345:
250:
139:
57:
226:, the acceptance angle is one dimensional, and the concentration has only weak dependence on off-pointing perpendicular to the focus direction. Point focus systems, on the other hand, are sensitive to off-pointing in both directions. In the general case, the acceptance angle in one direction may be different from the other.
327:
contributes to a decrease in the acceptance angle of the concentrator. The acceptance angle may then be seen as a "tolerance budget" to be spent on all these imperfections. At the end, the concentrator must still have enough acceptance to capture sunlight which also has some angular dispersion
364:, as indicated by the green rays. If the acceptance angle of the optic is wide enough, sunlight incident along the optical axis will be captured by the concentrator, as shown in the "angular aperture of sunlight" figure. However, for wider incidence angles
476:
in which the receiver is immersed. In practice, real concentrators either have a lower than ideal concentration for a given acceptance or they have a lower than ideal acceptance angle for a given concentration. This can be summarized in the expression
371:
Parallel rays and sunlight are therefore transmitted differently by a solar concentrator and the corresponding transmission curves are also different. Different acceptance angles may then be determined for parallel rays or for sunlight.
462:
595:
99:
to the optical axis. For an ideal concentrator, all rays are still captured. However, on the right, this figure shows yet another set of parallel rays, now incident on the concentrator at an angle
529:
246:, the more precise the tracking needs to be or the concentrator will not capture the incoming sunlight. It is, therefore, a measure of the tolerance a concentrator has to tracking errors.
91:. All rays end up on the receiver and, therefore, all light is captured. In the center, this figure shows another set of parallel rays, now incident on the concentrator at an angle
368:
some light may be lost, as shown on the right. Perfectly parallel rays (shown in blue) would be captured, but sunlight, due to its angular aperture, is partially lost.
535:
which defines a quantity CAP (concentration acceptance product), which must be smaller than the refractive index of the medium in which the receiver is immersed.
292:
now has undulations and some of the light rays that were captured before are now lost. This decreases the transmission of the concentrator for incidence angle
41:
in which the receiver is immersed. Maximizing the acceptance angle of a concentrator is desirable in practical systems and it may be achieved by using
337:
when seen from earth. It is, therefore, very important to design a concentrator with the widest possible acceptance angle. That is possible using
278:
to the optical axis. However, real optics are never perfect and the right part of the figure shows the effect of a badly made bottom surface
397:
706:
20:
352:
Figure "angular aperture of sunlight" on the right shows the effect of the angular dispersion of sunlight on the acceptance angle.
544:
48:
For concentrators that concentrate light in two dimensions, the acceptance angle may be different in the two directions.
483:
344:
604:. The higher the CAP, the closer the concentrator is to the maximum possible in concentration and acceptance angle.
189:
In practice, real transmission curves are not perfect and they typically have a shape similar to that of curve
249:
107:
to the optical axis. All rays now miss the receiver and all light is lost. Therefore, for incidence angles
138:
257:
However, other errors also affect the acceptance angle. The "optical imperfections" figure shows this.
355:
Sunlight is not a set of perfectly parallel rays (shown in blue), but it has a given angular aperture
56:
741:
655:
306:
147:
34:
722:
702:
673:
338:
42:
663:
219:
38:
473:
725:. Note that in this derivation theta is the full angle, not the half-angle defined here.
659:
239:
735:
296:, decreasing the acceptance angle. Actually, any imperfection in the system such as:
68:
260:
The left part of the figure shows a perfectly made lens with good optical surfaces
223:
123:
all light is lost. The concentrator is then said to have a (half) acceptance angle
88:
76:
692:
622:
16:
Maximum angle at which incoming sunlight can be captured by a solar concentrator
618:
600:
The
Concentration Acceptance Product is a consequence of the conservation of
698:
677:
156:
as shown in the "transmission curves" figure. Transmission (efficiency) is
668:
643:
30:
613:
601:
384:, for a point-focus concentrator, the maximum concentration possible,
457:{\displaystyle C_{\mathrm {max} }={\frac {n^{2}}{\sin ^{2}\theta }}}
238:
of a concentrator may be seen as a measure of how precisely it must
343:
248:
137:
55:
341:, which maximize the acceptance angle for a given concentration.
538:
For a linear-focused concentrator, the equation is not squared
37:. Its value depends on the concentration of the optic and the
723:
http://www.powerfromthesun.net/Book/chapter09/chapter09.html
590:{\displaystyle C_{\mathrm {max} }={\frac {n}{\sin \theta }}}
644:"High performance Fresnel-based photovoltaic concentrator"
211:
is typically defined as the angle for which transmission
75:. The left section of the figure shows a set of parallel
204: = 0. In that case, the real acceptance angle
64:
The "acceptance angle" figure illustrates this concept.
547:
486:
400:
589:
523:
456:
694:Introduction to Nonimaging Optics, Second Edition
524:{\displaystyle CAP={\sqrt {C}}\sin \theta \leq n}
115:all light is captured while for incidence angles
274:capturing all light rays incident at an angle
642:Benitez, Pablo; et al. (26 April 2010).
8:
317:finite stiffness of the supporting structure
19:For other uses of "Acceptance angle", see
667:
569:
553:
552:
546:
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485:
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399:
131:(since it accepts light within an angle ±
79:incident on the concentrator at an angle
175: = 0 for all incidence angles
160: = 1 for all incidence angles
634:
29:is the maximum angle at which incoming
376:Concentration acceptance product (CAP)
230:Acceptance angle as a tolerance budget
7:
242:the sun in the sky. The smaller the
146:Ideally, a solar concentrator has a
314:movements of the system due to wind
560:
557:
554:
413:
410:
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218:For line-focus systems, such as a
14:
323:other imperfections in the system
311:imperfectly assembled components
621:, acceptance angle context for
472:is the refractive index of the
303:imperfectly manufactured optics
127:, or a total acceptance angle 2
196:, which is normalized so that
1:
380:For a given acceptance angle
215:drops to 90% of its maximum.
348:Angular aperture of sunlight
285:. Instead of being smooth,
758:
18:
320:deformation due to aging
691:Chaves, Julio (2015).
591:
525:
458:
349:
254:
143:
135:to the optical axis).
67:The concentrator is a
61:
592:
526:
459:
347:
253:Optical imperfections
252:
234:The acceptance angle
141:
59:
33:can be captured by a
669:10.1364/OE.18.000A25
545:
484:
398:
660:2010OExpr..18S..25B
307:optical aberrations
300:tracking inaccuracy
220:trough concentrator
200: = 1 for
142:Transmission curves
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521:
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148:transmission curve
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35:solar concentrator
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339:nonimaging optics
43:nonimaging optics
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60:Acceptance angle
39:refractive index
27:Acceptance angle
21:Acceptance angle
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654:(S1): A25-40.
648:Optics Express
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224:Fresnel lens
222:or a linear
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89:optical axis
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742:Solar power
629:References
619:Guided ray
52:Definition
699:CRC Press
582:θ
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516:≤
513:θ
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449:θ
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736:Category
678:20588570
608:See also
31:sunlight
656:Bibcode
614:Etendue
602:etendue
87:to the
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267:and
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664:doi
576:sin
507:sin
437:sin
389:max
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