: 3745: 3740: 3738: 3733: 3729: 3727: 3714: 3710: 3706: 3702: 3698: 3694: 3690: 3686: 3682: 3678: 3674: 3672: 3664: 3657: 3649: 3642: 3638: 3634: 3627: 3620: 3613: 3606: 3602: 3598: 3591: 3590:. Also, Ray 3584: 3577: 3570: 3563: 3559: 3555: 3548: 3546: 3538: 3531: 3527: 3520: 3513: 3506: 3502: 3495: 3488: 3481: 3474: 3470: 3463: 3456: 3449: 3442: 3435: 3428: 3422: 3415: 3412:optical axis 3407: 3400: 3394: 3392: 3376: 3370: 3363: 3357: 3350: 3343: 3336: 3330: 3327:optical axis 3322: 3315: 3309: 3299: 3265: 3243: 3234: 3229: 3222: 3215: 3208: 3207:a new point 3201: 3194: 3193:a new point 3187: 3180: 3173: 3166: 3159: 3158:coming from 3152: 3145: 3138: 3131: 3124: 3123:coming from 3117: 3113: 3106: 3102: 3095: 3088: 3081: 3074: 3067: 3060: 3053: 3046: 3039: 3032: 3025: 3023: 3020:SMS 3D chain 3004: 2997: 2992: 2985: 2978: 2971: 2964: 2957: 2950: 2943: 2942:coming from 2936: 2935:. Now a ray 2929: 2922: 2915: 2908: 2901: 2894: 2887: 2880: 2879:coming from 2873: 2869: 2862: 2858: 2851: 2844: 2842: 2839:SMS skinning 2831: 2823: 2817: 2811: 2805: 2799: 2792: 2785: 2778: 2771: 2764: 2757: 2750: 2743: 2736: 2729: 2722: 2715: 2708: 2706: 2698: 2692: 2686: 2680: 2674: 2668: 2661: 2654: 2647: 2640: 2633: 2626: 2619: 2618:coming from 2612: 2605: 2598: 2591: 2584: 2577: 2570: 2569:coming from 2563: 2556: 2549: 2542: 2535: 2528: 2521: 2514: 2507: 2506:coming from 2500: 2493: 2486: 2479: 2472: 2465: 2458: 2451: 2450:coming from 2444: 2437: 2430: 2423: 2416: 2409: 2407: 2391: 2385: 2378: 2372: 2368: 2361: 2354: 2347: 2340: 2337: 2326: 2322: 2318: 2313: 2309: 2297: 2290: 2287: 2274: 2273:starting at 2267: 2260: 2259:starting at 2253: 2249: 2245: 2237: 2233: 2231: 2218: 2214: 2212: 2207: 2200: 2193: 2186: 2179: 2175: 2168: 2164: 2160: 2149: 2145: 2141: 2134: 2127: 2120: 2113: 2106: 2102: 2095: 2091: 2089: 2075: 2067: 2060: 2053: 2046: 2039: 2032: 2031:centered at 2025: 2018: 2011: 2004: 1997: 1990: 1980: 1978: 1962: 1955: 1949: 1944: 1940: 1936: 1935:at an angle 1929: 1925: 1921: 1920:at an angle 1914: 1913:Another ray 1912: 1896: 1892: 1891:at an angle 1885: 1881: 1877: 1875: 1863: 1856: 1849: 1842: 1835: 1828: 1821: 1815: 1813: 1797: 1793: 1786: 1779: 1775: 1774:ends at ray 1768: 1761: 1754: 1750: 1743: 1737: 1730: 1724: 1717: 1710: 1703: 1696: 1689: 1682: 1680: 1664: 1657: 1650: 1643: 1636: 1629: 1626: 1619: 1604: 1598:January 2016 1595: 1576: 1543: 1536: 1533: 1525: 1518: 1511: 1504: 1500: 1491: 1487: 1480: 1476: 1469: 1465: 1461: 1457: 1453: 1444: 1437: 1430: 1423: 1411: 1405: 1398: 1394: 1388: 1381: 1375: 1371: 1367: 1363: 1354: 1348: 1341: 1337: 1331: 1324: 1318: 1314: 1310: 1301: 1295: 1288: 1281: 1274: 1270: 1266: 1262: 1252: 1245: 1238: 1231: 1225: 1221: 1217: 1210: 1206: 1202: 1198: 1194: 1191: 898: 890: 883: 875: 869: 862: 856: 849: 845: 837: 836:. Also, ray 829: 823: 816: 810: 803: 799: 791: 787: 780: 773: 769: 762: 755: 748: 744: 740: 733: 726: 719: 715: 711: 704: 697: 693: 685: 681: 674: 667: 663: 659: 653: 640: 635: 631: 624: 616: 615:where index 553: 549:optimization 530: 519: 515: 508: 504: 497: 490: 486: 479: 475: 473: 468: 461: 454: 447: 440: 434: 418: 412: 405: 399: 395: 393: 385: 361: 354: 346: 342: 338: 330: 323: 316: 312: 296: 269: 229:light guides 226: 209: 198: 93: 84:radiant flux 81: 76:illumination 75: 69: 64: 61:Applications 34: 30: 29: 3306:illuminance 3284:phase space 1778:connecting 535:or Winston- 303:solar pipes 4454:Categories 4389:M. Ploke, 3917:References 3677:(red) and 3302:irradiance 3294:See also: 3278:possible. 2140:and point 1656:with foci 1635:with foci 1420:refraction 656:wavefronts 265:luminaires 257:LED lights 233:reflectors 3955:CRC Press 3817:θ 3788:θ 3785:⁡ 3705:The area 3274:with the 3228:on curve 2404:SMS chain 2244:at point 2236:. A line 1988:wavefront 1586:talk page 1170:τ 1161:τ 1158:− 1152:τ 1143:τ 1132:τ 1123:− 1117:τ 1108:τ 1086:τ 1072:τ 1067:∫ 1053:τ 1044:τ 1017:τ 1003:τ 998:∫ 970:∫ 945:τ 935:− 917:τ 743:at point 577:∑ 533:flow-line 4077:Archived 3896:Lighting 3865:See also 3080:between 3059:between 3005:The SMS 2963:between 2921:between 2872:. A ray 2784:between 2742:between 2639:between 2590:between 2527:between 2471:between 2329:aspheric 2300:caustics 2159:between 2157:distance 2121:n d 2114:n d 1579:disputed 739:crosses 680:, where 503:through 485:through 241:lighting 3871:Etendue 3833:History 3410:to the 3325:to the 3268:etendue 3262:Etendue 2242:tangent 2155:is the 1681:Mirror 537:Welford 394:Figure 321:tubes. 47:imaging 4465:Optics 4351: 4239:Nature 4223: 4199: 4179: 4159: 4046: 4012: 3992: 3961: 3855:CeDInt 3809:where 2611:a ray 2562:a ray 2126:where 790:. Ray 732:. Ray 335:Theory 237:lenses 114:wider 39:optics 2086:DTIRC 855:) = 51:image 43:light 4349:ISBN 4253:SPIE 4221:ISBN 4197:ISBN 4177:ISBN 4157:ISBN 4044:ISBN 4010:ISBN 3990:ISBN 3959:ISBN 3839:USSR 3697:and 3685:and 3648:and 3637:< 3612:and 3601:< 3569:and 3558:< 3537:and 3304:(or 3087:and 3066:and 3045:and 3031:and 2984:and 2970:and 2928:and 2907:and 2850:and 2791:and 2749:and 2646:and 2597:and 2534:and 2478:and 2266:and 2167:and 2163:and 1939:> 1924:< 1862:and 1848:and 1785:and 1663:and 1642:and 1510:and 1486:) = 1464:) = 1374:) = 1361:and 1317:) = 1294:) + 1273:) = 1260:and 1224:) = 1205:) − 889:and 809:) = 673:and 263:and 3776:sin 3703:DD' 3695:CC' 3679:DD' 3675:CC' 3349:to 2293:SMS 2045:to 2017:to 1810:CPC 1677:CEC 1624:). 1443:sin 1429:sin 1397:sin 1340:sin 786:on 768:on 621:ray 541:SMS 301:or 288:LED 214:or 106:or 4456:: 3973:^ 3957:. 3953:. 3925:^ 3861:. 3741:DC 3736:. 3730:DC 3717:. 3711:AB 3707:DC 3286:. 3177:23 3174:S 3142:14 3078:23 3057:14 3011:2D 3007:3D 2961:22 2954:01 2919:11 2898:01 2891:12 2866:12 2782:22 2740:11 2637:11 2588:22 2525:11 2469:22 2397:. 2280:. 2221:. 2210:. 2148:, 2073:. 1670:. 1542:= 1531:. 1462:dτ 1460:+ 1436:= 1404:+ 1395:dc 1387:+ 1372:dτ 1370:+ 1347:+ 1338:dc 1330:+ 1287:+ 1271:dτ 1269:+ 1251:+ 1237:+ 1203:dτ 1201:+ 868:+ 822:+ 424:. 305:. 267:. 259:, 247:, 4129:. 4099:. 4052:. 3967:. 3795:, 3780:2 3771:1 3766:= 3763:C 3734:F 3715:θ 3699:B 3691:A 3687:A 3683:B 3653:2 3650:R 3646:1 3643:R 3639:θ 3635:α 3631:1 3628:R 3624:2 3621:L 3617:4 3614:L 3610:3 3607:L 3603:θ 3599:α 3595:4 3592:r 3588:2 3585:R 3581:1 3578:L 3574:4 3571:L 3567:3 3564:L 3560:θ 3556:α 3552:3 3549:r 3542:2 3539:R 3535:1 3532:R 3528:θ 3524:1 3521:R 3517:2 3514:L 3510:3 3507:L 3503:θ 3499:2 3496:r 3492:2 3489:R 3485:1 3482:L 3478:3 3475:L 3471:θ 3467:1 3464:r 3460:1 3457:R 3453:2 3450:L 3446:2 3443:R 3439:1 3436:L 3432:4 3429:L 3426:3 3423:L 3419:3 3416:L 3408:θ 3404:2 3401:L 3398:1 3395:L 3380:2 3377:R 3374:1 3371:R 3367:2 3364:L 3361:1 3358:L 3354:4 3351:L 3347:3 3344:L 3340:4 3337:L 3334:3 3331:L 3323:α 3319:2 3316:L 3313:1 3310:L 3230:a 3226:0 3223:T 3219:0 3216:T 3212:4 3209:T 3205:4 3202:r 3198:2 3195:B 3191:3 3188:r 3184:2 3181:T 3170:2 3167:B 3163:3 3160:w 3156:2 3153:r 3149:2 3146:B 3139:S 3135:0 3132:T 3128:1 3125:w 3121:1 3118:r 3114:a 3110:0 3107:T 3103:a 3099:0 3096:T 3092:3 3089:w 3085:2 3082:w 3075:S 3071:4 3068:w 3064:1 3061:w 3054:S 3050:4 3047:w 3043:3 3040:w 3036:2 3033:w 3029:1 3026:w 2993:c 2989:4 2986:r 2982:3 2979:r 2975:2 2972:R 2968:2 2965:S 2958:S 2951:T 2947:2 2944:S 2940:2 2937:r 2933:1 2930:R 2926:1 2923:S 2916:S 2912:1 2909:T 2905:0 2902:T 2895:T 2888:B 2884:1 2881:R 2877:1 2874:r 2870:c 2863:B 2859:c 2855:2 2852:B 2848:1 2845:B 2827:6 2824:B 2821:4 2818:T 2815:4 2812:B 2809:2 2806:T 2803:2 2800:B 2796:2 2793:R 2789:2 2786:S 2779:S 2775:2 2772:T 2768:2 2765:B 2761:2 2758:R 2754:1 2751:R 2747:1 2744:S 2737:S 2733:2 2730:B 2726:0 2723:T 2719:1 2716:S 2712:0 2709:T 2702:5 2699:B 2696:3 2693:T 2690:3 2687:B 2684:1 2681:T 2678:1 2675:B 2672:0 2669:T 2665:5 2662:r 2658:5 2655:B 2651:1 2648:S 2644:1 2641:R 2634:S 2630:3 2627:T 2623:1 2620:R 2616:4 2613:r 2609:3 2606:B 2602:2 2599:R 2595:2 2592:S 2585:S 2581:3 2578:B 2574:2 2571:S 2567:3 2564:r 2560:1 2557:T 2553:1 2550:T 2546:1 2543:T 2539:1 2536:S 2532:1 2529:R 2522:S 2518:1 2515:B 2511:1 2508:R 2504:2 2501:r 2497:1 2494:B 2490:1 2487:B 2483:2 2480:R 2476:2 2473:S 2466:S 2462:0 2459:T 2455:2 2452:S 2448:1 2445:r 2441:0 2438:T 2434:2 2431:R 2427:2 2424:S 2420:1 2417:R 2413:1 2410:S 2395:2 2392:R 2389:1 2386:R 2382:2 2379:S 2376:1 2373:S 2369:n 2365:3 2362:w 2358:2 2355:w 2351:4 2348:w 2344:1 2341:w 2278:1 2275:R 2271:2 2268:p 2264:2 2261:R 2257:1 2254:p 2250:P 2246:P 2238:f 2234:α 2219:P 2215:θ 2208:θ 2204:1 2201:m 2197:2 2194:m 2190:1 2187:R 2183:2 2180:w 2176:Q 2172:3 2169:d 2165:Q 2161:P 2153:2 2150:d 2146:s 2142:P 2138:1 2135:w 2131:1 2128:d 2124:3 2119:+ 2117:2 2112:+ 2110:1 2107:d 2105:= 2103:S 2099:1 2096:m 2092:s 2071:2 2068:w 2064:1 2061:w 2057:1 2054:e 2050:2 2047:w 2043:1 2040:w 2036:1 2033:R 2029:2 2026:w 2022:1 2019:w 2015:1 2012:S 2008:1 2005:S 2001:1 1998:S 1994:1 1991:w 1984:1 1981:e 1966:1 1963:R 1959:1 1956:S 1945:θ 1941:θ 1937:β 1933:3 1930:r 1926:θ 1922:α 1918:2 1915:r 1900:1 1897:R 1893:θ 1889:1 1886:r 1882:θ 1878:θ 1867:2 1864:p 1860:1 1857:p 1853:2 1850:e 1846:1 1843:e 1839:2 1836:S 1832:1 1829:S 1825:2 1822:S 1819:1 1816:S 1801:1 1798:S 1794:r 1790:2 1787:R 1783:1 1780:S 1776:r 1772:2 1769:e 1765:1 1762:R 1758:2 1755:e 1751:S 1747:2 1744:R 1741:1 1738:R 1734:2 1731:S 1728:1 1725:S 1721:2 1718:R 1714:2 1711:S 1707:2 1704:e 1700:1 1697:R 1693:1 1690:S 1686:1 1683:e 1668:2 1665:R 1661:2 1658:S 1654:2 1651:e 1647:1 1644:R 1640:1 1637:S 1633:1 1630:e 1611:) 1605:( 1600:) 1596:( 1592:. 1582:. 1547:2 1544:n 1540:1 1537:n 1529:2 1526:w 1522:1 1519:w 1515:2 1512:w 1508:1 1505:w 1501:c 1497:) 1494:B 1492:τ 1490:( 1488:S 1483:A 1481:τ 1479:( 1477:S 1472:) 1470:τ 1468:( 1466:S 1458:τ 1456:( 1454:S 1448:2 1445:θ 1441:2 1438:n 1434:1 1431:θ 1427:1 1424:n 1415:4 1412:d 1409:2 1406:n 1402:1 1399:θ 1392:1 1389:n 1385:1 1382:d 1379:1 1376:n 1368:τ 1366:( 1364:S 1358:4 1355:d 1352:2 1349:n 1345:2 1342:θ 1335:2 1332:n 1328:1 1325:d 1322:1 1319:n 1315:τ 1313:( 1311:S 1305:4 1302:d 1299:2 1296:n 1292:2 1289:d 1285:1 1282:d 1280:( 1278:1 1275:n 1267:τ 1265:( 1263:S 1258:) 1256:4 1253:d 1249:3 1246:d 1244:( 1242:2 1239:n 1235:1 1232:d 1229:1 1226:n 1222:τ 1220:( 1218:S 1213:) 1211:τ 1209:( 1207:S 1199:τ 1197:( 1195:S 1174:. 1167:d 1155:) 1149:d 1146:+ 1140:( 1135:) 1129:( 1126:S 1120:) 1114:d 1111:+ 1105:( 1102:S 1091:B 1077:A 1063:= 1050:d 1041:d 1036:S 1033:d 1022:B 1008:A 994:= 991:S 988:d 982:B 975:A 966:= 956:) 950:A 941:( 938:S 928:) 922:B 913:( 910:S 894:B 891:r 887:A 884:r 879:8 876:d 873:2 870:n 866:7 863:d 860:1 857:n 853:B 850:τ 848:( 846:S 841:B 838:r 833:6 830:d 827:2 824:n 820:5 817:d 814:1 811:n 807:A 804:τ 802:( 800:S 795:A 792:r 788:c 784:B 781:τ 777:B 774:r 770:c 766:A 763:τ 759:A 756:r 752:A 749:τ 747:( 745:c 741:c 737:A 734:r 730:2 727:w 723:2 720:n 716:τ 714:( 712:c 708:1 705:n 701:1 698:w 694:τ 686:τ 684:( 682:c 678:2 675:n 671:1 668:n 664:τ 662:( 660:c 641:i 636:i 632:d 628:i 625:n 617:i 601:i 597:d 591:i 587:n 581:i 573:= 570:S 520:S 516:P 512:2 509:R 505:P 501:2 498:S 494:1 491:R 487:P 483:1 480:S 476:P 469:S 465:2 462:R 458:2 455:S 451:1 448:R 444:1 441:S 422:2 419:R 416:1 413:R 409:2 406:S 403:1 400:S 348:( 190:) 183:) 168:) 161:) 154:) 20:)

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Index