Non-imaging optics: the best framework for concentrator design

Non-imaging optics (also called anidolic optics) is the branch of optics that deals with maximum efficiency power transfer from a light source to a receiver [], and, thus, it is the best framework for PV concentrator design. The term non-imaging comes from the fact that for achieving high efficiency the image formation condition is not required (but neither is it excluded, as the RX showed!), and then, in contrast to imaging optical systems, the ray-to-ray correspondence will not be restricted (see figure 13.9). This idea emerged in the mid-1960s when the first non-imaging device, the compound parabolic concentrator (CPC), was invented, and it was possible to attain the thermodynamic limit of concentration in two dimensions with a very simple device that did not have any imaging properties.

Concentrator designs in non-imaging optics are carried out within the framework of geometrical optics. Then the concentrators act as transformers of extended ray bundles. In the PV framework, the bundle of rays impinging on the surface of the entry aperture of the concentrator within a cone of acceptance angle a is called the input bundle and is denoted by Mi. The bundle of rays that links the surface of the exit aperture of the concentrator with the cell is the exit bundle Mo. Collected bundle Mc is the name given to the set made up of the rays common to Mi and Mo, connected to one another by means of the concentrator. The exit bundle Mo is a subset of MMAX, the bundle formed by all the rays that
can impinge on the cell (i. e. MMAX is the ray bundle that illuminates the cell isotropically).

There are two main groups of design problems in non-imaging optics. Although both groups have been usually treated separately in the non-imaging literature, PV concentrators constitute an example of a non-imaging design that belongs to both groups.

In the first group, which we will refer to as ‘bundle-coupling’, the design problem consists in specifying the bundles Mi and Mo, and the objective is to design the concentrator to couple the two bundles, i. e. making Mi = Mo = Mc. When Mo = MMAX, the maximum concentration condition is achieved. This design problem is arises, for instance, in solar thermal concentration or in point – to-point IR wireless links (for both emitter and receiver sets).

For the second group of design problems, ‘prescribed-irradiance’, it is only specified that one bundle must be included in the other, for example, Mi in Mo (so that Mi and Mc will coincide), with the additional condition that the bundle Mc produces a certain prescribed irradiance distribution on one target surface at the output side. As Mc is not fully specified, this problem is less restrictive than the bundle-coupling one. These designs are useful in automotive lighting, the light source being a light bulb or an LED and the target surface is the far-field, where the intensity distribution is prescribed. It is also interesting for wide-angle ceiling IR receivers in indoor wireless communications, where the receiver sensitivity is prescribed to compensate for the different link distances for multiple emitters on the desks (in this case, Mo is included in Mi, and the irradiance distribution is prescribed at the input side, at the plane of the desks).

The design problem of the perfect PV concentrator performance, as defined in section 13.1.6, can be stated with the following two design conditions: (1) coupling Mi (defined with the acceptance angle a and the squared entry aperture) and MMAX (defined with the refractive index around the cell and the squared cell active area); and (2) defining that every bundle Mj, defined as the cone with arbitrary axis direction and the sun’s radius as, if contained in Mi, must produce the same relative irradiance distribution, which is prescribed to be uniform on the squared cell’s active area. Therefore, (1) is a bundle-coupling problem at maximum concentration, while (2) is a prescribed-irradiance problem for every subset Mj. Due to the clear difficulty of this design, traditionally only partial solutions have been found, some aim at condition (1) while others aim at condition

(2) .

The two groups of designs are carried out with the help of the edge-rays. If M is a ray bundle, the topological boundary of M as a set of the phase space is called the edge-ray bundle of M (and denoted by 8M). For the two-dimensional example in figure 13.10, the rays of bundle Mi are all the rays linking the light source with the entry aperture, while its edge-rays 8Mi are only the rays passing either by the source edges or the entry aperture edges. The same applies for Mo and 8Mo. For a more detailed discussion about the definition of edge rays and the application of the theorem, see [22].

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For the first group of designs, the edge-ray theorem states that in order to couple two bundles M; and Mo, it is sufficient to couple the edge rays 8M; and 8Mo. This theorem is very useful, since it is sufficient to design for edge rays, which form a ray bundle with fewer rays (it has one dimension less). Also in the prescribed-irradiance problem, only edge rays need to be considered for the design.

Several types of optical surfaces have been typically used in non-imaging design: first, conventional refractive surfaces and mirrors, which deflect the ray bundles as in classical imaging optical systems (lenses, mirror telescopes, etc); and second, a special mirror type, called the flow-line mirror, because it coincides with a flow line of the bundle. In 2D geometry, the flow line is defined as the line which is tangent to the bisector of the ray bundle at each point. This line indicates the direction of the energy flow. In a flow-line mirror, the ray bundle is guided by the mirror which acts like a light funnel. The main practical difference between conventional and flow-line mirrors is that to achieve a high concentration-acceptance angle product, the flow-line mirrors need to touch (or be very close) to the cell. This is usually considered inconvenient, especially if the cell is small.

The previously mentioned optical surfaces can be either continuous or microstructured. Examples of microstructured surfaces are those of Fresnel or TIR lenses. Microstructured surfaces with small facets can be studied as an apparent surface (obtained by enveloping the facet vertices) with a deflection law which differs from reflection or refraction laws. Usually, microstructured surfaces are not ideal in the sense that a fraction of the microstructure output is inactive, which implies that the transmitted ray bundle will not fill the cell bundle MMAX totally. As a consequence, in these microstructures the concentration-acceptance

angle product will necessarily be lower than the bound of equation (13.1). As an example, the microstructure of a Fresnel lens concentrator is not ideal: the cell is not illuminated from the inactive nearly-vertical facets.

The non-imaging designs are usually done in 2D geometry, and the 3D device is generated by linear or by rotational symmetry. This means that only part of the real 3D rays are designed: typically, the meridian rays in the rotational concentrators and the normal rays in the linear ones. There are essentially four design methods in 2D geometry:

(1) The Welford-Winston method (also called the TERC method) [23-27]. This is the method that was used to invent the CPC and also other designs later applied to PVs, such as the DTIRC (which is a dielectric-filled CPC with a prefixed circular aperture).

(2) The flow-line method [28].

(3) The Poisson bracket method [29].

(4) The simultaneous multiple surface (SMS) design method [30].

The SMS method has proven to be, in our opinion, the most versatile and practical of the four methods. It consists in the design of at least two aspheric optical surfaces (refractive or reflective), which are calculated simultaneously and point-by-point, to produced the desired edge-ray transformation. Not only does the SMS method produce designs that can work close to the thermodynamic limit but the resulting devices also have such excellent practical features as high compactness or simplicity for manufacturing. Besides that, in contrast to the other three design methods, the SMS method does not need to use flow-line mirrors (however, flow-line mirrors can also be designed in the SMS [22]). In section 13.2.2, a description of SMS concentrators designed for high concentration systems is given.