Automotive headlamp reflector and method for its design

A reflector for a headlamp is divided into zones depending on the sizes of the light source images produced by the various parts of the reflector. Those parts of the reflector that provide smaller image sizes are used to supply light to the higher intensity parts of the road pattern. This allows greater control over glare and is particularly useful for headlamps having high intensity discharge as a light source. In one embodiment, a larger reflector is trimmed to be smaller and yet to retain portions that provide the small light source images.

TECHNICAL FIELD 
This invention relates to the art of lighting, and in particular to the art 
of headlamps for automobiles and their design. 
BACKGROUND 
Styling and performance requirements have directed the automotive industry 
toward headlamps with clear lenses and reflector optics. Further, demand 
for increased headlamp performance has heightened interest in high 
intensity discharge (HID) light sources. Marriage of these two 
technologies into one product requires that several technical problems be 
overcome. 
Two of the most difficult issues in designing reflector optics for a 
low-beam headlamp for use with an HID source are control of glare light 
and control of excess amounts of foreground light. These problems stem 
from the extended discharge area of the HID source, which is an ellipse of 
about 4.4 mm.times.4.4 mm.times.7.1 mm, compared to the typical tungsten 
halogen (TH) bulb, which is a cylinder 5.2 mm.times.1.2 mm. The extended 
discharge area of the HID source creates a large effective light source, 
which causes a large angular spread of light from a point on the reflector 
surface. This large angular spread can lead to excess amounts of glare 
light or foreground light. 
The angular spread of light (i.e., the angular image size) from any point 
on the reflector depends on the size of the light source and the distance 
between the source and the point on the reflector. The image sizes 
produced by the reflector, however, can be controlled to some extent. For 
example, the image size can be decreased by increasing the distance 
between the light source and the point on the reflector. 
SUMMARY OF THE INVENTION 
Different parts of a reflector produce images of different sizes and 
intensity. Generally, points on the reflector that are further from the 
source of light produce smaller images and lower light intensities. 
Similarly, points nearer the light source produce larger images and have 
greater intensities. When the reflector is nominally of parabolic shape 
but with individual facets for directing individual parts of the image to 
desired locations in the light pattern, it is possible to specify the 
shape of each facet such that characteristics of the individual images are 
correlated with the characteristics of selected portions of the desired 
light pattern. 
In general, the light pattern required for automotive lighting has a well 
defined region of greater intensity and other regions of lower intensity, 
but which cover a broader area. This required pattern is obtained in 
accordance with the invention by shaping the facets of the reflector to 
directing the smaller images of the source to the smaller part of the 
light pattern and using the larger images for the larger areas. As well, 
the areas of the pattern that require more light (lumens) are formed by 
the facets producing images carrying more light. This allows greater 
control of the light pattern. 
In accordance with the invention, a reflector that is nominally parabolic 
with individual facets is divided into zones of these facets. These zones 
are defined by the respective sizes of the images of the light source 
generated by the facets and the amount of light contained in the images. 
Then, the shapes of the facets are designed such that light from the 
images having the smaller sizes is used for the smaller, higher intensity 
portion of the light pattern, and light from images having larger sizes is 
used for horizontal image spread. In the preferred embodiment, the facets 
are divided into three zones, with the facets of the zone providing 
intermediate image sizes being used for smoothing the light pattern. 
When the reflector is divided into zones, a decision criteria in accordance 
with one embodiment of the invention divides the facets into three zones, 
A, B, and C. Zone A includes facets that will supply from 30% to 50% of 
the light in the pattern, zone B will supply from 25% to 45% of the light 
in the pattern, and zone C will supply 10% to 35% of the light in the 
pattern. In addition, the facets in zone A are selected to be the ones 
that will provide image sizes larger than 6.degree., the facets in zone B 
provide images sizes between 3.degree. and 6.degree., and the facets in 
zone C provide image sizes smaller than 3.degree., each of these 
dimensions being variable by .+-.1.degree.. 
The reflector contemplated in the preferred embodiment of the invention is 
a nominally parabolic reflector that is trimmed to be a given shape, e.g., 
rectangular, when viewed from the front. In one embodiment, the light 
source is located in the geometric center of the reflector, in which case 
the three zones of facets are generally symmetrical about the light 
source. This may be the case, for example, when the reflector is 90 mm in 
height and 150 mm in width. 
It is often required, however, that the reflector be made smaller. The 
smaller reflector presents the problem that the if the light source is 
centrally located, the distances between the source and the reflector will 
not be large enough to provide an adequate population of facets that 
produce the smaller images. That is, there are too few facets that provide 
an image size less than 3.degree.. This makes it very difficult to provide 
adequate definition for certain regions in the light pattern, such as the 
"hot spot." Thus, in accordance with a second embodiment of the invention, 
the position of the light source with respect to the reflector is selected 
to provide the optimum mix of image sizes and light intensities. This then 
provides the designer with the tools for generating the required light 
pattern. 
This second embodiment is particularly useful when the size of the 
reflector must be reduced to fit a physical restraint in an automobile, 
such as a small opening. If a reflector of a given curvature were reduced 
in size symmetrically, many of the facets producing small image sizes 
would be eliminated. If the size is reduced asymmetrically, however, many 
of the facets that produce small image sizes can be retained. This 
asymmetrical reduction in size results in the light source being displaced 
from the geometric center of the reflector.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 illustrates the geometry of a head lamp reflector and shows the 
reflection of light rays from a source S at an arbitrary point P on the 
reflector. A reflector can be considered an imaging device. If only 
specular reflection is assumed, images of a light source (filament or arc) 
are formed by each point on the reflector. When the light source geometry 
and location are defined, the image varies with respect to the points on 
the reflector. In geometric optics, the relationship between object, image 
and reflecting surface can be described using vector notations. 
Referring to FIG. 1, let a.sub.i be the direction of light from the light 
source S and incident of a surface, a.sub.r be the direction of light 
reflected from the surface, and n be the normal to the surface at the 
point of incidence. The vectors a.sub.i, a.sub.r, and n are unit vectors. 
For specular reflections, Snell's Law states that 
EQU ai.multidot.n=ar.multidot.n (1) 
where the vectors a.sub.i, a.sub.r, and n are coplanar, which means that 
a.sub.i, a.sub.r, and n are linearly dependent: 
EQU -ai+ar=rn (2) 
where r is a coefficient. 
For a given reflector, if the center of the light source is located at 
point (0,0,f) and extends from -1.sub.x to 1.sub.x, -1.sub.y to 1.sub.y, 
and -1.sub.z to 1.sub.z, then (.DELTA.1x, .DELTA.1y, f+.DELTA.1z) can 
represent an arbitrary point of the light source. The value for the 
incident vector from an arbitrary point of the light source to an 
arbitrary point on the reflector, p, can written 
##EQU1## 
where 
EQU d=[(p.sub.x -.DELTA.1.sub.x).sup.2 +(p.sub.y -.DELTA.1.sub.y).sup.2 
+(p.sub.z -f-.DELTA.1.sub.z).sup.2 ].sup.1/2 (4) 
At the center of light source, 
##EQU2## 
For simplicity, the reflector is approximated as a parabola with the center 
of the light source filament on the focal point (i.e., the light is 
reflected straight ahead from the reflector surface), so that a.sub.r 
=(0,0,1). That is approximately the case for the high intensity area of a 
low beam head lamp centered at 2R 1.5D, which is near the areas of 
greatest concern for both excess glare light and excess foreground light. 
The normal of surface is thus 
EQU rn=-a.sub.i +a.sub.r 
##EQU3## 
Solving for n and normalizing, we obtain for a parabolic surface: 
##EQU4## 
The direction of reflection for any point or light source is 
EQU a.sub.r =a.sub.i -2n (a.sub.i .multidot.n )=(I-2E).sub.a.sub.i(8) 
where 
##EQU5## 
EQU (a.sub.ix, a.sub.iy, a.sub.iz). 
Equation (11) determines the vector of the reflecting rays from any point 
on the reflector, (p.sub.x, p.sub.y, p.sub.z), given the incident ray 
vector, a.sub.i. For any point of the light source, the incident ray 
vector, a.sub.i, can be calculated by using equation (3). Thus given an 
arbitrary point on the reflector and an arbitrary origination point in the 
light source, the above provides a method to calculate a.sub.r. By 
calculating a.sub.r for light source points at a specific reflector point 
one can calculate an image size (in degrees) for that specific reflector 
point. The image size of the HID light source for a reflector using a 24 
mm "focal distance" has been calculated. The results are shown in FIG. 2. 
FIG. 2 shows the upper right hand portion of a reflector 2 in elevation and 
illustrates the image sizes produced by the reflector for light from a 
high intensity discharge source. The width of the portion shown in FIG. 2 
is 78 mm, and the height is 60 mm. The opening 4 in the reflector for 
receiving the light source is centrally located with respect to the entire 
reflector. As shown in FIG. 2, the images sizes created by the reflector 
are smaller for those portions of the reflector that are farther from the 
light source. 
FIG. 3 illustrates that the intensity of the light contained in the images 
also decreases for the areas farther from the light source. Thus, FIG. 3 
illustrates the lumen content for the images produced by individual facets 
in a reflector. 
FIGS. 2 and 3 also indicate the boundaries of the zones A, B, and C into 
which the reflector is divided during the design process. These zones 
define the facets 6 to be used for the high intensity part of the light 
pattern, the lower intensity part of the light pattern, and for smoothing 
the pattern. In the preferred embodiment, the zones are defined in 
accordance with the following criteria: 
______________________________________ 
Zone A B C 
______________________________________ 
Portion of total light 
40% 35% 25% 
Filament size (.degree.) 
&gt;6 3-6 &lt;3 
______________________________________ 
The facets in zone A are used to supply the light for the broader and lower 
intensity parts of the light pattern, the facets in zone C are used to 
supply the light for the smaller and higher intensity part of the light 
pattern, and the facets in zone B are used to supply light to smooth the 
light pattern. 
FIG. 4a shows an embodiment of the invention where the reflector is divided 
into seventy-eight facets 6 arranged in twenty-six columns and three rows. 
The reflector is one hundred fifty six millimeters in width and ninety 
millimeters in height. The zones are symmetrical about the high intensity 
discharge light source 8, and zone A extends from the light source to 
about 24 mm on either side of the source. Zone B extends from the outer 
boundary of zone A to about 42 mm on either side of the light source, and 
zone C extends from the outer boundary of zone B to the outer edges of the 
reflector. 
FIG. 4b is a side view of the reflector of FIG. 4a, and FIGS. 4c through 4e 
show the curvature along the lines C--C, D--D, and E--E, respectively. 
FIG. 5a illustrates a second embodiment of a reflector in accordance with 
the invention. In accordance with this embodiment, the reflector contains 
twelve vertical facets and is not symmetrical with respect to the geometry 
of the lens. The width of the reflector of FIG. 5a is about one hundred 
sixty millimeters, and the height is about eighty millimeters. The light 
source 8 is centrally located with respect to the width and about thirty 
millimeters from the lower edge of the reflector. The zones are 
symmetrical about the light source in the horizontal direction; zone A 
extends about 35 mm on either side of the source; zone B extends from the 
outer boundary of zone A to about 55 mm on either side of the source; zone 
C extends from the outer boundary of zone B to the outer edges of the 
reflector. 
FIG. 5b is a side view of the reflector of FIG. 5a and FIGS. 5c through 5e 
show the curvatures along lines C--C, D--D, and E--E. 
FIG. 6 shows a further embodiment wherein the reflector of FIG. 4a had been 
modified by trimming zones B and C on the left side of the reflector (when 
viewed from the front) from the reflector. This results in a reflector 
that is physically smaller than the reflector shown in FIG. 4a but, by 
retaining the facets of zones B and C on the right side of the reflector, 
retains the ability of the designer to provide light of small image sizes 
to the higher intensity parts of the light pattern. The physical geometry 
of the resulting new reflector is such that the light source is 
geometrically off-center. In the design method associated with this 
embodiment, a symmetrical reflector, such as that shown in FIG. 4a, is 
made to fit a smaller prescribed geometry while retaining the desirable 
light pattern associated with the larger reflector by retaining a large 
number of facets in zones B and C on the right side of the reflector. This 
greatly simplifies the design process and produces a reflector with 
superior properties. 
Modifications within the scope of the appended claims will be apparent to 
those of skill in the art.