WO1993002320A1

WO1993002320A1 - Non-imaging optical illumination system

Info

Publication number: WO1993002320A1
Application number: PCT/US1992/006032
Authority: WO
Inventors: Roland Winston
Original assignee: Nioptics Corporation
Priority date: 1991-07-19
Filing date: 1992-07-17
Publication date: 1993-02-04
Also published as: IL102530A; CA2113357A1; JP2763679B2; CA2113357C; DE69232264D1; US5289356A; AU2382992A; EP0596004A1; IL102530A0; EP0596004A4; EP0596004B1; DE69232264T2; ATE210263T1; AU670035B2; JPH06509210A; TW232724B

Abstract

A non-imaging 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

NON-IMAGING OPTICAL ILLUMINATION SYSTEM

The present invention is directed generally to a method and apparatus for providing user selected nonimaging optical outputs from electromagnetic energy sources of finite but small extent. More particularly, the invention is directed to a method and apparatus wherein the design profile of an optical apparatus for small, finite 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.

Methods and apparatus concerning illumination by light sources of finite extent are set forth in a number of U.S.

patents including 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 source 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 therefore arise when the optical design involves situations such as: (1) the source size is much less than the closest distance of approach to any reflective or refractive component or (2) the angle subtended by the source at any ref lective or ref ractive component is much smaller than the angular divergence of an optical beam.

It is therefore an object of the invention to provide an improved method and apparatus for producing a user selected nonimaging optical output.

It is another object of the invention to provide a novel method and apparatus for providing user selected nonimaging optical output of electromagnetic energy from optical designs using small, but finite, electromagnetic energy sources.

It is a further object of the invention to provide an improved optical apparatus and method of design wherein the optical acceptance angle for an electromagnetic ray is a function of the profile parameters 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.

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

FIGURE 1 shows a two-dimensional optical device for

providing nonimaging output;

FIGURE 2 illustrates a portion of the optical device of

FIG. 1 associated with the optical source and immediate

reflecting surface of the device.

FIGURE 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;

FIGURE 4A shows a perspective view of a three-dimensional optical system for nonimaging illumination and FIG. 4B

illustrates a portion of the optical system of FIG. 4A; and

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

Detailed Description of Preferred Embodiments

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, New York / (1989)). Polar coordinates R,Φ are used with the source as origin and θ for the angle of the ref lected 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 ( A ) 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 θ₁ 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

dθdΦ=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, dP/dΦ = 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=R₀/CoS^k(Φ/k) (6)

where,

k=2/(1-a), (7)

and R₀ is the value of R at Φ=0.

We note that the case a=0 (k=2) gives the parabola in polar form,

R=R₀/cos²(Φ/2), (8)

while the case θ=constant=θ₁ gives the off-axis parabola,

R=R₀cos²(θ₁/2)/cos²[Φ-θ₀)/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(Ω₀)dΩ₀ (10)

where Ω_o is the solid angle radiated by the source. By

spherical symmetry of the point source, P(Ω₀)=constant.

Moreover, we have dΩ=(2π)dcosθ and dΩ₀=(2π)dcosΦ; therefore, we need to make cosθ a linear function of cosΦ,

cosθ=a cosΦ + b (11)₁ With the boundary conditions that θ = 0 at Φ = θ, θ=θ₁ at Φ=Φ₀. we obtain,

a=(1-cosθ₁)/(1-cosΦ₀) (12)

b=(cosθ₁-cosΦ₀)/(1-cosΦ₀) (13)

[For example, for θ₁<<1 and Φ₀~π/2 we have, θ~√2θ₀sin(½Φ).] 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(sinΦ₁-cosΦ). Moreover,

RdΦ=Ldθ (15)

which is a consequence of the law of reflection. Therefore, r=R+t/(dθ/dΦ) (16)

In the previously cited case where θ is the linear function aΦ, the caustic curve is particularly simple,

r=R+t/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 θ-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 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:

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-Φ₀ in the equation θ=c(Φ-Φ₀);

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=Φ₀ 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 Φ₀, α varies from α₀ to ninety degrees. The angle α₀ 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 va lues of Φ greater than Φ₀ , the profile is the

solution to the differential equation:

d(lnr)/dΦ=tan{½[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 step 4. 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 Φ₀ 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 Φ₀ 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)=conεtant), a typical set of parameters is (also see FIG. l):

a = 0.055 in.

b = 0.100 in.

h = 12.36 in.

c = 0.05136

for θ(Φ) = c(Φ-Φ₀)

In the case of an exponential beam profile (P(θ)=ce^-aθ) a typical set of parameters is:

a ~ o h = 5.25

b = 0.100 c = 4.694

Θ(Φ) = 0.131ln(1-

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:

APP. DIX-COMPUTER SOFTWARE PROGRAM

1 program coordinates

2 dimension r(1:200), theta(1:200),

dzdx(1:200)

3 dimension xx(1:200), zz(1:200)

4 real 1, k1, k2, k3, k4

5 parameter (degtorad=3.1415927/180.0)

6 write(*,*) 'Enter radius of cylindrical absorber.'

7 read(*,*)a

8 write(*,*) 'Enter gap size.'

9 read(*,*)b

10 write(*,*) 'Enter constant.'

11 read(*,*)c

12 write(*,*) 'Enter maximum height.'

13 read(*,*)h

c GENERATE 50 POINTS OF AN INVOLUTE

14 alpha0=acos(a/(a + b) )

15 do 100 i=1,50,1

16 alpha= ((90*degtorad-alpha0)/49.0)

*float(i-50)+90*degtorad

17 d= (alpha-alpha0)*a + sqrt((a+b)

**2 - a**2)

18 x= a*sin(alpha) - d*cos(alpha)

19 z= -a*cos(alpha) - d*sin(alpha)

20 r(i)=sgrt(x**2 + z**2)

21 theta(i) = atan(z/x)

22 phi= theta(i) + (90.0*degtorad)

100 continue

101 theta(l)= -90.0*degtorad

c GENERATE 150 POINTS OF THE WINSTON-TYPE CONCENTRATOR

102 v= 0.0

103 h= 0.001

104 phi0= theta(50) + (90.0*degtorad) +0.001

105 phi = phi0

106 f= alog(r(50))

107 do 200 while(v.eq.0.0)

108 phi= phi + h

109 k1= h*tan(0.5*((1.0-c)*phi+

c*phi0+asin(a/exp(f))))

110 k2= h*tan(0.5*((1.0-c)*

(phi+0.5*h)+c*phi0+

& asin(a/exp(f+0.5*k1))))

111 k3= h*tan(0.5*((1.0-c)*

(phi+0.5*h)+c*phi0+

& asin(a/exp(f+0.5*k2)))) 112 k4= h*tan(0.5*((1.0-c)*(phi+h)+c*phi0+ & asin(a/exp(f+k3))))

113 f= f + (kl/6.0) + (k2/3.0) +

(k3/3.0) + (k4/6.0)

114 rad= exp(f)

115 z= rad*sin(phi-(90*degtorad))

116 if(z.ge.a) then

117 phimax- phi

118 write(*,*)'phimax=',phi/degtorad

119 v= 1.0

120 endif

200 continue

201 f= alog(r(50))

202 phi= (-1.0/149.0)*(phimax-phi0)+phi0

203 h= (phimax-ρhi0)/149.0

204 do 300 i-1, 150,1

205 phi= phi + h

206 k1= h*tan(0.5*((1.0-c)*phi+

c*phi0+asin(a/exp(f))))

207 k2= h*tan(0.5*((1.0-c)*

(phi+0.5*h)+c*phi0+

& asin(a/exp(f+0.5*kl))))

208 k3= h*tan(0.5*((1.0-c)*

(phi+0.5*h)+c*phi0+

& asin(a/exp(f+0.5*k2)))))

209 k4= h*tan(0.5*((1.0-c)*(phi+h)+c*phi0+ & asin(a/exp(f+k3))))

210 f= f + (kl/6.0) + (k2/3.0) +

(k3/3.0) + (k4/6.0)

211 r(i+50)= exp(f)

212 theta(i+50)= phi - (90.0*degtorad)

300 continue

301 stop

302 end

Claims

1. A nonimaging illumination optical device for producing a selected intensity output over an angular range θ, comprising:

a source of light having a characteristic dimension; a light reflecting surface positioned at least partially around said light source and said light source disposed opposite the aperature opening of said light reflecting surface and said characteristic dimension of said light source being small relative to at least one of the distance from said light source to said light

reflecting surface and the angle subtended by said light source at said light reflecting surface; and

the spatial position of said light reflecting surface for producing said selected intensity output being defined relative to a light ray originating from said light source in terms of radius vector R_i from the surface of said light source in conjunction with angle Φ_i between said radius vector R_i and a direction 180° from direct forward

illumination output from said device and an angle θ_i

between direct forward illumination and the light ray as reflected once from said light reflecting surface with said radius vector R_i defining said spatial position profile of said light reflecting surface varying as a function of said angle Φ_i in accordance with the expression:

R_i = (const.) exp. {∫ tan [(Φ_i - θ_i)/2] dΦ_i

2. The nonimaging illumination source as defined in

Claim 1 wherein said intensity output is constant as a function of θ_i such that the spatial position of said light reflecting surface is defined by said radius vector R_i in accordance with the expression:

R_i = R_o cos ^k (Φ_i/k)

where k = 2/(1 - a)

R_o = length of vector R in a direction 180° from direct forward illumination

and θ_i = aΦ_i

a = a constant value

3. A nonimaging illumination optical device for

selectively outputting light having a preselected intensity output over a particular angular range θ_i, comprising:

a source of light having negligible dimensions along at least two dimensions;

a light reflecting surface positioned at least partially around said light source and said, light source disposed opposite the opening of said light reflecting surface; and

the spatial position of said light reflecting surface being defined relative to said source of origin of a light ray from said light source in terms of a radius vector R_i from the surface of said light source in conjunction with an angle Φ_i between said radius vector R_i and a direction 180° from direct forward illumination output from said device and an angle θ_i between direct forward illumination and the light ray as reflected once from said light

reflecting surface with said radius vector R_i varying as a function of said angle θ_i in accordance with the expression:

R_i = (const.) exp {∫ tan [(Φ_i - θ_i)/2]dΦ}

4. The nonimaging illumination device as defined in

Claim 3 wherein said preselected intensity output comprises a substantially constant intensity over said particular angular range.

5. The nonimaging illumination device as defined in

Claim 1 wherein said intensity output produces on illumination distribution on a reference surface located at a distance from said illumination device which is large compared to the

aperature opening of said illumination device.

6. The nonimaging illumination device as defined in

Claim 1 wherein said intensity output comprises a substantially exponential behavior as a function of θ_i such that the spatial position of said light reflecting surface is defined by said radius vector R_i in accordance with the expression:

R_i = (const.) exp {∫tan[(Φ_i -θ_i)/2]dΦ_i) where θ_i = C₁log(1 - C₂Φ_i)]dΦ_i}

7. The nonimaging illumination device as defined in

Claim 1 wherein said intensity output comprises a substantially Gaussian behavior as a function of θ_i such that the spatial position of said light reflecting surface is defined by said radius vector R_i in accordance with the expression:

R_i = exp {∫tan[(Φ_i-θ_i)/2]dΦ_i)

wherein:

θ_i = C₁ Erf^-1(C₂Φ_i)

Erf^-1 is the inverse error function [Erf(x) = ∫exp(-x²/2) dx] and C₁ and C₂ = constants

8. The nonimaging illumination source as defined in

Claim 1 wherein said intensity output is substantially a cosine as a function of Φ_i such that the spatial position of said light reflecting surface is defined by said radius vector R_i in accordance with the expression: R_i = exp{ tan[(Φ_i - θ_i)/2]dΦ_i} wherein:

θ_i = C₁sin^-1(C₂Φ_i)

sin^-1 is the arc sine function

C₁ and C₂ = constants

9. The nonimaging illumination optical device as defined in Claim 1 wherein said selected intensity output behaves in accordance with the function P(Ω_i) wherein Ω_i is a solid angle and the spatial position of said light reflecting surface is defined by said radius vector R_i in accordance with the expression: R_i = exp {∫tan[(Φ_i - θ_i)/2] dΦ_i and ∫P (Ω_i) d(cos θ_i) is a linear function of cos Φ_i

10. The nonimaging illumination optical device as defined in Claim 1 where θ_i - θ'_i with said angle θ'_i calculated in accordance with an edge ray method such that: θ'_i = θ_i-δ

where δ = angle subtended by said light source at said light reflecting surface.

11. The nonimaging illumination optical device as defined in Claim 10 wherein said light source comprises a substantially circular shape of radius p wherein, δ = arc sine (p/R_i)

R = exp {∫ tan (Φ_i - θ_i + arc sin ( p/R_i ) dΦ_i}

12. The nonimaging illumination optical device as defined in Claim 10 wherein said spatial position of said light reflecting surface includes another surface portion involute to said light source.

13. The nonimaging illumination source as defined in

Claim 10 wherein said selected light output has different profiles in two orthogonal planes and said profiles are

determined in said orthogonal planes in accordance with at least a portion of said light reflecting surface being defined independently in association with each of said orthogonal planes by said radius vector R_i defined by the expression: R_i = exp{∫tan[(Φ_i-θ'_i)/2]dΦ_i}

wherein the angle θ_i is calculated in accordance with the edge-ray method such that:

θ'_i = θ_i -δ and said δ being the angle subtended by said light source at said light reflecting surface.

14. The nonimaging illumination device as defined in

Claim 13 wherein the functional dependence of θ_i on Φ_i is optimized to achieve a relatively uniform output over output angle θ_i in each of said planes.

15. The nonimaging illumination device as defined in Claim 13 wherein the functional -dependence of θ_i on Φ_i in each of said planes is optimized to achieve a preselected output over the angle θ_i including at least one of substantially exponential, Gaussian and cosine.

16. The nonimaging illumination optical device as defined in Claim 13 wherein said portion of said light reflecting surface is involute to said light source.

17. A nonimaging illumination optical device for

generating a selected intensity output for electromagnetic radiation over an angular range θ_i, comprising:

a source of electromagnetic radiation having a characteristic source dimension;

an electromagnetic radiation reflecting surface positioned at least partially around said source and said source disposed opposite the opening of said reflecting surface, said light reflecting surface having

characteristic surface contour parameters describing said surface with said characteristic dimensions of said source of electromagnetic radiation being small relative to dimensional parameters comprising at least one of distance from said source to said reflecting surface, an angle subtended by said light source defined in terms of

characteristic angles and radial vectors and the functional shape of said reflecting surface and the longitudinal cross sectional line length of; and

the spatial position of said reflecting surface being defined relative to an electromagnetic energy ray

originating from said source in terms of an angle θ_i between direct forward illumination and said

electromagnetic energy ray as reflected once from said reflecting surface with said θ_i a function of at least one of said characteristic surface contour parameters.

18. The nonimaging illumination optical device as defined in Claim 17 wherein said characteristic surface contour parameter includes at least one of a radius vector R_i from the surface of said source of electromagnetic radiation to said reflecting surface, an angle Φ_i between said radius vector R_i and a direction 180° from direct forward illumination output from said device and a measure of a distance along said reflecting surface.

19. The nonimaging illumination optical device as defined in Claim 17 wherein θ_i is a solid angle with said reflecting surface extending over three dimensions.

20. A nonimaging electromagnetic radiation collection device for collecting said radiation with uniform efficiency over an angular range θ_i, comprising:

a collector for receiving said electromagnetic radiation;

a light reflecting surface positioned at least partially around said collector and disposed opposite the opening of said light reflecting surface; and the spatial position of said light reflecting surface being defined relative to said collector for receiving an electromagnetic energy ray in terms of a radius vector R_i from the surface of said collector in conjunction with an angle Φ_i between said radius vector R_i and a direction 180º from direct forward illumination output from said device and an angle θ_i between direct forward illumination and said electromagnetic energy ray as reflected once from said light reflecting surface to said collector with said radius vector R_i varying as a function of said angle Φ_i in

accordance with the expression: R_i = (const.) exp {∫ tan [(Φ_i - θ'_i)/2]dΦ) θ_i'=θ_i-δ, δ=angle subtended by source at reflector

21. The nonimaging collection device as defined in

Claim 20 wherein said collector comprises an energy transducer wherein the functional dependence of Φ_i on Φ_i is optimized to achieve a relatively uniform input over the angle θ_i.

22. The nonimaging collection device as defined in

Claim 21 wherein said spatial position of said light reflecting surface includes another portion involute to said light source.

23. The nonimaging collection device as defined in

Claim 20 wherein said collector comprises an energy transducer wherein the functional dependence of θ_i on Φ_i is optimized to achieve a preselected input having at least one of a

substantially exponential, Gaussian and cosine distribution.

24. The nonimaging collection device as defined in

Claim 21 wherein said collector comprises an energy transducer wherein the functional dependence of θ_i on Φ_i is optimized to achieve a preselected input having at least one of a

substantially exponential, Gaussian and cosine distribution.

25. A nonimaging illumination optical device for producing substantially uniform intensity output as a function of solid angle Ω, comprising:

a point source of light;

a light reflecting surface positioned at least partially around said light source and said light source diposed opposite the aperature opening of said light reflecting surface; and the spatial position of said light reflecting surface for producing said substantially uniform intensity output being defined relative to a light ray originating from said light source in terms of radius vector R_i from the surface of said light source in conjunction with angle Φ_i between said radius vector R_i and a direction 180° from direct forward illumination output from said device and an angle θ_i between direct forward illumination and the light ray as reflected once from said light reflecting surface with said radius vector R_i defining said spatial position profile of said light reflecting surface varying as a function of said angle Φ_i in accordance with the expression: R_i = exp {∫ tan [(Φ_i - θ_i)/2] dΦ_i where cosθ_i is a linear function of cosΦ_i.