page_title: Acceptance angle (solar concentrator)
section_title: Acceptance angle as a tolerance budget
hierarchical_section_title: Acceptance angle (solar concentrator) / Acceptance angle as a tolerance budget
caption_attribution_description: English: Effect of imperfections in the acceptance angle
context_page_description: 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 acceptance angle of a concentrator is desirable in practical systems and it may be achieved by using nonimaging optics.
  For concentrators that concentrate light in two dimensions, the acceptance angle may be different in the two directions.
context_section_description: 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 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 s₁ and s₂ 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 s₂. Instead of being smooth, s₂ 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 aberrations
  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 θS 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 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 θS, 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.
caption: Optical imperfections
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