Nonimaging optical illumination system

Abstract

A nonimaging illumination optical device for producing selected intensity output over an angular range. The device includes a light reflecting surface (24, 26) around a light source (22) which is disposed opposite the aperture opening of the light reflecting surface (24, 26). The light source (22) has a characteristic dimension which is small relative to one or more of the distance from the light source (22) to the light reflecting surface (24, 26) or the angle subtended by the light source (22) at the light reflecting surface (24, 26).

Description

The present invention is directed generally to a method and apparatus for providing user selected nonimaging optical outputs from different types of electromagnetic energy sources. More particularly, the invention is directed to a method and apparatus wherein the design profile of an optical apparatus for optical sources can be a variable of the acceptance angle of reflection of the source ray from the optical surface. By permitting such a functional dependence, the nonimaging output can be well controlled using various different types of light sources.

Methods and apparatus concerning illumination by light sources are set forth in a number of U.S. patents including, for example, U.S. Pat. Nos. 3,957,031; 4,240,692; 4,359,265; 4,387,961; 4,483,007; 4,114,592; 4,130,107; 4,237,332; 4,230,095; 3,923,381; 4,002,499; 4,045,246; 4,912,614 and 4,003,638 all of which are incorporated by reference herein. In one of these patents the nonimaging illumination performance was enhanced by requiring the optical design to have the reflector constrained to begin on the emitting surface of the optical source. However, in practice such a design was impractical to implement due to the very high temperatures developed by optical sources, such as infrared lamps, and because of the thick protective layers or glass envelopes required on the optical source. In other designs it is required that the optical reflector be separated substantial distances from the optical source. In addition, when the optical source is small compared to other parameters of the problem, the prior art methods which use the approach designed for finite size sources provide a nonimaging output which is not well controlled; and this results in less than ideal illumination. Substantial difficulties arise when a particular illumination output is sought but cannot be achieved due to limitations in optical design. These designs are currently constrained by the teachings of the prior art that one cannot utilize certain light sources to produce particular selectable illumination output over angle.

It is therefore an object of the invention to provide an improved method and apparatus for producing a user selected nonimaging optical output from any one of a number of different light sources.

It is another object of the invention to provide a novel method and apparatus for providing user selected nonimaging optical output of light energy from optical designs using a selected light source and a matching optical reflecting surface geometry.

It is a further object of the invention to provide an improved optical apparatus and method of design wherein the illumination output over angle is a function of the optical reflection geometry of both two and three dimensional optical devices.

It is a further object of the invention to provide an improved optical apparatus and method of design for radiation collection.

It is yet another object of the invention to provide a novel optical device and method for producing a user selected intensity output over an angular range of interest.

It is still an additional object of the invention to provide an improved method and apparatus for providing a nonimaging optical illumination system which generates a substantially uniform optical output over a wide range of output angles regardless of the light source used.

Other objects, features and advantages of the present invention will be apparent from the following description of the preferred embodiments thereof, taken in conjunction with the accompanying drawings described below wherein like elements have like numerals throughout the several views.

DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a two-dimensional optical device for providing nonimaging output;

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

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

FIG 4A shows a perspective view of a three dimensional optical system for nonimaging illumination, FIG. 4B shows a partial section of a reflecting side wall portion, FIG. 4C is an end view of the reflecting side wall of FIG. 4B and FIG. 4D is an end view of the optical system in FIG. 4A;

FIG. 5A shows intensity contours for an embodiment of the invention and FIG. 5B illustrates nonimaging intensity output contours from a prior art optical design;

FIG. 6A shows a schematic of a two dimensional Lambertian source giving a cos.sup.3 .theta. illuminace distribution; FIG. 6B shows a planar light source with the Lambertian source of FIG. 6A; FIG. 6C illustrates the geometry of a nonimaging refector providing uniform illuminance to .theta.=40.degree. for the source of FIG. 6A; and FIG. 6D illustrates a three dimensional Lambertian source giving a cos.sup.4 .theta. illuminance distribution; and

FIG. 7A shows a two dimensional solution ray trace analysis, FIG. 7B illustrates a first emperical fit to the three dimensional solution with n=2.1, FIG. 7C is a second emperical fit with n=2.2 and FIB. 7D is a third emperical fit with n=3;

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

A. Small Optical Sources

In the design of optical systems for providing nonimaging illumination using optical sources which are small relative to other system parameters, one should consider the limiting case where the source has no extent. This is in a sense the opposite of the usual nonimaging 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 nonimaging 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 nonimaging optics (see, for example, W. T. Welford and R. Winston "High Collection Nonimaging Optics," Academic Press, New York, N.Y. (1989)). Polar coordinates R,.phi. are used with the source as origin and .theta. for the angle of the reflected ray as shown in FIG. 3. The geometry in FIG. 3 shows that the following relation between source angle and reflected angle applies:

d/d.phi.(logR)=tan.alpha., (1) where .alpha. is the angle of incidence with respect to the normal. Therefore, .alpha.=(.phi.-.theta.)/2 (2) Equation (1) is readily integrated to yield, log(R)=.intg. tan.alpha.d.phi.+const. (3) so that, R=const. exp(.intg. tan.alpha.d.phi.) (4) This equation (4) determines the reflector profile R(.phi.) for any desired functional dependence .theta.(.phi.).

Suppose we wish to radiate power (P) with a particular angular distribution P(.theta.) from a line source which we assume to be axially symmetric. For example, P(.theta.)=const. from .theta.=0 to .theta..sub.1 and P(.theta.).about.0 outside this angular range. By conservation of energy P(.theta.)d.theta.=P(.phi.)d.phi. (neglecting material reflection loss) we need only ensure that

d.theta./d.phi.=P(.phi.)/P(.theta.) (5) to obtain the desire radiated beam profile. To illustrate the method, consider the above example of a constant P(.theta.) for a line source. By rotational symmetry of the line source, P(.phi.) =a constant so that, according to Equation (4) we want .theta. to be a linear function of .phi. such as, .theta.=a.phi.. Then the solution of Equation (3) is R=R.sub.0 / cos.sup.k (.phi./k) (6) where, k=2/(1-a), (7) and R.sub.0 is the value of R at .phi.=0. We note that the case a=0(k=2) gives the parabola in polar form, R=R.sub.0 / cos.sup.2 (.phi./2), (8) while the case .theta.-constant-.theta..sub.1 gives the off-axis parabola, R=R.sub.0 cos.sup.2 (.theta..sub.1 /2)/ cos.sup.2 [(.phi.-.theta..sub.1)/2](9) Suppose we desire instead to illuminate a plane with a particular intensity distribution. Then we correlate position on the plane with angle .theta. and proceed as above.

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

P(.OMEGA.)d.OMEGA.=P(.OMEGA..sub.0)d.OMEGA..sub.0 (10) where .OMEGA..sub.0 is the solid angle radiated by the source. By spherical symmetry of the point source, P(.OMEGA..sub.0)=constant. Moreover, we have d.OMEGA.=(2.pi.)d cos.theta. and d.OMEGA..sub.0 =(2.pi.)d cos.phi.; therefore, we need to make cos.theta. a linear function of cos.phi., cos.theta.=a cos.phi.+b (11.sub.1) With the boundary conditions that .theta.=0 at .phi.=.theta., .theta.=.theta..sub.1 at .phi.=.phi..sub.0, we obtain, a(1-cos.theta..sub.1)/(1-cos.phi..sub.0) (12) b(cos.theta..sub.1 -cos.phi..sub.0)/(1-cos.phi..sub.0) (13) For example, for .theta..sub.1 <<1 and .phi..sub.0 .about..pi./2 we have, .theta..about..sqroot.2.theta..sub.0 sin(1/2.phi.).] This functional dependence is applied to Equation (4) which is then integrated, such as by conventional numerical methods.

A useful way to describe the reflector profile R(.phi.) is in terms of the envelope (or caustic) of the reflected rays r(.phi.). This is most simply given in terms of the direction of the reflected ray t=(-sin.theta., cos.theta.). Since r(.phi.) lies along a reflected ray, it has the form,

r=R+Lt. (14) where R=R(sin.phi..sub.1 -cos.phi.). Moreover, Rd.phi.=Ld.theta. (15) which is a consequence of the law of reflection. Therefore, r=R+Rt/(d.theta./d.phi.) (16) In the previously cited case where .theta. is the linear function a.phi., the caustic curve is particularly simple, r=R+Rt/a (17) In terms of the caustic, we may view the reflector profile R 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 .theta.=0 with an involute to a virtual source. Thus, the reflector design should be involute to the "ice cream cone"0 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. Pat. 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 nonimaging designs. This method can be implemented and a profile calculated using the computer program of the Appendix (and see FIG. 2) and an example of a line source and profile is illustrated in FIG. 1. Also, in case the beam pattern and/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(.phi.) determined hereinbefore as explained in expressions (5) to (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 Equations (10) through (13).

A preferred form of nonimaging optical system 20 is shown in FIG. 4A with a representative nonimaging output illustrated in FIG. 5A. Such an output can typically be obtained using conventional infrared optical sources 22 (see FIG. 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 FIG. 5B, the prior art paraboloidal reflector systems (not shown) provide a nonuniform intensity output, whereas the optical system 20 provides a substantially uniform intensity output as shown in FIG. 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 1.09Ratio of Azimuth Edge to On Axis 0.70 0.68Ratio of Elevation Edge to On Axis 0.63 0.87Ratio of Corner to On Axis 0.33 0.52Percent of Radiation Inside Useful Angles 0.80 0.78Normalized 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:

1. a=the radius of a circular absorber; 2. b=the size of the gap; 3. c=the constant of proportionality between .theta. and .phi.-.phi..sub.0 in the equation .theta.=c(.phi.-.phi..sub.0); 4. 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 .phi.=0 to .phi.=.phi..sub.0 in FIG. 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 .alpha. (see FIG. 3A). As can be seen in FIG. 3B, as .phi. varies from 0 to .phi..sub.0, .alpha.varies from .alpha..sub.0 to ninety degrees. The angle .alpha..sub.0 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,.theta.) points are read to arrays r(i), and theta(i), respectively.

For values of .phi. greater than .phi..sub.0, the profile is the solution to the differential equation:

d(lnr)d.phi.=tan{1/2[.phi.-.theta.+arc sin(a/r)]} where .theta. is a function of .phi.. This makes the profile r(.phi.) a functional of .theta.. In the sample calculation performed, .theta. is taken to be a linear function of .phi. as in item 3 above. Other functional forms are described in the specification. It is desired to obtain one hundred fifty (r, theta) points in this region. In addition, the profile must be truncated to have the maximum height, h. We do not know the (r,theta) point which corresponds to this height, and thus, we must solve the above equation by increasing phi beyond .phi..sub.0 until the maximum height condition is met. This is carried out using the conventional fourth order Runga-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,theta) point at the maximum height is known, we can set our step sizes to calculate exactly one hundred fifty (r,theta) points between .phi..sub.0 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), theta(i).

In the end, we are left with two arrays: r(i) and theta(i), each with two hundred components specifying two hundred (r,theta) 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(.theta.)=constant), a typical set of parameters is (also see FIG. 1):

a=0.055 in. b=0.100 in. h=12.36 in. c=0.05136 for .theta.(.phi.)=c(.phi.-.phi..sub.o)

In the case of an exponential beam profile (P(.theta.)=ce.sup.-a.theta.) a typical set of parameters is:

a.about.o h=5.25 b=0.100 c=4.694 .theta.(.phi.)=0.131ln(1-.phi./c)

B. General Optical Sources

Nonimaging illumination can also be provided by general optical sources provided the geometrical constraints on a reflector can be defined by simultaneously solving a pair of system. The previously recited equations (1) and (2) relate the source angle and angle of light reflection from a reflector surface,

d/d.phi.(logR.sub.i)=tan (.phi..sub.i -.theta..sub.i)/2 (18) and the second general expression of far field illuminance is, L(.theta..sub.i).multidot.R.sub.i sin (.phi..sub.i -.theta..sub.i)G(.theta..sub.i)=I(.theta..sub.i) (19) where L (.theta..sub.i) is the characteristic luminance at angle .theta..sub.i and G (.theta..sub.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 FIG. 6A, the radiated power versus angle for constant illuminance varies as cos.sup.-2 .theta.. For a three dimensional Lambertian light source shown in FIG. 6D, the radiated power versus angle for constant illuminance varies as cos.sup.-3 .theta..

Considering the example of a two dimensional Lambertian light source and tile planar source illustrated in FIG. 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 .theta. in FIG. 6B is negative. In this example we will solve equations (18) and (19) simultaneously for a uniform far field illuminance using the two dimensional Lambertian source. In this example, equation (19) because,

R.sub.i sin (.phi..sub.i -.theta..sub.i) cos.sup.2 .theta..sub.i =I(.theta..sub.i)

Generally for a bare two dimensional Lambertian source,

I(.theta..sub.i).about..delta. cos .theta..sub.i .delta..about.a cos .theta..sub.i /l l.about.d/ cos .theta.

Therefore, I.about. cos.sup.3 .theta..

In the case of selecting a uniform far field illuminance I(.theta..sub.i)=C, and if we solve equations (18) and (19),

d/d.phi. (log R.sub.i)=tan (.phi..sub.i -.theta..sub.i)/2 and log R.sub.i +log sin (.phi..sub.i -.theta..sub.l)+2 log cos .theta..sub.i =log C=constant solving d.phi..sub.i /d.theta..sub.i =-2 tan.theta..sub.i sin (.phi..sub.i -.theta..sub.i)-cos (.phi..sub.i -.theta..sub.i) or let .psi..sub.i =.phi..sub.i -.theta..sub.i d.psi..sub.i /d.theta..sub.i -1+sin .psi..sub.i -2 tan .theta..sub.i cos .psi..sub.i

Solving numerically by conventional methods, such as the Runge-Kutta method, starting at .psi..sub.i =0 at .theta..sub.i, for the constant illuminance,

d.psi..sub.i /d.theta..sub.i =1+sin .psi..sub.i -n tan .theta..sub.i cos .psi..sub.i where n is two for the two dimensional source. The resulting reflector profile for the two dimensional solution is shown in FIG. 6C and the tabulated data characteristic of FIG. 6C is shown in Table III. The substantially exact nature of the two dimensional solution is clearly shown in the ray trace fit of FIG. 7A. The computer program used to perform these selective calculation is included as Appendix B of the Specification. For a bare three dimensional Lambertian source where I(.theta..sub.i).about. cos.sup.4 .theta..sub.i, n is larger than 2 but less than 3.

The ray trace fit for this three dimensional solution is shown in FIG. 7B-7D wherein the "n" value was fitted for desired end result of uniform far field illuminance with the best fit being about n=2.1 (see FIG. 7B).

Other general examples for different illuminance sources include,

(1) I(.theta..sub.i)-A exp (B.theta..sub.i) for a two dimensional, exponential illuminance for which one must solve the equation, d.psi..sub.i /d.theta..sub.i 1+sin .psi..sub.i -2 tan .theta..sub.i cos .psi.+B (2) I(.theta..sub.i)=A exp (-B.theta..sub.i.sup.2 /2) for a two dimensional solution for a Gaussian illuminance for which one must solve, d.psi..sub.i /d.theta..sub.i =1+sin .psi..sub.i -2 tan .theta..sub.i cos .psi..sub.i -B.theta..sub.i

Equations (18) and (19) 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 FIG. 1 is shown in a tabular form of output in Table II below:

__________________________________________________________________________AZIMUTH 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______________________________________Phi Theta 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 96.0302 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 1.23607100.251 8.89545 1.24522100.553 9.12933 1.25454100.854 9.36213 1.26402101.156 9.59390 1.27367101.457 9.82466 1.28349101.759 10.0545 1.29349102.060 10.2833 1.30366102.362 10.5112 1.31402102.663 10.7383 1.32457102.965 10.9645 1.33530103.266 11.1899 1.34624103.568 11.4145 1.35738103.869 11.6383 1.36873104.171 11.8614 1.38028104.472 12.0837 1.39206104.774 12.3054 1.40406105.075 12.5264 1.41629105.377 12.7468 1.42875105.678 12.9665 1.44145105.980 13.1857 1.45441106.281 13.4043 1.46761 1.48108107.789 14.4898 1.53770108.090 14.7056 1.55259108.392 14.9209 1.56778108.693 15.1359 1.58329108.995 15.3506 1.59912109.296 15.5649 1.61529109.598 15.7788 1.63181109.899 15.9926 1.64868110.201 16.2060 1.66591110.503 16.4192 1.68353110.804 16.6322 1.70153111.106 16.8450 1.71994111.407 17.0576 1.73876111.709 17.2701 1.75801112.010 17.4824 1.77770112.312 17.6946 1.79784112.613 17.9068 1.81846112.915 18.1188 1.83956113.216 18.3309 1.86117113.518 18.5429 1.88330113.819 18.7549 1.90596114.121 18.9670 1.92919114.422 19.1790 1.95299114.724 19.3912 1.97738115.025 19.6034 2.00240115.327 19.8158 2.02806115.628 20.0283 2.05438115.930 20.2410 2.08140116.231 20.4538 2.10913116.533 20.6669 2.13761116.834 20.8802 2.16686117.136 21.0938 2.19692117.437 21.3076 2.22782117.739 21.5218 2.25959118.040 21.7362 2.29226118.342 21.9511 2.32588118.643 22.1663 2.36049118.945 22.3820 2.39612119.246 22.5981 2.43283119.548 22.8146 2.47066119.849 23.0317 2.50967120.151 23.2493 2.54989120.452 23.4674 2.59140120.754 23.6861 2.63426121.055 23.9055 2.67852121.357 24.1255 2.72426121.658 24.3462 2.77155121.960 24.5676 2.82046122.261 24.7898 2.87109122.563 25.0127 2.92352122.864 25.2365 2.97785123.166 25.4611 3.03417123.467 25.6866 3.09261123.769 25.9131 3.15328124.070 26.1406 3.21631124.372 26.3691 3.28183124.673 26.5986 3.34999124.975 26.8293 3.42097125.276 27.0611 3.49492125.578 27.2941 3.57205125.879 27.5284 3.65255126.181 27.7640 3.73666126.482 28.0010 3.82462126.784 28.2394 3.91669127.085 28.4793 4.01318127.387 28.7208 4.11439127.688 28.9638 4.22071127.990 29.2086 4.33250128.291 29.4551 4.45022128.593 29.7034 4.57434128.894 29.9536 4.70540129.196 30.2059 4.84400129.497 30.4602 4.99082129.799 30.7166 5.14662130.101 30.9753 5.31223130.402 31.2365 5.48865130.704 31.5000 5.67695131.005 31.7662 5.87841131.307 32.0351 6.09446131.608 32.3068 6.32678131.910 32.5815 6.57729132.211 32.8593 6.84827132.513 33.1405 7.14236132.814 33.4251 7.46272133.116 33.7133 7.81311133.417 34.0054 8.19804133.719 34.3015 8.62303134.020 34.6019 9.09483134.322 34.9068 9.62185134.623 35.2165 10.2147134.925 35.5314 10.8869135.226 35.8517 11.6561135.528 36.1777 12.5458135.829 36.5100 13.5877136.131 36.8489 14.8263136.432 37.1949 16.3258136.734 37.5486 18.1823137.035 37.9106 20.5479137.337 38.2816 23.6778137.638 38.6625 28.0400137.940 39.0541 34.5999138.241 39.4575 45.7493138.543 39.8741 69.6401138.844 40.3052 166.255139.146 40.7528 0.707177E-01139.447 41.2190 0.336171E-01139.749 41.7065 0.231080E-01140.050 42.2188 0.180268E-01140.352 42.7602 0.149969E-01140.653 43.3369 0.129737E-01140.955 43.9570 0.115240E-01141.256 44.6325 0.104348E-01141.558 45.3823 0.958897E-02141.859 46.2390 0.891727E-02142.161 47.2696 0.837711E-02142.462 48.6680 0.794451E-02142.764 50.0816 0.758754E-02143.065 48.3934 0.720659E-02143.367 51.5651 0.692710E-02143.668 51.8064 0.666772E-02143.970 56.1867 0.647559E-02144.271 55.4713 0.628510E-02144.573 54.6692 0.609541E-02144.874 53.7388 0.590526E-02145.176 52.5882 0.571231E-02145.477 50.8865 0.550987E-02145.779 53.2187 0.534145E-02146.080 52.1367 0.517122E-02146.382 50.6650 0.499521E-02146.683 49.5225 0.481649E-02146.985 45.6312 0.459624E-02147.286 56.2858 0.448306E-02147.588 55.8215 0.437190E-02147.889 55.3389 0.426265E-02148.191 54.8358 0.415518E-02148.492 54.3093 0.404938E-02148.794 53.7560 0.394512E-02149.095 53.1715 0.384224E-02149.397 52.5498 0.374057E-02149.698 51.8829 0.363992E-02150.000 51.1597 0.354001E-02______________________________________ ##SPC1##

Claims

1. A nonimaging illumination optical device for producing a selected far field illuminance output I(.theta.) over an angular range .theta., comprising:

a source of light having a surface and a characteristic luminance L(.theta.) and related to said selected far field illuminance output I(.theta.) by the expression:

L(.theta..sub.i)R.sub.i sin(.phi..sub.i -.theta..sub.i)Q(.theta..sub.i)=I(.theta..sub.i) (A)

where R.sub.i is a radius vector from a point within said source of light, .phi..sub.i is an angle between said radius vector and a direction 180.degree. from direct forward illumination output from said nonimaging illumination optical device, .theta..sub.i is an angle between direct forward illumination and light rays reflected once from a light reflecting surface having an aperture opening and a spatial position and also disposed at least partially around said light source and said light source disposed opposite the aperature opening of said light reflecting surface and G(.theta..sub.i) is a geometrical factor that is a function of the geometry of said light source; and

the spatial position of said light reflecting surface for producing said selected far field illuminance output I(.theta..sub.i) being defined in terms of said R.sub.i, .phi..sub.i and .theta..sub.i and said R.sub.i functionally describing a profile for said spatial position of said light reflecting surface and varying as a function of said angle .phi..sub.i in accordance with the expression:

R.sub.i =(const.)exp {.intg. tan [(.phi..sub.i -.theta..sub.i)/2]d.phi..sub.i } (b)

and said light reflecting surface satisfying equations (a) and (b) simultaneously.

2. The nonimaging optical device as defined in claim 1 where said .theta..sub.i can range from a positive to a negative angle.

3. A nonimaging illumination optical device for producing a selected far field illuminates output I(.theta.) over an angular range .theta., comprising:

a source of light having a characteristic luminance L(.theta..sub.i) and related to said I(.theta.) by the expression:

L(.theta..sub.i)R.sub.i sin (.phi..sub.i -.theta..sub.i) cos.sup.11 .theta..sub.i =I(.theta..sub.i) (a)

where R.sub.i is a radius vector from a point within said source of light, .phi..sub.i is an angle between said radius vector and a direction 180.degree. from direct forward illumination output from said device, n is a number determined by the geometry of said light source and .theta..sub.i is an angle between direct forward illumination and light rays reflected once from a light reflecting surface having an aperature opening and a spatial position and also positioned at least partially around said light source and said light source disposed opposite the aperature opening of said light reflecting surface; and

the spatial position of said light reflecting surface for producing said selected far field illuminance output I(.theta..sub.i) being defined in terms of said R.sub.i, .phi..sub.i, and .theta..sub.i and said R.sub.i functionally describing a profile for said spatial position of said light reflecting surface varying as a function of said angle .phi..sub.i in accordance with the expression:

R.sub.i =(const.)exp {.intg. tan [(.phi..sub.i -.theta..sub.i)/2]d.phi..sub.i } (b)

and said light reflecting surface satisfying equations (a) and (b) simultaneously.

4. The nonimaging illumination optical device as defined in claim 3 wherein said "n" exponent is 2 for two dimensional light source solutions and is greater than two for three dimensional light source solutions.

5. The nonimaging optical device as defined in claim 3 where said n is almost 2.1 for three dimensional sources.

6. The nonimaging illumination optical device as defined in claim 3 wherein said selected far field illuminance output I(.theta.) comprises a substantially constant illuminance over said angular range .theta..

7. The nonimaging illumination optical device as defined in claim 3 wherein said selected far field illuminance I(.theta..sub.i) is a constant and said light reflecting surface is described in accordance with the expression:

d.psi..sub.i /d.theta..sub.i =1+sin.psi..sub.i -n tan(.theta..sub.i) cos .psi..sub.i

where .psi..sub.i =.phi..sub.i -.theta..sub.i -.pi./2.

8. The nonimaging illumination optical device as defined in claim 3 wherein said I(.theta..sub.i)=A exp (B.theta..sub.i) for two-dimensional light source solutions where A and B are constants and said light reflecting surface is described in accordance with the expression:

d.psi./d.theta..sub.i =1+sin.psi..sub.i -2 tan(.theta..sub.i) cos.psi..sub.i +B;

where .psi..sub.i =.phi..sub.i -.theta..sub.i =.pi./2

9. The nonimaging illumination optical device as defined in claim 3 wherein said selected far field illuminance I(.theta..sub.i)=A exp (-B.theta..sub.i.sup.2 /2) for two-dimensional light source solutions and Gaussian illuminance and A and B are constants and said light reflecting surface is described in accordance with the expression:

d.psi..sub.i /d.theta..sub.i =1+sin.psi..sub.i -2 tan (.theta..sub.i) cos .psi..sub.i -B.theta..sub.i

10. A nonimaging illumination optical device for producing a selected far field illuminance output I(.theta.) over an angular range .theta., comprising:

a light reflecting surface having an aperature opening and a spatial position and also a light source having a surface and disposed opposite the aperature opening of said light reflecting surface, said light source having a characteristic luminance L(.theta..sub.i) and related to said selected far field illuminance output I(.theta.) by the expression:

L(.theta..sub.i)R.sub.i sin (.phi..sub.i -.theta.i)G(.theta..sub.i)=I(.theta..sub.i) (a)

where R.sub.i is a radius vector from a point within said light source, .phi..sub.1 is an angle between said radius vector and a direction 180.degree. from direct forward illumination output from said nonimaging illumination optical device, .theta..sub.i is an angle between direct forward illumination and light rays reflected once from said light reflecting surface and G(.theta..sub.i) is a geometrical factor that depends on the geometry of said light source; and

the spatial position of said light reflecting surface for producing said selected far field illuminance output I(.theta..sub.i) being defined in terms of said R.sub.i, .psi..sub.i and .theta..sub.i and said R.sub.i functionally describing a profile for said spatial position of said light reflecting surface and varying as a function of said angle .phi..sub.i in accordance with the expression:

R.sub.i =(const.) exp {.intg. tan[(.phi..sub.i -.theta..sub.i)/2]d.phi..sub.i } (b)

with said light reflecting surface satisfying equations (a) and (b) simultaneously.

11. The nonimaging optical device as defined in claim 10 wherein said .theta..sub.i can range from a positive to a negative angle.