Abstract:
A quasi-parabolic reflector and method are provided for a solar concentrator which produces a unique radiation pattern which is less susceptible to surface defects, less sensitive to target distance irregularities, and having greater uniformity of intensity for PV applications in comparison to that produced by true parabolic reflectors. Cross-sections of the quasi-parabolic reflector include spaced reflective surfaces which have focal areas spaced one from the other about an axis of symmetry. A method for forming petals of a quasi-parabolic reflector includes stamping them into shape using a stamping apparatus with a higher radius of curvature than the finished petal and iteratively testing and stamping the petal until the petal passes or fails a quality and accuracy threshold.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to solar concentrators, and more particularly to the shape and manufacture of solar reflectors for concentrating sunlight onto photovoltaic or thermal absorption devices. 
       BACKGROUND OF THE INVENTION 
       [0002]    Solar concentrators are used to collect energy emitted by the sun in the form of radiation. Known solar concentrators are shaped so as to direct sunlight incident on a large area spanned by the solar concentrator into a much smaller target area occupied by a device which converts the sun&#39;s radiation in the form of light and/or heat into usable energy. Generally the configurations of solar concentrators include a combination of reflectors, lenses, and radiation diffusers. Typical known solar concentrators often utilize a large single or compound reflector for concentrating sunlight incident upon a relatively large area into a smaller target area at which location further reflectors, lenses and/or diffusers are used to further focus and/or diffuse the incident radiation prior to its falling incident upon the target device for conversion into usable energy. 
         [0003]    One known base shape that is often used for solar concentrators is the parabola. A two-dimensional parabola has the property that, at any point on the parabola, the angle between a line passing through the point parallel with the axis of symmetry of the parabola, and the normal of the curve at that point on the parabola, is the same as the angle between the normal and a line passing through the point and what is known as the focus of the parabola. Consequently, parallel rays from infinity are focused into a single point or a relatively small area located at the focus. 
         [0004]    Two widely used types of parabolic reflectors, having a three-dimensional form based on the parabola, are the parabolic trough and the parabaloid or parabolic dish reflector. 
         [0005]    A parabolic trough is a trough shaped reflector which has, in any plane perpendicular to its length, a two-dimensional profile in the shape of a parabola, and hence has a three-dimensional shape of that parabola extruded along the length of the trough. This kind of reflector has a focal line running the length of the trough and passing through the foci of the parabolas in the planes perpendicular to its length. 
         [0006]    A parabolic dish reflector is a parabaloid shaped reflector which has, in any plane parallel with and intersecting the reflector&#39;s axis of rotational symmetry, a two-dimensional profile in the shape of a parabola, and hence has a three-dimensional shape of that parabola rotated about its axis of symmetry. This kind of reflector has a focal point located along the axis of symmetry and at the foci of all the rotationally symmetric parabolas in the planes parallel with and intersecting the axis. 
         [0007]      FIG. 1  is a two-dimensional cross-sectional view of a known parabolic concentrator  100  which view is illustrative of both a parabolic trough and a parabolic dish reflector. For simplicity the parabola of the two-dimensional profile of the parabolic reflector of the parabolic concentrator  100  is simply referred to as the parabola  110 . Incoming radiation  105   i  from infinity or the sun which is parallel to the axis of symmetry  102  of the parabola  110  is reflected by the parabola  110  as reflected radiation  105   r , which converges at focus  103 . 
         [0008]    Known systems which collect solar radiation and convert it into thermal energy, typically use a reservoir or conduit such as a pipe containing a liquid which is heated up by the radiation focused by the parabola  110 , the thermal energy of which is used ultimately for the generation of electrical energy.  FIG. 1  depicts a cross-section of a pipe  122  which is for conducting fluid to be heated near the focus  103  of the parabola  110 . The pipe  122  is located at a distance  101   b  from the parabola  110  which is substantially at the focus  103  of the parabola  110  such that most or all of the reflected radiation  105   r  of the parabola  110  is incident upon the surface of the pipe  122 . The materials used for the pipe  122 , or other reservoir or conduit, at least in the region substantially at the focus  103  of the parabola  110 , are such that they are capable of withstanding the intensity of the reflected radiation  105   r  focused by the parabolic reflector  100  and are ideal for converting the reflected radiation  105   r  into thermal energy and transferring that energy in the form of heat to the fluid passing therethrough. 
         [0009]    Known systems which collect solar energy by converting light directly into electricity typically utilize photovoltaic (PV) cells arranged in a PV panel or unit to collect the light focused by the parabola  110  and convert it into electrical current. Typically, PV units are of finite dimensions, having a finite area spanned by a number of PV cells, and have maximal efficiency when the radiation incident upon the photovoltaic cells of the PV unit have the same intensity i.e. when the incident radiation upon the active area of the PV unit is homogeneous. In general a PV unit&#39;s efficiency is limited by the lowest intensities incident upon its radiation collecting surface, and consequently, localized shadows or minima in the incident radiation are a concern whereas localized bright areas or maxima are generally not. Additionally, there are limits to the intensity of the radiation to which any portion of a PV unit may be subjected without it malfunctioning or undergoing permanent irreparable damage. Hence, a PV unit is typically positioned either between the focus  103  and the parabola  110  such as a PV unit  120   a  at a distance  101   a  from the parabola  110 , or at a distance beyond the focus  103  from the parabola  110 , such as a PV unit  120   b  at a distance  101   c  from the parabola  110 . Due to the finite area of the PV unit, not all of the incident radiation  105   i  near the axis of symmetry  102  will be incident upon the parabola  110 . Specifically, a shadow is cast by the PV unit  120   a ,  120   b  which is reflected as a shadow  108  within the reflected radiation  105   r.    
         [0010]    In some known systems utilizing PV units, a radiation diffuser in the form of a substantially transparent plate or lens (not shown for clarity) is positioned so as to intercept and diffuse the radiation reflected by the parabola  110  prior to its falling incident upon the photovoltaic cells of the PV unit  120   a ,  120   b . Although this technique improves homogeneity of the intensity of the radiation incident upon the PV unit  120   a ,  120   b , efficiency is sacrificed due to the energy lost in the form of the radiation reflected or refracted away from the PV unit  120   a ,  120   b  by the plate or lens and/or the radiation absorbed by the plate or lens and converted into heat at the plate or lens which is lost to the surrounding environment. As is discussed hereinbelow, the smaller the proportion of the reflected radiation which is diffused with use of a diffuser, the higher the efficiency of the parabolic concentrator  100 . 
         [0011]    The foregoing applies equally to known parabolic concentrators of both the parabolic trough and parabolic dish types, the difference between them being only that the parabolic dish is rotationally symmetric about a single axis and the parabolic trough is bilaterally symmetric in a plane passing through the axes of the parabolas of the trough. 
       SUMMARY OF THE INVENTION 
       [0012]    According to one aspect, an embodiment of the invention provides for a quasi-parabolic reflector for a solar concentrator comprising: a concave reflective surface, the concave reflective surface comprising a cross-section substantially symmetric about an axis of symmetry, wherein the cross-section comprises: a first reflective portion on a first side of the axis of symmetry, the first reflective portion having a first focal area, the first focal area located on a concave side of the concave reflective surface and on the first side of the axis of symmetry and at a first distance away from the axis of symmetry; and a second reflective portion on a second side of the axis of symmetry, the second side of the axis of symmetry opposite the first side of the axis of symmetry, the second reflective portion having a second focal area, the second focal area located on the concave side of the concave reflective surface and on the second side of the axis of symmetry and at a second distance away from the axis of symmetry; and wherein the first focal area and the second focal area are substantially at a focal distance away from the concave side of the concave reflective surface, and wherein incident radiation which is incident upon the concave side of the concave reflective surface and propagating in a direction substantially parallel to the axis of symmetry is reflected from the concave reflective surface as reflected radiation such that reflected radiation reflected from the first reflective portion and reflected radiation reflected from the second reflective portion propagate to a radiation absorbing target. 
         [0013]    According to another aspect, an embodiment of the invention provides for a method of processing petals for a solar concentrator comprising: performing an iterative procedure comprising: stamping the petal with a stamping apparatus comprising stamping surfaces having a greater curvature than a target curvature of a reference petal; determining at least one of a quality and an accuracy of the petal by taking multiple measurements with use of a laser beam reflected from the petal upon a target; and determining deviations of the multiple measurements from a reference set of measurements which would have been obtained with a reference petal; during each iteration of the iterative procedure, determining whether the deviations of the multiple measurements meet at least one of a quality and an accuracy criteria threshold, and if the deviations of the multiple measurements meet at least one of a quality and an accuracy criteria threshold, passing the petal as a finished petal and stopping the iterative procedure, and if the deviations of the multiple measurements do not meet at least one of a quality and an accuracy criteria threshold: determining if either the deviations of the multiple measurements exceed an absolute threshold or if the iterative procedure has been performed more times than a predetermined number, and performing one of: failing the petal and stopping the iterative procedure if either the deviations of the multiple measurements exceed an absolute threshold or if the iterative procedure has been performed more times than a predetermined number; and performing another iteration of the iterative procedure if the deviations of the multiple measurements do not exceed the absolute threshold and the iterative procedure has not been performed more times than the predetermined number. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]    The features and advantages of the invention will become more apparent from the following detailed description of the preferred embodiment(s) with reference to the attached figures, wherein: 
           [0015]      FIG. 1  is a diagram illustrating a known parabolic concentrator having a known parabolic reflector; 
           [0016]      FIG. 2  is a diagram illustrating a quasi-parabolic reflector for quasi-parabolic concentrators according to an embodiment of the invention; 
           [0017]      FIG. 3  is a diagram of a quasi-parabolic concentrator according to an embodiment of the invention; 
           [0018]      FIG. 4  is a diagram of the reflected radiation from a quasi-parabolic reflector according to an embodiment of the invention; 
           [0019]      FIG. 5  is a diagram of the reflected radiation from a quasi-parabolic reflector according to an embodiment of the invention illustrating sensitivity to changes in distance; 
           [0020]      FIG. 6  is a diagram of the reflected radiation from a parabolic reflector illustrating sensitivity to changes in distance; 
           [0021]      FIG. 7  is a diagram further comparing the reflected radiation from a parabolic reflector and a quasi-parabolic reflector according to an embodiment of the invention; 
           [0022]      FIG. 8  is a diagram further comparing the reflected radiation from a parabolic reflector and a quasi-parabolic reflector according to an embodiment of the invention; 
           [0023]      FIG. 9A  is a graph depicting a magnitude of intensity across a PV unit of a known parabolic concentrator; 
           [0024]      FIG. 9B  is a graph depicting a magnitude of intensities across a PV unit of a quasi-parabolic concentrator at various distances; 
           [0025]      FIG. 10  is a diagram of a stamping apparatus for use in forming a petal of a quasi-parabolic dish reflector according to an embodiment of the invention; 
           [0026]      FIG. 11  is a diagram of a testing apparatus for use in testing a petal of a quasi-parabolic dish reflector according to an embodiment of the invention; and 
           [0027]      FIG. 12  is a functional block diagram of a process for forming and testing a petal of a quasi-parabolic dish reflector according to an embodiment of the invention. 
       
    
    
       [0028]    It is noted that in the attached figures, like features bear similar labels. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0029]    Referring to  FIG. 2 , a cross-section of a quasi-parabolic reflector  200  in accordance with a first embodiment of the invention will now be discussed in terms of its structure. 
         [0030]    The shape of the cross-section of the quasi-parabolic reflector  200  is a quasi-parabola  211  which comprises two partial parabolas  211   a  and  211   b  each of which is shifted a distance R f  away from the axis of symmetry  202  of the quasi-parabola  211 . 
         [0031]    For simplicity of description, and for comparison with the known parabolic concentrator  100  depicted in  FIG. 1 , each partial parabola of the quasi-parabola  211 , namely the left partial parabola  211   a  and the right partial parabola  211   b  have the same shape as respectively the left-half and the right-half of the parabola  110  of  FIG. 1 . Consequently, the left partial parabola  211   a  has a focal point  207   a  a distance R f  to the left of the axis of symmetry  202 , while the right partial parabola  211   b  has a focal point  207   b  a distance R f  to the right of the axis of symmetry  202 . The left partial parabola  211   a  and the right partial parabola  211   b  are either separated by a gap or void, or joined by a portion of the quasi-parabola  211  which need not serve to reflect any of the incident radiation  205   i  in any meaningful way. 
         [0032]    The interaction between the incident radiation  205   i  and the quasi-parabola  211  provides reflected radiation  205   r  which differs significantly from reflected radiation  105   r  of the known parabola  110  of  FIG. 1 . 
         [0033]    The foci  207   a ,  207   b  respectively of the left partial parabola  211   a  and the right partial parabola  211   b  are at a focal distance  206   a  away from quasi-parabola  211 . As can be seen in  FIG. 2 , the reflected radiation  205   r  reflected from the outer portions of the left partial parabola and the right partial parabola crossover to become the inner portions of the reflected radiation  205   r  at a distance just greater than focal distance  206   a . Reflected radiation  205   r  reflected from the inner portions of the left partial parabola and the right partial parabola crossover to become the outer portions of the reflected radiation  205   r  at a distance just greater than the focal distance  206   a.    
         [0034]    The overall nature of the radiation pattern reflected by the quasi-parabola  211  will now be described. 
         [0035]    Between the quasi-parabola  211  and the foci  207   a ,  207   b  of the left and right partial parabolas, the radiation pattern comprises two converging sections on either side of the axis of symmetry  202  separated by a gap equal to twice the distance R f . Between the focal distance  206   a  and an initial crossover distance  206   b , the reflected radiation  205   r  from each focus  207   a ,  207   b  diverges such that the gap, which is twice the distance R f  at the focal distance  206   a , reduces to  0  at the initial crossover distance  206   b , while the outer edge of the radiation pattern in this region maintains a generally constant radius R f  from the axis of symmetry  202 . At the initial crossover distance  206   b  from the quasi-parabola  211 , reflected radiation  205   r  reflected from the outer portions of the left partial parabola and the right partial parabola just begin to intersect. At distances between the initial crossover distance  206   b  and a complete crossover distance  206   c  from the quasi-parabola  211 , the portion of overlap between the reflected radiation  205   r  of the left partial parabola and the right partial parabola at the center of the radiation pattern increases from an infinitesimal amount at the initial crossover distance  206   b  to a complete overlap at the complete crossover distance  206   c . At the complete crossover distance  206   c , reflected radiation  205   r  reflected from the left partial parabola and the right partial parabola completely overlap with each other. At distances beyond the complete crossover distance  206   c , the reflected radiation  205   r  reflected from the outer portions of the left partial parabola and the right partial parabola diverge such that they progressively overlap less and less with reflected radiation  205   r  from the other of the left partial parabola and the right partial parabola. 
         [0036]    Referring now to  FIG. 3 , a quasi-parabolic concentrator  300  in accordance with an embodiment of the invention will now be described. The quasi-parabolic concentrator  300  comprises a quasi-parabolic dish reflector  311  which is rotationally symmetric about the axis of symmetry  302 , and has a two-dimensional profile in any plane parallel to and intersecting the axis of symmetry  302  similar to the quasi-parabola  211  depicted in  FIG. 2 . The quasi-parabolic dish reflector  311  is made up of petals  315  arranged in a rotationally symmetric and periodic pattern. The quasi-parabolic dish reflector  311  of  FIG. 3  is made up of a total of 16 petals  315 , only one of which is shown for clarity. 
         [0037]    Incident radiation  305   i  from the sun is reflected by the quasi-parabolic dish reflector  311  as reflected radiation  305   r . As can be seen in  FIG. 3 , the resulting radiation pattern formed by the reflected radiation  305   r  is a converging cone shaped pattern with a cylindrical gap of radius R f . The reflected radiation  305   r  focuses at a focal distance  306   a  from the quasi-parabolic dish reflector  311  to form a focal ring  307  having a radius R f . Between the focal distance  306   a  and an initial crossover distance  306   b , the reflected radiation  305   r  from the focal ring  307  diverges such that the resulting radiation pattern is a cylinder roughly of radius R f  with a cone shaped gap having a radius of R f  at the focal distance  306   a  and converging to a point at the initial crossover distance  306   b . At the initial crossover distance  306   b  from the quasi-parabolic dish reflector  311 , reflected radiation  305   r  reflected from the outer portions of quasi-parabolic dish reflector  311  just begin to overlap in the center at the axis of symmetry  302 . At distances between the initial crossover distance  306   b  and a complete crossover distance  306   c  from the quasi-parabolic dish reflector  311 , the resulting radiation pattern is made up of a cylinder roughly of radius R f  having reflected radiation  305   r  with no overlap and a cone of overlapping reflected radiation  305   r  growing from a point at the initial crossover distance  306   b  to a radius of R f  at the complete crossover distance  306   c . At the complete crossover distance  306   c , the reflected radiation  305   r  reflected from the left partial parabola and the right partial parabola of any cross section of the quasi-parabolic dish reflector  311  completely overlap with one another. As distances increase beyond the complete crossover distance  306   c , the reflected radiation  305   r  reflected from the quasi-parabolic dish reflector  311  diverges such that it progressively overlaps proportionally less with itself The resulting radiation pattern in this region is a conical section of non overlapping radiation having an initial radius of about R f  at the complete crossover distance  306   c  to an infinite radius at infinity, with a core of overlapping radiation generally in the shape of a cylinder of radius R f , which makes-up proportionally 100% of the radiation pattern at the complete crossover distance and proportionally 0% of the radiation pattern at infinity. 
         [0038]    For completeness, a circular PV unit  326  of the quasi-parabolic concentrator  300  having a radius R f  and located at the initial crossover distance  306   b  is shown in  FIG. 3 . 
         [0039]    Referring to  FIG. 4 , a configuration of the target devices in a radiation pattern produced by the quasi-parabolic dish reflector  311  of  FIG. 3  will now be discussed. A single two dimensional cross-section taken through the axis of rotational symmetry is shown. Reflected radiation  405   r  converges at a focal ring  407  at a focal distance  406   a  from the quasi-parabolic dish reflector. A PV unit having a radius roughly the same as R f  is generally placed between an initial crossover distance  406   b  from the quasi-parabolic dish reflector as illustrated by PV unit  426   a , and a complete crossover distance  406   c  from the quasi-parabolic dish reflector as illustrated by PV unit  426   b . Due to the finite angular size of the sun in the sky, and with use of further lenses or diffusers, the PV unit  426   a  may be placed at a distance just closer to or just farther from the quasi-parabolic dish reflector than the initial crossover distance  406   b . This is made possible due to a smoothing out of the gap or the overlap that otherwise would be sharply defined near the center at the axis of symmetry. 
         [0040]    As can be seen in  FIG. 4 , substantially all of the reflected radiation  405   r  is spread over the entire area of the PV unit  426   a , at the initial crossover distance  406   b  such that there is singular coverage, and at the complete crossover distance  406   c  substantially all of the reflected radiation  405   r  is spread over the entire area of the PV unit  426   b  such that there is double coverage. The consequences of the radiation pattern having singular coverage and double coverage will be discussed in more detail hereinbelow. 
         [0041]    To convert solar energy into thermal energy a reservoir or conduit such as pipe  422  or large pipe  423  is used. As with the PV units, a pipe sufficiently large may be located at distances around and between the initial crossover distance  406   b  and the complete crossover distance  406   c , although if the pipe has a radius smaller than R f  as is the case for pipe  422 , it may be placed at a distance such that the overlapping cone of double coverage is incident upon the pipe  422  to ensure a large proportion of the entire reflected radiation is incident upon the surface of the pipe  422 . A large pipe  423  may also be placed at a distance within the cylinder of double coverage beyond the complete crossover distance  406   c , and may be mounted permanently in association with a non-permanently mounted PV unit  426   a ,  426   b . In such embodiments, the quasi-parabolic concentrator has dual modes of operation, thermal and photo-voltaic. 
         [0042]    Referring now to  FIG. 5  and  FIG. 6 , the effects of a variation in distance of a PV unit from the quasi-parabolic reflector of a quasi-parabolic concentrator and the effects of a variation of a distance of a PV unit from a known parabolic concentrator will now be compared. 
         [0043]      FIG. 5  depicts the radiation pattern  500  of a quasi-parabolic dish reflector such as that illustrated in  FIG. 3 . Reflected radiation  505   r  converges into a focal ring  507  at a focal distance from the quasi-parabolic dish reflector which has a vertical axis of symmetry  502 . A PV unit  520  of radius R 0  is located between the initial crossover distance and the focal distance, at a distance D 0  such that the radius to the outer edge of the reflected radiation  505   r  is also R 0 . The total amount of reflected radiation  505   r  is incident upon the PV unit  520  and has an area of πR 0   2 −πR 1   2 =π(R 0   2 −R 1   2 ). If the PV unit  520  were to shift by ΔD to a distance D 0 ′, the total amount of reflected radiation  505   r  would be incident upon the PV unit  520  and would have an area of πR 0   2 −R 2   2 =π(R 0   2 −R 2   2 ). Designating the absolute value of the slope of the reflected radiation  505   r  from the outside of the quasi-parabolic dish reflector as m, the magnitude of the change in radius ΔR is ΔD/m, hence R 2 =R 1 +ΔD/m. The change in area due to the shift is ΔA=−π(2R 1 ΔD/m+(ΔD/m) 2 ). The reduction in area in shifting from D 0  to D 0 ′ is reflected in an increase in intensity. The closer the set position of the PV unit  520  is to the location of interest at which it would have complete singular coverage, namely the initial crossover distance, the closer R 1  is to 0, and small shifts in distance result in a change in area having one term proportional to the square of the change in distance (πΔD 2 /m 2 ) and another term proportional to R 1  (π2R 1 ΔD/m) which vanishes at the initial crossover distance. 
         [0044]      FIG. 6  depicts the radiation pattern  600  of a parabolic dish reflector. For comparison to the radiation pattern  500  of  FIG. 5  it should be kept in mind that the slope of the reflected radiation  505   r  from the outside portions of the quasi-parabolic dish reflector is substantially the same as the slope of the reflected radiation  605   r  from the outside portions of the parabolic dish reflector (not shown) generating the radiation pattern  600  in  FIG. 6 . 
         [0045]    Reflected radiation  605   r  converges into a focal point  603  at a focal distance from the parabolic dish reflector which has a vertical axis of symmetry  602 . A PV unit  620  of radius R 0  is located at a distance D 1  such that the radius if the outer edge of the reflected radiation  605   r  is also R 0 . The total amount of reflected radiation  605   r  is incident upon the PV unit  620 , and has an area of πR 0   2 . If the PV unit  620  were to shift by ΔD to a distance D 1 ′, the total amount of reflected radiation  605   r  would be incident upon the PV unit  620  and would have an area of πR 0 ′ 2 . The absolute value of the slope of the reflected radiation  605   r  from the outside of the parabolic dish reflector is m, the same as that of the quasi-parabolic dish reflector of  FIG. 5 , and hence the magnitude of the change in radius ΔR is ΔD/m, and therefore R 0 =R 0 ′+ΔD/m. The change in area due to the shift is ΔA=−π(2R 0 ′ΔD/m+(ΔD/m) 2 ). The reduction in area in shifting from D 1  to D 1 ′ is reflected in an increase in intensity. At the set position of interest for the PV unit  620 , at which it would have complete singular coverage, namely at distance D 1  from the focus  603 , small shifts in distance result in a change in area having one term proportional to the square of the change in distance (πΔD 2 /m 2 ) and another term proportional to R 0 ′ (π2R 0 ′ΔD/m) which approaches the non-zero value R 0  for smaller and smaller shifts in position. 
         [0046]    As such a change in area and hence intensity due to a shift in the position of a PV unit for a quasi-parabolic dish reflector is smaller than a change in area and intensity due to a shift in the position of a PV unit for the parabolic dish reflector. The performance, stability, and behavior of the quasi-parabolic concentrator thus is less susceptible to changes in the distance of the PV unit from the reflector. 
         [0047]    Referring now to  FIG. 7 , radiation patterns  700  of reflected radiation from a quasi-parabolic dish reflector  710  and a parabolic dish reflector  711  are shown superimposed for direct comparison. As discussed above, the quasi-parabolic dish reflector  710  comprises, in any cross section a left partial parabola and a right partial parabola, each of which is shifted a distance R f  and each similar in shape to a respective half of a known parabola. The quasi-parabolic dish reflector therefore has a gap (which may or may not be reflective or even spanned by the dish structure) having a radius of R f . 
         [0048]    The known parabolic dish reflector  711  has a focus  703  a focal distance  706   a  away from the parabolic dish reflector  711 . A PV unit  720   a  or  720   b  is ideally positioned at a distance less than or greater than the focal distance  701   b  such that the outer radius of the radiation pattern is the same size as the radius of the PV unit  720   a  or  720   b . At either distance  701   a ,  701   c , the PV unit  720   a ,  720   b  encounters its own shadow  708  which forms a circle centered on the axis of symmetry  702  which is absent reflected radiation. Such a local minimum of radiation intensity would greatly harm the efficiency of the PV unit  720   a ,  720   b  and hence diffusers and/or lenses are often used in an attempt to scatter the radiation, otherwise incident outside of the shadow and evenly over a relatively large area, so as to redirect it into the central area of the shadow. As described hereinabove techniques utilizing diffusers and/or lenses have their limits and some energy of radiation will be lost due to reflection, refraction, or absorption at the diffusers and/or lenses. For clarity, incident radiation from the source, only out to a radius of Rd is depicted in  FIG. 7 . 
         [0049]    The quasi-parabolic dish reflector  710  has a focal ring  707  a focal distance  701   b  away from the quasi-parabolic dish reflector  710 . A PV unit  726   a  or  726   b  is ideally positioned at the complete crossover distance  706   c  or at the initial crossover distance  706   b  or anywhere between, such that the outer radius of the radiation pattern is substantially the same size as the radius of the PV unit  726   a  or  726   b . Since the PV unit  726   a ,  726   b  has a radius substantially the same as the focal ring  707 , and the radius of the gap, no shadow is cast by the PV unit  726   a ,  726   b  onto reflecting portions of the quasi-parabolic dish reflector, and hence at distances between the initial crossover distance  706   b  and the complete crossover distance  706   c , no shadow or extreme local minima in intensity exists. Beyond the initial crossover distance  706   b , there is an increasingly growing central area of double coverage as discussed above, which does not serve to limit the efficiently of the PV unit  726   a ,  726   b . However, if the central hotspot encountered just beyond the initial crossover distance  706   b  would otherwise cause damage to the PV unit  726   a , a small diffuser and/or lens may be used to spread or redirect the hotspot outward. Since the hotspot is relatively small, the likewise small diffuser and/or lens would have a minimal footprint. Generally, utilizing diffusers and/or lenses to spread out a small hotspot is less disruptive than attempting to evenly gather radiation from a larger area to fill in a hole in the radiation pattern (i.e. a shadow). 
         [0050]    It is clear that no matter what distance the PV unit  720   a ,  720   b  is located at, reflected radiation from any one point Q of the parabolic dish reflector  711  is incident upon the PV unit  720   a ,  720   b  at one spot on the active surface of the PV unit  720   a ,  720   b , and that spot on the active surface of the PV unit  720   a ,  720   b  has radiation incident upon it from only that one point Q of the parabolic dish reflector  711 . 
         [0051]    In a case that the PV unit  726   b  is located at the complete crossover distance  706   c , it is clear that every spot on the active surface of the PV unit  726   b  has radiation incident upon it from two points of the quasi-parabolic dish reflector  710 , radiation from one point of the left partial parabola and radiation from one point of the right partial parabola. For example, spot P on the PV unit  726   b  surface is illuminated by point P′ of the left partial parabola of the quasi-parabolic dish reflector  710 , as well as being illuminated by point P″ of the right partial parabola of the quasi-parabolic dish reflector  710 . It is due to the illumination by two distinct points of the quasi-parabolic dish reflector  710  that the PV unit  726   b  is referred to as subject to double coverage at the complete crossover distance  706   c.    
         [0052]    A consequence of the partial double coverage on the PV unit  726   b  between the initial crossover distance  706   b  and the complete crossover distance  706   c , and the complete double coverage at the complete crossover distance  706   c , is that a quasi-parabolic concentrator is much more robust in the face of surface defects such as post-installation localized damage, blemishes, dirt or interfering matter such as bird feces than a known parabolic concentrator subject to the same surface defect. For the same reason, the quasi-parabolic concentrator is more robust than the known parabolic concentrator in the face of pre-installation damage and or any other surface defect which could arise during manufacture, assembly, or during shipment. 
         [0053]    Referring now to  FIG. 8 , a qualitative illustration of relative intensity across a PV unit  826   a  is discussed. It is known that a known parabolic concentrator reflecting incident radiation from a distant object illuminates a flat PV unit with a circularly symmetric pattern having an intensity maximum near the center (outside of any shadow) and monotonically decreasing to a minimum at the edges. As such, in  FIG. 8 , the reflected radiation from point p 1  on the parabola  811  passing through the focus  803  and falling on the PV unit  826   a  at spot q 1 , has a higher intensity than that from point p 2  on the parabola  811  passing through the focus  803  and falling on the PV unit  826   a  at spot q 2 . 
         [0054]    An equivalent point to p 1 , on the left partial portion of the quasi-parabola  810 , p 1 ′, is shifted a distance R f  away from p 1  and away from the axis of symmetry  802 . The point p 1 ′ reflects radiation from the quasi-parabola  810  at the same angle as that reflected from p 1  of the parabola  811 , to pass through the focal ring  807  and fall on the PV unit  826   a  at a spot q 1 ′ at the same angle that the incident radiation falls on q 1  after being reflected by the parabola  811 . An equivalent point to p 2 , on the left partial portion of the quasi-parabola  811 , p 2 ′, is shifted a distance R f  away from p 2  and away from the axis of symmetry  802 . The point p 2 ′ reflects radiation from the quasi-parabola  810  at the same angle as that reflected from p 2  of the parabola  811 , to pass through the focal ring  807  and fall on the PV unit  826   a  at a spot q 2 ′ at the same angle that the incident radiation falls on q 2  after being reflected by the parabola  811 . 
         [0055]    It is to be noted that the pattern reflected by the parabola  811  is such that radiation from the relatively central areas of the reflector, such as from point p 1 , is reflected to the relatively central area of the PV unit  826   a , such as at spot q 1 , and radiation from the relatively outer areas of the reflector, such as from point p 2 , is reflected to the relatively outer areas of the PV unit  826   a , such as at spot q 2 . In contrast to the pattern reflected by the parabola  811 , the pattern reflected by the quasi-parabola  810  is such that radiation from the relatively central areas of the reflector, such as from point p 1 ′, is reflected to the relatively outer areas of the PV unit  826   a , such as at spot q 1 ′, and radiation from the relatively outer areas of the reflector, such as from point p 2 ′, is reflected to the relatively central area of the PV unit  826   a , such as at spot q 2 ′. 
         [0056]    This reversal of inner and outer intensity plays a role in the generally homogeneous intensity resulting from solar radiation reflecting from the quasi-parabolic concentrator of the invention. 
         [0057]    With reference to  FIG. 9A  and  FIG. 9B  intensities of the radiation patterns of a known parabolic reflector and a quasi-parabolic reflector are discussed. Each graph shows a plot of intensity I against position X across a PV unit. 
         [0058]      FIG. 9A  shows an intensity plot of a radiation pattern from a known parabola falling incident on a PV unit as discussed above. As can be seen, intensity is largest in the center of the PV unit (position X=0) and falls off to zero intensity on either side of the axis of symmetry. For clarity,  FIG. 9A  does not show the shadow or the correction applied to it by a diffuser or lens. 
         [0059]      FIG. 9B  shows a number of intensity plots of a radiation pattern from a quasi-parabolic reflector according to the invention falling incident on a PV unit as discussed above. Each plot shows the intensities resulting for a specific distance between the PV unit and the quasi-parabolic reflector. Intensity plot  930  shows intensities when the distance is just beyond the initial crossover distance. Each of intensity plots  910 ,  915 ,  920 ,  925 ,  935 ,  940 ,  945 ,  950  correspond to the intensities across a PV unit at respectively distances offset from the initial crossover distance of: −50 mm; −25 mm; −12.5 mm; −5 mm; +25 mm; +50 mm; +75 mm; +100 mm. 
         [0060]    Clearly intensities near the initial crossover distance, indicated by  930 , are generally homogenous over a large area of the PV unit. Also of note is the intense concentration at the central areas at distances beyond the initial crossover distance, allowing for thermal applications to sit behind the PV applications, and since the intensities at the central area are relatively concentrated for a large range (up to 75 mm), tolerances of thermal applications are improved and hence so are efficiencies. 
         [0061]    With reference to  FIGS. 10 ,  11 , and  12  a system and method of manufacturing and testing a petal of the quasi-parabolic reflector will now be discussed. 
         [0062]    Although many different methods may be utilized to construct a petal of the quasi-parabolic reflector discussed above, a person skilled in the art will understand different methods will be appropriate for different materials from which the petal is made. In the manufacturing embodiment depicted in  FIG. 10 , each petal is constructed from a lightweight metal such as aluminum with a hard reflective coating deposited thereon. In some embodiments the reflective material is anodized and laminated to the aluminum base material and may be nonmetallic such as a hard plastic-based material. 
         [0063]    Rather than being die cast or machined, the aluminum base material, in the form of a plate or sheet, is cut to roughly the same shape as, although a little larger than, the finished petal but having no appreciable curvature. This petal is treated so that the reflective coating is deposited thereon, and then the composite material petal is stamped. 
         [0064]      FIG. 10  depicts a stamping apparatus  1000  for stamping the composite material petal into a shape for use in a reflector of a solar concentrator. The stamping apparatus  1000  includes an upper stamping portion  1020  and a lower stamping portion  1030 , the upper stamping portion  1020  having an upper stamping surface  1025  and the lower stamping portion  1030  having a lower stamping surface  1035 . The shape of the upper stamping surface  1025  and the lower stamping surface  1035  are substantially the same as each other, which is a modified version of the desired petal shape. Specifically, in the embodiment depicted in  FIG. 10 , the upper and lower stamping surfaces  1025 ,  1035  have curvatures whose magnitudes are greater than the magnitudes of the curvature of the final petal, for example, the magnitude of the convex curvature of the upper stamping surface  1025  is greater than a magnitude of the concave curvature of a desired petal, and the magnitude of the concave curvature of the lower stamping surface  1035  is greater than a magnitude of the convex curvature of a desired petal. By stamping with magnitudes of curvatures which are greater than what is desired in the produced stamped petal, this stamping process takes into account the rigid nature of the composite material petal which will exhibit a certain amount of spring back once stamped. In order to prevent the hard reflector material from peeling-off or cracking, the level of overcompensation of the curvature (the amount by which the stamp curvature is greater than a curvature of a desired petal) of the upper and lower stamping portions does not exceed the limit ratio of the curvature of the petal at which the reflector material would be damaged. Although this may require a greater number of multiple stampings, the quality and durability of the final product is greatly enhanced. 
         [0065]    Referring now also to  FIG. 11 , a testing apparatus  1100  for testing and refining a petal  1130  will now be described. 
         [0066]    After each stamping cycle through the stamping apparatus  1000  depicted in  FIG. 10 , the stamped composite material petal is subjected to testing in the testing apparatus  1100 . The testing apparatus  1100  includes a frame  1110  for supporting and holding in place the stamped composite material petal  1130 , a laser light source  1150 , and a target  1160 . To facilitate loading of the petal  1130 , which is of considerable weight, a platform  1112  is provided in front of the support structure  1111  on which the composite material petal  1130  is mounted for testing. 
         [0067]    The laser light source  1150  is mounted such that it provides a beam of light  1152  in a direction which, relative to the composite material petal  1130 , is parallel to the direction light rays would travel from the sun when the quasi-parabolic concentrator in which the petal  1130  is installed is aligned with the sun. The laser light source  1150  is mounted on a first translating mount  1114  for translating the laser light source  1150  in a first direction within a plane substantially perpendicular to the beam of light  1152 , and is also mounted on a second translating mount  1113  for translating the laser light source  1150  in a second direction within a plane substantially perpendicular to the beam of light  1152  and also substantially perpendicular to the first direction. This enables laser light source  1150  to target various points on the stamped composite material petal  1130  for testing, such as point  1135 . 
         [0068]    The beam of light  1152  from the laser light source  1150  reflects from the composite material petal  1130  as reflected beam  1154  which strikes the target  1160  at a point of incidence  1165 . In some embodiments the target  1160  is placed at a distance substantially equal to the distance which would exist between the focal area and the petal of a parabolic reflector. In the embodiment depicted in  FIG. 11 , the laser light source  1150  is positioned at various predetermined locations at different first direction and second direction coordinates. In one embodiment of the invention the laser light source  1150  is located at 16 different predetermined locations during testing of a petal. The target area  1160  is either marked, or monitored by light scanning apparatus (not shown for clarity) in order to compare the actual point of incidence  1165  with the calculated point of incidence for an ideal petal. Depending upon the level of accuracy or inaccuracy of each of the points of actual incidence, the composite material petal  1130  may be sent back for additional stamping, may be discarded, or may be determined to be within quality and accuracy tolerances meeting the standard of a final finished composite material petal. In some embodiments each point of incidence upon the target area is also inspected for quality by inspecting the spread and/or shape of the incident light on the target. In some embodiments an average of the deviations is determinative of an overall accuracy which is measured against an overall accuracy threshold. In other embodiments a deviation exceeding a maximum threshold is determinative of a failed petal which should be discarded, and in other embodiments a weighted average of deviations is compared to a maximum weighted average deviation threshold. 
         [0069]    Referring now to  FIG. 12 , a method of iteratively stamping and testing of a composite material petal will now be described. 
         [0070]    At  1200  a composite material petal is first stamped in accordance with an assumed number of stampings required to bring an average composite material petal to its proper shape. At  1220  the petal is mounted on the testing apparatus and multiple measurements are taken with the laser light source at multiple locations. The resulting incident locations on the target as well as the quality of the incident radiation are recorded and a determination is made as to how much these deviate from the ideal petal in  1230 . The next step is to determine if the petal meets the quality/accuracy threshold at  1240 . The quality of the incident beam is determined with use of the spread and/or shape of the incident light on the target, while in general accuracy may be determined by determining the difference between the location of the center of an incident beam on the target area and the location where the beam would have been incident upon the target had it been reflected by a reference petal having an ideal or target curvature. If the petal meets the quality and accuracy criteria thresholds it is passed as a finished petal for use in a parabolic concentrator in step  1250  and then the process ends. If the petal does not meet the quality and accuracy criteria, at step  1260  it is determined whether the petal either has deviations which exceed an absolute threshold level or has been stamped more times than is acceptable. If either of these conditions exist, the petal is determined in step  1270  to be a failure and unsuitable for use in a quasi-parabolic concentrator. If neither of these conditions exist, the petal is determined to be worth attempting to rectify through further processing and the process returns to a further step of stamping  1200 . 
         [0071]    The process of  FIG. 12  allows for multiple stamping of petals based on a measurement of the actual quality and accuracy of the petal. This allows early identification of petals which are unsuitable, and also early identification of petals which are suitable after relatively few stamping cycles. This reduces stresses on the reflective material and the risk of cracking or peeling due to stamping, by eliminating unnecessary stamping cycles. 
         [0072]    Although embodiments of the quasi-parabolic concentrator discussed above have been described in the context of a circularly or rotationally symmetric dish reflector, elliptical variations of the quasi-parabolic concentrator and linear extruded variations of the quasi-parabolic concentrator are also contemplated by the invention. In such embodiments, instead of a focal ring, a focal ellipse or two parallel focal lines result. Although embodiments of the quasi-parabolic concentrator discussed above have been described as comprising two separated partial parabolas on either side of an axis or plane of symmetry, other shapes may be utilized to give rise to the equivalent radiation patterns to those disclosed above such as parabolas which are separated and rotated toward or away from the axis or plane of symmetry, or parabolas which are not separated but are rotated, compound parabolas, or other forms substantially forming and having two focal areas on either side of the axis of symmetry. 
         [0073]    In these embodiments, cross sections of the reflector possess two separate foci, such that there is overlap or double coverage within the radiation pattern. As long as there exist areas within the radiation pattern in which there is double coverage, the concentrator provides robust performance in the face of surface defects whether due to post-installation or pre-installation activities and/or incidents. 
         [0074]    Although embodiments of the quasi-parabolic concentrator discussed above have been described as comprising two distinct foci, other embodiments may utilize partial parabolas or other shapes to give rise to areas of radiation which are nearly focal referred to as focal areas. In such embodiments there would exist crossover of radiation but the areas of crossover would not necessarily be restricted to a point, ring or line, but instead could be a surface, such as a cylinder, or a volume, such as a torus. As long as the nearly focal regions are such that the radiation pattern has areas of double coverage, the concentrator will still remain robust in the face of surface defects. Also, as long as the quasi-parabolic reflector generates a radiation pattern in which radiation from the central areas of the reflecting surface are reflected to the outer areas of a PV unit and radiation from the outer areas of the reflecting surface are reflected to the central areas of the PV unit, improvements to the homogeneity of the radiation on the PV unit may be obtained. 
         [0075]    Although, the embodiments described above include a straight trough of constant width and a circular or elliptical dish, the invention applies also to non-straight troughs and/or troughs having varying widths, as well as non-rotationally symmetric dishes which nonetheless are symmetric at each angle through a single axis. Other forms such as troughs which are contiguous and having no ends such as a trough which describes a circle or an ellipse in a horizontal plane are also contemplated. Skilled persons in the art will understand that various forms utilizing reflective cross-sections with two focal areas in accordance with the teachings hereinabove are in accordance with the invention. 
         [0076]    The embodiments presented are exemplary only and persons skilled in the art would appreciate that variations to the embodiments described above may be made without departing from the scope of the invention. The scope of the invention is solely defined by the appended claims.