Sunlight has been used to light interior spaces from the time the window was invented. The glass window in use today that lets sunlight in, however, is the source of much heat loss in the winter and the source of a considerable air-conditioning load in the summer, even if it is a double-pane window with a partial vacuum between the panes. The primary source of heat in most offices in office buildings, at least in the summer, is the electricity used to light the offices. While heat from the lighting load reduces the need for more conventionally-supplied heat in the winter, it is a significant part of the cooling load for the office building in the summer.

Solar collectors, and especially non-imaging solar collectors, have come increasingly into use to supply heat for heating and to drive air conditioners. This includes both fixed collectors and tracking collectors. Tracking collectors are in general more efficient in collecting solar energy than fixed collectors, but they are more complicated mechanically and electrically. The current state of the art is summarized in U. S. Patents 5,586,013, entitled Nonimaging Optical Illumination System, 5,816,693, entitled "Nonimaging Optical Illumination System,"and 5,610,768, entitled"Nonimaging Radiant Energy Device." In most solar collectors, all the visible, infrared and ultraviolet radiation is desired for efficient operation; the radiation in the visible range is only a portion of the useful flux for operation of these collectors, as is the ultraviolet radiation. This situation is reversed when considering the collection of sunlight for illumination. There the infrared radiation is an undesirable quantity that will normally be screened out, and the ultraviolet radiation is similarly undesired because it will damage some of the equipment, particularly the plastics used in light pipes. In contrast, it may be desirable to keep the heat during the wintertime and distribute it inside along with the light.

It is an object of the present invention to provide a method of and means for collecting sunlight and distributing the collected sunlight for lighting interior spaces.

It is a further object of the present invention to provide a method of and means for reducing the electrical load used to light interior spaces electrically.

Other objects will become apparent in the course of a detailed description of the invention.

SUMMARY OF THE INVENTION Sunlight is collected by one or more solar collectors and concentrators. The collected sunlight, either including the infrared portion or having that portion removed, is piped to the inside of a building or other structure where it is distributed to supply interior lighting. The greatest energy efficiency is achieved with a windowless building. All of the sunlight that is collected may be used both to heat and to light the building or other structure.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 shows a two-dimensional optical device for providing non-imaging output.

Figure 2 illustrates a portion of the optical device of Figure 1 associated with the optical source and immediate reflecting surface of the device.

Figure 3A illustrates a bottom portion of an optical system and Figure 3B shows the involute portion of the reflecting surface with selected critical design dimensions and angular design parameters associated with the source.

Figure 4A shows a perspective view of a three-dimensional optical system for non-imaging illumination and Figure 4B illustrates a portion of the optical system of Figure 4A. Figure 4C and 4D are respectively an end view and a side view of the system of Figure 4A.

Figure 5A shows intensity contours for an embodiment of the invention and Figure 5B illustrates non-imaging intensity output contours from a prior-art optical design.

Figure 6A shows a schematic of a two-dimensional Lambertian source giving a cos3r illuminance distribution. Figure 6B shows a planar light source with the Lambertian source of Figure 6A. Figure 6C illustrates the geometry of a non-imaging reflector providing uniform illuminance to r=40° for the source of Figure 6A, and Figure 6D illustrates a three-dimensional Lambertian source giving a cos4r illuminance distribution.

Figure 7A shows a two-dimensional solution of a ray-trace analysis and Figure 7B illustrates three empirical fits to the three-dimensional solution.

Figure 8 shows an acceptance angle function which produces a constant irradiance on a distant plane from a narrow one-sided Lambertian strip source (two- dimensional) with a=l.

Figure 9 illustrates a reflector profile which produces a constant irradiance on a distant plane from a one-sided Lambertian strip source (two-dimensional) at the origin, R (C=7i/2) = 1, a= 1. CEC (inner curve) and CHC-type solutions (outer truncated curve) are shown.

Figure 10 shows a reflector designed to produce a reflected image adjacent to the source; the combined intensity radiated in the direction-9 is determined by the separation of the two edge rays, Rsin2a.

Figure 11 illustrates an acceptance angle function which produces a constant irradiance on a distant plane from a finite one-sided Lambertian strip source; there is only a CHC-type solution.

Figure 12 shows a reflector profile which produces a constant irradiance on a distant plane from a finite one-side Lambertian strip source of width two units; note that there is only a CHC-type solution and it is truncated.

Figure 13 illustrates a deviation of the reflector depicted in Figure 12 from a true V-trough.

Figure 14 shows a desired irradiance distribution on a distant plane perpendicular to the optical plane divided by the irradiance produced along the axis by the source alone; a broken line shows the irradiance of a truncated device.

Figure 15 illustrates an angular power distribution corresponding to the irradiance distribution shown in Figure 13; a broken line refers to a truncated device.

Figure 16 shows an acceptance angle function corresponding to the desired irradiance distribution plotted in Figure 13.

Figure 17 illustrates a reflector profile which produces the desired irradiance shown in Figure 13 on a distant plane from a finite one-sided Lambertian strip source of width two units; note that there is only a CHC-type solution and it is truncated.

Figure 18 shows the slope of the reflector as a function of vertical distance from the source.

Figure 19 illustrates the deviation of the reflector depicted in Figure 16 from a true V-trough.

Figure 20 shows the effect of truncation indicated by the angle up to which the truncated device matches the desired power distribution, and plotted as a function of the vertical length of the reflector.

Figure 21 illustrates a light source and family of edge rays along a reference line with identifying vectors.

Figure 22A illustrates a source, reflector, reference line and edge rays for a CEC reflector.

Figure 22B illustrates a source, reflector, reference line and edge rays for a CHC reflector.

Figure 23 illustrates the effect of termination of the reflector on boundary illumination.

Figure 24 shows a reflector for illumination of both sides of a target zone.

Figure 25 shows irradiance as a function of angle on a distant plane from a finite cylindrical source of uniform brightness.

Figure 26 shows a CEC-type reflector profile producing a constant irradiance on a distant plane from a cylindrical source.

Figure 27 shows some edge rays corresponding to the angles designated in Figure 25.

Figure 28a is a block diagram of a system for the practice of the present invention.

Figure 28b is a perspective view of an alternate version of a portion of the system.

Figure 29 is a perspective view of a building that includes an apparatus for the practice of the present invention.

Figure 30 is a perspective view of a collector for the practice of the present invention.

Figure 31 is a perspective view of a high-rise building equipped for the practice of the present invention.

Figure 32 is a diagram of a preferred embodiment of a solar light concentrator for conveying sunlight into a building.

DETAILED DESCRIPTION OF THE INVENTION A. Small Optical Sources In the design of optical systems for providing non-imaging illumination using optical sources which are small relative to other system parameters, one should consider the limiting case where the source has no extent. That is, for example, the size of the source is much less than the closest distance of approach to any reflective or refractive component.

Thus, the angle subtended by the source at any reflective or refractive component may be regarded as small. Our approximation of small source dimension, d, and large observer distance, D, amounts to d « Ro << D. This is in a sense the opposite of the usual non- imaging problem where the finite size and specific shape of the source is critical in determining the design. In any practical situation, a source of finite, but small, extent can better be accommodated by the small-source non-imaging design described herein rather than by the existing prior-art finite-source designs.

We can idealize a source by a line or point with negligible diameter and seek a one-reflection solution in analogy with the conventional"edge-ray methods"of non- imaging optics (see, for example, W. T. Welford and R. Winston"High Collection Non- imaging Optics,"Academic Press, New York, New York (1989)). Polar coordinates R and d) are used with the source as origin and 0 for the angle of the reflected ray as shown in Figure 3. The geometry in Figure 3 shows that the following relation between source angle and reflected angle applies, D/d (logR) =tana, (1) where a is the angle of incidence with respect to the normal.

Therefore, α=(#-#)/2. (2) Eq. (1) is readily integrated to yield, log (R) =JtanadO + constant, (3) so that, R-constant-exp [J (tan a cfO)]. (4) Eq. (4) determines the reflector profile R (#) for any desired functional dependence A (0).

Suppose we wish to radiate power P with a particular angular distribution (q>) from a line source which we assume to be axially symmetric. For example, P ( =constant. from #=0 to 01 and P (0) 0 outside this angular range. By conservation of energy P (e) dO=P () dO (neglecting material reflection loss) we need only ensure that, d#d#=P(#)/P(#), (5) to obtain the desire radiated beam profile. To illustrate the method, consider the above example of a constant P (9) for a line source. By rotational symmetry of the line source, dP/d#=a constant so that, according to Eq. (4) we want 9 to be a linear function of 0 such as #=a#. Then the solution of Eq. (3) is, R=Ro/cosk (C/k), (6) where, k=2/ (l-a), (7) and Ro is the value of R at 0=0.

We note that the case a=0 (k=2) gives the parabola in polar form, R=Ro/cos2 (C/2), (8) while the case #=constant=#1 gives the off-axis parabola, R=R0cos2(#1)/cos2[#-#0)/2]. (9) Suppose we desire instead to illuminate a plane with a particular intensity distribution. Then we correlate position on the plane with angle q and proceed as above.

Turning next to a spherically symmetric point source, we consider the case of a constant P (Q) where Q is the radiated solid angle. Now we have by energy conservation.

P (Q) d#=P(#0)d#0, (10) where Q0 is the solid angle radiated by the source. By spherical symmetry of the point source P (#0) =constant. Moreover, we have dQ= (2s) dcos0 and d30=(2#)dcos#; therefore, we need to make cos0 a linear function of cos (D, cos6=acos<I) +b. (11) With the boundary conditions that #=0 at 0=6 and #=#1 at #=#0, we obtain, a=(1-cos#1)/(1-cos#0), (12) b (cos#1-cos#0)/(1-cos#0). (13) For example, for Ol << 1 and (Do=-7t/2 we have ###2#0sin(1/2#). This functional dependence is applied to Eq. (4) which is then integrated by conventional numerical methods.

A useful way to describe the reflector profile R (0) is in terms of the envelope (or caustic) of the reflected rays, r ( (D). This is most simply given in terms of the direction of the reflected ray, t= (-sin0, cos6). Since r ( (D) lies along a reflected ray, it has the form, r=R+Lt. (14) where R=R (sin#1-cos#). Moreover, Rd#=Ld#, (15) which is a consequence of the law of reflection. Therefore, r=R+t/ (d#/d#). (16) In the previously cited case where 0 is the linear function aO, the caustic curve is particularly simple, r=R+t/a. (17) In terms of the caustic, we may view the reflector profile as the locus of a taut string; the string unwraps from the caustic, r, while one end is fixed at the origin.

In any practical design the small but finite size of the source will smear--by a small amount--the"point-like"or"line-like"angular distributions derived above. To prevent radiation from returning to the source, one may wish to"begin"the solution in the vicinity of #=0 with an involute to a virtual source. Thus, the reflector design should be involute to the"ice cream cone"virtual source. It is well known in the art how to execute this result (see, for example, R. Winston,"Appl. Optics,"Vol. 17, p. 166,1978). Also, see U. S. Patent No. 4,230,095 which is incorporated by reference herein. Similarly, the finite size of the source may be better accommodated by considering rays from the source to originate not from the center but from the periphery in the manner of the"edge rays"of non-imaging designs. This method can be implemented and a profile calculated using the computer program of the Appendix (and see Figure 2) and an example of a line source and profile is illustrated in Figure 1. Also, in case the beam pattern or source is not rotationally symmetric, one can use crossed two-dimensional reflectors in analogy with conventional crossed parabolic shaped reflecting surfaces. In any case, the present methods are most useful when the sources are small compared to the other parameters of the problem.

Various practical optical sources can include a long arc source which can be approximated by an axially symmetric line source. We then can utilize the reflector profile, R ( (D), determined here as explained in Eqs. (5) through (9) and the accompanying text. This analysis applies equally to two and three-dimensional reflecting surface profiles of the optical device.

Another practical optical source is a short arc source which can be approximated by a spherically symmetric point source. The details of determining the optical profile are shown in Eqs. (10) through (13).

A preferred form of non-imaging optical system 20 is shown in Figures 4A, 4B, 4C, and 4D with a representative non-imaging output illustrated in Figure 5A. Such an output can typically be obtained using conventional infrared optical sources 22 (see Figure 4A)--for example, high-intensity arc lamps or graphite glow bars. Reflecting side walls 24 and 26 collect the infrared radiation emitted from the optical source 22 and reflect the radiation into the optical far field from the reflecting side walls 24 and 26. An ideal infrared generator concentrates the radiation from the optical source 22 within a particular angular range (typically a cone of about % 15 degrees) or in an asymmetric field of % 20 degrees in the horizontal plane by % 6 degrees in the vertical plane. As shown from the contours of Figure SB, the prior-art paraboloidal reflector systems (not shown) provide a non-uniform intensity output, whereas the optical system 20 provides a substantially uniform intensity output as shown in Figure 5A. Note the excellent improvement in intensity profile from the prior-art compound parabolic concentrator (CPC) design. The improvements are summarized in tabular form in Table I, below.

Table I: Comparison of CPC with Improved Design CPC New Design Ratio of Peak to On Axis Radiant Intensity 1.58 1.09 Ratio of Azimuth Edge to On Axis, 0.70 0.68 Ratio of Elevation Edge to On Axis 0.63 0.87 Ratio of Corner to On Axis 0.33 0.52 Percent of Radiation Inside Useful Angles 0.80 0.78 Normalized Mouth Area 1.00 1.02 In a preferred embodiment, designing an actual optical profile involves specification of four parameters. For example, in the case of a concentrator design, these parameters are, a = the radius of a circular absorber, b = the size of the gap, c = the constant of proportionality between 9 and 4) 0 in the equation #=c(#-#0), and h = the maximum height.

A computer program has been used to carry out the calculations, and these values are obtained from the user (see lines six and thirteen of the program which is attached as a computer software Appendix included as part of the specification).

From (D = 0 to (D = (Do in Figure 3B the reflector profile is an involute of a circle with its distance of closest approach equal to b. The parametric equations for this curve are parameterized by the angle a (see Figure 3A). As can be seen in Figure 3B, as C varies from 0 to #0, α varies from oxo to ninety degrees. The angle ao depends on a and b, and is calculated in line fourteen of the computer software program. Between lines fifteen and one hundred and one, fifty points of the involute are calculated in polar coordinates by stepping through these parametric equations. The (r, #) points are read to arrays r (i) and 6 (i), respectively.

For values of 0 greater than (Do the profile is the solution to the differential equation, d (lnr)/d# = tan { [<D-6 + arcsin (a/r)]}. where 6 is a function of 0. This makes the profile, r (C), a functional of 8. In the sample calculation performed, 9 is taken to be a linear function of as in step 4. Other functional forms are described in the specification. It is desired to obtain one hundred fifty (r, 9) points in this region. In addition, the profile must be truncated to have the maximum height, h.

We do not know the (r, #) point which corresponds to this height, and thus, we must solve the above equation by increasing 0 beyond (Do until the maximum height condition is met.

This is carried out using the conventional fourth-order Runge-Kutta numerical integration method between lines one hundred two and one hundred and fifteen. The maximum height condition is checked between lines one hundred sixteen and one hundred twenty.

Once the (r, #) point at the maximum height is known, we can set our step sizes to calculate exactly one hundred fifty (r, 9) points between (Do and the point of maximum height. This is done between lines two hundred one and three hundred using the same numerical integration procedure. Again, the points are read into arrays r (i) and 0 (i).

In the end, we are left with two arrays, r (i) and 0 (i), each with two hundred components specifying two hundred (r, #) points of the reflector surface. These arrays can then be used for design specifications and ray trace applications.

In the case of a uniform beam design profile, (P (8) = constant), a typical set of parameters is (also see Figure 1), a = 0.055 in., b = 0.100 in., h = 12.36 in., and c = 0.05136, for (<D) =c (<M) o).

In the case of an exponential beam profile (P (9) =ce-a#)) a typical set of parameters is: a # 0 in., b = 0. 100 in., h = 5. 25 in., and c = 4. 694, for #(#)=0.131 ln(#/c-1).

Power can be radiated with a particular angular distribution, P° (0), from a source which itself radiates with a power distribution P° (cD). The angular characteristic of the source is the combined result of its shape, surface brightness and surface angular emissivity, at each point. A distant observer viewing the source fitted with the reflector under an angle, 0, will see a reflected image of the source in addition to the source itself This image will be magnified by some factor, M, if the reflector is curved. Ideally both the source and its reflected image have the same brightness, so the power each produces is proportional to the apparent size. The intensity perceived by the observer, P° (9), will be the sum of the two, po (e) =P (0) + lMlP° (0) (18) The absolute value of the magnification has to be taken, because if the reflected image and the source are on different sides of the reflector, and if we therefore perceive the image as reversed or upside down, then the magnification is negative.

Actually, at small angles the source and its reflection image can be aligned so that the observer perceives only the larger of the two. But if M is large, one can neglect the direct radiation from the source.

Thus, one is concerned with the magnification of the reflector. A distant observer will see a thin source placed in the axis of a trough reflector magnified in width by a factor, Mm=d#/d#. (19) This can be proved from energy conservation since the power emitted by the source is conserved upon reflection: Ps3#=MPsd#.

For a rotationally symmetric reflector, the magnification, Mm, as given in Eq. (19), refers to the meridional direction. In the sagittal direction the magnification is, Ms=(dµ1/dµ2)=(sin#/sin#), (20) where, ut and p2 are now small angles in the sagittal plane, perpendicular to the cross section shown in Figure 2. Eq. (20) can be easily verified by noting that the sagittal image of an object on the optical axis must also lie on the optical axis. The reason for this is that because of symmetry, all reflected rays must be coplanar with the optical axis.

The total magnification, Mt, is the product of the sagittal and the meridional magnification, Mt=MsMm =dcos (O) Idcos (O (21) Actually Eq. (21) could also have been derived directly from energy conservation by noting that the differential solid angle is proportional to dcos (0) and dcos (C) respectively.

Thus, inserting the magnification given in Eq. (21) or Eq. (19), as the case may be, into Eq. (18), yields the relationship between cD and 6 which produces a desired power distribution, P (0), for a given angular power distribution of the source, Ps. This relationship then can be integrated as outlined in Eq. (17) to construct the shape of the reflector which solves that particular problem.

There are two qualitatively different solutions depending on whether we assume the magnification to be positive or negative. If Mm > 0, this leads to CEC-type devices; whereas, Mm < 0 leads to CHC-type devices. The term CEC means Compound Elliptical Concentrator and CHC means Compound Hyperbolic Concentrator.

Now the question arises of how long we can extend the reflector or over what angular range we can specify the power distribution. From Eq. (17) one can see that if C- jazz then R diverges. In the case of negative magnification, this happens when the total power seen by the observer, between 6=0 and 6=9, approaches the total power radiated by the source, between (D = 0 and (D = 7c. A similar limit applies to the opposite side and specifies omit. The reflector asymptotically approaches an infinite cone or V-trough. There is no power radiated or reflected outside the range o n < 0 < oman.

For positive magnification, the reflected image is on the opposite side of the symmetry axis (plane) to the observer. In this case, the limit of the reflector is reached as the reflector on the side of the observer starts to block the source and its reflection image.

For symmetric devices this happens when <D+6=. In this case too one can show that the limit is actually imposed by the first law. However, the reflector remains finite in this limit.

It always ends with a vertical tangent. For symmetric devices where #max=-#minand#max= - (D min, the extreme directions for both the CEC-type and the CHC-type solution are related by, #max+max=#. (22) In general, CEC-type devices tend to be more compact. The mirror area needed to reflect a certain beam of light is proportional to l/cos (a). The functional dependence of 9 and C for symmetrical problems is similar except that they have opposite signs for CHC-type devices and equal signs for CEC-type solutions. Therefore, a increases much more rapidly for the CHC-type solution, which therefore requires a larger reflector-- assuming the same initial value, R (,. This is visualized in Figure 8 where the acceptance angle function as well as the incidence angle a are both plotted for the negative magnification solution.

To illustrate the above principles, consider a strip source as an example. For a narrow, one-sided Lambertian strip, the radiant power is proportional to the cosine of the angle. In order to produce a constant irradiance on a distant target, the total radiation of source and reflection should be proportional to 1/cos2 (A). This yields, cos#+# cos ( d#/d##=α/cos2(#). (23) In this case, the boundary condition is 0 = 0, at C=Tc/2, because we assume that the strip only radiates on one side, downward. Eq. (11) can only be integrated for a = 1, sin#=1-# tan (0)-sin (H) {. (24) The acceptance angle function 0 as well as the incidence angle for the CEC- type solution are shown in Figure 8. Integrating Eq. (24) yields the reflector shapes plotted in Figure 9.

The analytical tools described herein can be used to solve real problems which involve reflectors close to the source. This is done by combining the above technique with the edge ray method which has proved so effective in non-imaging designs. That is, the above methods can be applied to edge rays. As a first example, a reflector is designed for a planar, Lambertian strip source so as to achieve a predetermined far-field irradiance. The reflector is designed so that the reflected image is immediately adjacent to the source. This is only possible in a negative-magnification arrangement. Then the combination of source and its mirror image is bounded by two edge rays as indicated in Figure 10. The combined angular power density for a source of unit brightness radiated into a certain direction is given by the edge ray separation, Rsin (2a) = P° (0). (25) By taking the logarithmic derivative of Eq. (25) and substituting, d (log (R))/d#=tanα, (26) we obtain, da/d6=sin (2a) dlog (P° (0))/2d0-sin2 (a). (27) This describes the right-hand side, where A < 0. The other side is the mirror image.

For 2a=7r, R diverges just as in the case of the CHC-type solutions for small sources. Thus, in general, the full reflector extends to infinity. For practical reasons it will have to be truncated. Let's assume that the reflector is truncated at a point, T, from which the edge ray is reflected into the direction, 0,. For angles 9 in the range _0TX the truncation has no effect because the outer parts of the reflector do not contribute radiation in that range.

Therefore, within this range the truncated reflector also produces strictly the desired illumination. Outside this range the combination of source plus reflector behaves like a flat source bounded by the point, T, and the opposite edge of the source. Its angular power density is given by Eq. (13), with R=R#=constant. The total power, P#, radiated beyond ## is thus, In order to produce an intensity P0(##) at #, R(##) must be, <BR> <BR> P0(##)<BR> R(##) = (29) sin(2α#) The conservation of total energy implies that the truncated reflector radiates the same total power beyond OT as does the untruncated reflector, This equation must hold true for any truncation 0=eT. It allows us to explicitly calculate a, and with it O and R, in closed form as functions of 0, if B (0)--that is, the integral of P° (0)--is given in closed form. The conservation of total energy also implies that the untruncated reflector radiates the same total power as the bare source. This leads to the normalizing condition, This condition may be used to find (3mat, it is equivalent to setting ##=0 and 2aT=7t/2 in Eq. (30). Solving Eq. (30) for a yields, Substitutingα=(#-#)/2, yields the acceptance angle function.

#(#)=#+2α. (33) From Eq.(25) the radius is given by, R(#)=P0(#)B2+1/2B.

These equations specify the shape of the reflector in a parametric polar representation for any desired angular power distribution, P° (0). A straightforward calculation shows that Eq. (32) is indeed the solution of the differential equation (27). In fact, Eq. (27) was not needed for this derivation of the reflector shape. We have presented it only to show the consistency of the approach.

For example, to produce a constant irradiance on a plane parallel to the source we must have P° (0) =1/cos2 (A), and thus B (e) =cos2 (0)-tan (0)-tan (Om"ç)).

Using Eq. (31), we find Omax =-7E/4, so that B (A) =cos2 (0) (tan (0) + 1) with no undetermined constants.

The resulting acceptance angle function and the reflector profile are shown in Figure 11 and Figure 17, respectively. The reflector shape is close to a V-trough. Though, the acceptance angle function is only poorly approximated by a straight line, which characterizes the V-trough. In Figure 13 we show the deviation of the reflector shape depicted in Figure 12 from a true V-trough. Note that a true V-trough produces a markedly non-constant irradiance distribution proportional to cos (Q + toc/4) cos (9), for 0 <-0 < w/4.

As a second example for a specific non-constant irradiance a reflector produces the irradiance distribution on a plane shown in Figure 14. The corresponding angular power distribution is shown in Figure 15. The acceptance angle function according to Eq. (33) and (32) and the resulting reflector shape according to Eq. (34) are visualized in Figure 16 and Figure 17.

Although the desired irradiance in this example is significantly different from the constant irradiance treated in the previous example, the reflector shape again superficially resembles the V-trough and the reflector of the previous example. The subtle difference between the reflector shape of this example and a true V-trough are visualized in Figure 18 and Figure 19, where we plot the slope of our reflector and the distance to a true V-trough. Most structure is confined to the region adjacent to the source. The fact that subtle variations in reflector shape have marked effects on the power and irradiance distribution of the device can be attributed to the large incidence angle with which the edge rays strike the outer parts of the reflector.

As mentioned before, in general the reflector is of infinite size. Truncation alters, however, only the distribution in the outer parts. To illustrate the effects of truncation for the reflector of this example, we plot in Figure 20 the angle up to which the truncated device matches the desired power distribution as a function of the vertical length of the reflector. Thus, for example, the truncated device shown in Figure 17 has the irradiance distribution and power distribution shown in broken line in Figure 14 and Figure 15. Note that the reflector truncated to a vertical length of 3 times the source width covers more than 5/6 of the angular range.

B. General Optical Sources Non-imaging illumination can also be provided by general optical sources, provided that the geometrical constraints on a reflector can be defined by simultaneously solving a pair of system. The previously recited Eqs. (l) and (2) relate the source angle and the angle of light reflection from a reflector surface, d/d (logRi) =tan (<))/2, and the second general expression of far-field illuminance is, L(#i)#Risin(#i-#i)G(#j)=I(#i), where L (0i) is the characteristic luminance at angle 0i, and G (#i) is a geometrical factor which is a function of the geometry of the light source. In the case of a two-dimensional Lambertian light source, as illustrated in Figure 6A, the throughput versus angle for constant illuminance varies as cos 6. For a three-dimensional Lambertian light source, as shown in Figure 6D, the throughput versus angle for constant illuminance varies as cos3#.

Considering the example of a two-dimensional Lambertian light source and the planar source illustrated in Figure 6B, the concept of using a general light source to produce a selected far field illuminance can readily be illustrated. Notice with our sign convention, angle 9 in Figure 6B is negative. We solve Eqs. (18) and (19) simultaneously for a uniform far field illuminance using the two-dimensional Lambertian source. In this example, Eq. (19) becomes, risin(#i-#i)cos23i=I(#i).

Generally, for a bare two-dimensional Lambertian source, I(#i) 3 #cos#i, # s a cos6//, and I _ d/cos0.

Therefore, I s cos 9.

In the case of selecting a uniform far-field illuminance, I (0i) =C, if we solve the equations at the end of the first paragraph of Section B, d/d (logR ;) = tan (Ci-ej)/2, and log Ri+log sin (#i-#i)+2 log cos Oi = logC = constant, solvingd#i/d#i = -2tan#isin(#i-#i)-cos(#i-#i), or letting #i = #i-#I, d#i/d#i=1+sin#i-2tant#icos#i-B#i.

Solving numerically by conventional methods, such as the Runge-Kutta method, starting at Ti=0 at 0j, for the constant illuminance, dTild0i = 1 + sint,-n tan OicosTi, where n=2 for the two-dimensional source.

The resulting reflector profile for the two-dimensional solution is shown in Figure 6C and the tabulated data characteristic of Figure 6C is shown in Table III. The substantially exact nature of the two-dimensional solution is clearly shown in the ray-trace fit of Figure 7A. The computer program used to perform these selective calculations is included as Appendix B. For a bare three-dimensional Lambertian source where I (0i) _ cos462<n<3.

The ray-trace fit for this three-dimensional solution is shown in Figure 7B where the"n"value was fitted for desired end result of uniform far-field illuminance with the best fit being about n=2. 1.

Other general examples for different illuminance sources include: (1) I (#i) =A exp (BO ;) for a two-dimensional exponential illuminance for which one must solve the equation, d#i/d#i=1+sin#i-2tan#icos#+B ; and (2) I (0j) A exp (-BOj2/2) for a two-dimensional solution for a Gaussian illuminance for which one must solve, d#i/d#i=1+sion#i-2tan#icos#i-B#I.

The equations in the first paragraph of Section B can of course be generalized to include any light source for any desired for field illuminance for which one of ordinary skill in the art would be able to obtain convergent solutions in a conventional manner.

A ray trace of the uniform beam profile for the optical device of Figure 1 is shown in a tabular form of output in Table II below: TABLE II 114 202 309 368 422 434 424 608 457 448 400 402 315 229 103 145 295 398 455 490 576 615 699 559 568 511 478 389 298 126 153 334 386 465 515 572 552 622 597 571 540 479 396 306 190 202 352 393 452 502 521 544 616 629 486 520 432 423 352 230 197 362 409 496 496 514 576 511 549 508 476 432 455 335 201 241 377 419 438 489 480 557 567 494 474 482 459 421 379 230 251 364 434 444 487 550 503 558 567 514 500 438 426 358 231 243 376 441 436 510 526 520 540 540 482 506 429 447 378 234 233 389 452 430 489 519 541 547 517 500 476 427 442 344 230 228 369 416 490 522 501 539 546 527 481 499 431 416 347 227 224 359 424 466 493 560 575 553 521 527 526 413 417 320 205 181 378 392 489 485 504 603 583 563 530 512 422 358 308 194 150 326 407 435 506 567 602 648 581 535 491 453 414 324 179 135 265 382 450 541 611 567 654 611 522 568 446 389 300 130 129 213 295 364 396 404 420 557 469 435 447 351 287 206 146 ---ELEVATION-- TABLE III (D 0 r 90.0000 0.000000 1.00526 90.3015 0.298447 1.01061 90.6030 0.593856 1.01604 90.9045 0.886328 1.02156 91.2060 1.17596 1.02717 91.5075 1.46284 1.03286 91.8090 1.74706 1.03865 92.1106 2.02870 1.04453 92.4121 2.30784 1.05050 92.7136 2.58456 1.05657 93.0151 2.85894 1.06273 93.3166 3.13105 1.06899 93.6181 3.40095 1.07536 93.9196 3.66872 1.08182 94.2211 3.93441 1.08840 94.5226 4.19810 1.09507 94.8241 4.45983 1.10186 95.1256 4.71967 1.10876 95.4271 4.97767 1.11576 95.7286 5.23389 1.12289 96.03 02 5.48838 1.13013 96.3317 5.74120 1.13749 96.6332 5.99238 1.14497 96.9347 6.24197 1.15258 97.2362 6.49004 1. 16031 97.5377 6.73661 1.16817 97.8392 6.98173 1.17617 98.1407 7.22545 1.18430 98.4422 7.46780 1.19256 98.7437 7.70883 1.20097 99.0452 7.94857 1.20952 99.3467 8.18707 1.21822 99.6482 8.42436 1.22707 99.9498 8.66048 1. 23607 100.251 8.89545 1.24522 100.553 9.12933 1.25454 100.854 9.36213 1.26402 101.156 9.59390 1.27367 101.457 9.82466 1.28349 101.759 10.0545 1.29349 A r 102.060 10. 2833 1.30366 102.362 10.5112 1.31402 102.663 10.7383 1.32457 102.965 10.9645 1.33530 103.266 11.1899 1.34624 103.568 11.4145 1.35738 103.869 11.6383 1.36873 104.171 11.8614 1.38028 104.472 12. 0837 1.39206 104.774 12.3054 1.40406 105.075 12.5264 1.41629 105.377 12.7468 1. 42875 105.678 12.9665 1.44145 105.980 13.1857 1.45441 106.281 13.4043 1.46761 107.789 14.4898 1.48108 108.090 14.7056 1.53770 108.392 14.9209 1.55259 108. 693 15.1359 1.56778 108.995 15.3506 1.58329 109.296 15.5649 1.59912 109.598 15.7788 1.61529 109.899 15.9926 1.63181 110.201 16.2060 1.64868 110.503 16.4192 1.66591 110.804 16.6322 1.68353 111.106 16.8450 1.70153 111.407 17.0576 1.71994 111.709 17.2701 1.73876 112.010 17.4824 1.75801 112.312 17.6946 1.77770 112.613 17.9068 1.79784 112.915 18.1188 1.81846 113.216 18.3309 1.83956 113.518 18.5429 1.86117 113.819 18.7549 1.88330 114.121 18.9670 1.90596 114.422 19.1790 1.92919 114.724 19.3912 1.95299 115.025 19.6034 1.97738 115.327 19.8158 2.00240 (D r 115.628 20. 0283 2.02806 115.930 20.2410 2.05438 116.231 20.4538 2. 08140 116.533 20.6669 2.10913 116.834 20.8802 2.13761 117. 136 21. 0938 2.16686 117.437 21.3076 2.19692 117.739 21.5218 2.22782 118.040 21.7362 2.25959 118.342 21.9511 2.29226 118. 643 22.1663 2.32588 118.945 22.3820 2.36049 119.246 22.5981 2.39612 119.548 22.8146 2.43283 119.849 23.0317 2.47066 120.151 23.2493 2.50967 120.452 23.4674 2.54989 120.754 23.6861 2.59140 121.055 23.9055 2.63426 121.357 24.1255 2.67852 121.658 24.3462 2.72426 121.960 24.5676 2.77155 122.261 24.7898 2.82046 122.563 25.0127 2.87109 122.864 25.2365 2.92352 123.166 25.4611 2.97785 123.467 25.6866 3.03417 123.769 25.9131 3.09261 124.070 26.1406 3.15328 124.372 26.3691 3.21631 124.673 26.5986 3.28183 124.975 26.8293 3.34999 125.276 27.0611 3.42097 125.578 27.2941 3.49492 125.879 27.5284 3.57205 126.181 27.7640 3.65255 126.482 28.0010 3.73666 126.784 28.2394 3.82462 127.085 28.4793 3.91669 127.387 28.7208 4.01318 127.688 28.9638 4.11439 6 r 127.990 29. 2086 4.22071 128.291 29.4551 4.33250 128. 593 29.7034 4.45022 128.894 29.9536 4.57434 129.196 30.2059 4.70540 129.497 30.4602 4.84400 129.799 30.7166 4.99082 130.101 30.9753 5.14662 130.402 31.2365 5.31223 130.704 31.5000 5.48865 131. 005 31.7662 5.67695 131.307 32.0351 5.87841 131.608 32.3068 6.09446 131.910 32.5815 6.32678 132.211 32.8593 6.57729 132.513 33.1405 6.84827 132.814 33.4251 7.14236 133.116 33.7133 7.46272 133.417 34.0054 7.81311 133.719 34.3015 8.19804 134.020 34.6019 8.62303 134.322 34.9068 9.09483 134.623 35.2165 9.62185 134.925 35.5314 10.2147 135.226 35.8517 10.8869 135.528 36.1777 11.6561 135.829 36.5100 12.5458 136.131 36.8489 13.5877 136.432 37.1949 14.8263 136.734 37.5486 16.3258 137.035 37.9106 18.1823 137.337 38.2816 20.5479 137.638 38.6625 23.6778 137.940 39.0541 28.0400 138.241 39.4575 34.5999 138.543 39.8741 45.7493 138.844 40.3052 69.6401 139.146 40.7528 166.255 139.447 41.2190 0.707177E-01 139.749 41.7065 0.336171E-01 140.050 42.2188 0.231080E-01 (D 0 r 140.352 42. 7602 0. 180268E-01 140.653 43.3369 0.149969E-01 140.955 43.9570 0.129737E-01 141.256 44.6325 0.115240E-01 141.558 45.3823 0.104348E-01 141.859 46.2390 0.958897E-02 142.161 47.2696 0.891727E-02 142.462 48.6680 0.837711E-02 142.764 50.0816 0.794451E-02 143.065 48.3934 0.758754E-02 143.367 51.5651 0.720659E-02 143.668 51.8064 0.692710E-02 143.970 56.1867 0.666772E-02 144.271 55.4713 0.647559E-02 144.573 54.6692 0.628510E-02 144.874 53.7388 0.609541E-02 145.176 52.5882 0.590526E-02 145.477 50.8865 0.571231E-02 145.779 53.2187 0.550987E-02 146.080 52.1367 0.534145E-02 146.382 50.6650 0.517122E-02 146.683 49.5225 0.499521E-02 146.985 45.6312 0.481649E-02 147.286 56.2858 0.459624E-02 147.588 55.8215 0.448306E-02 147.889 55.3389 0.437190E-02 148.191 54.8358 0.426265E-02 148.492 54.3093 0.415518E-02 148.794 53.7560 0.404938E-02 149.095 53.1715 0.394512E-02 149.397 52.5498 0.384224E-02 0.374057E-02 C. Extended Finite-Sized Sources In this section we demonstrate how compact CEC reflectors can be designed to produce a desired irradiance distribution on a given target space from a given finite-sized source. The method is based on tailoring the reflector to a family of edge-rays, but at the same time the edge rays of the reflected source image are also controlled.

In order to tailor edge rays in two dimensions, for example, one can assume a family of edge rays, such as are produced by a luminaire source. Through each point in the space outside the luminaire source there is precisely one edge ray. The direction of the edge rays is a continuous and differentiable vector function of position. If we have a second tentative family of edge rays represented by another continuous vector function in the same region of space, we can design a reflector which precisely reflects one family onto the other.

Each point in space is the intersection of precisely one member of each family. Therefore, the inclination of the desired reflector in each point in space can be calculated in a conventional, well known manner. Thus, one can derive a differential equation which uniquely specifies the reflector once the starting point is chosen.

We can, for example, formalize this idea for the case where the tentative family of edge rays is given only along a reference line which is not necessarily a straight line. This pertains to the usual problems encountered in solving illumination requirements.

Referring to Figure 21, let a=a (x) be the two-dimensional unit vector 100 pointing toward the edge of a source 102 as seen from a point x, where k = k (t) is a parameterization of reference line 104 according to a scalar parameter t. Let u (t) be a unit vector 106 pointing in the direction of an edge ray 107 desired at the reference location specified by t. We can parameterize the contour of a reflector 108 with respect to the reference line 104 by writing the points on the reflector 108 as, R (t) =k (t) + Du (t). (35) Here the scalar D denotes the distance from a point on the reference line 104 to the reflector 108 along the desired edge ray 107 through this point.

Designing the shape of the reflector 108 in this notation is equivalent to specifying the scalar function D=D (t). An equation for D is derived from the condition that the reflector 108 should reflect the desired edge ray 107 along u (t) into the actual edge ray a (R (t)) and vice versa, <BR> <BR> <BR> is perpendicular to (a (R (t))-u (t)). (36)<BR> <BR> dt Inserting Eq. (35) from above yields, <BR> <BR> <BR> <BR> dD dk/dt#(a-u)+D(du/dt) - a<BR> <BR> <BR> <BR> dt (1-a)#u Here the dots indicate scalar products. Eq. (37) is a scalar differential equation for the scalar function D (t). By solving this equation, we can determine the reflector 108 which tailors the desired family of the edge ray 107 specified by the unit vector 106, u, to the source 102 characterized by the vector function, a.

This approach can also be used to tailor one family of the edge rays 107 onto another with refractive materials rather then reflectors. Eq. (36) then is replaced by Snell's law.

Consequently, the condition for the existence of a solution in this embodiment is that each point on the reflector 108 is intersected by precisely one member of the family of tentative edge rays. To be able to define this family of edge rays 107 along the reference line 104, each point on the reference line 104 must also be intersected by precisely one tentative edge ray. This is less than the requirement that the tentative edge rays define a physical surface which produces them. The family of the edge rays 107 of a physical contour (for example right edge rays) must also satisfy the further requirement that precisely one edge ray passes through each point of the entire space exterior to the contour. Indeed we can produce families of such edge rays by tailoring, but which cannot be produced by a single physical source. This is confirmed by observations that curved mirrors produce not only a distorted image of the source, but furthermore an image is produced that appears to move as the observer moves.

The condition that each point on the reflector 108, as well as each point on the reference line 104, should be intersected by precisely one of the desired edge rays 107 implies that the caustic formed by these edge rays 107 cannot intersect the reflector 108 or the reference line 104. The caustic is defined to be the line of tangents to the rays. The caustic must therefore either be entirely confined to the region between the reflector 108 and the reference line 104, or lie entirely outside this region. The first of these alternatives characterizes the CEC-type solutions, while the second one defines CHC-type solutions.

In order to determine the desired edge rays 107, the irradiance, for example, from a Lambertian source of uniform brightness B is given by its projected solid angle or view factor. In a conventional, known manner the view factor is calculated by projecting the source 102 first on a unit sphere surrounding the observer (this yields the solid angle) and then projecting the source 102 again onto the unit circle tangent to the reference plane.

The view factor is determined by the contour of the source 102 as seen by the observer. In two dimensions for example, the irradiance E is, E=B (sin rR-sin rL), (38) where rR and rL, are the angles between the normal to the reference line and the right and left edge rays striking the observer, respectively. If we know the brightness B, the desired irradiance E, and one edge ray, then Eq. (38) can be used to determine the desired direction of the other edge ray.

Consider the example of a source 110 of given shape (see Figures 22A and B). We then know the direction of the edge rays as seen by an observer as a function of the location of the observer. The shape of the source 110 can be defined by all its tangents. We can now design the reflector 108 so that it reflects a specified irradiance distribution onto the given reference line 104 iteratively.

In this iterative process, if an observer proceeds, for example, from right to left along reference line 112, the perceived reflection moves in the opposite direction for a CEC-type solution. As shown in Figure 22A, a right edge ray 114, as seen by the observer, is the reflection of the right edge, as seen from reflector 116, and further plays the role of leading-edge ray 114'along the reflector 116. A left edge ray 118 is just trailing behind, and this is shown in Figure 22A as reflected trailing edge ray 118'. For a CHC-type reflector 126 (see Figure 22B) the reflected image of the source 110 moves in the same direction as the observer, and the right edge as seen by the observer is the reflection of the left edge. If part of the reflector 126 is known, then a trailing-edge ray 128'which has been reflected by the known part of the reflector 126 can be calculated as a function of location on the reference line 112. Eq. (38) consequently specifies the direction of leading-edge ray 130. Eq. (37) can then be solved to tailor the next part of the reflector profile to this leading-edge ray 130.

Considering the boundary conditions, if the reflector 116 or 126 is terminated, then the reflected radiation does not terminate where the leading edge from the end of the reflector 116 or 126 strikes the reference line 112. Rather, the reflected radiation ends where the trailing edge from the end of the reflector 116 or 126 strikes the reference line 112 (see Figure 23). Thus, there is a'decay'zone 130 on the reference line 112 which subtends an equal angle at the source 110 as seen from the end of the reflector 116 or 126.

In this region the previously leading edge is at an end location 131 of the reflector 116 or 126, while the trailing edge gradually closes in. An analogous'rise'zone 132 exists at the other end of the reflector 116 or 126, where the trailing edge is initially fixed to a'start' position 134 of the reflector 116. However, there is an important conceptual difference between these two regions, in that the'rise'of the irradiance can be modeled by tailoring the reflector 116 or 126 to the leading edge, while the'decay'cannot be influenced once the reflector 116 or 126 is terminated. Therefore, there is a difference in which way we can proceed in the iterative tailoring of the reflector 116 or 126.

If the source 110 radiates in all directions and we want to avoid trapped radiation (that is, radiation reflected back onto the source 110), then the reflected radiation from each side of the reflector 140 should cover the whole target domain of the reflector 140 (see Figure 24). At the same time, the normal to the reflector surface should not intersect the source 110. Therefore, left and right side portions 142 and 143, respectively, of the reflectors 140 are joined in a cusp. An observer in the target domain thus perceives radiation from two distinct reflections of the source 110, one in each of the portions 142 and 143 of the reflector 140, in addition to the direct radiation from the source 110.

If we assume symmetry as shown in Figure 24 and assume the surface of the reflector 140 is continuous and differentiable (except for the cusp in the symmetry plane), then we require that, as seen from the symmetry plane, the two perceived reflections be equal. For all other points in the target domain we now have the additional degree of freedom of choosing the relative contributions of each of the portions 142 and 143 of the reflector 140. In CEC-type solutions both reflections appear to be situated between the target space and the reflector 140. Thus, as the observer moves, both reflection images move in the opposite direction. When the observer approaches the outermost part of the illuminated target region, the reflection on the same side first disappears at the cusp in the center. Thereafter, the reflection opposite to the observer starts to disappear past the outer edge of the opposite reflector, while the source itself is shaded by the outer edge of the other reflector portion on the observer side. These events determine the end point of the reflector 140 because now the total radiation in the target region equals the total radiation emitted by the source 110.

D. CEC-Type Reflector for Constant Irradiance A CEC-type reflector 150 can produce a constant irradiance on a distant plane from a finite size cylindrical source 152 of uniform brightness. This requires the angular power distribution to be proportional to 1/cos (6). In Figure 25 we show the necessary power from both reflections so that the total power is as required. The reflector 150 is depicted in Figure 26. The reflector 150 is designed starting from cusp 154 in the symmetry axes. Note that each reflection irradiates mostly the opposite side, but is visible from the same side too. Some angles have been particularly designated by the letters A through E in Figure 12. The corresponding edge rays are indicated also in Figure 27.

Between-A and A angles the reflections are immediately adjacent to the source 152. The cusp 154 in the center is not visible. Between A and B angles the reflection from the same side as the observer slowly disappears at the cusp 154, while the other increases in size for compensation. Starting with C, the source 152 is gradually eclipsed by the end of the reflector 150. The largest angle for which a constant irradiance can be achieved is labeled D. The source 152 is not visible. The power is produced exclusively by the opposite side reflection. The reflector 150 is truncated so that between D and E the reflection gradually disappears at the end of the reflector 150.

The inner part of the reflector 150, which irradiates the same side, is somewhat arbitrary. In the example shown, we have designed it as an involute because this avoids trapped radiation and at the same time yields the most compact design. At the center the power from each reflection is very nearly equal to that of the source 152 itself. Once the power radiated to the same side is determined, the reflector 150 is designed so that the sum of the contributions of the two reflections and the source 152 matches the desired distribution. Proceeding outward, the eclipsing of the source 152 by the reflector 150 is not known at first, because it depends on the end point. This problem is solved by iterating the whole design procedure several times.

The point of truncation is determined by the criterion that the reflector 150 intersects the edge rays marked B from the cusp 154, because the preferred design is based on a maximum of one reflection. This criterion is also the reason for designing the inner part as an involute.

The angular decay range D to E in Figures 25 and 27 depends only on the distance of the end point to the source 152. Depending on the starting distance from the cusp 154 to the source 152, the device can be designed either more compact, but with a broader decay zone, or larger, and with a more narrow decay zone. The reflector 150 shown has a cusp distance of 2.85 source diameters. The end point is at a distance of 8.5 source diameters. This ensures that a constant irradiance is produced between-43 and 43 degrees. The decay zone is only 7 degrees. This design was chosen so that the source 152 is eclipsed just before the angle of truncation.

The reflector 150 cannot be made much more compact as long as one designs for a minimum of one reflection. At the angle D the opening is nearly totally filled with radiation as seen in Figure 27. The distance the reflector 150 extends downward from the source 152 is also determined by the maximum power required to produce at angle D. The distance of the cusp 154 also cannot be diminished, otherwise the criterion for the end of the reflection 150 is reached sooner, the reflector 150 has to be truncated and the maximum power produced is also less.

In the preceding description we have discussed structures where the profile curve is along the x-and z-axes, or in the x-z plane, and is translationally invariant along the y-axis. In other words, the structures have embodied cylindrical symmetry. It may be advantageous to allow the profile curve to be a function of y as well; in other words, to exhibit no symmetry. In this case, y becomes a non-trivial variable. This parametric dependence would be arrived at through numerical optimization, making use of such standard codes as TRNSYS from the University of Wisconsin.

The embodiments described here involve at most one reflection. However, in other forms of the invention various systems based on multiple reflections can be designed using the teachings provided here. As more reflections contribute, the freedom of the designer increases. This freedom can be used to adapt the reflector to other criteria, such as- a need for compactness. In any case, independent of the number of reflections, once the general architecture has been determined, tailoring the reflector to one set of edge rays determines its shape without the need for approximations or a need to undergo optimizations. We emphasize that in this technology total internal reflection may have an important role.

A useful adjunct to the present system is described in an article entitled"A Dielectric Omnidirectional Reflector,"published in"Science,"Vol. 282,27 November 1998, which article is incorporated here by reference as if set forth fully. In that article, a design criterion that permits truly omnidirectional reflectivity for all polarizations of incident light over a wide selectable range of frequencies was used in fabricating an all-dielectric omnidirectional reflector consisting of multilayer films. The reflector was simply constructed as a stack of nine alternating micrometer-thick layers of polystyrene and tellurium and demonstrates omnidirectional reflection over the wavelength range from 10 to 15 micrometers. Because the omnidirectionality criterion is general, it can be used to design omnidirectional reflectors in many frequency ranges of interest. Potential uses depend on the geometry of the system. For example, coating of an enclosure will result in an optical cavity. A hollow tube will produce a low-loss, broadband waveguide, whereas a planar film could be used as an efficient radiative heat barrier or collector in thermoelectric devices. A commercial reflector with similar properties was announced by 3M Company in Photonics spectra of May 1999.

Figure 28a is a block diagram of a system for the practice of the present invention, and Figure 28b is a perspective view of an alternate version of a portion of the system. In Figure 28a, a solar collector 210 is placed so as to receive light from the sun.

The solar collector 210 may either track the sun or it may be fixed in place to receive solar energy over a wide range of angles. The solar collector 210 is indicated here as a single collector, but it may be a plurality of collectors. In Figure 28b, light pipes 231 are brought out of the bottom of the solar collectors 210.

The solar collector 210 is connected to a light pipe 212 which carries the collected solar radiation to an interior space 214. There may also be one or more light pipes 214 used as additional means of carrying light from the solar collector 210. It may be desirable to have an infrared shield 216 to keep heat out of the light pipe 212 and also an ultraviolet shield 218 to turn away or absorb ultraviolet radiation. In one embodiment of the invention the infrared shield 216 may be used in the summer when heat is not wanted in the interior space 214 and may be removed in the winter to admit heat. This is a matter of design choice and operating choice. The solar collector 210 may also includes one or more light pipes 216 exiting below the solar collector 210.

Figure 29a is a perspective view of a building 220 that includes an apparatus for the practice of the present invention. In Figure 29a, an array of solar collectors 222 is located on the roof 224 of the building 220, which can be seen to have one story. In general, a one-story building will not require much roof space to locate enough solar collectors to provide adequate interior illumination. In contrast, a high-rise building can be expected to need to have its roof covered with collectors and it will be necessary to place at least some solar collectors on the exterior walls to get enough light. The solar collectors 222 are connected to a light pipe 226 which is connected to a switch 228 that divides the light for distribution to different interior spaces 230. The switch 228 will normally be set to correspond to the area of each separate interior space 230 but it will need to be capable of adjustment if room sizes are changed by construction or if a different use of an interior space 230 requires a different lighting level. Light pipes 232 are connected to the switch 228 to convey light to reflectors 234 in each interior space 230. The reflectors 234 may distribute only collected solar energy, but it is more likely that the reflectors 234 will distribute light produced electrically as well, so that the reflectors are usable at night and on days when the level of sunlight is inadequate to meet the entire lighting load. As in Figure 28b, Figure 29b shows that one or more light pipes 235 may exit from the bottom of the solar collectors 222.

Figure 30 is a perspective view of a solar collector 210 for the practice of the present invention. In Figure 30, a reflector 240 is supported on a base 242 that may either be fixed or driven, If the base 242 is fixed, the reflector 240 will need to have a relatively large acceptance angle for solar radiation, and will thus generally have a lower average collection efficiency. If the base 242 is driven so as to track the sun, the acceptance angle may be smaller and the average collection efficiency will be higher. This is a matter of design choice. The reflector concentrates light on a light pipe 244 that will serve as an intermediate light source for a building. As with Figures 28b and 29b, there may be one or more light pipes (not shown) exiting from the bottom of the solar collector 210. When the only object of the invention is to use the light, it will be advantageous to filter infrared and ultraviolet radiation to leave only the visible light, which is relatively cool. This can be accomplished by a filter 246 that is essentially transparent to visible light but blocks or reflects away the infrared and ultraviolet radiation. When it is desired to use heat as well as light in the interior spaces 230 of Figure 29a, the filter 246 is constructed to prevent the passage of ultraviolet light but permit both visible and infrared radiation to pass. This means there may be a summer filter 246, removing the infrared, and a winter filter 246, admitting the infrared radiation to help heat the interior spaces. For comparable reasons, it may be desirable to use a summer reflector 210 and a winter reflector 210. This is likely to be the case with a passive or non-tracking reflector 210; a tracking reflector 210 can normally be aimed as desired in a direction that is appropriate to the season. It is almost never desirable to pass the ultraviolet radiation, since this radiation tends to cause relatively rapid degradation of light pipes, but if this radiation is desired and can be transmitted, it may be left with the collected radiation.

Figure 31 is a perspective view of a high-rise building 250 that is adapted for the practice of the present invention. In Figure 31, the roof 252 of building 250 is equipped with a plurality of reflectors 254 that may be passive or tracking reflectors. The walls 256 of the building that are exposed to sunlight are also covered with reflectors 258 and 260.

The reflectors 258 are here shown as horizontal and the reflectors 260 are vertical, but this is just a matter of design choice. The objective is to convert as much as possible of the sunlight incident upon the building 250 into light that is usable for interior illumination, heating, or both. Connections to the reflectors 254,258, and 260 are like those shown in Figures 28a, 28b, 29a and 29b. Entrances to the building 250 are not shown, but would be made most effectively on the shaded side.

Figure 32 is a perspective view of an apparatus for attachment as one of the reflectors 258 or 260 of Figure 31. A structure 280 is caused by a tracking or adjustment means 281 to track or substantially follow the sun and convey sunlight through a Fresnel lens 282. The maximum amount of focussed sunlight will be passed by a square, rectangular, or hexagonal Fresnel 282 lens that can be arrayed with similar Fresnel lenses to cover a relatively large area. Light passing thro ugh the Fresnel lens 282 is directed at a convex secondary lens 284 that captures the light and conducts it to a light pipe 286 for distribution. There will normally, although not necessarily, be one Fresnel lens 282 for each secondary lens 284, and the light pipe 286 may supply light directly to an interior space or it may join other light pipes to add the light from more than one Fresnel lens 282. The light pipe 286 may be circular in cross-section or it may be a substantially planar sheet or strip or a plurality of sheets or strips. The system could also be configured to work without the Fresnel lens.

At the other end of the light pipe that terminates inside the building technologies similar to those used for collection can be used to distribute the light to interior spaces.

APPENDIX-COMPUTER SOFTWARE PROGRAM program coordinates dimension r (1: 200), theta (1 : 200), dzdx (1 : 200) dimension xx (1 : 200), zz (1: 200) real l, kl, k2, k3, k4 parameter (degtorad=3.1415927/180.0) write (*, *)'Enter radius of cylindrical absorber.' read (*, *) a write (*, *)'Enter gap size.' read (*, *) b write (*, *)'Enter constant.' read (*, *) c write (*, *)'Enter maximum height.' read (*, *) h GENERATE 50 POINTS OF AN INVOLUTE alpha0=acos (a/ (a + b)) do 100 i =1, 50,1 alpha= ( (90*degtorad-alpha0)/49. 0) *float (i-50) + 90*degtorad d= (alpha-alpha0) *a + sqrt ( (a+b) **2-a**2) x= a*sin (alpha)-d*cos (alpha) z=-a*cos (alpha)-d*sin (alpha) r (i) = sqrt (x**2 +z**2) theta (i) = atan (z/x) phi= theta (i) + (90.0*degtorad) continue theta (1) =-90.0*degtorad GENERATE 150 POINTS OF THE WINSTON-TYPE CONCENTRATOR v= 0.0 h= 0.001 phi0= theta (50) + (90.0*degtorad) + 0.001 phi= phi f= alog (r (50)) do 200 while (v. eq. 0.0) phi= phi + h kl = h*tan (0. 5* ( (1. 0-c) *phi+c*phi0+asin (a/exp (f)))) k2-h-tan (0. 5* ( (1. 0-c) * (phi+0.5*h) +c*phiO+ & asin (a/exp (f+0. 5*kl)))) k3= h*tan (0. 5* ( (1. 0-c) * (phi+0.5*h) +c*phiO+ & asin (a/exp (f+0. 5*k2)))) k4 =b*tan (0. 5* ((1. 0-c) * (phi+h) +c*phi0+ & asin (a/exp (f+k3)))) f-f' (kl/6.0) + (k2/3.0) + (k3/3.0) + (k4/6.0) rad=exp (f) z = rad*sin (phi- (90*degtorad)) if (z. ge. a) then phimax=phi write (*, *)'phimax =', phi/degtorad v=1. 0 endif continue f=alog (r (50)) phi=(01.0/149. 0) * (phimax-phiO) +phi0 h=(phimax phi0)/149. 0 do 300 i=1, 150,1 phi =phi + h kl = h*tan (0. 5* ((1. 0-c) *phi+c*phi0+asin (a/exp (f)))) k2=h*tan (0. 5* ((1. 0-c) * (phi+0.5*h) +c*phi0+ & asin (a/exp (f+0.5*kl)))) k3=h*tan(0.5*((1.0-c) * (phi+0.5*h)+c*phi0+ & asin (a/exp (f+0.5*k2)))) k4=h*tan(0.5*((1. 0-c) * (phi+h)+c*phi0+ & asin (a/exp (f+k3)))) f=f + (kl/6.0) + (k2/3.0) + (k3/3.0) + (k4/6. 0) r (i+50) =exp (f) theta (i+50) =phi- (90.0*degtorad) continue stop end