Uniform LED illuminator for miniature displays

Vladimir Medvedev, David Pelka, and Bill Parky&Teledyne Lighting & Display Products, Inc.12525 Daphne Ave. , Hawthorne CA 90250

ABSTRACT

The Total Internally Reflecting (TIR) lens is a faceted structure composed of prismatic elements that collect a source's lightover a much larger angular range than a conventional Fresnel lens. It has been successfully applied to the efficientcollimation of light from incandescent and fluorescent lamps, and from light-emitting diodes (LEDs)' . Anovel LED-poweredcollimating backlight is presented here, for uniformly illuminating 0.25"-diagonal miniature liquid-crystal displays, whichare a burgeoning market for pagers, cellular phones, digital cameras, camcorders, and virtual-reality displays. The backlightlens consists of a central dual-asphere refracting section and an outer TIR section, properly curved with a curved exit face.

1. IMAGE ILLUMINATION

Projection displays pose problems connected with image definition and correction for uniformity of illuminance.This paper reviews methods of applying nonimaging optics to this topic, methods that may be useful for some commonimaging optical systems.

We will begin with how to define illuminance. The illuminance E at point P on surface S' in the image space ofan optical system may be defined as the scalar product of an illumination vector e and the surface normal vector n at P

E=en (1)

where the illumination vector e is defined by

e = fB . d with d = ' d (2)

B is brightness or luminance, (1 is the full solid angle for all rays that intercept point P from all point sources, do, is thedifferential solid angle vector, equal to the solid angle of a small bundle of rays multiplied by the unit direction vector a'of its central ray.

This theory of the light field has been used for the creation of optical systems and in software4 for the definitionof image-space illuminance in both centered and decentered optical systems, initially in spectroscopy, which utilizesdecentered optical systems. The numerical integration of (2) is a result of reverse raytracing for an array of rays from pointP through the optical system to the source. In actual practice, one must consider extended sources with spatially varyingbrightness, as well as diaphragms (stops) in the optical system, which can result in vignetting. For these conditions it ispossible to define the fme structure of an image, if its size and sizes of its aberrations are comparable.

Referring to Figure 1 , consider a centered optical system with a small source, such as the filament of anincandescent lamp, the arc of a xenon lamp, or a light-emitting diode (LED). The fine structure of the image is investigatedin the space near the Gaussian image. If the source has a non-uniform distribution of luminance, it is difficult to achieveuniform image illuminance. When an illuminated point P is far from the Gaussian image, the full bundle of rays has to benarrow and ( in (2) is small due to vignetting of most of the rays from source to point P. This simplifies the expression

a' 1(a)fore. e =K

Here a and a' are unit vectors of central ray in object and image space, 1(a) is the luminous intensity of the source as a

112525 Daphne Ave., Hawthorne CA 90250, (213) 242-1900, FAX (213) 242-1924, e-mail: bparkyn@teledyne.com

Part of the SPIE Conference on Illumination and Source Engineering • San Diego. California • July 1998142 SPIE Vol. 3428. 0277-786X/981$1O.OO

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function of unit direction vector a of the central ray in object space, and is a coefficient that depends upon properties ofthe narrow bundle of rays and the characteristics of the central ray.

Let this small source be installed on the optical axis, as shown in Figure 2. Then the central ray is in the meridionalplane, which contains the optical axis, and Coddington equations (or Young equations, in European literature) can be usedto describe the properties of this bundle of rays. The illumination vector e may be defmed by

e =a" 1(a) m m3 (4)

Pt. Pwhere p and p are the absolute values of the distances of image point t and sagittal image point s from illuminated pointP, n-is and m the absolute values of their magnifications. The points t and s are defined sequentially by Coddingtonequations, which define astigmatism. The simplest event is when central ray is traced along the optical axis. Then m =Ills = m0 and p, = p3 = po . For projection systems, m is the source magnification in the exit pupil of the objective(assuming that source is not cut by any diaphragm), and is the distance from this exit pupil to the final display screen.Assume the distribution of the source's luminous intensity is rotationally symmetric (I = 1(0) in object space), and that allother elements are parts of a typical centered optical system. The illuminance E can be defined on a plane perpendicularto optical axis.

E=I(u) sinu g (5)r dr

As shown in Figure 2, u is the polar angle of the central ray, distance r is defined by the point of interception of thecentralray with the illuminated plane S. It is possible to consider "meridional paraxial" optics (or "parabasal" optics in Americanliterature5), which may be constructed by meridional Coddington equations alone. For narrow meridional bundle of rays,therefore, another ray, from the center of the source, with angle du from the central ray may be traced to the interceptionwith the illuminated plane. Then de/dr is a function only of the central ray data.

2. ACHIEVING UNIFORMITY OF ILLUMINATION

The topic of this paper is the correction of non-uniform illuminance in imaging optical systems, by consideringmethods of nonimaging optics. For instance, the method of numerical integration is used in nonimaging optics for the designof reflecting concentrators for complex light sources, using the edge-ray principle6. in conventional optical systems, suchas projectors, it is also possible to create uniform illumination on an image plane by numerical integration methods. Insteadof the edge-ray principle, however, the flux-conservation law is usually applied to the properties of narrow bundles of rays.It is well known that this can result in some coma or an image of source structure7. We will unite these methods for narrowbundles of ray, resulting in a considerably more compact illuminating illumination system. Consider a centered opticalsystem, shown in Figure 2, having on the optical axis a compact source with rotationally symmetric intensity 1(u) and it hasa rotational symmetry. Then the useable flux is

F(u) = 2fI(u) sin u du (6)

and the average illuminance is

= F(u) ii(7)

ltRmax

where , is the flux reduction due to Fresnel reflections and absorption.

2.1 Modified Winston Method

The illumination system consists of n continuous optical surfaces with specified positions and aspheric coefficients,and the illuminated plane S. The exception is for surfaces j and j +k, which have undefined coefficients. The meridionalray from A (center of source) with small angle u1 is traced to surface j through the first part of optical system (before surfacej). Interception point A1 can be found because for small u paraxial optics is valid, so that a small element of surface j near

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by r0 = O l(O)IEa(8)

with the condition2 2

ii0F(u1) = T)01tU1 1(0) = EaltT0

The paraxial ray may be defined jn the source's space by point A, or by angle u1, which may be choose arbitrarily,or in the screen's space by r0 = R, from (7), the height of the paraxial ray. Its direction may be defined by the positionof the entrance pupil of the projecting objective or for simplicity, it may be assumed that this ray is parallel to optical axis,which would be desirable if a polarizer and LCD are used. The straight raytracing may be done from source's space to thepoint A on surface j , or analogously the reverse raytracing can done from screen's space to the point A2 the surface j +k.For the simple case of k = 1 , we can connect points A1 and A2 by a straight line. If k > 1 , it means that there are somesurfaces between surface j and surface j +k. Again, we know the radii of these intermediate surfaces, so that we can definethe paraxial image of AL in space before surface j +k and connect it with A2 (see Figure 3). Paraxial raytracing from A1to A2 will suffice. We thus have three separate raytraces:

1) before surface j2) between surface j and surface j +k,3) after surface j +k.

To combine these three traces into one it is necessary to define meridional radii R and RJ+k at points A1 and A0,2 forsurfaces j and j +k on the optical axis (by the methods of paraxial optics). This is possible because all data are known afterthese separate raytracings.

Additional calculations are necessary for more exact values of A1 and A2 and for the trajectory of the real ray (vs.the paraxial one, where the surfaces 'are planes), based on 01 and r0. This is the path of the central ray for the subsequentiterations, where the first step gets the initial data for next step:

1)Points A1 and A2 (and all other points of interceptions with surfaces)2)Angles of ray Uj before A1, u+ after A1 and u+k before A2, uJ+k÷L after A2 (and all other angles for other media).

These are the data for the ray, without data of surfaces i near point AL and i+k near point A2. The data for othersurfaces (angles of incidence, reflection or refraction, normals and meridional radiuses at points of interceptions) must beknown. As for the central part of the optical system, it is necessary to solve a problem that is complementary to conventionalraytracing. From u and u +L (refractive indices are known), it is possible to define angles i , i ' of incidence and refraction(or reflection) and angle for normal at A1 , hence one can consider a small element of surface j as a plane, or a straightinclined line on meridional plane. Including the transmittance due to Fresnel reflections we have

T1 dF(u) = 2rr 1(u) sin(u) du = 2ic EaT 'jr (10)

As previously, the law of conservation energy holds. For this case, however, u1 has to be changed to du: a smallangle with central ray and corresponding screen separation dr. In this annular differential solid angle, the source flux is

dF(u) = F(u+du) — F(u) (11)

As many authors have realized4, it is possible to create and use meridional and sagittal paraxial optics, based on Young orCoddmgton formulae. Only for this case is meridional paraxial optics required and the relevant data are known: i and i'surfaces j and j +k. In the numerical iteration, (8) is valid even for the first step, with UL = du.

3. EXAMPLES

3.1 Non-imaging optics

Figure 4a shows a Winston reflective luminaire with a planar source and a far-field target plane S' ,with uniformilluminance desired. Figure 4b shows a compound parabolic concentrator (CPC) with a round source. Direct and reflectedlight illuminate a nearby plane S'. This system can illuminate S' uniformly if its parameters are chosen properly inaccordance with source characteristics. Both of these systems are straightforward to design, but the choice of sources forthese systems is restricted. It is their design methodology that inspired the methods discussed here.

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3.2 TW lens with auxiliary "mushroom" lens

Figure 5 shows a TIR lens with an auxiliary mushroom-shaped lens8. The modified Winston method was first usedto design this system9. This method had additional transformations because the unknown outer surface (j +k=3) is acompound one. A high-power arc lamp is shown for the illumination of a large LCD (200 or 210 mm diagonal). The iimersurface of the mushroom lens is spherical and the cross-section of the outer surface is defined by sequence of points. Thecentral part of the TIR lens is an asphere, and the rest of it is faceted with internally reflecting annular prisms. Of course,the mushroom lens should be manufactured from heat-resistant material, such as pyrex or fuzed quartz.

A numerical calculation of the relative distribution of illuminance is shown by the dashed line. The source modelfor this calculation is a spherical source with uniform brightness, which is supported by actual measurements of distributionof luminous intensity. These measurements show rotational symmetry and constant intensity for degrees from the YZplane. The axis of the lamp is perpendicular to the plane of Figure 5(along the Y-axis). The screen is rectangular. Anauxiliary reflector below the lamp could be used to collect additional flux.

4. ILLUMINATING SYSTEM FOR SMALL SOURCE AND SMALL SCREEN

The application of an optical system with a mushroom lens encounters with difficulties for small sizes. With an LEDsource, with its quarter-millimeter dimensions, and a 0.25" diagonal screen, the mushroom lens and the TIR facets wouldbe impractically small, necessitating the revised design shown in Figure 6. This system is intended for used with miniaturedisplays having magnification systems that utilize only a small cone-angle from the LCD screen, so that a conventionalLambertian backlight, or even one using brightness-enhancing film, would be wasteful.

The central part redirects rays that are within 45° of the optical axis. Around it is a single correctively curved TIRsurface (j =2) with an outer corrective surface (j +k=3). The LED source is immersed in a protective transparent glob.The luminous intensity 1(u) for this source is defined as for a parallelopiped with the main square surface 0.25*0.25 mm2with height of 0.01 mm. This source is considered as Lambertian one with constant brightness B. For these approximations,the function 1(u) is defined easily9. The dashed curve shows the calculated illuminance, with a discontinuity at the borderbetween the central and outer TIR sections. In practice, this may be removed by an intermediate holographic diffuser,between the lens and the LCD screen, with a 1O scattering angle.

5. HIGH-COLLECTION LENSES FOR INCANDESCENT SOURCES

A particular advantage of this illumination system is the ability to extend the lens below the level of the source, thatis to large values of the angle u of Figure 3. Figure 7 shows such a design, for u = 135°. This limit was merely that ofTotal internal Reflection, and may be extended by an external mirror coating. As a purely collimating device, it isconsiderably more efficient than a conventional parabola. Such a device is currently being marketed as a bicycle light, underthe trademark "Photon Funnel". For the screen illumination application shown here, the dashed line that graphs thecalculated illuminance has a discontinuity between the inner refractive section and the outer reflective section. As previouslymentioned, a holographic diffuser could eliminate this effect, which would be less for a non-point source. The chiefdisadvantage is sensitivity to source misalignment. Most incandescent lamps have some variance in filament location, leavinglittle system tolerance for variations in lamp position. A larger more powerful filament, although it would lessen this effect,would exceed the temperature limits of a plastic lens.

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6. REFERENCES

1 . William A. Parkyn and David G. Pelka, "Compact Non-Imaging Lens with Totally Internal Reflective Facets, " SPIEVol. 1528, pp. 70-81

2. Gershun A., "The Light Field", Journal Mathematics and Physics XVII, 1938, MIT Press (translated from Russian).

3. Paritskaya G.G. et a!., Optika 1 spectrockopia (USSR) 23, 5, pp8l9-823 1967

4. Peisaxon I.V. et al., Optiko-Mekhanicheskaya Promyshlennost, 10,pp 22-24, State Optical Institute St.Petersburg 1971

5. Optical Society of America, Handbook of optics, 1, pp 1-47, McGraw Hill 1995

6. W.T. Welford and R.Winston, High Collection Nonimaging Optics, Academic Press, San Diego 1989.

7. Slyusarev G.G., Aberrations and OpticalDesign Theory, Hilger, Bristol, 1984.

8. Parkyn, William A. & Pelka, David, United States Patent "Auxiliary Lens to Modify the Output Flux Distribution of aTIR Lens"

9. Vladimir Medvedev, William A. Parkyn, David G. Pelka, "Uniform High-Efficiency Condenser For Projection Systems"SPIE Vol. 3139, pp. 122-134.

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