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 3  θ 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 θ=40° for the source of FIG. 6A; and FIG. 6D illustrates a three dimensional Lambertian source giving a cos 4  θ 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 &#34;edge-ray methods&#34; of nonimaging optics (see, for example, W. T. Welford and R. Winston &#34;High Collection Nonimaging Optics,&#34; Academic Press, New York, N.Y. (1989)). Polar coordinates R,φ are used with the source as origin and θ 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/dφ(logR)=tanα,                                 (1) 
    
     where α is the angle of incidence with respect to the normal. Therefore, 
     
         α=(φ-θ)/2                                  (2) 
    
     Equation (1) is readily integrated to yield, 
     
         log(R)=∫ tanαdφ+const.                      (3) 
    
     
         so that, 
    
     
         R=const. exp(∫ tanαdφ)                      (4) 
    
     This equation (4) determines the reflector profile R(φ) for any desired functional dependence θ(φ). 
     Suppose we wish to radiate power (P) with a particular angular distribution P(θ) from a line source which we assume to be axially symmetric. For example, P(θ)=const. from θ=0 to θ 1  and P(θ)˜0 outside this angular range. By conservation of energy P(θ)dθ=P(φ)dφ (neglecting material reflection loss) we need only ensure that 
     
         dθ/dφ=P(φ)/P(θ)                        (5) 
    
     to obtain the desire radiated beam profile. To illustrate the method, consider the above example of a constant P(θ) for a line source. By rotational symmetry of the line source, P(φ) =a constant so that, according to Equation (4) we want θ to be a linear function of φ such as, θ=aφ. Then the solution of Equation (3) is 
     
         R=R.sub.0 / cos.sup.k (φ/k)                            (6) 
    
     
         where, 
    
     
         k=2/(1-a),                                                 (7) 
    
     and R 0  is the value of R at φ=0. We note that the case a=0(k=2) gives the parabola in polar form, 
     
         R=R.sub.0 / cos.sup.2 (φ/2),                           (8) 
    
     while the case θ-constant-θ 1  gives the off-axis parabola, 
     
         R=R.sub.0 cos.sup.2 (θ.sub.1 /2)/ cos.sup.2 [(φ-θ.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 θ and proceed as above. 
     Turning next to a spherically symmetric point source, we consider the case of a constant P(Ω) where Ω is the radiated solid angle. Now we have by energy conservation, 
     
         P(Ω)dΩ=P(Ω.sub.0)dΩ.sub.0          (10) 
    
     where Ω 0  is the solid angle radiated by the source. By spherical symmetry of the point source, P(Ω 0 )=constant. Moreover, we have dΩ=(2π)d cosθ and dΩ 0  =(2π)d cosφ; therefore, we need to make cosθ a linear function of cosφ, 
     
         cosθ=a cosφ+b                                    (11.sub.1) 
    
     With the boundary conditions that θ=0 at φ=θ, θ=θ 1  at φ=φ 0 , we obtain, 
     
         a(1-cosθ.sub.1)/(1-cosφ.sub.0)                   (12) 
    
     
         b(cosθ.sub.1 -cosφ.sub.0)/(1-cosφ.sub.0)     (13) 
    
     For example, for θ 1  &lt;&lt;1 and φ 0  ˜π/2 we have, θ˜√2θ 0  sin(1/2φ).] 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(φ) is in terms of the envelope (or caustic) of the reflected rays r(φ). This is most simply given in terms of the direction of the reflected ray t=(-sinθ, cosθ). Since r(φ) lies along a reflected ray, it has the form, 
     
         r=R+Lt.                                                    (14) 
    
     where R=R(sinφ 1  -cosφ). Moreover, 
     
         Rdφ=Ldθ                                          (15) 
    
     which is a consequence of the law of reflection. Therefore, 
     
         r=R+Rt/(dθ/dφ)                                   (16) 
    
     In the previously cited case where θ is the linear function aφ, 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 &#34;point-like&#34; or &#34;line-like&#34; angular distributions derived above. To prevent radiation from returning to the source, one may wish to &#34;begin&#34; the solution in the vicinity of θ=0 with an involute to a virtual source. Thus, the reflector design should be involute to the &#34;ice cream cone&#34;0 virtual source. It is well known in the art how to execute this result (see, for example, R. Winston, &#34;Appl. Optics,&#34; 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 &#34;edge rays&#34; 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(φ) 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 θ and φ-φ 0  in the equation θ=c(φ-φ 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 φ=0 to φ=φ 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 α (see FIG. 3A). As can be seen in FIG. 3B, as φ varies from 0 to φ 0 , αvaries from α 0  to ninety degrees. The angle α 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,θ) points are read to arrays r(i), and theta(i), respectively. 
     For values of φ greater than φ 0 , the profile is the solution to the differential equation: 
     
         d(lnr)dφ=tan{1/2[φ-θ+arc sin(a/r)]} 
    
     where θ is a function of φ. This makes the profile r(φ) a functional of θ. In the sample calculation performed, θ is taken to be a linear function of φ 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 φ 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 φ 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(θ)=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 θ(φ)=c(φ-φ o ) 
     In the case of an exponential beam profile (P(θ)=ce -a θ) a typical set of parameters is: 
     a˜o 
     h=5.25 
     b=0.100 
     c=4.694 
     θ(φ)=0.131ln(1-φ/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/dφ(logR.sub.i)=tan (φ.sub.i -θ.sub.i)/2    (18) 
    
     and the second general expression of far field illuminance is, 
     
         L(θ.sub.i)·R.sub.i sin (φ.sub.i -θ.sub.i)G(θ.sub.i)=I(θ.sub.i)          (19) 
    
     where L (θ i ) is the characteristic luminance at angle θ i  and G (θ 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 -2  θ. For a three dimensional Lambertian light source shown in FIG. 6D, the radiated power versus angle for constant illuminance varies as cos -3  θ. 
     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 θ 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 (φ.sub.i -θ.sub.i) cos.sup.2 θ.sub.i =I(θ.sub.i) 
    
     Generally for a bare two dimensional Lambertian source, 
     
         I(θ.sub.i)˜δ cos θ.sub.i 
    
     
         δ˜a cos θ.sub.i /l 
    
     
         l˜d/ cos θ 
    
     Therefore, I˜ cos 3  θ. 
     In the case of selecting a uniform far field illuminance I(θ i )=C, and if we solve equations (18) and (19), 
     d/dφ (log R i )=tan (φ i  -θ i )/2 and 
     log R i  +log sin (φ i  -θ l )+2 log cos θ i  =log C=constant 
     solving dφ i  /dθ i  =-2 tanθ i  sin (φ i  -θ i )-cos (φ i  -θ i ) 
     or let ψ i  =φ i  -θ i   
     dψ i  /dθ i  -1+sin ψ i  -2 tan θ i  cos ψ i   
     Solving numerically by conventional methods, such as the Runge-Kutta method, starting at ψ i  =0 at θ i , for the constant illuminance, 
     
         dψ.sub.i /dθ.sub.i =1+sin ψ.sub.i -n tan θ.sub.i cos ψ.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(θ.sub.i)˜ cos.sup.4 θ.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 &#34;n&#34; 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(θ i )-A exp (Bθ i ) for a two dimensional, exponential illuminance for which one must solve the equation, 
     
         dψ.sub.i /dθ.sub.i 1+sin ψ.sub.i -2 tan θ.sub.i cos ψ+B 
    
     (2) I(θ i )=A exp (-Bθ i   2  /2) for a two dimensional solution for a Gaussian illuminance for which one must solve, 
     
         dψ.sub.i /dθ.sub.i =1+sin ψ.sub.i -2 tan θ.sub.i cos ψ.sub.i -Bθ.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##