Abstract:
The present invention relates to apparatus and methods to provide a control system for the purpose of redirecting light from a source onto a target. The present invention appreciates that the diffraction pattern for light that is both diffracted and re-directed by a heliostat is a function of how the light redirecting element is aimed. This means that the aim of the light redirecting element can be precisely determined once the aim of the diffracted light is known. Advantageously, the characteristics of diffracted light indicative of how the diffracted light is aimed can be determined from locations outside the zone of concentrated illumination in which sensors are at undue risk. This, in turn, means that diffracted light characteristics can be detected at a safe location, and this information can then be used to help precisely aim the light redirecting element onto the desired target, such as a receiver in a CSP system. The aim of the diffracted light is thus an accurate proxy for the light beam to be aimed at the receiver.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional application No. 61/465,171 filed Mar. 14, 2011, titled ROOFTOP CENTRALIZED CONCENTRATED SOLAR POWER COLLECTION SYSTEM; U.S. Provisional application No. 61/465,165 filed Mar. 14, 2011, titled APPARATUS AND METHOD FOR POINTING LIGHT SOURCES; and U.S. Provisional application No. 61/465,216 filed Mar. 16, 2011, titled TIP-TILT TRACKER, each of which is incorporated herein by reference in its respective entirety for all purposes. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to control systems that use diffraction information to help aim light redirecting elements at desired target(s). More specifically, these strategies are used to controllably aim heliostats in the field of concentrating solar power (CSP). 
       BACKGROUND OF THE INVENTION 
       [0003]    The use of heliostats in the field of concentrating solar power (CSP) is well established in the prior art. A typical CSP system includes at least one centralized tower and a plurality of heliostats corresponding to each centralized tower. The tower is centralized in the sense that the tower serves as the focal point onto which a corresponding plurality of heliostats collectively redirect and concentrate sunlight onto a target (also referred to as a focus or a receiver) associated with the tower. The concentration of sunlight at the tower receiver is therefore directly related to the number of heliostats associated with the tower up to certain fundamental limits. This approach concentrates solar energy to very high levels, e.g., on the order of 1000× or more if desired. In practical application, many systems concentrate sunlight in a range from 50× to 5000×. The high concentration of solar energy is converted by the tower into other useful forms of energy. One mode of practice converts the concentrated solar energy into heat to be used either directly or indirectly, such as by generating steam, to power electrical generators, industrial equipment, or the like. In other modes of practice, the concentrated solar energy is converted directly into electricity through the use of any number of photovoltaic devices, also referred to as solar cells. 
         [0004]    Heliostats generally include a mirror or other suitable optical device to redirect sunlight, support structure to hold the mirror and to allow the mirror to be articulated, and actuators such as motors to effect the articulation. At a minimum, heliostats must provide two degrees of rotational freedom in order to redirect sunlight onto a fixed tower focus point. Heliostat mirrors are may be planar, but could possibly have more complex shapes. Heliostat articulation can follow an azimuth/elevation scheme by which the mirror rotates about an axis perpendicular to the earth&#39;s surface for the azimuth and then rotates about an elevation axis that is parallel to the earth&#39;s surface. The elevation axis is coupled to the azimuth rotation such that the direction of the elevation is a function of the azimuth angle. Alternatively, heliostats can articulate using a tip/tilt scheme in which the mirror rotates about a fixed tip axis that is parallel to the earth&#39;s surface and a further tilt axis. The tip axis often is orthogonal to the tilt axis but its axis of rotation tips as a function of the tip axis rotation. The tilt axis is parallel to the earth&#39;s surface when the heliostat mirror normal vector is parallel to the normal vector of the earth&#39;s surface. 
         [0005]    Heliostats are pointed so that the reflected sunlight impinges on the central tower receiver, which often is fixed in space relative to the heliostat. Because the sun moves relative to the heliostat site during the day, the heliostat reflectors must track the sun appropriately to keep the reflected light aimed at the receiver as the sun moves. 
         [0006]      FIG. 1  schematically illustrates a typical CSP system  403 . CSP system  403  has tower  405  with focus region  407  and a plurality of corresponding heliostats  409  (only one of which is shown for purposes of illustration) that aim reflected sunlight at region  407 . Sunlight represented by vector  411  reflects off the heliostat mirror  413  oriented with surface normal represented by vector  415 . Mirror  413  is accurately aimed so that reflected sunlight according to vector  417  is aimed at focus  407  generally along heliostat focus vector  419 , which is the line of sight from the heliostat mirror  413  and the tower focus  407 . If mirror  413  were to be aimed improperly so that vector  417  is not aimed at focus  407 , these two vectors would diverge. Consequently, the reflected light  417  impinges on the tower focus  407 . For such conditions to be realized, the laws of reflection require that the angle formed between the sunlight vector  411  and mirror normal  415  must be equal to the angle formed between vector  419  and mirror normal  415 . Further, all three vectors  411 ,  415 , and  419  must lie on the same plane. It can be shown using vector algebra that given a sunlight vector  411  and focus vector  419 , there is a unique solution for mirror normal  415  that is simply the normalized average of vectors  411  and  419 . 
         [0007]    Many control strategies use open loop control, closed loop control, or combinations of these. Many heliostat control systems employ open loop algorithms based on system geometry and sun position calculators in order to determine the sun and heliostat-focus vectors as a function of time. These calculations result in azimuth/elevation or tip/tilt commands to each heliostat device. Such control systems generally assume that the location of the heliostats are static and well defined and/or otherwise rely on periodic calibration maintenance to correct for settling and other lifetime induced drifts and offsets. Open loop solutions are advantageous in that they do not require any feedback sensors to detect how well each heliostat is pointed. These systems simply tell every heliostat how to point and assume that the heliostats point correctly. A major drawback is that open loop systems demand components made with high precision if accuracy is to be realized. Incorporating precision into the system components is very expensive. Additionally, it can be cost prohibitive to perform the precise surveying needed to perform open loop calculations with sufficient accuracy. The expense of precision and surveying escalates as the number of heliostats in a heliostat field increases. Consequently, systems that rely only on open loop control tend to be too expensive. 
         [0008]    Closed loop heliostat control relies on feedback from one or more sensors capable of measuring differences, or errors, between the desired condition and an actual condition. These errors are then processed into compensation signals to heliostat actuators to articulate the mirrors so that reflected sunlight impinges on the tower focus. Closed loop pointing has an advantage that it does not require precise components or installation or knowledge of the system geometry. The system also can be made less sensitive to lifetime drifts. Less demand for precision means that these systems are much less expensive than systems that rely solely on open loop control. These advantages become more important for smaller scale, commercial rooftop CSP applications. Such installations cannot provide sufficiently stable mounting surfaces because of weight load limitations to maintain accurate open loop control over time without increased maintenance demands. Consequently it is highly desirable that such small scale commercial rooftop installations track the sun using at least some degree of closed loop techniques in order to be cost effective and otherwise practical. Closed loop systems offer the potential to use control software rather than predominantly precision, and control is much less expensive to implement than precision. 
         [0009]    A difficulty in applying closed loop pointing methods on CSP systems is that the pointing condition requires the bisection of two vectors rather than alignment to a single vector. This is challenging, because there is no optical signal available at the nominal aim point (i.e., mirror normal  415  in  FIG. 1 ). CSP system designers have contemplated that an ideal location for a feedback sensor would be to place the sensor in the path of the reflected beam, such as at the tower focus  407 . Unfortunately, this is not feasible because no practical sensor could withstand the extreme temperatures or the UV dosage that result from highly concentrated sunlight. This poses a significant technical challenge of how to track and correct the aim of a beam if the beam cannot be tracked. Consequently, there remains a strong need for techniques that would allow closed loop pointing to be feasible. 
       SUMMARY OF THE INVENTION 
       [0010]    The present invention relates to apparatus and methods to provide a closed loop pointing system for the purpose of redirecting light from a source onto a target. Whereas the principles of the invention disclosed herein are presented in the context of concentrating solar power, the apparatus and methods are generally applicable to any pointing system in which light is redirected onto one or more fixed and/or moving targets. 
         [0011]    The present invention appreciates that the diffraction pattern for light that is both diffracted and redirected by a heliostat is a function of how the light redirecting element is aimed. This means that the aim of the light redirecting element can be precisely determined once the aim of the diffracted light is known. Advantageously, the characteristics of diffracted light indicative of how the diffracted light is aimed can be determined from locations outside the zone of concentrated illumination in which sensors are at undue risk. This, in turn, means that diffracted light characteristics can be detected at a safe location, and this information can then be used to help precisely aim the light redirecting element onto the desired target, such as a receiver in a CSP system. The aim of the diffracted light is thus an accurate proxy for the light beam to be aimed at the receiver. 
         [0012]    Advantageously, one or more centralized sensors can be used to aim multiple light redirecting elements. This means that common sensor(s) can detect diffraction characteristics of multiple heliostats. This facilitates incredibly simple implementation of the control system in large or small heliostat arrays in which the array is deployed over a large or small area. 
         [0013]    The system is extremely accurate. For example, the sun diameter generally spans about ½ degree of the sky. In more preferred embodiments, the pointing control system of the invention may provide accuracy of at least 1/20 th  of a degree so that the sun, not the system, is the limiting factor on accuracy. 
         [0014]    Diffracted light has different characteristics that are a function of how the light redirecting element is aimed. These include wavelength (color or frequency), intensity, diffraction orders, combinations of these, and the like. The present invention may detect and use one or more of these diffraction characteristics to aim light redirecting elements using closed loop control. In utility-scale CSP installations, control systems that comprise closed loop strategies advantageously facilitate cost-effective deployment of a large number of small heliostats. Such an architecture would otherwise be cost-prohibitive if each individual heliostat were to require careful installation, alignment, and calibration. Embodiments of the invention that use smaller heliostats are advantageously easier to handle and install, resulting in further cost reduction. 
         [0015]    In preferred modes of practice, the present invention teaches that a portion of the incident light impinging on a light redirecting element can be diffracted into one or more diffraction orders. The diffracted light furthermore can be detected by suitable sensor(s) such as an imaging system proximal to the receiver target (nominal target location) but sufficiently spaced from the nominal target so the sensor(s) are outside a zone of concentrated illumination associated with undue risk of sensor damage. The detected property(ies) of the diffracted light, including wavelength and intensity, can be used by the control system to determine if the light redirecting element is oriented such that the non-diffracted, redirected light substantially impinges on the nominal target. Furthermore, the control system uses the detected diffraction information, such as wavelength and intensity information to know how to articulate and correct the aim of the light redirecting element when the redirected light does not substantially impinge on the target location. 
         [0016]    The present invention teaches that a portion of the incident light impinging on a light redirecting element can be diffracted using a variety of different techniques. For example, a portion of the incident light can be diffracted using one or more diffraction gratings. Diffraction gratings are well known in the field of spectroscopy for their ability to split light into its constituent wavelengths or colors. While linear (one-dimensional) gratings may be used in the practice of the present invention, they are less preferred; the present invention teaches that intrinsically two-dimensional structures, such as circular (incorporating concentric rings) or spiral (incorporating single or multiple spiral features) gratings, are particularly advantageous for heliostat tracking. Such structures are capable of diffracting in two dimensions, thusly broadcasting light broadly into three dimensions. 
         [0017]    Gratings can have uniform spacing between features or may have spacing variations as a function of location on the grating. Both the orientation and spacing of the grating lines affect the diffractive properties of the grating, allowing gratings to be tuned for specific applications. 
         [0018]    While standard linear gratings can be used by the present invention, individual linear gratings provide more limited utility compared to 2-D gratings. By way of example, when used to sense pointing of the sun, in the non-dispersing direction, a single linear grating broadcasts light over only a very narrow angle of slightly less than ½ degree (the width of the sun.) Two linear gratings may be provided, oriented ½-degree differently from one another, to provide a 1-degree broadcast angle. Similarly, four linear gratings may be provided to provide a 2-degree broadcast angle, and so on. 
         [0019]    Since many practical applications require broadcast angles of 90 to 360 degrees, a large number of linear gratings may be required to provide a sufficient broadcast angle. For this reason, two-dimensional gratings such as circular or spiral are preferred by the present invention. 
         [0020]    In other embodiments, the present invention teaches that a portion of the incident light impinging on a light redirecting element can be diffracted using one or more diffractive elements in the form of an embossed or otherwise fabricated sheet (including a laminated sheet) incorporating one or more diffraction gratings, wherein the sheet in some modes of practice has been manufactured using techniques similar to those used to fabricate holographic stickers commonly used in commercial applications for security and authenticity validation. In some embodiments, the sheets may have diffraction features incorporated into two or more sub-elements. For instance, such a sheet may comprise an array comprising a plurality of spiral or circular diffraction gratings. Such manufacturing techniques easily implement diffractive optics and can produce complex diffraction patterns inexpensively compared to scientific-grade diffraction gratings. Sheets made using the techniques used to manufacture holographic stickers can be readily mass produced and can provide cost effective diffractive elements in the systems disclosed herein. 
         [0021]    The present invention teaches that diffractive elements may be used with either reflective and/or transmissive light redirecting elements. In the case of reflective light redirecting elements, incident light hitting the diffractive element also is partially reflected by the diffractive element according to the laws of reflection. The pattern of the resultant diffractive orders is produced and positioned in a manner that correlates accurately relative to the vector of the reflected rays to be aimed at the desired target(s). Such reflected rays are also referred to herein as the 0 th  diffraction order. 
         [0022]    In the case of transmissive light redirecting elements, incident light is refracted and diffracted by the diffractive element and refracted or otherwise altered by the light redirecting element. An exemplary refractive light redirecting element is a refractive type optic such as a lens. 
         [0023]    The present invention teaches that multiple diffractive elements may be used. Each diffractive element may be used to produce different diffractive properties with respect to a particular light redirecting element. This can be done for the purpose of extending the dynamic range of the feedback system and/or to eliminate ambiguities related to symmetries, such as positive and negative diffractive orders and multiple axes of rotation. 
         [0024]    The present invention teaches that a single diffractive element may be used with respect to a particular light redirecting element, wherein the diffractive element incorporates multiple sub elements. This also can provide different diffractive properties for the purpose of extending the dynamic range of the feedback system and/or to eliminate ambiguities related to symmetries, such as positive and negative diffractive orders and multiple axes of rotation. 
         [0025]    The present invention teaches that the detection features used to detect diffraction characteristics may be in the form of an imaging system proximal to the receiver target but at a safe distance so that the detection features avoid undue exposure risk to the concentrated light. The imaging system may include a plurality of imaging devices such as cameras and more specifically digital cameras capable of spatially and spectrally resolving diffractive elements mechanically coupled to light redirecting elements. The field of view of each imaging device is preferably fixed. Alternatively, the field of view may be adjustable via actuation capabilities such as pan and tilt actuation and/or zoom functionality. Similarly the total net field of view of a particular imaging device may include the entire set of diffractive elements in the system or a subset therein. Regardless of the field of view constraints of a given imaging device, the imaging system as a whole desirably has a field of view that together sufficiently covers the diffractive elements used for aiming control. 
         [0026]    In one aspect, the present invention relates to a method of concentrating sunlight, comprising the steps of:
       a) redirecting and diffracting sunlight; and   b) observing the diffracted sunlight; and   c) using the observed diffracted sunlight in a closed loop control system to controllably actuate a plurality of light redirecting elements in a manner that concentrates the sunlight onto at least one target.       
 
         [0030]    In another aspect, the present invention relates to a method of aiming re-directed sunlight, comprising the step of using a diffraction characteristic of the sunlight to aim the sunlight onto a target. 
         [0031]    In another aspect, the present invention relates to a system for concentrating sunlight onto a centralized target, comprising:
       a) a plurality of heliostats, each heliostat comprising:
           i. a redirecting element that redirects incident sunlight;   ii. a diffractive element that diffracts incident sunlight, wherein a characteristic of the diffracted sunlight is indicative of the orientation of sunlight redirected by the redirecting element;   
           b) a device that observes the diffractive element; and   c) a control system that uses observed diffracted light to determine a compensation that articulates the redirecting elements to concentrate the redirected sunlight onto the centralized target.       
 
         [0037]    In another aspect, the present invention relates to a heliostat that redirects sunlight, comprising:
       a) a redirecting element that redirects incident sunlight; and   b) a diffractive element that diffracts a portion of the sunlight incident on the heliostat, said diffractive element coupled to the redirecting element such that a characteristic of the diffracted sunlight is indicative of the orientation of sunlight redirected by the redirecting element.       
 
         [0040]    In another aspect, the present invention relates to a heliostat system for concentrating sunlight onto a target, comprising:
       a) a plurality of heliostats that redirect, diffract, and concentrate sunlight onto the first centralized target; each heliostat comprising:
           i. a redirecting element that redirects incident light onto the centralized target; and   ii. at least one diffractive element provided on the redirecting element;   
           b) an imaging device comprising a field of view that observes the diffractive element; and   c) a control system that uses a characteristic of the observed diffractive element to determine a compensation that articulates the redirecting elements to concentrate the redirected sunlight onto the centralized target.       
 
         [0046]    In another aspect, the present invention relates to a closed loop pointing system that controls the pointing of a plurality of heliostats to concentrate light onto a centralized target, comprising:
       a) a plurality of heliostats that diffract and redirect sunlight that is incident on the heliostats; and   b) a control system that uses the diffracted sunlight to control the articulation of the heliostats so that the redirected sunlight is concentrated onto the centralized target.       
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0049]      FIG. 1  is a simplified perspective view of an exemplary concentrating solar power system; 
           [0050]      FIG. 2A  is a perspective view of an exemplary embodiment of the present invention applied to a concentrating solar power system; 
           [0051]      FIG. 2B  is a perspective view of an exemplary imaging subsystem of the present invention applied to a concentrating solar power system; 
           [0052]      FIG. 2C  is a perspective view of an exemplary heliostat with an exemplary diffractive element of the present invention; 
           [0053]      FIG. 3  is a perspective view of an exemplary heliostat; 
           [0054]      FIGS. 4A through 4D  schematically show front views of exemplary reflective elements fitted with exemplary diffractive elements of the present invention; 
           [0055]      FIG. 5  schematically shows a front view of a linear diffraction grating; 
           [0056]      FIG. 6A  is a side view of the linear diffraction grating of  FIG. 5  illuminated by an on axis light ray; 
           [0057]      FIG. 6B  is a side view of the linear diffraction grating of  FIG. 5  illuminated by an off axis light ray that is orthogonal to the diffraction lines; 
           [0058]      FIG. 7A-C  is a front view of exemplary diffractive element including concentric or spiral diffraction lines; 
           [0059]      FIG. 8A  is a front view of an exemplary diffractive element including a plurality of concentric or spiral diffraction lines; 
           [0060]      FIG. 8B  is a front view illustration of observed spectra of an exemplary diffractive element; 
           [0061]      FIG. 9A-C  is a perspective view of exemplary layered diffractive elements; 
           [0062]      FIG. 10   a  shows a perspective view of an exemplary imaging device; 
           [0063]      FIG. 10   b  shows an exploded perspective view of the imaging device of  FIG. 10   a;    
           [0064]      FIG. 11  is a schematic diagram of an exemplary tracking control system incorporating an imaging subsystem; 
           [0065]      FIG. 12   a  is a schematic diagram of an exemplary imaging subsystem; 
           [0066]      FIG. 12   b  is a schematic diagram of an exemplary imaging subsystem; 
           [0067]      FIG. 13   a  is a schematic diagram of an exemplary articulation subsystem; 
           [0068]      FIG. 13   b  is a schematic diagram of an exemplary articulation subsystem; 
           [0069]      FIG. 14A-B  is a schematic diagram of an exemplary computation subsystem; 
           [0070]      FIG. 15  is a schematic diagram of an alternate exemplary computation subsystem; 
           [0071]      FIG. 16A-C  is an exemplary 2D ray trace of a diffractive element; 
           [0072]      FIG. 17  is an exemplary perspective ray trace of a diffractive element; 
           [0073]      FIG. 18  is an exemplary perspective ray trace of a diffractive element from two viewpoints; 
           [0074]      FIG. 19  is an exemplary perspective ray trace of a diffractive element from two viewpoints; 
           [0075]      FIG. 20  is an exemplary perspective ray trace of a diffractive element from two viewpoints; 
           [0076]      FIG. 21  is an exemplary perspective ray trace of a diffractive element from three viewpoints; 
           [0077]      FIG. 22  is an exemplary tracking system with a single target; 
           [0078]      FIG. 23  is an exemplary tracking system with a plurality of targets and 
           [0079]      FIG. 24  is an exemplary tracking system with a plurality of targets. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0080]    The apparatus and methods presented herein describe closed loop tracking systems that use diffractive properties of light to sense orientation and effect articulation of a plurality of light redirecting elements in a preferred manner. Embodiments described herein are exemplary and do not represent all possible embodiments of the principles taught by the present invention. In particular, embodiments of the present invention have direct application in the field of concentrating solar power, particularly concentrating solar power including the use of heliostats to redirect sunlight onto a fixed focus in which concentrated sunlight may be converted into other forms of energy such as heat or electrical energy. Nevertheless, the apparatus and methods described herein can be applied and adapted by those skilled in the art for use in alternative applications in which light from a source must be redirected onto a plurality of targets, particularly light from a source that is not stationary. 
         [0081]      FIGS. 2A-2C  and  3  show an exemplary CSP system  1  incorporating principles of the present invention that is deployed for purposes of illustration on mounting surface  21 , which may be a roof of a building in some embodiments. CSP system  1  includes an array of heliostats  9  that redirect and concentrate sunlight onto focus area  7  of tower  5 . An imaging subsystem  11  is mounted to tower  5  to detect diffraction information produced by heliostats  9 . 
         [0082]    A control system (not shown) uses the detected diffraction information in a closed loop control system to articulate and thereby aim redirected sunlight from the heliostats  9  onto focus area  7 . The control system desirably includes a plurality of computational devices (not shown) coupled electronically to imaging subsystem  11  and heliostats  9 . The control system includes software to process diffraction information acquired by imaging subsystem  11  in order to effect articulation of the plurality of heliostats  9  for the purpose of controllably redirecting sunlight onto the system focus area  7 . 
         [0083]    Each heliostat  9  generally includes diffractive element  23 , a light redirecting element in the form of reflecting element  25 , and a support structure including pivot mechanisms  27  and  31 , mechanical support  33 , and base  35 . The diffractive element  23  and its associated reflecting element  25  form an assembly that articulates so that the assembly can track the sun and aim redirected sunlight onto the focus area of tower  5 . Diffractive element  23  is coupled to reflecting element  25  so that the diffraction information produced from the diffractive element  25  can be used to controllably aim light redirecting element  25  via aiming strategies comprising closed loop control techniques optionally in combination with other control strategies, e.g, open loop control and/or feedforward techniques. In particular, imaging subsystem  11  detects diffraction information produced by diffractive element  23 . The information correlates to the manner in which reflecting element  25  is aimed. Accordingly, the information can be used to articulate reflecting element  25  in a manner effective to correct and/or maintain the aim of redirected light onto focus area  7 . 
         [0084]    Pivot mechanism  31  is mechanically coupled to support structure  34  and incorporates tip axis  33  such that tip axis  33  is fixed relative to the orientation of the support structure  34 . Pivot mechanism  27  is pivotably coupled to pivot mechanism  31  and can be actuated to pivot on tip axis  33 . Pivot mechanism  27  incorporates tilt axis  29  such that tilt axis  29  has an orientation that is a function of the rotation of pivot mechanism  31  about the tip axis  33 . Reflecting element  25  is pivotably coupled to pivot mechanism  27  and can be actuated to pivot on tilt axis  29 . Pivot mechanisms  27  and  31  provide two degrees of rotational freedom about axes  29  and  33 , respectively, for articulating the reflecting element  25  and diffractive element  23 . The orientation and position of reflecting element  25  and diffractive element  23  are thereby affected by both rotational degrees of freedom provided by tip axis  33  and tilt axis  29 . In the embodiment shown tilt axis  29  and tip axis  33  are substantially orthogonal to each other but do not lie on the same plane. Articulation of the components around axes  29  and  33  allows the reflecting element  25  to be controllably aimed at focus area  7 . 
         [0085]    The embodiment of heliostat  9  shown in  FIGS. 2A-2C  and  3  incorporates two rotational degrees of freedom for articulating the diffractive element  23  and reflecting element  25 . In an alternative embodiment, the orientation and position of the diffractive element  23  and reflecting element  25  may be affected by zero or more rotational degrees of freedom and one or more translational degrees of freedom. In yet another alternative embodiment, the orientation and position of the diffractive element  23  and reflecting element  25  may be affected by one or more rotational degrees of freedom and zero or more translational degrees of freedom. 
         [0086]    Diffractive element  23  preferably is located on reflective element  25  in such a manner that diffractive element  23  can be observed by imaging subsystem  11  irrespective of orientation of reflective element  25  over the functional articulation range of heliostat  9 . For purposes of illustration,  FIG. 2   c  shows diffractive element  23  centrally located along a top edge of reflecting element  25 . Other positioning strategies may be used such as those described below with respect to  FIGS. 4A-4D . 
         [0087]    In addition to the functional articulation range of individual heliostat devices  9 , the ability to observe diffraction element  23  by imaging subsystem  11  is affected by the position and orientation of the heliostats  9  relative to the imaging subsystem  11  and the proximity of heliostats  9  to one another. Consequently it is possible in some embodiments that portions of reflecting element  25  might be obstructed by one or more other reflecting elements  25  of other heliostats  9  from the viewpoint of the imaging subsystem  11 . Because of this, in some embodiments there may be regions on reflective surface  25  where it is not practical to locate diffractive element  23 . 
         [0088]    Diffractive element  23  preferably has a sufficient size such that diffractive element  23  can be resolved by imaging subsystem  11  over the functional articulation range of heliostat  9 . At the same time, it is also preferable to minimize the area of diffractive element or elements  23  such that these occupy a small fraction of the total area of reflecting element  25 . This is particularly true in the case of a concentrating solar power system in which efficiency is affected by the net reflecting area of the heliostat  9 . Consequently the minimum size of diffractive element  23  is dependent on the resolution of imaging subsystem  11 , and the location of the diffractive element  23  relative to the imaging subsystem  11 . As a limiting factor, the minimum area of diffractive element  23  is determined by the resolution of the imaging subsystem  11  and the location of the most distant heliostat  9  in the system  3 . 
         [0089]    In one embodiment of tracking control system  1 , all diffractive elements  23  among the heliostats  9  or a particular subset of heliostats  9  have areas that are substantially uniform in magnitude. Having all diffractive elements substantially uniform in size advantageously reduces manufacturing complexity and requires less specificity when installing heliostats  9  to ensure that heliostats  9  are located properly relative to imaging subsystem  11 . A disadvantage of this embodiment is that the amount of power that could be generated by a given CSP system is not maximized, as some of the diffractive elements  23  will be larger than needed to ensure that all the elements  23  in the array can be resolved by the imaging subsystem  11  regardless of distance from subsystem  11 . 
         [0090]    An alternative embodiment incorporates diffractive elements  23  having a plurality of sizes such that the area of diffractive elements  23  is correlated, e.g., inversely proportional, to their distance from imaging subsystem  11 . The embodiment has an advantage in that it can be designed so that the effective area of diffractive elements  23  in the image space of imaging subsystem  11  is substantially uniform. Additionally this embodiment increases the total throughput of a CSP system by minimizing parasitic losses from diffractive elements  23  that are too large with respect to some heliostats  9 . The major disadvantage to this embodiment is in increased manufacturing and installation complexity. 
         [0091]    The shape of diffractive element  23  as shown is substantially square, but a variety of shapes may be used. In alternative embodiments the shape of diffractive element  23  may have a substantially rectangular shape. In yet another alternative embodiment the shape of diffractive elements  23  may be substantially circular. In still another alternative embodiment the shape of diffractive element  23  may have a freeform outline. Furthermore embodiments of the present invention may include diffractive elements  23  having a plurality of shapes. 
         [0092]    Imaging subsystem  11  is used to detect or otherwise capture diffraction information produced by diffractive elements  23 . The subsystem  11  is able to detect, sense, observe, or otherwise capture diffraction information including but not limited to intensity and color of light reflected, scattered, or diffracted by diffractive elements  23 . The diffraction information correlates to the aim of reflecting elements  25 , and therefore can be used by a control system to aim and concentrate redirected sunlight from heliostats  9  onto focus area  7 . 
         [0093]    Imaging subsystem  11  generally includes a plurality of sensors preferably in the form of imaging devices  28 . In one embodiment, each imaging device  28  is a commercially available digital camera device. In an alternative embodiment, imaging device  28  is to varying degrees a customized device. Imaging devices  28  are mechanically coupled to a support structure  30  and arranged proximal to focus area  7 . Support structure  30  is mechanically coupled to tower  5  proximal to focus area  7 . In another embodiment, support structure  30  is mechanically coupled to the focus area  7 . In another embodiment, support structure  30  is mounted to a separate structure other than tower  5 . 
         [0094]    As illustrated, imaging devices  28  are arranged about the focus  7  in a generally radially symmetric fashion. Other arrangements may be used. For example, an alternate embodiment of imaging subsystem  11  includes a plurality of imaging devices  28  that are arranged about focus  7  in a generally linear symmetric manner. In an alternative embodiment, imaging subsystem support structure  30  is substantially free standing, being independently mechanically coupled to mounting surface  21 . Imaging devices  28  are sufficiently close to focus area  7  so that detected diffraction information can be used in a closed loop control system to actuate reflecting elements  25  for aiming at focus area  7 . However, the devices  28  are far enough away from focus area  7  to avoid undue risk that the devices  28  would be damaged by concentrated sunlight. 
         [0095]    Imaging subsystem  11  includes a plurality of imaging devices  28  having suitable field of view characteristics by which the plurality of diffractive elements  23  are observed. In one exemplary embodiment, each imaging device  28  has an effective field of view such that it can observe the entire plurality of diffractive elements  23  either statically or by the use of opto-mechanical mechanisms or other actuation techniques allowing a plurality of fields of view. In an alternative embodiment individual imaging devices  28  have an effective field of view to observe a subset of the plurality of diffractive elements  23  either statically or by use of optic-mechanical mechanisms allowing a plurality of fields of view. In such an embodiment the union of the plurality of fields of view includes the entire plurality of diffractive elements  23 . In another alternative embodiment a plurality of subsets of imaging devices  28  have effective fields of view such that their intersection and union of observable diffractive elements are equivalent with a given subset and/or the union of all effective fields of view includes the entire plurality of diffractive elements  23 . 
         [0096]    Generally, it desirable that imaging devices  28  provide a color imaging function having sufficient spectral resolution to measure variations in the orientation of diffractive element  23  within fractions of one degree of actuation of reflecting elements  25 . The required spectral resolution is a function of the diffractive properties of diffractive element  23 . In some embodiments of diffractive element  23 , the required spectral resolution is such that a 10-bit color imaging device provides sufficient resolution to measure the orientation of diffractive element  23 . Such embodiments advantageously reduce the cost of imaging device  28 . In other embodiments of diffractive element  23 , the required spectral resolution is such that a 24-bit color imaging device provides sufficient resolution to measure the orientation of diffractive element  23 . 
         [0097]    In addition to providing sufficient spectral resolution, imaging devices  28  must also provide sufficient spatial resolution of diffractive elements  23  included inside respective field of view or views. Spatial resolution of imaging device  28  is affected by the size of pixels provided by focal plane array  131 , and optical properties of lenses  127 . Whether a given diffractive element  23  can be sufficiently resolved depends on these factors, as well as, the physical dimensions of diffractive element  23 , the position of the diffractive element  23  within the field of view, and the distance between diffractive element  23  and imaging device  28 . For a given diffractive element  23  within the effective field of view of imaging device  28 , the minimum spatial resolution preferably is such that diffractive element  23  can resolve at least a single pixel in the image space of imaging device  28 . Because the orientation of diffractive element  23  relative to imaging device  28  is not fixed but can vary within the range of its associated articulation mechanism, the size of diffractive element  23  in the image space of imaging device  28  is not fixed but is rather a function of diffractive element  23  orientation. Consequently, the spatial resolution of imaging device  28  must be sufficient to resolve diffractive element  23  to a minimum of a single pixel in image space over the full range of orientation of diffractive element  23 . 
         [0098]    In one embodiment the spatial resolution of imaging device  28  is such that for each diffractive element  23  included in the effective field of view the minimum respective size in image space is a single pixel over the range of articulation orientations. Such embodiment advantageously minimizes the required resolution of imaging device  28  and consequently the cost of the device as cost is generally directly proportional to spatial resolution. 
         [0099]    In an alternative embodiment, the spatial resolution of imaging device  28  is such that for each diffractive element  23  included in the effective field of view the minimum respective size in image space is an n×m array of pixels over the range of articulation orientations where n and m are integers where at least one of the integers is greater than 1. Such embodiment does not necessarily minimize the spatial resolution of imaging device  28 , however, it advantageously provides a resolution margin. Additionally such embodiments enable imaging device  28  to be deployed in tracking control systems  1  having varying topologies and number of diffractive elements  23  with its effective field of view. 
         [0100]      FIGS. 4A through 4D  schematically show front views of exemplary reflective elements fitted with exemplary diffractive elements of the present invention.  FIG. 4   a  shows an embodiment of diffractive element  23  on reflective element  25  according to the heliostat  9  of  FIG. 2   c  such that diffractive element  23  is substantially centered in the horizontal direction and substantially along the top edge of reflective element  25 . Such location of diffractive element  23  is advantageous in concentrating solar power systems as it minimizes the risk that diffractive element  23  would be obstructed by neighboring heliostats throughout a full range of functional articulation. 
         [0101]      FIG. 4   b  shows diffractive element  24  substantially close to the center of reflecting element  26 . This embodiment may allow obstruction-free observation of diffractive element  24  but may impose a minimum spacing requirement on a CSP system. This embodiment may provide an advantage in minimizing the displacement of diffractive element  24  as a function of rotation of elements  26  and  24  about tip and tilt axes provided that element  24  is located proximal one or more axes of rotation. 
         [0102]    In yet another alternative embodiment of  FIG. 4   c , a plurality of diffractive elements  32  are provided on reflective element  38 . The location of diffractive elements  32  are such that at least one diffractive element  32  is not obstructed over the functional articulation range. Such exemplary embodiments include locating two diffractive elements  32  substantially proximal to adjacent corners of reflecting element  38 .  FIG. 4   d  shows a similar embodiment in which diffractive elements  37  are positioned at opposite corners of reflecting element  36 . Still yet other alternative embodiments may locate any number of diffractive elements on a corresponding reflecting element. 
         [0103]    To understand the use of diffractive elements in the practice of the present invention, we will review the operation of linear diffraction gratings.  FIG. 5  shows a linear diffraction grating  51  having regularly spaced grating lines  53 . Diffraction gratings have long been used in devices such as spectrometers to split polychromatic light into its constituent colors in order to characterize the light source or the material that is reflecting/absorbing the light. There are various types of linear diffraction gratings, but in principle they generally incorporate a set of parallel grooves or lines suitably sized and spaced for diffraction, e.g., on the order of the wavelength or even 10× or more of the light band to be diffracted. The spacing of the grooves sets up constructive and destructive interference that result in light of different wavelengths constructively interfering at different angles relative to the incident light beam. Consequently white light passing through a transmission grating or reflecting off of a reflective grating will generate a spectrum of colors similar to the effect of a rainbow. The diffraction angle is a function of both the line spacing, the wavelength of the diffracted light, and the angle of incidence on the grating. The equation below gives the relationship between the diffraction angle θ m , the groove spacing d, the incidence angle θ i  and the wavelength λ. The equation has multiple solutions since the interference maxima are periodic. The integer m is the diffraction order and can be positive, negative, or 0. 
         [0000]        d (sin(θ m )+sin(θ i ))= mλ   (1)
 
         [0000]    The m=0 or 0 th  order diffraction is a special case and is equal to the angle of reflection in the case of a reflective grating or the angle of refraction in the case of a transmission grating. 
         [0104]      FIG. 6A  shows reflective linear diffraction grating  51  of  FIG. 5  viewed on edge and being illuminated with a single polychromatic ray of light  55  that impinges on the diffraction grating  51  perpendicular to its plane. The grating reflects the light, ray  57  and also diffracts the light into multiple diffractive orders  59  through  65 . Each diffractive order is represented schematically by three monochromatic light rays. Angle  67  represents the angle between the 0 th  order reflected light ray  57  and the 1 st  order diffracted ray  59 . From the above equation we see that angle  67  is independent of the angle of incidence. This means that detection of any of rays  59  through  65  provides information concerning the location of reflected ray  57 . 
         [0105]      FIG. 6B  shows incident ray  55  impinging on grating  51  of  FIG. 5  at non normal incidence. The reflected 0 th  order ray  57  reflects from grating  51  at an angle that is equal to the angle of incidence of ray  55 . The 1 st  order diffracted rays  59  maintains the same angular separation  67  relative to the 0 th  order reflected ray as does the −1 st  order rays  61  regardless of the angle of incidence of ray  55 . The same is true for higher order diffracted rays  63  and  65 . 
         [0106]    Referring to  FIGS. 6A and 6B , one skilled in the art will appreciate that a ray of light diffracted from a linear grating  51  is dispersed in one dimension only, into a narrow plane. In the case of a light source like the sun that is less than ½ degree in size, the dispersed light will be confined to a narrow ½-degree region of space. 
         [0107]    Further consideration of this result illustrates that a linear diffraction grating although useful is less than optimum to serve as a more preferred diffraction element  23  of the present invention, since the diffracted light is not observable by an imaging detector  28  unless it happens to lie in that narrow ½-degree region of space, and can be readily detected by more than one of the detectors  28  in only the most fortuitous of circumstances. Further, as the sun moves through the sky during the day and light redirecting element  25  changes angles, this ½-degree region of space moves widely across the sky. 
         [0108]    To solve this problem, more preferred embodiments of the present invention introduce using a diffraction element that has structure in two dimensions, that broadcasts light broadly into three dimensions, so that a large two-dimensional area proximal to target  7 , including at least the area including imaging detectors  28 , is illuminated by the broadcast light. 
         [0109]    The present invention teaches that preferred embodiments of diffractive elements incorporate a circular or spiral grating. For example,  FIG. 7   a  shows diffractive element  91  having a circular grating formed from concentric rings  93 .  FIG. 7   b  shows diffractive element  94  having spiral grating  95 . Other less preferred embodiments may use superposed and/or an array of linear gratings that increase the window for observing diffraction effects as compared to a further less preferred embodiment, wherein only a single linear grating is used. 
         [0110]    The aforementioned embodiments describe diffractive elements including sub-elements having uniformly spaced diffraction lines. Alternative embodiments may include sub-elements having non-uniformly spaced diffraction lines. Likewise alternative embodiments may include a plurality of sub-elements having diffraction lines arranged so that respective lines are parallel but having different spacing. Diffractive elements including sub-elements with a plurality of line spacings advantageously allow diffractive elements to provide greater dynamic range by tuning the diffractive orders to overlap. 
         [0111]    Advantageously, circular and spiral gratings effectively provide a continuous set of linear gratings about their center point. This is schematically shown in  FIG. 7   c . Consider narrow portion  97  of diffractive element  91  ( FIG. 7   a ). This portion  97  approximates a linear grating with horizontal lines and thereby will generate a diffraction spectrum when illuminated by light orthogonal to the horizontal axis  105 . Likewise, portions  99 , 101 , and  103 , respectively, approximate linear diffraction gratings having a diffractive axes  102 ,  104 , and  108  orthogonal to the angle of the cross section, respectively. In the limit that the width of the cross-section goes to zero, there are an infinite number of linear diffraction gratings having diffraction axes completely filling 0° to 360°. The same benefits are provided by circular and spiral gratings. Advantageously, circular or spiral gratings overcome the problems of non-linear effects encountered with linear gratings and are more preferred. 
         [0112]    A single circular or spiral grating, however, does have a disadvantage that the width of the observed spectrum is confined to a narrow line proportional to the angular width of the illuminating source. Consequently such gratings may require a higher resolution imaging subsystem than might be desired in order to observe diffraction spectra of all diffractive elements in the tracking control system  1 . Accordingly, to overcome resolution limitations of single circular or spiral gratings, alternative embodiments of more preferred diffractive elements preferably include a plurality of circular or spiral gratings arranged in a two dimensional array. For example, referring to  FIG. 8   a , diffractive element  112  includes a plurality of circular or spiral grating sub-elements  115 . Each sub-element  115  is capable of diffracting incident light in all diffractive axes that when viewed from a relatively close view point can be resolved as a set of parallel spectra  117  as shown in  FIG. 8B , e.g., one spectrum for each sub-element  115  in  FIG. 8   a . When viewed from relatively far away, the set of parallel spectra  117  of  FIG. 8B  are resolved as a single spectrum. 
         [0113]    Other embodiments of diffractive elements use sheets incorporating diffraction gratings, similar to the techniques used to make holographic stickers, to produce diffraction information in ways that are more cost effective than using other kinds of linear, spiral, and/or circular gratings. The sheets may be single layers or a laminate of two or more layers. In particular, holographic manufacturing techniques may generate specific dot matrix patterns for a high level of control of the diffractive properties that approximate the effect of linear and circular gratings described herein. Advantageously, holographic manufacturing techniques advantageously provide a low cost method to manufacture high volumes of diffractive elements, as evidenced by the readily available low cost holographic stickers commonly used for security and authentication purposes on consumer goods and packaging. 
         [0114]    To illustrate this,  FIGS. 9A through 9C  schematically show another embodiment of a diffractive element  106  that includes a plurality of layers including a diffractive layer  107 . Diffractive layer  107  is in the form of an embossed or otherwise fabricated sheet (including a laminated sheet) incorporating one or more diffraction gratings. Desirably, the sheet in some modes practice has been manufactured using techniques similar to those used to fabricate holographic stickers. Element  106  further includes an adhesive layer  109 . Diffractive layer  107  provides any of the aforementioned diffractive properties whereas adhesive layer  109  provides a mechanism by which to mechanically couple diffractive element  106  to a reflective element or associated structure. Diffractive element  106  may include a removable backing layer  111  that prevents diffractive element  106  from prematurely adhering to other entities. This advantageously allows diffractive element  106  to be manufactured in volume, stored, and handled efficiently prior to the removal of backing layer  111  and coupling to a reflective element during assembly. Optionally, diffractive element  106  may include a UV resistant layer  113  applied over diffractive layer  107  that increases the lifetime of diffractive element  23  when exposed to UV doses as in the case of outdoor sun exposure. As another option, the diffractive layer  107  itself may include UV resistant components such as dyes that improve the lifetime under outdoor sun exposure. Furthermore, diffractive element  106  may include additional layers that provide additional diffractive layers, and or mechanical advantages such as stiffness to improve repeatability during the manufacturing or assembly processes. 
         [0115]      FIGS. 10   a  and  10   b  show an exemplary imaging device  120  suitable in the practice of the present invention. Imaging device  120  includes a mechanical housing  121 , lens housing  123 , and electronic interconnect  125 . Mechanical housing  121  provides general structural support and environmental protection of imaging electronics  129 . Likewise lens housing  123  positions and protects one or more lenses  127 . Imaging electronics  129  includes a focal plane array  131  onto which lenses  127  image objects within the field of view imaging device  120 . 
         [0116]      FIG. 11  shows how imaging subsystem  11  shown in  FIGS. 2A and 2B  may be incorporated into a tracking control system  150  of the present invention. The tracking control system  150  includes imaging subsystem  11 , computation subsystem  151 , and a plurality of articulation subsystems  153 . Imaging subsystem is electronically coupled to computation subsystem  151  via interconnect  155  by which computation subsystem  151  acquires image data. Computation subsystem  151  is likewise electronically coupled to a plurality of articulation subsystems  153  via interconnects  157  by which computation subsystem  151  delivers pointing instructions to and receives status telemetry from articulation subsystems  153 . Electronic interconnects  155  and  157  may be realized by wired and/or wireless communication topologies. The articulation subsystems  153  actuate corresponding heliostats (not shown) to aim redirected light at a desired target. 
         [0117]      FIGS. 12   a  and  12   b  show illustrative embodiments of imaging subsystem  11 . Referring to  FIG. 12   a , imaging subsystem  11  includes a plurality of imaging devices  152  connected independently or through a common electronic bus  155  to computation subsystem  151  (shown in  FIG. 11 ). In an alternative embodiment of  FIG. 12   b , imaging subsystem  11  further includes image processing controller  159  coupled electronically to a plurality of imaging devices  152  via a plurality of interconnects  161 . Interconnects  161  include wired and/or wireless communication topologies. Image processing controller  159  provides localized coordination of one or more of the following functions that include image acquisition, image pre-processing, and image transmission to computation subsystem  151  ( FIG. 11 ) via interconnect  155 . 
         [0118]      FIGS. 13   a  and  13   b  show illustrative embodiments of articulation subsystem  153 . Referring to  FIG. 13   a , articulation subsystem  153  includes an articulation processor  163  electrically coupled to articulation mechanism  167  via interconnect  165 . Mechanism  167  is mechanically coupled to a diffractive element (not shown). Articulation processor  163  receives pointing instructions from computation subsystem  151  ( FIG. 11 ) via interconnect  157  to effect articulation of articulation mechanism  167  and the corresponding diffractive element. In an alternative embodiment shown in  FIG. 13   b , articulation processor  163  is electrically coupled to a plurality of articulation mechanisms  167  via a plurality of interconnects  165 . Interconnects  165  may be distinct interconnects or be combined in one or more bus topologies. 
         [0119]      FIG. 14   a  shows an embodiment of computation system  151  ( FIG. 11 ) in more detail. Computation subsystem  151  includes a plurality of parallel processors  169 . Parallel processors  169  are electrically coupled to imaging subsystem  11  via interconnect  155  and to a plurality of articulation subsystems  155  via interconnect  157 . In some embodiments parallel processors  169  are coupled so that the interconnect  155  and interconnect  157  are distinct logical and/or physical buses. In alternative embodiments such as shown in  FIG. 14   b , interconnect  155  and  157  are combined into a single logical and/or physical bus. 
         [0120]      FIG. 15  shows an alternative embodiment of computation system  151  ( FIG. 11 ) in more detail. Computation subsystem  151  includes a master processor  171  and a plurality of slave processors  173  and  179  electrically coupled via interconnect  177 . Master processor  171  provides supervisory control over the plurality of slave processors  173  and  179 , including but not limited to timing and external diagnostic interfacing. Slave processors  179  provide image acquisition and processing via interconnect  155 , whereas slave processors  173  provide articulation control via interconnects  157 . 
         [0121]    The optical properties of diffractive elements according to the present invention advantageously provide a method whereby imaging subsystem  11  ( FIG. 11 ) in conjunction with a computation subsystem  151  ( FIG. 11 ) is able to use observed diffraction information to sense and determine the angular displacement of the 0 th  order reflected beam relative to the observation point.  FIGS. 16   a  through  16   c  illustrate this schematically with respect to CSP system  1  of  FIGS. 2   a - 2   c  and  3 . Referring to  FIG. 16   a , diffractive element  23  is illuminated by a distant polychromatic source such that the incident rays  201  that hit diffractive element  23  are substantially parallel. Imaging device  28  receives light scattered, reflected, or diffracted by diffractive element  23  through its lens aperture  127 . The collected ray bundles represented by the edge rays  203  are focused by the imaging device onto a focal plane array  131 . The focused ray bundle is represented by edge rays  205 . As shown in  FIG. 16   c , the resulting image  219  contains the sub image  225  of the diffractive element  23 . In the case where imaging device  28  is substantially far away from diffractive element  23  relative to the size of the diffractive element  23 , the angular extent of collected rays  203  is relatively small. Under these conditions we approximate the optics using just the central rays. Exemplary image  219  acquired by imaging device  28  has sub-image  225  that is the mapping of the diffractive element  23  into image space. The location of diffractive element  23  in image space represented by sub-image  225  is given by horizontal coordinate  221  and vertical coordinate  223 . 
         [0122]      FIG. 16   b  shows how diffraction information can be used to help determine the location vector of redirected light. In  FIG. 16   b , source ray  207  impinges on diffractive element  23 . The reflected ray  211  makes angle  213  relative to the diffractive element normal  212 . The central, collected ray  209  observed by imaging device  28  makes an angle  215  relative to the reflected ray  211 . Angle  217  represents the nominal angular position of diffractive element  23  in imaging device&#39;s  27  field of view. Due to the optical effects of diffractive element  23 ; the color of sub-image  225  ( FIG. 16   b ) is a function of angle  215 . In the case that angle  215  lies within one of the non-zero diffractive orders of diffractive element  23 , sub-image  225  will be substantially monochromatic. In the case that angle  215  is 0° (coincident with the reflected beam) sub-image  225  will be the image of the source and will be substantially the color of the source. In the case that angle  215  is between the 0 th  and ±1 st  diffractive orders of visible light sub-image  225  will be a diffuse image of diffractive element  23  as generally there will be some level of Lambertian scattering. 
         [0123]    Of particular interest is the case in which angle  215  lies within the visible portion of a non-zero diffractive order. Under this condition the color of sub-image  225  provides information about the possible magnitude of angle  215 .  FIG. 17  schematically shows this in more detail. Referring to  FIG. 17 , imaging device  28  observes diffractive element  23  illuminated by a substantially collimated white light source (not shown) from a distance substantially far away such that sub image  225  ( FIG. 16   c ) is substantially monochromatic and may be characterized by a central wavelength λ. Given the specific diffractive properties of the diffractive element  23  and the observed wavelength λ, the angle between the line of sight  231  between element  23  and imaging device  28  (the camera-element line of sight) and the 0 th  order reflected ray, θ m , is constrained to be a member of the set of angles corresponding to this wavelength; one angle for each possible diffractive order. Two such possible angles θ −1    233  and θ −2    235  are shown and correspond to the −1 st  and −2 nd  order rays for exemplary reflected rays  237  and  239  respectively. Note that these angles and orders are exemplary and do not represent the full set of possible angles for a given observed wavelength λ. 
         [0124]    Furthermore for each possible angle solution for the observed wavelength λ, there are in fact an infinite number of possible reflected ray vectors that lie along the surface of a cone with vertex angle 2θ m . The set of cones share a common axis coincident with the line of sight vector  231 . The cones are represented by their circular bases  241  and  243  for the angles  233  and  235 , respectively. Given the set of possible reflection vectors for the observed wavelength, using the laws of reflection the set of possible incident light vectors also can be determined. The set of all possible incident light vectors lie along the set of cones having a common axis  236 , which is the reflection (off diffractive element  23 ) of the line of sight  231  of imaging device  28 , and having vertex angles  245  and  247 . These cones are represented by their circular bases  249  and  251  in the exemplary solution. By the laws of reflection, angle  245  equals angle  233 , and angle  247  equals angle  235 . Thus, the observed diffraction information allows candidate vector locations of reflected light to be propagated backwards to determine candidate incident light vectors. The set of candidate solutions generally form cones with an apex at the diffractive element  23 , main axes  236  which is the reflection of imaging device line of sight  231 , and cone apex angles that can be determined from the observed diffraction information. 
         [0125]    Whereas the image of a diffractive element  23  from a single viewpoint such as provided by a single imaging device can provide some information about the orientation of the reflected ray, multiple viewpoints provide more specific information. This allows the reflected and incident light vectors to be precisely identified from the diffraction information. The loci of candidate solutions can be narrowed to a single solution very accurately. 
         [0126]    For example, a two viewpoint embodiment provides sufficient information by which to constrain reflected ray orientation to at most two possible vectors and in some limited cases, can uniquely constrain the reflected ray orientation.  FIG. 18  shows this schematically. Referring to  FIG. 18 , a diffractive element is represented as point  261  having a normal vector  265  lying in plane  285  and passing through the intersection of planes  285  and  287 . Imaging devices having viewpoints represented by points  269  and  271  lie on plane  285  at the intersection with plane  287 . Light ray  273  is incident on point  261  representing the diffractive element and is in plane  285 . Reflected and diffracted ray  275  also is in plane  285  and passes through plane  287  at point  267 . At the outset, the location of ray  275  is unknown, but the location can be determined from diffraction information according to principles of the present invention. Lines of sight  277  and  279  form angles  291  and  292  with the reflected ray  279  respectively resulting in observed diffraction information, e.g., an observed color, per viewpoint of diffractive element  261 . Circles  281  and  283  represent the locus of possible reflected rays that would result in the color observed at viewpoints  267  and  271  respectively. The intersection of  281  and  283  is a single point  267  which is in fact the unique solution to the two viewpoint observation. Thus, the vector corresponding to ray  275  is precisely determined using two viewpoints in this illustration. 
         [0127]      FIG. 19  shows another instance in which two viewpoints provide a single solution. Referring to  FIG. 19  a similar two viewpoint constraint is demonstrated in which incident ray  273  reflects and diffracts from diffractive element  261  such that reflected and diffracted ray  275  is in plane  285  and intersects plane  287  at point  267 . In this example the location of intersection  267  is such that it is not located between viewpoints  269  and  271 , although at the outset the location of point  267  is unknown but can be determined using principles of the present invention. In this instance the locus of constant color rays represented by circle  283  for viewpoint  271  is encircled by locus of constant color rays  281  for viewpoint  269 . The two loci have a single intersection point  267 . This is the unique solution for reflected ray  275  provided by the observed diffraction information from locations  269  and  271 . In fact, it can be shown that for any reflected ray  275  lying along plane  285 , the loci of constant color points from viewpoints  269  and  271  have a single intersection  267 . This allows the location of reflected ray  275  to be precisely determined. 
         [0128]    In many cases, however, the plane of incidence and reflection is not coplanar with plane  285  (which is the line of sight plane between diffractive element and the observation point), and a unique locus intersection does not exist using only two viewpoints. Using principles of the present invention, however, observing diffraction information from more than two viewpoints provides a unique solution in this circumstance. Three viewpoints is sufficient. Four viewpoints allows a unique solution with very high precision and extra information for redundancy. More than four can be used, but may not be needed. This is shown in  FIG. 20 . 
         [0129]    Referring to  FIG. 20 , incident ray  273  and reflected ray  275  lie in plane  291  that is not coplanar with plane  285 . Resulting constant color loci  281  and  283  for viewpoints  269  and  271  respectively intersect at point  267  which lies along reflected ray  275 . In addition, loci  281  and  283  have a secondary intersection at point  293 . This intersection represents an alternative reflected ray that would result in the same set of observed colors from the two viewpoints  269  and  271 . At the outset, it would not be known which solution is correct in many situations. Consequently, observation of diffractive element  261  from two viewpoints alone does not provide unique determination of the reflected ray vector  275 . In some possible embodiments, existence of certain constraints may provide sufficient knowledge to overcome the aforementioned ambiguity associated with the two viewpoint observation. One such constraint includes constraints on the location of the light source. In particular, in the case of a concentrating solar power system, it is possible that one of the two possible solutions  267  and  293  is not feasible because it would imply a sun position that is below the horizon. In alternate applications various other constraint(s) may be used to resolve which of the two possible solutions is correct. 
         [0130]    Another approach to resolve the possible ambiguity with the two viewpoint observation is a step and observe method. This method uses multiple observations as a function of orientation of diffractive element  261  to determine which of the two solutions  267  or  293  describes the real reflected ray  275 . In effect, this adds additional viewpoints, allowing the solution to be solved. 
         [0131]    Yet another approach to overcome ambiguity present in the two viewpoint observation is the addition of at least a third viewpoint. This is shown in  FIG. 21 . Referring to  FIG. 21 , third viewpoint  295  having line of sight  297  to point  261  is added. Viewpoint  295  lies in plane  287  to observe diffraction information such as color that is a function of the angle formed between line of sight  297  and reflected ray  275 . The locus of constant color for viewpoint  295  is represented by circle  299 . Points  293  represent the set of intersections between exactly two loci circles  283 / 281  and  283 / 299 . In contrast, point  267  represents the unique intersection of all three loci circles  281 ,  283 , and  299 . Consequently, color observation from three distinct viewpoints  269 ,  271 , and  295  provides unique determination of the vector corresponding to reflected ray  275 . 
         [0132]    Thus, three distinct viewpoints are sufficient to uniquely determine the orientation of reflected ray vectors originating from a known point (e.g., point  261  in  FIGS. 18-20 ) in space. In general four or more distinct viewpoints may be used. In such embodiments, viewpoints in excess of three may provide redundancy function, which may be helpful, for instance, in case a particular viewpoint is obstructed. 
         [0133]    The diffraction information used for illustrative purposes in  FIGS. 18-20  is color. A variety of different kinds of diffraction information can be used singly or in combination in control systems of the present invention. For example, in addition or as an alternative to observed color of diffractive element  261  from a plurality of viewpoints, the relative intensity of the observed light also provides information that may be used to determine the orientation of a reflected ray. In particular, relative intensity is useful for determining whether two or more viewpoint observation correspond to the same or different diffraction orders. 
         [0134]      FIGS. 20-21  and the corresponding discussion show how three or more distinct viewpoints provide a unique characterization of the orientation of a ray  275  reflected from a viewpoint  261 . The relationship can be represented by equation 2: 
         [0000]        C   i   =A   i   ·R   i   (2)
 
         [0000]    Where C, is a vector having an element corresponding to the color observed from the i th  diffractive element  23 , R i  is a unit vector corresponding to the orientation of reflected and diffracted ray  275  for the i th  diffractive element  261  relative to a known reference coordinates space, and A i  is a transformation matrix that maps reflected ray unit vector into the color vector for the i th  diffractive element  261 . Given color observation from three or more viewpoints and transformation A i , it is possible to determine the orientation of the reflected ray by using the inverse of equation 2: 
         [0000]        R   i   =A   i   −1   ·C   i   (3)
 
         [0135]    Furthermore, referring to  FIG. 22 , in a typical mode of practice such as with respect to CSP system  1  of  FIGS. 2A-2C  and  3 , it is desirable that light redirecting elements  25  be oriented in such a manner such that reflected rays  305  from each light redirecting element  25  resulting from incident rays  303  substantially intersect a known point in space referred to herein as the nominal target  301  of the light redirecting elements  25  when these are aimed as desired to concentrate sunlight. In  FIGS. 2A-2C , this corresponds to the focus area  7 . Consequently, for each light redirecting element  25 , there is a vector that describes the desired orientation of the reflected ray  305  from a light redirecting element  25  to the nominal track point  301 .  FIG. 22  shows a single nominal track point  301  for the entire plurality of light redirecting elements  25 , and this nominal track point  301  preferably is substantially fixed in position relative to the control system 
         [0136]    Referring to  FIG. 23 , in an alternative embodiment, there may be a plurality of nominal track points  301 . In such alternative embodiments each nominal track point  301  may be associated with a subset of the plurality of light redirecting elements  25 . 
         [0137]    Referring to  FIG. 24 , in another alternative embodiment, the nominal track point  301  is substantially fixed for a period of time and then moved to another location  309  for another period of time. After the track point is shifted to location  309 , new aiming vectors  307  result. The number of fixed locations and the duration of respective periods are not constrained. In yet another alternative embodiment the location of the nominal track point is a substantially continuous function of time. 
         [0138]    In illustrative modes of practice, at a given instant in time there is a substantially fixed nominal track point associated with a single light redirecting element from which a desired reflected ray vector r i,0  can be determined such that reflected rays generally intersect the desired nominal track point. Consequently, according to equation 2 there is a color observation vector c i,0  that represents this desired reflected ray vector. Given a color observation c i,j  that corresponds to the multi-viewpoint observation of the i th  diffractive element at a known orientation represented by a unit normal vector n i,j . The value of the unit normal is a function of the orientation of the articulation mechanism associated with the diffractive element. Mathematically, the unit normal of a diffractive element can be described by the following vector equation: 
         [0000]        N   i   =B·X   i   (4)
 
         [0000]    Where N i  is the unit normal of the i th  diffractive element, X i  is a vector describing the quantities of each degree of freedom of articulation mechanism, and B is the transformation matrix that maps articulation coordinates into the diffractive element unit normal. 
         [0139]    An exemplary method of performing closed loop tracking of a plurality of articulating diffractive elements in order that the reflected rays substantially intersect a known location includes the following steps, desirably implemented for every diffractive element and light redirecting element within the scope of the control system. Procedure 1 is as follows:
       1. Sample the color vector C i  including as vector elements the observed color from a plurality of distinct viewpoints.   2. Compute the difference between the observed color vector C i  and the nominal on target color vector C i0  herein referred to as ΔC i .   3. Compute articulation compensation vector ΔX i  such that       
 
         [0000]    
       
         
           
             
               
                 lim 
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       C 
                       i 
                     
                   
                   -&gt; 
                   D 
                 
               
                
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   X 
                   i 
                 
               
             
             = 
             0 
           
         
       
       
         
           
             4. Apply ΔX i  to articulation mechanism. 
             5. Repeat steps 1-4 
           
         
       
     
         [0145]    An alternative method of performing closed loop tracking of a plurality of articulating diffractive elements in order that the reflected rays substantially intersect a known location includes the following steps for every diffractive element according to Procedure 2:
       1. Compute open loop articulation coordinate X i  based on geospatial coordinates, local date and time, and position relative to the target position.   2. Apply open loop articulation coordinate Xi to articulation mechanism   3. Sample the color vector C i  including as vector elements the observed color from a plurality of distinct viewpoints.   4. Compute the difference between the observed color vector C i  and the nominal on target color vector C i0  herein referred to as ΔC i .   5. Compute articulation compensation vector ΔX i  such that       
 
         [0000]    
       
         
           
             
               
                 lim 
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       C 
                       i 
                     
                   
                   -&gt; 
                   D 
                 
               
                
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   X 
                   i 
                 
               
             
             = 
             0 
           
         
       
       
         
           
             6. Apply ΔX i  to articulation mechanism. 
             7. Repeat steps 1-6 
           
         
       
     
         [0153]    Yet another alternative method includes the following steps according to Procedure 3:
       1. Generating a lookup table of articulation coordinates X i [t] where t is the local time of day such that X i [t] is the last known substantially on target articulation coordinate at time t.   2. Interpolate X i  coordinate for the current time based on lookup table.   3. Apply interpolated X i  coordinate for the current time based on lookup table.   4. Sample the color vector C i  including as vector elements the observed color from a plurality of distinct viewpoints.   5. Compute the difference between the observed color vector C i  and the nominal on target color vector C i0  herein referred to as ΔC i .   6. Compute articulation compensation vector ΔX i  such that       
 
         [0000]    
       
         
           
             
               
                 lim 
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       C 
                       i 
                     
                   
                   -&gt; 
                   D 
                 
               
                
               
                 Δ 
                  
                 
                     
                 
                  
                 
                   X 
                   i 
                 
               
             
             = 
             0 
           
         
       
       
         
           
             7. Apply ΔX i  to articulation mechanism. 
             8. Repeat steps 2-6 
           
         
       
     
         [0162]    In illustrative modes of practice, any of Procedures 1 to 3 is used in a CSP system in which a plurality of heliostats concentrate sunlight onto one or more targets. The heliostats include light redirecting elements that allow sunlight to be redirected. The light redirecting elements are mechanically coupled to articulation mechanisms allowing controlled articulation of the light redirecting elements. Corresponding diffractive elements are coupled to the light redirecting elements so that diffraction information produced by the diffractive elements is indicative of how the light redirecting elements are aimed. The system includes an imaging subsystem comprising one or more imaging devices in a position effective to observe diffraction information produced by the diffractive elements that is indicative of the aim of the corresponding light redirecting elements. Preferably, the imaging devices are mechanically coupled to a support structure and are arranged proximal to the one or more targets. A computational subsystem including one or more computational devices is operationally coupled to the imaging devices so that the diffraction information captured by the imaging devices can be used to controllably aim the light redirecting elements at the desired target(s). 
         [0163]    The complete disclosures of the patents, patent documents, technical articles, and other publications cited herein are incorporated by reference in their entirety as if each were individually incorporated. Various modifications and alterations to this invention will become apparent to those skilled in the art without departing from the scope and spirit of this invention. It should be understood that this invention is not intended to be unduly limited by the illustrative embodiments and examples set forth herein and that such examples and embodiments are presented by way of example only with the scope of the invention intended to be limited only by the claims set forth herein as follows.