Acceptance Angle (solar Concentrator)
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Acceptance angle is the maximum angle at which incoming
sunlight Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when t ...
can be captured by a
solar concentrator 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 ...
. Its value depends on the concentration of the optic and the
refractive index 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 ...
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
nonimaging optics 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 concerned wi ...
. For concentrators that concentrate light in two dimensions, the acceptance angle may be different in the two directions.


Definition

The "acceptance angle" figure illustrates this concept. The concentrator is a
lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
with a receiver ''R''. The left section of the figure shows a set of parallel rays incident on the concentrator at an angle ''α'' < ''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 propagat ...
. 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 ''α'' = ''θ'' 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 ''α'' > ''θ'' to the optical axis. All rays now miss the receiver and all light is lost. Therefore, for incidence angles ''α'' < ''θ'' all light is captured while for incidence angles ''α'' > ''θ'' all light is lost. The concentrator is then said to have a (half) acceptance angle ''θ'', or a total acceptance angle 2''θ'' (since it accepts light within an angle ±''θ'' to the optical axis). Ideally, a solar concentrator has a
transmission curve The transmission curve or transmission characteristic is the mathematical function or graph that describes the transmission fraction of an optical or electronic filter as a function of frequency or wavelength. It is an instance of a transfer fu ...
''c''I as shown in the "transmission curves" figure. Transmission (efficiency) is ''τ'' = 1 for all incidence angles ''α'' < ''θ''I and ''τ'' = 0 for all incidence angles ''α'' > ''θ''I. In practice, real transmission curves are not perfect and they typically have a shape similar to that of curve ''c''R, which is normalized so that ''τ'' = 1 for ''α'' = 0. In that case, the real acceptance angle ''θ''R is typically defined as the angle for which transmission ''τ'' drops to 90% of its maximum. For line-focus systems, such as a trough concentrator or a linear
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 ...
, 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.


Acceptance angle as a tolerance budget

The acceptance angle ''θ'' of a concentrator may be seen as a measure of how precisely it must
track Track or Tracks may refer to: Routes or imprints * Ancient trackway, any track or trail whose origin is lost in antiquity * Animal track, imprints left on surfaces that an animal walks across * Desire path, a line worn by people taking the shorte ...
the sun in the sky. The smaller the ''θ'', 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. However, other errors also affect the acceptance angle. The "optical imperfections" figure shows this. The left part of the figure shows a perfectly made lens with good optical surfaces ''s''1 and ''s''2 capturing all light rays incident at an angle ''α'' 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 ''s''2. Instead of being smooth, ''s''2 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 ''α'', decreasing the acceptance angle. Actually, any imperfection in the system such as: *tracking inaccuracy *imperfectly manufactured optics *
optical aberration In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with th ...
s *imperfectly assembled components *movements of the system due to wind *finite stiffness of the supporting structure *deformation due to aging *other imperfections in the system 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 ''θ''''S'' when seen from earth. It is, therefore, very important to design a concentrator with the widest possible acceptance angle. That is possible using
nonimaging optics 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 concerned wi ...
, which maximize the acceptance angle for a given concentration. Figure "angular aperture of sunlight" on the right shows the effect of the angular dispersion of sunlight on the acceptance angle. Sunlight is not a set of perfectly parallel rays (shown in blue), but it has a given angular aperture ''θ''''S'', 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 ''α'' 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. 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.


Concentration acceptance product (CAP)

For a given acceptance angle ''θ'', for a point-focus concentrator, the maximum concentration possible, ''C''max, is given by :C_\mathrm = \frac , where ''n'' is the refractive index of the
medium Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane * Tecma Medium, a French hang glider design Communication * Media (communication), tools used to store and deliver information or data * Medium of ...
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 :CAP = \sqrt \sin\theta \le n , 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. For a linear-focused concentrator, the equation is not squaredSee: http://www.powerfromthesun.net/Book/chapter09/chapter09.html . Note that in this derivation theta is the full angle, not the half-angle defined here. :C_\mathrm = \frac The Concentration Acceptance Product is a consequence of the conservation of
etendue Etendue or étendue (; ) is a property of light in an 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 include a ...
. The higher the CAP, the closer the concentrator is to the maximum possible in concentration and acceptance angle.


See also

*
Etendue Etendue or étendue (; ) is a property of light in an 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 include a ...
*
Guided ray A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber, which is confined by the core. For step index fiber, light entering the fiber will be guided if it falls within the acceptance cone of the fiber, that i ...
, acceptance angle context for
optic fibre An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to ...
s


References

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