# Acceptance angle (solar concentrator)

Acceptance angle is the maximum angle at which incoming sunlight can be captured by a solar concentrator . Its value depends on the concentration of the optic and the refractive index in which the receiver is immersed. Maximizing the consensus angle of a concentrator is desirable in practical systems and it can be achieved by using nonimaging optics .

For concentrators that concentrate in two dimensions, the acceptance angle may be different in two directions.

## Definition

Acceptance angle

The “acceptance angle” is an example of this concept.

The concentrator is a lens 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 . 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 > θto 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 angle α > θ all light is lost. The concentrator is then said to have an (half) acceptance angle θ , or a total acceptance angle  (since it accepts light within an angle ± θ to the optical axis).

Transmission curves

Ideally, a solar concentrator: has a transmission curve I have shown in the “transmission curves” figure. Transmission (efficiency) is τ = 1 for all angles α < θ I and τ = 0 for all angles α > θ I .

In practice, real transmission curves are not perfect Typically And They-have a shape similar to That of curve R , qui est normalized That so τ = 1 for α = 0. In That case, the real acceptance angle θ R is defined as Typically the angle for which transmission τ drops to 90% of its maximum. 

For line-focus systems, such as has a concentrator or a linear Fresnel lens , the 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 the sun in the sky. The smaller the θ , the more precise the tracking needs to be the concentrator will not catch the incoming sunlight. It is, therefore, a measure of the tolerance has concentrator has to tracking errors.

Optical imperfections

However, other errors also affect the acceptance angle. The “optical imperfections” figure shows this.

The left portion of the Figure shows a perfectly made lens with good optical surfaces 1 and 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 2 . Instead of being white smooth, 2 now HAS Undulations and Reviews some of the light rays That Were captured before are now lost. This decreases the transmission of the concentrator for angle α incidence , decreasing the acceptance angle. Actually, any imperfection in the system such as:

• tracking inaccuracy
• imperfectly manufactured optics
• optical aberrations
• imperfectly assembled components
• movements of the system
• finite stiffness of the supporting structure
• deformation due to aging
• other imperfections in the system

to decrease in the angle of the concentrator. The acceptance angle can be seen as a “tolerance budget” to be all these imperfections. At the end, the concentrator must still have acceptance of 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 , which maximizes the acceptance angle for a given concentration.

Angular aperture of sunlight

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 angle of the optic is wide enough, the sunlight incident will be captured by the concentrator, as shown in the “angular aperture of sunlight” figure. HOWEVER, for ‘wider 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 thus 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 angle θ , for a concentrator point-focus, the maximum possible concentration, max , is given by

{\ displaystyle C _ {\ mathrm {max}} = {\ frac {n ^ {2}} {\ sin ^ {2} \ theta}}},

Where n is the refractive index of the medium in the receiver qui est Immersed.  In practice, real concentrators have a lower than ideal concentration for a given acceptance. This can be summarized in the expression

{\ displaystyle CAP = {\ sqrt {C}} \ sin \ theta \ leq n},

which defines a concentration (CAP), which must be smaller than the refractive index of the medium in which the receiver is immersed.

For a linear-focuss concentrator, the equation is not squared 

{\ displaystyle C _ {\ mathrm {max}} = {\ frac {n} {\ sin \ theta}}}

The Concentration Acceptance Product is a consequence of the extended preservation . The higher the CAP, the closer the concentrator is to the maximum possible in concentration and acceptance angle.

• Extended
• Guided ray , angle angle for optic fibers

## References

1. Jump up^ Benitez, Pablo; et al. (26 April 2010). “High performance Fresnel-based photovoltaic concentrator”. Optics Express . 18 (S1): A25. doi : 10.1364 / OE.18.000A25 .
2. Jump up^ Chaves, Julio (2015). Introduction to Nonimaging Optics, Second Edition . CRC Press . ISBN  978-1482206739 .
3. Jump up^ See:http://www.powerfromthesun.net/Book/chapter09/chapter09.html. Note that this derivation is the full angle, not the half-angle defined here. 