Machine tools abstract
An adjustable beam flashlight according to this invention is based
in part on the teachings of Ellion U.S. Pat. Nos. 4984140 and
5459649 but adds important new concepts to describe a theoretical
reflector having a broad beam that is uniformly illuminated with
no bright and dull rings and no unilluminated center disc. This
theoretical reflector requires manufacturing tolerances that are
not available with conventional machine tools. A method is described
to modify this theoretical reflector so that a practical reflector
can be produced using existing machine tools. In one embodiment,
the practical reflector surface is made up of a multitude of small
concentric cones which reflect the light in the form of small fans.
A uniformly illuminated broad beam is formed by fabricating specific
groups of these cones of varying size and slope to form the reflector
surface in order to project the light so as to overlap the required
number of fans to produce the uniformity of illumination.
Machine tools claims
I claim:
1. An improved reflector for a flashlight, said reflector having
an internal reflective surface, a central axis, a smaller end with
a region of smaller diameter and a larger end with a region of larger
diameter, said surface near its smaller end having an aperture there
through to pass a light emitting source and said surface at its
larger end open so as to project the reflected light out of the
reflector, the improvement comprising:
said reflective surface at the smaller end having the same coordinates,
focal point, and slope of a true paraboloid but whose coordinates
and slope deviate from those of the true paraboloid as the reflective
surface extends toward the larger end, and wherein the angle between
tangents between said surface and the central axis along said reflector
are such that when said source is axially positioned along the central
axis to a broad beam position spaced from the focal point the pattern
of the reflected rays crosses the central axis in a controlled fashion
in order to project a uniformly illuminated broad beam, and when
the source is disposed at the focus, the reflected rays form a substantially
continuous spot beam pattern.
2. A reflector according to claim 1 in which the rays emitted from
the larger diameter region of the reflector surface diverge from
the central axis in order to intensify the illumination at the center
of said broad beam.
3. A reflector according to claim 1 in which the light source is
positioned farther from the minimum diameter of the reflector than
the focal point location in order to project said broad beam.
4. A reflector according to claim 1 in which the light source is
positioned closer to the minimum diameter of the reflector than
the focal point location in order to project said broad beam.
5. A reflector according to claim 3 in which the reflector surface
has a slope at the minimum diameter equal to that of a true paraboloid
but which slope increases as the reflector extends toward the maximum
diameter of the surface where the reflected light is projected substantially
parallel to the axis, said surface being such that rays from the
light source when located at the broad beam position that are emitted
towards the larger end of said reflector tend progressively to be
emitted at smaller angles to the axis in such a manner that the
broad beam is uniformly illuminated from its outer rim to the center.
6. A reflector according to claim 4 in which the reflector surface
has a slope at the minimum diameter equal to a true paraboloid but
which decreases from it to a maximum diameter of the surface where
the reflected light is projected substantially parallel to the axis,
the said surface being such that rays from the light source when
located at the broad beam position that are emitted towards the
larger end of said reflector tend progressively to be emitted at
smaller angles to the axis in manner so that the broad beam is uniformly
illuminated from its outer rim to the center.
7. The reflector according to claim 3 in which the reflective surface
is a complete surface of revolution.
8. The reflector of claim 3 in which the portion of the reflector
which is a surface of revolution is not complete and the reflector
has one or more intermediate reflecting surfaces to decrease the
size of the reflector in the direction of said intermediate surfaces.
9. The reflector according to claim 4 in which the reflective surface
is a complete surface of revolution.
10. The reflector of claim 4 in which the portion of the reflector
which is a surface of revolution is not complete and the reflector
has one or more intermediate reflecting surfaces to decrease the
size of the reflector in the direction of said intermediate surfaces.
11. The reflector according to claim 3 in which the angle between
the emitted light rays and the central axis is related to the angle
between the reflected light rays and the central axis according
to the relation
where "a" is the angle between the central axis and the
emitted rays, "b" is the angle between the reflected rays
and the central axis, C.sub.1 and C.sub.2 are constants.
12. The reflector according to claim 4 in which the angle between
the emitted light rays and the central axis is related to the angle
between the reflected light rays and the central axis according
to the relation:
where "a" is the angle between the central axis and the
emitted rays, "b" is the angle between the reflected rays
and the central axis, C.sub.1 and C.sub.2 are constants.
13. The reflector according to claim 7 in which the diameter of
said surface is less than the diameter of a true paraboloid as the
diameter of the reflective surface increases to provide said broad
beam.
14. The reflector according to claim 8 in which the diameter of
said surface is less than the diameter of a true paraboloid as the
diameter of the reflective surface increases to provide said broad
beam.
15. The reflector according to claim 7 in which the diameter of
said surface is greater than the diameter of a true paraboloid as
the diameter of the reflective surface increases to provide said
broad beam.
16. The reflector according to claim 8 in which the diameter of
said surface is greater than the diameter of a true paraboloid as
the diameter of the reflective surface increases to provide said
broad beam.
17. The reflector of claim 13 in which the radius to any point
on the reflective surface is related to smaller neighboring point
on the surface by the expression: ##EQU6## where: a.sub.n is the
angle between the central axis and the emitted light ray to the
point on the reflector, R.sub.n is the radius to the smaller neighboring
point, X.sub.0 is the location of the light source along the central
axis, X.sub.n is the axial position of the smaller neighboring point,
C.sub.1 and C.sub.2 are constants.
18. The reflector of claim 14 in which the radius to any point
on the reflective surface is related to smaller neighboring point
on the surface by the expression: ##EQU7## where: a.sub.n is the
angle between the central axis and the emitted light ray to the
point on the reflector, R.sub.n is the radius to the smaller neighboring
point, X.sub.0 is the location of the light source along the central
axis, X.sub.n is the axial position of the smaller neighboring point,
C.sub.1 and C.sub.2 are constants.
19. The reflector of claim 13 in which the axial position of any
point on the reflective surface is related to smaller neighboring
point on the surface by the expression: ##EQU8## where: a.sub.n
is the angle between the central axis and the emitted light ray
to the point on the reflector, R.sub.n is the radius to the smaller
neighboring point, X.sub.0 is the location of the light source along
the central axis, X.sub.n is the axial position of the smaller neighboring
point, C.sub.1 and C.sub.2 are constants.
20. The reflector of claim 14 in which the axial position of any
point on the reflective surface is related to smaller neighboring
point on the surface by the expression: ##EQU9## where: a.sub.n
is the angle between the central axis and the emitted light ray
to the point on the reflector, R.sub.n is the radius to the smaller
neighboring point, X.sub.0 is the location of the light source along
the central axis, X.sub.n is the axial position of the smaller neighboring
point, C.sub.1 and C.sub.2 are constants.
21. The reflector according to claim 13 in which the reflective
surface is composed of a series of small conical segments.
22. The reflector according to claim 14 in which the reflective
surface is composed of a series of small conical segments.
23. The reflector according to claim 15 in which the reflective
surface is composed of a series of small conical segments.
24. The reflector according to claim 16 in which the reflective
surface is composed of a series of small conical segments.
25. The reflector of claim 21 in which the number of conical segments
that project light to any region is given by the relation:
where: b.sub.n is the angle between the central axis and a reflected
light ray from a point on the reflector surface at location n, b.sub.n+1
is the angle between the central axis and a reflected light ray
from a point on the reflector at location n+1 d.sub.n is the angle
between the central axis and a reflected light ray from a point
on the reflector surface at location n, d.sub.n-1 is the angle between
the central axis and a reflected light ray from a point on the reflector
at location n+1.
26. The reflector of claim 22 in which the number of conical segments
that project light to any region is given by the relation:
where: b.sub.n is the angle between the central axis and a reflected
light ray from a point on the reflector surface at location n, b.sub.n+1
is the angle between the central axis and a reflected light ray
from a point on the reflector at location n+1 d.sub.n is the angle
between the central axis and a reflected light ray from a point
on the reflector surface at location n, d.sub.n-1 is the angle between
the central axis and a reflected light ray from a point on the reflector
at location n+1.
27. The reflector of claim 23 in which the number of conical segments
that project light to any region is given by the relation:
where: b.sub.n is the angle between the central axis and a reflected
light ray from a point on the reflector surface at location n, b.sub.n+1
is the angle between the central axis and a reflected light ray
from a point on the reflector at location n+1 d.sub.n is the angle
between the central axis and a reflected light ray from a point
on the reflector surface at location n, d.sub.n-1 is the angle between
the central axis and a reflected light ray from a point on the reflector
at location n+1.
28. The reflector of claim 24 in which the number of conical segments
that project light to any region is given by the relation:
where: b.sub.n is the angle between the central axis and a reflected
light ray from a point on the reflector surface at location n, b.sub.n+1
is the angle between the central axis and a reflected light ray
from a point on the reflector at location n+1 d.sub.n is the angle
between the central axis and a reflected light ray from a point
on the reflector surface at location n, d.sub.n-1 is the angle between
the central axis and a reflected light my from a point on the reflector
at location n+1.
29. A reflector according to claim 1 in which said reflective surface
is generated by a cutting tool which leaves a track, and in which
said surface includes a smooth layer of lacquer that covers said
track, and a deposited highly reflective metal layer on said lacquer
layer.
Machine tools description
FIELD OF THE INVENTION
This invention is a flashlight which can selectively project uniformly
illuminated beams of sizes ranging from a spot to a broad beam having
no occluded center disc.
BACKGROUND OF THE INVENTION
The conventional adjustable beam flashlight employs a paraboloidal
reflector to direct the light. If the light originates from a point
source and is located at the focal point of the paraboloid, a concentrated
spot beam is projected. As the light source is positioned farther
away from the focal point, the projected beam becomes larger. The
beam becomes less uniformly illuminated as the light source is positioned
farther from the focal point until the center of the beam is no
longer illuminated and is surrounded by a series of bright and dull
rings. This dark disc is at the center of the object to be illuminated
and is highly undesirable. The non uniformity with the bright and
dull rings over the remaining area of the broad beam is also undesirable.
Because of the accuracy limits of the machine tools employed, the
state-of-the-art reflector is not a true paraboloid. The slope of
the reflector surface in numerous places differs from the paraboloid.
In order to ameliorate the deviations from a true paraboloid, the
reflector surface or mold from which the reflector is to be formed,
is polished to smooth out the differences. While polishing will
improve the performance of the reflector when projecting a sport
beam, there will remain the problems for the broad beam of non uniformity
of illumination, the appearance of several approximately concentric
bright and dull rings and an unilluminated center disc.
The Ellion U.S. Pat. Nos. 4984140; 5376446; 5440463 and 5459649
describe two unique methods to produce a spot or broad beam without
the unilluminated center disc. U.S. Pat. Nos. 5367446 and 5440463
describe unique lamps to produce the desired beams; U.S. Pat. Nos.
4984140 and 5459649 describe unique reflectors that produce
the desired beams. Although the patented lamps and reflectors eliminate
the unilluminated center disc, none of the four patents teaches
how to produce a broad beam that is perfectly uniform in illumination.
Additionally, while the reflector patents teach how to design a
theoretical reflector having the desired properties to eliminate
the dark center disc, the reflector can not be fabricated to the
accuracy that is required using available machine tools. As a result,
although the broad beam does not have a dark center disc, the beam
is not uniformly illuminated and has a series of bright and dull
rings of illumination.
It is the object of this invention to define the design criteria
for a reflector that projects a uniformly illuminated broad beam.
Another object of this invention is to teach how to use the design
criteria to design a theoretical reflector that projects a uniform
intensity broad beam of illumination and that will have no unilluminated
center disc.
A further object of this invention is to teach how the theoretical
reflector which has uniform illumination and no unilluminated center
disc can be modified so that a practical reflector can be produced
using existing machine tools.
BRIEF DESCRIPTION OF THE INVENTION
This invention is a flashlight reflector that can project a spot
beam approximately the same size as a conventional paraboloidal
reflector but can project a broad beam of uniform illumination without
the occluded center spot. This reflector is based on the principles
of the Ellion U.S. Pat. Nos. 4984140 and 5450649 but describes
three unique enhancements: (1) A design criteria is taught that
defines the relation between the angle of the reflected light from
any location on the surface of the reflector and the angle to that
location from the light source, both angles referred to the axis
of the axially symmetric reflector. A design using this criteria
will not have the multitude of bright and dull rings in the projected
broad beam as occurs with the paraboloidal reflector. (2) Using
this criteria, a method is developed to design a "theoretical"
reflector. However, this theoretical reflector can not be manufactured
using conventional machine tools. (3) A technique is taught to modify
the design of the theoretical reflector to produce a "practical"
reflector using available tools. In one embodiment, the surface
of the practical reflector is made up of a multitude of concentric
cones. The slope and number of these conical segments is determined
from the coordinates of the theoretical reflector. The final result
is a reflector that has a uniformly illuminated spot and broad beam
with no occluded center disc and which can be fabricated using existing
machine tools.
The above and other features of this invention will be fully understood
from the following detailed description and the accompanying drawings,
in which:
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates light rays reflecting from a segment of a reflector.
FIG. 2a illustrates light rays emitted from a reflector as seen
from a distance.
FIG. 2b illustrates a ring of illumination from the light rays
of FIG. 2a
FIG. 3 shows an imaginary sphere surrounding the point light source.
FIG. 4 shows the angles of emitted light rays and reflected light
rays at the maximum and minimum diameters of a reflector.
FIG. 5 defines the angles and coordinates needed to develop a digital
equation.
FIG. 6 shows the actual level of illumination and the level that
is perceived by the human eye.
FIG. 7 illustrates a segment of the theoretical reflector shown
in phantom and one conical segment of the practical reflector.
FIG. 8 illustrates a side view of a truncated reflector to reduce
its size.
FIG. 9 illustrates an end view of a truncated reflector to reduce
its size.
DETAILED DESCRIPTION OF THE INVENTION
The ultimate object of this invention is to enhance the Ellion
inventions described in U.S. Pat. Nos. 4984140 and 5459649 so
that the broad beam has uniform illumination without bright and
dull rings of light and the reflector can be fabricated using existing
machine tools.
This detailed description is organized into three principal sections:
1. The design criteria for a reflector that will project a uniformly
illuminated broad beam.
2. The design of the theoretical reflector that has uniform illumination
using the design criteria
3. The design of the practical reflector based on the theoretical
reflector coordinates that can be manufactured using conventional
machine tools.
1. The design criteria for uniform illumination
It will be necessary to employ a few geometric relations in order
to develop the criteria for uniform illumination. In order to reduce
the teachings of this patent to the simplest form without sacrificing
the rigor of the analysis, the equations will be developed in two
dimensions and will assume that the light originates from a point
source. Since the reflector is axially symmetric, the two dimensional
equations can be transformed easily to the actual three dimensional
beam. It will be made clear later how the finite length of the incandescent
filament in place of a point light source affects the analysis.
The first relation to be developed will be the one that controls
the uniformity of the illumination in the broad beam.
It will be helpfuil to remind the reader of the definitions of
some terms that are related to light. The rate at which a point
source emits light energy, evaluated in terms of its visual effects,
is known as light flux. This flux is measured in lumens which is
the amount of light flux radiating from a uniform one candle power
source throughout a solid angle of size to surround a unit area
at a distance from the source. The illumination of a surface is
defined as the amount of light it receives per unit area. For uniform
illumination of a surface, the ratio of total flux divided by the
illuminated surface area would be equal to a constant. This requirement
forms the basis for the reflector design to produce a uniformly
illuminated broad beam.
In order to determine the illuminated surface area, consider FIG.
1. FIG. 1 illustrates a cross-sectional view of a segment of the
theoretical axially-symmetric reflector 1 whose surface 2 is changing
monotonically. The point light source 3 located on the axis 6 is
positioned at X.sub.0 to project a broad beam. Two light rays 4
and 5 are shown originating from the point light source 3 at angles
"a" and "a+da" relative to the reflector axis
6 where "da" is a differentially small increment (For
clarity of illustration, the light rays are shown far apart rather
than the very small increment "da".) These two rays 4
and 5 bound a continuum of light 7. The continuum of light 7 that
is bounded by rays 4 and 5 is reflected from the surface 2 to form
a continuum of light 10 that is bounded by rays 8 and 9 at angles
"b" and "b+db" relative to the axis 6.
FIG. 2a is a view of the same axially symmetrical reflector 1 and
the two light rays 8 and 9 as viewed from a distance. FIG. 2a illustrates
a side view of the reflector and light rays while FIG. 2b illustrates
the resulting ring shaped illumination from rays 8 and 9. Since
the reflector is axially symmetric, the two light rays 8 and 9 bound
a continuum of light 10 to form the illuminated ring 11 at distance
as illustrated. The area of this differential ring of light will
be equal to:
where "l" is the distance from the reflector to the illuminated
object and d(l tan b) is the thickness of the differentially small
ring of illumination.
Equation 2 relates the illuminated differential area "dA"
to the angle "b" of the reflected light.
It now will be shown how to determine the quantity of light flux
leaving the source in terms of the angle "b" that illuminates
the differential area "dA". FIG. 3 illustrates an imaginary
sphere 31 of arbitrary radius "r" surrounding the point
light source 3. The light can be assumed to radiate equally in all
directions with flux equal to "i". The illumination on
any differential area "dB" of the sphere is equal to the
constant value of the flux "i" times the area "dB".
The light rays 33 and are shown at angles "a" and "a+da"
passing through the area "dB" of width "rda"
on the imaginary sphere. As with FIG. 2 the light rays 33 and 34
are considered to bound a continuum of rays 35. If the axis of the
sphere 36 is aligned to the reflector axis 6 the area of the portion
of the sphere through which the continuum of light will pass is
equal to:
The total light flux passing through the area "dB" will
be equal to:
Since the angle "a" is the same in FIG. 1 and FIG. 3
the light rays 33 and 34 are the same as rays 4 and S. Consequently,
"idB" as given in equation 5 is the total flux quantity
of light that will be reflected to illuminate the differential area
"dA" of equation 2. Since it is desired to have uniform
illumination across the entire broad beam, the ratio of equation
5 and 2 should equal a constant for all values of the angle "a":
Integrating equation 7 and rearranging terms gives:
where: C.sub.1 and C.sub.2 are constants that define the size of
the reflector. The method to determine the value of these two constants
will be explained later.
Equation 8 is the fundamental relation between the angle of the
reflected ray "b" and the angle "a" of the light
my leaving the source to establish a uniformly illuminated broad
beam. This equation forms the basis to define the desired theoretical
reflector; it is the design criteria for uniform illumination.
2. The theoretical reflector
The theoretical reflector will be described next. Based on the
criteria for uniform illumination represented by equation 8 this
reflector will produce a broad beam that has uniform illumination
with no bright/dull rings and does not have an unilluminated disc
at the center. After describing this theoretical reflector, it will
be shown that it is impossible to fabricate it precisely with conventional
machine tools. (Although the theoretical reflector can not be fabricated,
the coordinates of it are needed to design the practical reflector.)
The unique practical reflector of this invention will then be described
that can be manufactured. The practical reflector possesses the
same performance as the theoretical reflector as far as the ability
to adjust from a spot beam to a broad beam, or any size in between,
and where the broad beam will appear to be of uniform illumination
with no bright/dull rings and will have no unilluminated disc in
the center.
Although equation 8 is the criteria that shows how angles "a"
and "b" must be related to obtain a uniformly illuminated
broad beam, in order to design the reflector, it is necessary also
to relate the reflector coordinates, the reflector surface slope
and the position of the light source. As a result, a few additional
relations must be employed.
The relation between the angle of the reflected light rays "b",
the slope of the reflector surface "c" and the angle at
which the light leave the source "a" has been derived
by Ellion in U.S. Pat. No. 4984140 to be:
where all angle are expressed in degrees.
This equation results from the fact that the angle of incident
light is equal to the angle of reflection from the reflector surface.
FIG. 4 illustrates the three angles where "b" is the
angle of the reflected light ray relative to the reflector axis
and is negative in a clockwise direction, and "a" is the
angle of the light ray leaving the source relative to the reflector
axis and "c" is the slope of the reflector surface where
the light ray impacts the reflector and is also relative to the
reflector axis. Both angles "a" and "c" are
always positive in this analysis and angle "b" is always
negative.
Solving equation 9 for "c" gives:
Replacing angle "b" from equation 8 gives:
Equation 11 defines the slope "c" of the reflector surface
in terms of the angle "a" for uniform illumination; it
is another form of equation 8 for the criteria for uniform illumination.
There remains the requirement to obtain a relation between the
angles and the radial and axial coordinates of the reflector that
will project a uniformly illuminated broad beam. A complicated differential
equation that relates the radial coordinates and the angle "a"
can be derived: ##EQU1## However, since this relation can not be
integrated to determine the coordinates "R" in terms of
"a", its complex derivation is of no practical interest.
Similarly, a differential relation for the axial position "X"
in terms of angle "a" can be derived but it also can not
be integrated and is of no practical interest
While it is not possible to relate the radial and axial coordinates
to the various angles in a closed form they can be related in digit
form; i.e. they can be specified with a step-by-step method.
FIG. 5 illustrates a section of the reflector 61. Points 62 and
63 on the reflector surface 61 are spaced an infinitesimal distance
apart. The coordinates of point 62 will be designated "R.sub.n
", "X.sub.n " and "a.sub.n " while those
of point 63 are "R.sub.n+1 ", "X.sub.n+1 " and
"a.sub.n+1 ". For clarity, the points are shown greatly
separated from one another. The point light source 3 is shown located
in the broad beam position at X.sub.0 on the reflector axis 6. A
continuum of light 66 bounded by rays 64 and 65 impact the reflector
61 between points 62 and 63. The tangent to the reflector surface
between points 62 and 63 has an angle "c.sub.n " relative
to the axis 6.
It can be seen from FIG. 5 that: ##EQU2## Solving for R.sub.n+1
gives:
The value of the slope of the reflector surface at any point may
be written as:
and solving for X.sub.n+1 gives:
Equations 14 15 and 16 provide the relations to conduct a step-by-step
process to design the theoretical reflector. The step-by-step method
is not rigorously accurate. However, it will provide a design that
the human eye can not differentiate from the precise "perfect"
reflector. The accuracy of the coordinates as determined by this
digital technique will depend upon the size of the steps that are
taken. For example, if the digital increments for angle "a"
are chosen as da=0.2 degrees, the error in angle "c" and
the coordinates "R" and "X" will be insignificant
for a typical 2D battery size flashlight reflector which projects
a 6 foot diameter broad beam at a range of 10 feet; The reason that
such a crude increment of da=0.2 degrees will not affect the apparent
performance of the theoretical reflector is that the human eye does
not react to light intensity in a linear fashion. Instead, the eye
responds to a logarithmic variation. FIG. 6 from U.S. Pat. No. 4984140
illustrates the actual illumination along the abscissa and the relative
effectiveness of seeing by the human eye (i.e. the perceived brightness)
along the ordinate. It is seen from FIG. 6 that for a large 100
percent change in the actual intensity from 320 to 160 lumens, the
human eye can only perceive a change of less than 10 percent. Similarly,
a change in actual illumination of 10 percent from 320 to 297 lumens
results in a perceived change of only one percent.
The method for determining the value of the two constants in equation
8 can now be explained. For the desired size of the reflector and
the desired size of the broad beam, the value of the constants can
be determined readily by considering FIG. 4. When the light source
is located at the broad beam setting, X.sub.0 the light rays 43
that are reflected from the maximum diameter 41 of the reflector
emerge 44 parallel to the axis to shine on the center of the illuminated
object and those 45 reflected from the minimum diameter 42 emerge
at angle "b" which illuminates the outer region of the
object. Equation 8 can be written for these two beams to give two
equations (one for b=0 and a=a.sub.max and one for b=the maximum
angle and a=a.sub.min). Having two equations and two unknowns (C.sub.1
and C.sub.2) the value of the two constants can be determined. The
angle "a" to the minimum radius can be seen to be related
to the radial and axial coordinates by considering FIG. 4:
If the incremental steps for (a.sub.n -a.sub.n+1) are chosen as
0.2 degrees, the value of a.sub.n+1 is given by:
Equations 11 14 15 16 and 18 can be combined to give: ##EQU3##
Equations 11 18 and 19 can be combined to give: ##EQU4##
All of the information that is needed to design the theoretical
reflector has been presented. The steps to following in designing
the reflected can be summarized as:
1. Determine the value of the constants C.sub.1 and C.sub.2 in
equation 8 by choosing the size of the reflector and the size of
the broad beam.
2. Calculate the values "X", "R" and "c"
at the minimum diameter of a paraboloid that will fit into the flashlight.
These are initial values for "X.sub.n ", "R.sub.n
" and "c.sub.n ".
3. Using equation 17 calculate the value of "a.sub.n "
at the minimum diameter.
4. Using equation 18 calculate the value of "c.sub.n+1 ".
5. Using equation 19 calculate the value of "R.sub.n-1 ".
6. Using equation 20 calculate the value of "X.sub.n+1 ".
7. Continue this step-by-step process until the value of "R.sub.n+1
" equals the desired maximum radius of the reflector.
By following this digital technique, a theoretical reflector can
be designed that would project a broad beam that is uniformly illuminated
as perceived by the human eye and which has no unilluminated center
disc. However, because the tolerances of current machine tools is
.+-.0.0001 inches, the theoretical reflector can not be fabricated
to the required tolerances. An example will be instructive:
Consider two points on the theoretical reflector surface for which
the axially displacement is 0.0100 inches. The computer controlled
lathe will move in a straight line between these two points. Consider
the example where it is desired to have the slope of the surface
between these two points equal to 44.9 degrees. From equation 9
the error in the reflected angle,b, will be twice the error in the
slope of the surface. The tangent of 44.9 degrees is 0.9965154.
The radial displacement to form this angle would be 0.009965154
inches. The lathe can only move 0.0100 or 0.0099 inches. The result
is that the radial displacement would be 0.010 and the axial displacement
also would be 0.010 inches resulting in a surface having a slope
of 45 degrees. The difference between the desired 44.9 degrees and
the actual 45.0 degrees would produce a reflected light ray that
is 2.times.0.1 degrees from the desired location. This would displace
the actual light ray from the desired location by 0.4189 inches
at a range of 10 feet to the object being illuminated as determined
by equation 21. This would result in a dull ring of light of thickness
0.42 inches. If the entire reflector were analyzed in a similar
manner, it would be seen that the broad beam would have a multitude
of bright and dull rings of illumination.
A broad beam of light made up of discrete bright/dull rings is
highly undesirable. Existing paraboloidal reflectors manufactured
on existing lathes that have tolerances of .+-.0.0001 inches are
improved by polishing out the very small conical sections that result.
However, in addition to the unilluminated center disc, the polished
paraboloidal reflector would have a broad beam with bright/dull
rings of illumination. A reflector that is manufactured from the
theoretical design would produce a broad beam that has a fully illuminated
center disc but would have a series of bright/dull rings. The intensity
and number of these bright/dull rings would increase as the number
of coordinate points is increased. If the two coordinate points
are farther apart, the problem can be ameliorated. This consideration
forms the basic concept for designing the "practical"
reflector.
3. The Practical Reflector
It has been shown that the accuracy available from existing machine
tools will produce a reflector with a broad beam that has bright/dull
rings of illumination. The greater the values of (R.sub.n -R.sub.n+1)
and (X.sub.n -X.sub.n+1), the easier it will be to obtain the precise
values of the desired slope of the surface between the two points
and consequently eliminate the rings. With this background, it is
now possible to describe a reflector that approaches the performance
of the theoretical reflector that has a small spot beam and a broad
beam that has uniform illumination with no bright/dull rings and
no unilluminated center disc.
The concept for the design of the practical reflector is to increase
the incremental distance between each coordinate to the level where
the slope is precisely the desired value given the possible axial
and radial tolerances of .+-.0.0001 inches. In the simplest embodiment
to describe this invention, the reflector surface is formed by a
multitude of concentric cones. The size, location, slope and number
of these cones are determined by the criteria for uniform illumination
(equation 8 and 11) and the theoretical reflector.
The first step in designing the practical reflector is to design
the theoretical reflector with the coordinates calculated to several
decimal paces (e.g. 7 places). The design of the theoretical reflector
will provide the information that determines the number of cones
that are need to reflect light to any specific area in order to
provide uniform illumination.
FIG. 7 will be helpful in explaining how to determine the number
of cones that are needed. The figure illustrates a segment of the
theoretical reflector shown in phantom 70 and one cone of the practical
reflector 71 that is tangent to the theoretical segment at the minimum
diameter location that is designated with subscript "n".
Consider the segment of the theoretical reflector bounded by light
rays 73 and 74 reflected as rays 75 and 76 having angles of 77 and
78 relative to the axis 6 as determined by equation 9. The same
light rays 73 and 74 and, therefor, the same amount of total flux
would reflect from the conical segment as rays 79 and 80 at angles
77 and 81. Using equation 21 it is seen that the segment of the
theoretical reflector would project an illuminated ring of light
with a minimum diameter D.sub.1 equal to the tangent of the angle
78 times twice the distance between the reflector and the illuminated
object. Similarly, the maximum diameter D.sub.2 of the ring of light
would be equal to the tangent of the angle 77 times twice the distance
to the object. The maximum diameter of the illuminated ring of light
D.sub.3 that is projected by the conical segment would be the same
as is reflected from the segment of the theoretical reflector since
the slopes of the two surfaces are equal at the minimum diameter.
However, the minimum diameter D.sub.4 would be less than that projected
by the segment of the theoretical reflector since angle 81 is less
than angle 78 The segment of the theoretical reflector illuminates
a ring having an area equal to .pi./4(D.sub.1.sup.2 -D.sub.2.sup.2)
and the conical segment illuminates a ring having an area equal
to .pi./4(D.sub.3.sup.2 -D.sub.4.sup.2). The level of illumination
is inversely related to the area for a given value of total flux.
Consequently, it is necessary to have N cones to provide the same
illumination with the conical practical reflector as with the theoretical
monotonically changing surface where N is: ##EQU5## The procedure
to follow in designing the entire practical reflector is as follows:
1. Choose the value for (a.sub.n -a.sub.n+1) so that the desired
slope of the reflector surface can be machined with existing tools.
For a reflector in a typical 2D battery flashlight that value would
be greater than one degree. A convenient and practical value is
two degrees.
2. Draw a conical segment tangent to the minimum radius of the
theoretical reflector at R.sub.n and X.sub.n that has a slope equal
to c.sub.n.
3. Determine the value of R.sub.n+1 and X.sub.n+1 for the end of
the conical segment having the desired slope c.sub.n. The value
of these coordinates should be precise within the tolerances of
the machine tool (0.0001 inches) in order to produce the slope c.sub.n.
The slope can deviate from the desired value by .+-.0.02 degrees
and only affect the broad beam diameter by less than 0.084 inches,
which is less than the dispersion resulting from a finite filiment
rather than a point source of light.
4. Determine the angle of the reflected rays from the segment of
the theoretical reflector and the segment of the cone by equation
9 the resulting radius of the illuminated areas by equation 21
and finally the number of cones required to illuminate the area
by equation 24.
5. If it is required to have a second cone illuminating the same
ring as determined by equation 24 determine the slope of the second
conical segment from equation 9 in order to place the reflected
rays at the same location as from the first cone.
6. After providing the-required number of cones for the first ring
of illumination, the next conical segment should reflect light to
the edge of the light from the first group of cones.
7. Continue for the number of cones necessary to provide uniform
illumination. This process continues until the minimum radius is
reached.
The discussion to this point has been concerned with the broad
beam. This section will discuss the spot beam. In a typical paraboloidal
reflector, the spot beam is larger than the maximum diameter of
the reflector because the light is not originating from a point
source. The result of the bulb having a finite length filament is
to produce a spot beam from a typical D-battery size flashlight
that diverges from the reflector axis by approximately 4 degrees.
At a range of ten feet, this divergence will produce a spot beam
of approximately 1.4 feet in diameter as calculated using equation
21. When the bulb is positioned away from the focal point towards
the maximum diameter (or towards the minimum diameter) in order
to project a broad beam having a diameter of 6 feet, an unilluminated
center disc is formed that has a diameter of approximately 1.5.
feet for a D-batttery size flashlight at a range of 10 feet. The
theoretical reflector previously described will fill in this unilluminated
center disc by having the slope at the maximum diameter of the theoretical
reflector equal to that of the paraboloidal reflector plus (or minus)
one-half of the angle 4 degrees as calculated by equation 9. This
increased slope will direct the reflected light from the maximum
diameter towards the center by the required 4 degrees and illuminate
the dark disc. Conversely, when the bulb is located at the spot
beam position, the light that is projected from the maximum diameter
of the theoretical reflector will diverge 4 degrees from the axis
of the reflector and produce a spot beam that is approximately 1.5
feet in diameter. The light that is reflected from smaller diameters
of the theoretical reflector will project into the spot beam within
the 1.5 feet diameter. It is seen that the theoretical reflector
will project a broad beam that is uniformly illuminated and that
will project a spot beam that is approximately the same size as
that from a paraboloidal reflector.
It has been shown in a previous section that in order to design
the theoretical reflector, the minimum diameter segment is chosen
as a small portion of a paraboloidal reflector that would fit into
the flashlight. The focal point of this imaginary paraboloid is
also the "focal point" of the theoretical reflector. The
theoretical reflector does not have a precise focal point as does
the paraboloid since it is a slightly modified paraboloid. However,
placing the bulb at the focal point of the imaginary parabloid will
generate a spot beam that is approximately the same size as one
projected a paraboloid as was explained above.
One additional practical consideration is that the surface of the
reflector should be highly polished to project the brightest beams.
When the reflector is machined or if it is injection molded there
would be slight helical grooves since the lathe that was used for
fabrication moves a small axial distance for every revolution. Using
the current state of the art, inexpensive production reflectors
are coated with a thin layer of lacquer, then aluminum is deposited
in a vacuum (vapor deposited aluminum, VDA) and finally a second
layer of lacquer is applied in order to protect the aluminum reflective
surface. The first layer of lacquer will ameliorate the small helical
grooves and result in a smooth reflective surface.
The foregoing has disclosed complete surfaces of revolution which
would produce the maximum illumination. However, the reflector will
always have a larger diameter than the body of the flashlight. Although
this is true of all conventional flashlights, it may be desirable
to have a smaller product. For example in FIGS. 8 and 9 a reflector
90 according to the foregoing discussion has a dimension of width
in one lateral axis at its larger end reduced by forming two planar
reflecting faces 91 and 92 extending from the edges 93 and 94 respectively,
to near adjacency to the center hole 95. It may or may not extend
through the reflecting region immediately to the hole. These slanting
faces will also reflect light, but not in the same controlled pattern
as the remainder of the reflector, which still will produce beams
of uniform illumination and without an occluded disc. Anyone skilled
in the art can envision a multitude of other truncated reflectors.
While this invention will find its greatest use in hand held flashlights,
and the specifications and claims use this term, it can be scaled
to any size from small hand held lamps to large searchlights that
may use arcs in place of filaments as a source of the light.
This invention is not to be limited by the embodiments shown in
the drawings and described in the description, which are given by
way of example and not of limitations, but only in accordance with
the scope of the accompanying claims. |