U.S. patent application number 14/503748 was filed with the patent office on 2015-02-05 for control of luminous intensity distribution from an array of point light sources.
The applicant listed for this patent is Ian Ashdown, Michael A. Tischler. Invention is credited to Ian Ashdown, Michael A. Tischler.
Application Number | 20150036339 14/503748 |
Document ID | / |
Family ID | 47505298 |
Filed Date | 2015-02-05 |
United States Patent
Application |
20150036339 |
Kind Code |
A1 |
Ashdown; Ian ; et
al. |
February 5, 2015 |
CONTROL OF LUMINOUS INTENSITY DISTRIBUTION FROM AN ARRAY OF POINT
LIGHT SOURCES
Abstract
In various embodiments, a lens array comprises a plurality of
aspheric lens elements each optically coupled to a light-emitting
element and producing an out-of-focus image thereof. The images
combine to generate a target luminous intensity distribution, e.g.,
providing constant illuminance on a plane.
Inventors: |
Ashdown; Ian; (West
Vancouver, CA) ; Tischler; Michael A.; (Vancouver,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Ashdown; Ian
Tischler; Michael A. |
West Vancouver
Vancouver |
|
CA
CA |
|
|
Family ID: |
47505298 |
Appl. No.: |
14/503748 |
Filed: |
October 1, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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14199375 |
Mar 6, 2014 |
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14503748 |
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13693632 |
Dec 4, 2012 |
8746923 |
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14199375 |
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61566899 |
Dec 5, 2011 |
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61583691 |
Jan 6, 2012 |
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Current U.S.
Class: |
362/235 |
Current CPC
Class: |
F21V 5/007 20130101;
G02B 2207/113 20130101; G02B 3/08 20130101; F21V 5/045 20130101;
F21Y 2115/10 20160801; G02B 3/0056 20130101; F21V 5/08 20130101;
F21V 5/10 20180201; G02B 27/0961 20130101; Y10T 29/49 20150115;
F21V 33/00 20130101; G02B 19/0066 20130101; F21Y 2105/10 20160801;
G02B 19/0028 20130101 |
Class at
Publication: |
362/235 |
International
Class: |
F21V 5/00 20060101
F21V005/00; F21V 5/04 20060101 F21V005/04 |
Claims
1-27. (canceled)
28. A luminaire comprising: a substantially planar array of
light-emitting elements; and a lens array comprising a continuous
layer of transparent material having a first surface for receiving
light from the light-emitting elements and, formed on a second
surface thereof opposed to the first surface, a two-dimensional
array of aspheric lens elements, at least some of which are
optically coupled to a closest one of the light-emitting elements,
wherein (i) the light-emitting elements each have an optical axis
shifted relative to an optical axis of the closest lens element,
(ii) the light-emitting elements are spaced apart from the first
surface by a first distance, and (iii) a light distribution pattern
of the luminaire is radially asymmetric with respect to a direction
perpendicular to a plane defined by the array of light-emitting
elements.
29. The luminaire of claim 28, wherein the aspheric lens elements
in the two-dimensional array are substantially co-linear in a first
direction, and the light distribution pattern of the luminaire is
(i) tilted along the first direction and (ii) substantially
spatially constant with respect to a plane not parallel to the
plane defined by the array of light-emitting elements.
30. The luminaire of claim 29, wherein the aspheric lens elements
in the two-dimensional array are substantially co-linear in a
second direction substantially perpendicular to the first
direction.
31. The luminaire of claim 28, wherein the lens elements each have
a lens profile described by the lowest-order mathematical equation
that generates a predetermined luminous intensity distribution when
light emitted by the light-emitting elements and passing through
the lens elements is combined, the profile specifying a lens shape
and a lens thickness.
32. The luminaire of claim 31, wherein the equation comprises
parameters including a refractive index of the lens and dimensions
of the light-emitting element, the thickness corresponding to a
distance from a front surface of the lens element to the
light-emitting element.
33. The luminaire of claim 31, wherein the equation is a quadratic
equation.
34. The luminaire of claim 31, wherein the equation is a cubic
equation.
35. The luminaire of claim 28, wherein each lens element has an
aspheric cubic lens profile.
36. The luminaire of claim 28, wherein each lens element has an
aspheric cubic linear lens profile.
37. The luminaire of claim 28, wherein the light-emitting elements
have rectangular emission surfaces.
38. The luminaire of claim 28, wherein each lens element is shaped
to produce a batwing luminous distribution profile when the optical
axis of the lens element is not shifted relative to the optical
axis of the closest light-emitting element.
39. The luminaire of claim 28, wherein each lens element is shaped
to produce a substantially collimated light distribution profile
when the optical axis of the lens element is not shifted relative
to the optical axis of the closest light-emitting element.
40. The luminaire of claim 39, wherein the substantially collimated
light distribution profile has a beam angle less than
15.degree..
41. The luminaire of claim 28, wherein the asymmetric light
distribution pattern is an asymmetric collimated light distribution
pattern.
42. The luminaire of claim 41, wherein the asymmetric collimated
light distribution pattern has a beam angle less than
40.degree..
43. The luminaire of claim 28, wherein the asymmetric light
distribution pattern is an asymmetric batwing light distribution
pattern.
44. The luminaire of claim 28, wherein the first distance is
essentially zero.
45. The luminaire of claim 44, wherein each light-emitting element
is directly bonded to the first surface.
46. The luminaire of claim 28, wherein the light distribution
pattern of the luminaire has a cutoff angle varying with changes in
the first distance.
47. The luminaire of claim 28, wherein the first distance is less
than about 4.3 mm.
48. The luminaire of claim 28, wherein the optical axis of each
light-emitting element is shifted by about 1.5 mm.
49. The luminaire of claim 28, wherein the light distribution
pattern has a beam angle less than 40.degree..
50. The luminaire of claim 28, wherein the two-dimensional array of
aspheric lens elements forms a linear lens array.
51. The luminaire of claim 28, wherein a thickness of the luminaire
is less than about 9 mm.
52. The luminaire of claim 28, wherein the aspheric lens elements
in the two-dimensional array are substantially co-linear in a first
direction, and the light distribution pattern of the luminaire is
(i) tilted along the first direction and (ii) substantially
radially symmetric with respect to a direction not perpendicular to
the plane defined by the array of light-emitting elements.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 13/693,632, filed on Dec. 4, 2012, which
claims the benefit of and priority to U.S. Provisional Patent
Application No. 61/566,899, filed on Dec. 5, 2011, and U.S.
Provisional Patent Application No. 61/583,691, filed on Jan. 6,
2012, the entire disclosures of which are hereby incorporated by
reference.
TECHNICAL FIELD
[0002] The present invention relates to the control of luminous
intensity distribution from an array of point light sources. More
particularly, the invention relates to modification of the
Lambertian luminous intensity distribution of an array of
light-emitting elements into a distribution that provides spatially
constant illumination of a planar surface.
BACKGROUND
[0003] Bare phosphor-coated lighting-emitting diodes (i.e.,
unencapsulated light-emitting diode (LED) die with a conformal
phosphor coating) typically exhibit a Lambertian luminous intensity
distribution that is described by:
I(.theta.)=I.sub.n.times.cos(.theta.)
where I.sub.n is the intensity measured perpendicular to the
light-emitting surface and I(.theta.) is the intensity measured at
angle .theta. from the surface normal. A schematic luminous
intensity plot of such a Lambertian emitter is shown in FIG. 1,
where the light source is located at the center of the large sphere
and points on the smaller sphere represent the intensity
plot--i.e., the intensity value as a function of angle from the
normal. As shown in the figure, the apparent brightness to an
observer is the same regardless of the observer's angle of
view.
[0004] For many lighting applications, however, it is desirable for
luminaires to have a luminous intensity distribution such that the
illuminance of the workplane below the luminaire or the ceiling
above the luminaire is substantially constant. For an infinite
linear source, the illuminance E of a plane parallel to and at a
distance d.sub.n from the light source is given by:
E(.theta.)=I(.theta.).times.cos.sup.2(.theta.)/d.sub.n
where .theta. is the angle in the direction perpendicular to the
linear light source. To maintain spatially constant illuminance
with a linear light source, it is therefore necessary that:
I(.theta.)=I.sub.n/cos.sup.2(.theta.)
in the direction perpendicular to the light source axis.
[0005] Again, however, for architectural applications, and in
particular for office lighting, luminaires with linear fluorescent
lamps are typically arranged in parallel rows such that their
luminous intensity distributions overlap. As such, a more desirable
intensity distribution is:
I(.theta.)=I.sub.n/cos(.theta.)
[0006] Luminaires designed for office lighting applications
generally also comply with the recommendations of ANSI/IES RP-1,
Office Lighting, which limits the luminous intensity at oblique
viewing angles. A theoretical luminous intensity distribution
satisfying these requirements over the range
-30.degree.<.theta.<30.degree. is shown in FIG. 2. One
attempt to realize this distribution is the direct-indirect linear
fluorescent luminaire (Model 7306T02IN as manufactured by Ledalite,
Langley, BC, Canada), the measured luminous intensity distribution
of which is shown in FIG. 3A (viewed perpendicular to the lamp
axis) and FIG. 3B (viewed parallel to the lamp axis).
[0007] The downward component illustrated in FIG. 3A exhibits a
distribution similar to that of FIG. 2, while the downward
component of FIG. 3B exhibits a substantially Lambertian
distribution similar to FIG. 1. The latter distribution is a
consequence of the fact that four-foot fluorescent lamps are
essentially linear light sources, so the luminous intensity
distribution in the direction parallel to the lamp axis cannot be
controlled without substantial light losses, and also need not
satisfy the inverse cosine relationship: the continuous
distribution of light along the length of the luminaires will tend
to provide constant illuminance on the workplane or ceiling in the
same direction. However, the recommendations of ANSI/IES RP-1 must
still be satisfied for many commercial applications.
[0008] For illuminated ceilings in open-plan offices, ANSI/IES
RP-1, Office Lighting, also recommends a brightness uniformity
ratio of 8:1 or less, and preferably 4:1 or even 2:1 if possible.
This is typically accomplished with linear fluorescent luminaires
having a so-called "batwing" luminous intensity distribution, such
as is exhibited, for example, by the upward component of the
luminous intensity distribution shown in FIGS. 3A and 3B. The ideal
batwing distribution is similar to FIG. 2, but with a wider range.
Assuming a typical suspension distance of 16 inches below the
ceiling and a luminaire row operation of 6 feet, the range of
constant illuminance should be at least
-65.degree.<.theta.<65.degree.. Another approach is to
optically couple high-power LED packages with external optics. The
resulting distribution, however, may be too collimated for most
architectural lighting applications, and the optical assembly too
large for most luminaire designs.
[0009] There are in addition applications requiring an asymmetric
luminous intensity distribution. As one example, linear fluorescent
luminaires are often mounted on walls near the ceiling of a room as
"cove lighting" to provide substantially constant illumination of
the wall surface, typically with the use of physically large
asymmetric reflectors.
[0010] There is, therefore, a need for a monolithic optical lens
design that can generate a luminous intensity distribution from an
array of light-emitting elements to provide spatially constant
illumination of a surface, such as a workplane, ceiling or wall,
and in a form factor that is compatible with the optical,
mechanical and aesthetic design requirements of luminaires intended
for architectural applications such as office lighting.
SUMMARY
[0011] In various embodiments, the present invention exploits the
ability to achieve a predetermined light intensity distribution
from a light source by intentionally designing an optical element
to produce an out-of-focus image of the source. This approach is
used, for example, to design single-lens optical elements for
light-emitting element arrays. In one exemplary implementation, the
constant illuminance distribution of a plane is achieved with a
single aspheric lens. In contrast to free-form lens designs, the
present approach may begin with a spherical lens profile, which is
modified until the resulting profile is described by the
lowest-order mathematical equation that will generate the desired
luminous intensity distribution. An evolutionary algorithm, for
example, may be employed to determine the lowest-order mathematical
equation that will generate the desired luminous intensity
distribution. Typically, the equation is a cubic or lower-order
equation, and the lens may have a conventional or Fresnel design.
In some embodiments the lens profile is hyperbolic, and in other
embodiments it is conical. A luminaire based on a light-emitting
element array may utilize single-lens optical elements designed in
accordance herewith to produce spatially constant illumination over
a planar surface.
[0012] Accordingly, in one aspect, the invention pertains to a
luminaire producing a light distribution that provides
predetermined luminous intensity distribution. In various
embodiments, the luminaire comprises an array of light-emitting
elements, and, disposed over the light-emitting elements, a lens
array that itself comprises a plurality of aspheric lens elements
each optically coupled to a respective one of light-emitting
elements and producing an out-of-focus image thereof; the images
combine to generate a predetermined luminous intensity
distribution. In some embodiments, the lens elements each have a
lens profile described by the lowest-order mathematical equation
that generates a predetermined luminous intensity distribution when
light emitted by the light-emitting elements and passing through
the lens elements is combined, and the profile specifies a lens
shape and a lens thickness. The predetermined luminous intensity
distribution may, for example, correspond to spatially constant
illumination of a planar surface.
[0013] In some embodiments, the lens elements each produce a narrow
beam and collectively produce the predetermined luminous intensity
distribution. The equation may comprise parameters including a
refractive index of the lens and dimensions of the light-emitting
element, and the thickness may correspond to a distance from a
front surface of the lens element to the light-emitting element.
The equation may, for example, be a quadratic equation, a cubic
equation, or other suitable expression.
[0014] Each lens element may be a Fresnel lens or a conventional
lens. The lens elements may each have a rotationally symmetric
profile, e.g., an aspheric cubic lens profile, an aspheric cubic
linear lens profile, a hyperbolic lens profile, or a conic linear
lens profile, and the luminaire may have lens elements with a
single profile or a combination of profiles. In some embodiments,
each lens element produces a batwing luminous distribution profile
or a substantially collimated light distribution profile, e.g.,
having a beam angle or full width at half maximum (FWHM) less than
15.degree.. The light distribution of each lens element may be
asymmetric, e.g., an asymmetric collimated light distribution. The
center of each light-emitting element may be shifted relative to
the center of the corresponding aspheric lens element, or may be
substantially aligned with the center of the corresponding aspheric
lens element.
[0015] In another aspect, the invention relates to a method of
manufacturing a luminaire for achieving a predetermined luminous
intensity distribution. In various embodiments, the method
comprises the steps of designing one or more optical elements to
produce an out-of-focus image of a light source by computationally
modifying an initial lens profile (e.g., a spherical profile) until
a resulting profile is described by the lowest-order mathematical
equation that will generate the predetermined light intensity
distribution from the light source; providing a plurality of the
light sources arranged in an array; manufacturing a plurality of
the optical elements; and associating the optical elements with the
light sources such that each of the optical elements produces an
out-of-focus image of an associated light source, such that the
images combine to generate the predetermined luminous intensity
distribution.
[0016] In still another aspect, the invention pertains to a method
of manufacturing an optical element for achieving a predetermined
luminous intensity distribution. In various embodiments, the method
comprises the steps of generating a design for one or more optical
elements to produce an out-of-focus image of a light source by
computationally modifying an initial lens profile (e.g., a
spherical profile) until a resulting profile is described by the
lowest-order mathematical equation that will generate the
predetermined luminous intensity distribution from the light
source; and manufacturing the optical element in accordance with
the design. In various embodiments, the optical element is a lens,
and the lens is manufactured by molding or embossing.
[0017] These and other objects, along with advantages and features
of the present invention herein disclosed, will become more
apparent through reference to the following description, the
accompanying drawings, and the claims. Furthermore, it is to be
understood that the features of the various embodiments described
herein are not mutually exclusive and can exist in various
combinations and permutations. Reference throughout this
specification to "one example," "an example," "one embodiment," or
"an embodiment" means that a particular feature, structure, or
characteristic described in connection with the example is included
in at least one example of the present technology. Thus, the
occurrences of the phrases "in one example," "in an example," "one
embodiment," or "an embodiment" in various places throughout this
specification are not necessarily all referring to the same
example. Furthermore, the particular features, structures,
routines, steps, or characteristics may be combined in any suitable
manner in one or more examples of the technology. The headings
provided herein are for convenience only and are not intended to
limit or interpret the scope or meaning of the claimed technology.
The term "light" broadly connotes any wavelength or wavelength band
in the electromagnetic spectrum, including, without limitation,
visible light, ultraviolet radiation, and infrared radiation.
Similarly, photometric terms such as "illuminance," "luminous
flux," and "luminous intensity" extend to and include their
radiometric equivalents, such as "irradiance," "radiant flux," and
"radiant intensity." The term "substantially" means.+-.10%, and in
some embodiments, .+-.5%.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] In the drawings, like reference characters generally refer
to the same parts throughout the different views. Also, the
drawings are not necessarily to scale, with an emphasis instead
generally being placed upon illustrating the principles of the
invention. In the following description, various embodiments of the
present invention are described with reference to the following
drawings, in which:
[0019] FIG. 1 graphically depicts a luminous intensity plot of a
Lambertian emitter.
[0020] FIG. 2 graphically depicts a luminous intensity distribution
satisfying the recommendations of ANSI/IES RP-1, Office
Lighting.
[0021] FIGS. 3A and 3B graphically depict the measured luminous
intensity distribution of a direct-indirect linear fluorescent
luminaire viewed, respectively, perpendicular and parallel to the
lamp axis.
[0022] FIG. 4 is a schematic sectional view of a portion of a
planar array of light-emitting and optical elements in accordance
with embodiments of the present invention.
[0023] FIG. 5 graphically depicts the profile of a cubic lens
profile in accordance with an embodiment of the invention, where
(as in similar depictions herein) the ordinate axis represents lens
thickness (height) and the abscissa corresponds to distance from
the lens center (at the origin).
[0024] FIG. 6 is a perspective view of an array of lenses having
the profile shown in FIG. 5.
[0025] FIGS. 7A and 7B graphically depict the luminous intensity
distribution generated by a lens having the profile shown in FIG.
5, with FIG. 7A reflecting a horizontal view and FIG. 7B providing
a nadir view (i.e., looking "up" from the "bottom").
[0026] FIGS. 8 and 9 graphically depict horizontal luminous
intensity distributions generated by a lens having the profile
shown in FIG. 5 with the vertical offset decreased and increased,
respectively.
[0027] FIG. 10 graphically depicts the horizontal luminous
intensity distribution generated by a lens having the profile shown
in FIG. 5 with an altered horizontal offset.
[0028] FIGS. 11A and 11B graphically depict horizontal luminous
intensity distributions generated by a lens having the profile
shown in FIG. 5 with phosphor layers of different thicknesses.
[0029] FIG. 12 is a perspective view of an array of lenses in
accordance with a Fresnel embodiment corresponding to the cubic
profile of FIG. 5.
[0030] FIG. 13 graphically depicts the profile of a Fresnel lens as
shown in FIG. 12.
[0031] FIGS. 14A and 14B graphically depict the luminous intensity
distribution generated by a lens having the profile shown in FIG.
12, with FIG. 14A reflecting a horizontal view and FIG. 14B
providing a nadir view.
[0032] FIG. 15 graphically depicts the profile of a Fresnel
embodiment with variable width segments, and corresponding to the
cubic profile of FIG. 5.
[0033] FIG. 16 is a perspective view of a lens having the profile
shown in FIG. 15.
[0034] FIG. 17 graphically depicts the horizontal luminous
intensity distribution generated by a lens having the profile shown
in FIG. 15.
[0035] FIG. 18 graphically depicts a lens profile that may be
formed using a laser-fabricated embossing mold.
[0036] FIG. 19 graphically depicts the horizontal luminous
intensity distribution generated by a lens made from a mold with
the profile shown in FIG. 18.
[0037] FIG. 20 is a perspective view of an array of linear lenses
in accordance with an embodiment of the invention.
[0038] FIG. 21 graphically depicts the profile of a lens as shown
in FIG. 20.
[0039] FIGS. 22A-22C graphically depict the luminous intensity
distribution generated by a lens having the profile shown in FIG.
20, with FIG. 22A reflecting a lateral view, and FIG. 22B providing
a longitudinal view, and FIG. 22C a nadir view.
[0040] FIG. 23 is a perspective view of an array of lenses in
accordance with an embodiment having a hyperbolic lens profile.
[0041] FIG. 24 graphically depicts the profile of a lens as shown
in FIG. 23.
[0042] FIGS. 25A and 25B graphically depict the luminous intensity
distribution generated by a lens having the profile shown in FIG.
24, with FIG. 25A reflecting a horizontal view and FIG. 25B
providing a nadir view; FIGS. 26A and 26B show the corresponding
profiles that result when the LED die is offset horizontally.
[0043] FIG. 27 graphically depicts the profile of a conic lens in
accordance with an embodiment of the invention.
[0044] FIGS. 28A and 28B graphically depict the luminous intensity
distribution generated by a lens having the profile shown in FIG.
27, with FIG. 28A reflecting a horizontal view and FIG. 28B
providing a nadir view.
[0045] FIG. 29 is a perspective view of an array of Fresnel lenses
corresponding to the profile shown in FIG. 27.
[0046] FIG. 30 graphically depicts the profile of the Fresnel lens
shown in FIG. 29.
[0047] FIGS. 31A and 31B graphically depict the luminous intensity
distribution generated by a lens having the profile shown in FIG.
29, with FIG. 31A reflecting a horizontal view and FIG. 31B
providing a nadir view.
[0048] FIG. 32 graphically depicts the profile of a lens having a
cubic profile in accordance with an embodiment of the
invention.
[0049] FIGS. 33A and 33B graphically depict the luminous intensity
distribution generated by a lens having the profile shown in FIG.
32, with FIG. 33A reflecting a horizontal view and FIG. 33B
providing a nadir view.
[0050] FIGS. 34A and 34B show, respectively, simulated and measured
light-distribution patterns for a lens in accordance with a cubic
embodiment of the invention.
[0051] FIG. 35 shows, simulated and measured light-distribution
patterns for a lens in accordance with a hyperbolic embodiment of
the invention.
[0052] FIG. 36 shows simulated and measured light-distribution
patterns for a lens in accordance with another hyperbolic
embodiment of the invention.
DETAILED DESCRIPTION
[0053] The approach of the present invention is based upon an
aesthetic photographic quality called "bokeh." As discussed in
Nasse, H. H., Depth of Field and Bokeh, Oberkochen, Germany: Carl
Zeiss Camera Lens Division (2010) (hereafter "Nasse," the entire
disclosure of which is hereby incorporated by reference), bokeh is
"a collective term for all attributes of [out-of-focus] blurring"
of photographic images. It is a subjective metric in that
out-of-focus blurring is dependent upon a large number of
parameters, including picture format, focal length, f-number
(effective aperture), t-number (lens transmission),
camera-to-subject distance, distance to the background or
foreground, shapes and patterns of the subject, aperture iris
shape, lens aberrations, foreground/background brightness, and
color.
[0054] With an ideal lens and a point light source, out-of-focus
blurring is described by the "circle of confusion," which is a
hard-edged circle of light. However, diffraction effects and lens
aberrations invariably result in an out-of-focus image of a point
light source having smooth edges and color fringing. As further
discussed in Nasse, photographic camera lenses may be intentionally
designed to produce aesthetically pleasing out-of-focus blurring.
In contrast, Maksutov telescopes and other catadioptic lens-mirror
designs produce severe "doughnut" bokeh patterns due to obstruction
by their secondary mirrors.
[0055] There are, however, physical limits on the control the lens
designer has over the bokeh characteristics of a given lens design.
Embodiments of the present invention apply the concept of bokeh to
the distribution of light from light-emitting elements, such as an
array of LEDs. In particular, there is a continuum of bokeh
characteristics from the uniform circle of confusion for an ideal
lens to the doughnut pattern of catadioptic lens-mirror designs. It
therefore follows from the Helmholtz reciprocity principle (i.e.,
the direction of light can always be reversed) that the projected
image of a physical light source will exhibit bokeh
characteristics. As such, it becomes possible to achieve a
predetermined light intensity distribution (such as, for example,
FIG. 3A) from a light source by intentionally designing an optical
element to produce an out-of-focus image of the source.
[0056] This approach is particularly advantageous for the design of
single-lens optical elements for light-emitting element (e.g., LED)
arrays. In accordance with the approach described herein, the
constant illuminance distribution of a plane can be achieved with a
single aspheric lens. In contrast to free-form lens designs (which
may arbitrarily impose a refractive-total internal reflection (TIR)
design constraint), the present approach may begin with an optical
element consisting of a spherical lens profile, which is modified
until the resulting profile is described by the lowest-order
mathematical equation that will generate the desired luminous
intensity distribution.
[0057] Using the lowest-order mathematical equation (such as for
example a linear, quadratic, or cubic equation) is advantageous.
Profiles described by higher-order equations (such as, for example,
quintic equations) have higher degrees of curvature that tend to
produce caustics in the near-field luminous intensity distribution
and possibly visible striations on the plane illuminance
distribution. The higher orders (e.g.,
z=ax.sup.5+bx.sup.4+cx.sup.3+dx.sup.2+ex+f) also introduce more
design parameters that must be optimized, thereby increasing the
size of the search space and decreasing the probability of
converging to a local rather than global optimum.
[0058] A particular advantage of the present approach to optical
elements used in architectural applications is that it represents a
non-imaging application. Unlike the photographic lens design issues
discussed in Nasse, most of the enumerated design parameters (which
relate to precise image reproduction) become immaterial, thereby
simplifying the design process and minimizing the search space for
a globally optimal lens profile.
[0059] A representative approach to determining the lowest-order
mathematical equation that will generate the desired luminous
intensity distribution is an evolutionary algorithm that comprises
the following steps: [0060] 1. Specify a target luminous intensity
distribution; [0061] 2. Specify one or more candidate equations
with different terms and constants; [0062] 3. Calculate the
luminous intensity distribution for each candidate equation; [0063]
4. Compare each candidate intensity distribution with the target
intensity distribution; [0064] 5. Modify the constants of the best
candidates; and [0065] 6. Repeat steps 3 to 5 until the best
candidate meets the target design criteria. wherein the luminous
intensity distribution comparisons in Step 4 may be based, for
example, on the Hausdorff distance metric as disclosed in Ashdown,
I., "Comparing Photometric Distributions," Journal of the
Illuminating Engineering Society 29(1):25-33. (1999) (the entire
disclosure of which is hereby incorporated by reference).
[0066] For Step 3, one calculation method for determining the
luminous intensity distribution is to model the light source
(typically as an areal or volumetric emitter rather than as point
source) and lens using a non-sequential ray-tracing program.
Suitable commercial software products include LightTools from
Optical Research Associates (Pasadena, Calif.), FRED from Photon
Engineering (Tucson, Ariz.), ZEMAX from Radiant ZEMAX LLC
(Bellevue, Wash.), ASAP from Breault Research (Tucson, Ariz.), and
TracePro from Lambda Research (Littleton, Mass.).
[0067] One approach to implementing this methodology is based on a
particle-swarm optimization algorithm, as described, for example,
in Xiangdong, Z. L, and X. Duan, "Comparative Research on Particle
Swarm Optimization and Genetic Algorithm," Computer and Information
Science 3(1):120-127 (2010) and Sancho-Pradel, D. L., "Particle
Swarm Optimization for Game Programming," in Game Programming 8,
pp. 152-167, the entire disclosures of which are hereby
incorporated by reference. In accordance with this approach, the
algorithm models the behavior of a flock of birds in pursuit of
feeding opportunities. Adapted to the present problem, the flock of
birds (or "particles") is represented by the set of candidate
equations with different terms and constants, while the feeding
opportunity (i.e., the solution) is represented by the target
luminous intensity distribution.
[0068] Like genetic algorithms, particle-swarm optimization
algorithms are instances of evolutionary algorithms, and so can be
used to implement the six steps outlined above. In Step 2, however,
the terms and constants of the equations represent the
multidimensional "equations of motion" of each candidate equation.
In canonical form, these equations can be expressed as:
v(t+.DELTA.t)=v.sub.inertia(t)+v.sub.cognitive(t)+v.sub.social(t)
x(t+.DELTA.t)=x(t)+v(t+.DELTA.t)
where x(t) and v(t) are m-dimensional vectors that represent the
particle's position and velocity in the multidimensional space at
time t, with .DELTA.t=1 representing the iteration step time, and
the dimension m of the multidimensional space being the maximum
number of terms (i.e., order) of the equations under consideration.
(Of course, non-polynomial equations may also be considered.)
[0069] The three terms of the velocity update are based on
cognitive information (experience gained during the particle's
search, represented by the best solution x.sub.best in the
particle's history); social information (experience gained by the
swarm's search, represented by the best solution
X.sub.global.sub.--.sub.best in the swarm's history) and inertia
(inertial constraint .omega..epsilon.(0,1) based on the particle
current direction of movement and velocity) and:
v.sub.inertia(t)=.omega..times.v(t)
v.sub.cognitive(t)=c.times.r.sub.cognitive(x.sub.best-x(t))
v.sub.social(t)=c.times.r.sub.social(x.sub.global.sub.--.sub.best-x(t))
where c is a multiplication constant; r.sub.cognitive and
r.sub.social are random-valued vectors taken from a uniform random
distribution (i.e., r.sub.j.epsilon.(0,1).A-inverted.j=1, 2, . . .
, m), and is the component-wise vector-vector multiplication
operator. The choices of c and .omega. are typically dependent on
the problem domain, and may be straightforwardly determined by
those skilled in the art without undue experimentation; moreover,
one or both parameters may be varied during the iterative solution
process. Typically, however, a high value of inertia .omega.
encourages "exploration" of the entire problem domain, while a low
value results in "exploitation" of the local neighborhood. A
representative implementation of the algorithm suitable for use in
connection with the present invention is set forth below. While
this particular implementation was found to yield acceptable
results, it will be apparent to those skilled in the art that other
variants may yield similar results, differing, for example, in the
computational time needed to converge to a global solution.
Similarly, other evolutionary algorithms, particularly those known
to yield successful results with real-valued (as opposed to
discrete-valued) problems, may be employed.
[0070] To determine the lowest-order equation for a lens profile
capable of generating a luminous intensity distribution such as
that shown in FIG. 2 (for producing constant illuminance on a
plane), it has been found that a cubic equation (e.g.,
z=ax.sup.3+b) is generally sufficient as a candidate equation for
purposes of step 2, with parameter values that are optimized by the
algorithm. The cubic term a determines the shape of the lens, while
the constant term b determines the distance of the front lens
surface from the light source. Surprisingly, this relationship
applies even when an areal light source (such as a bare LED die) or
a volumetric light source (such as an LED die embedded in a
phosphor matrix) is used, at least for dimensions that do not
exceed approximately 10 to 20 percent in width of the diameter of
the lens and approximately 10 percent in height of the lens-source
distance b. The examples set forth below were designed by applying
an evolutionary algorithm to the equations based on arbitrary
initial values. In general, evolutionary algorithms will converge
to an optimal solution over a wide range of initial values. The
hyperbolic lens of Example 5 below was generated from the conic
design of Example 6, with its linear profile. Expressing the lens
curve as a hyperbolic equation with initial values that produced
the linear profile and then iteratively varying the parameters
resulted in the hyperbolic lens profile with its narrower luminous
intensity distribution. More generally, those skilled in the art of
mathematical analysis will understand that an arbitrary smooth
curve or surface can be approximated by a low-order mathematical
equation using a conventional "curve-fitting" algorithm. The
parameters of this equation can then be optimized by the
evolutionary algorithm.
[0071] Optical elements in accordance herewith may be manufactured
in conventional fashion. Individual optical elements can be
fabricated from any transparent material (glass, polymer, etc.) by
molding, grinding and polishing, casting, or other suitable
technique. Particularly in the case of arrays of optical elements,
which tend to be polymeric, molding is a suitable fabrication
method. The shape of an optical element is designed in accordance
with the techniques discussed above, and the complement of this
shape is replicated in the mold in the desired array pattern, e.g.,
by machining, laser etching, 3D printing, or other conventional
method. Alternatively, the optical elements may be embossed onto a
polymer sheet. Embossing may be accomplished by drawing the polymer
sheet through heated roller dies, one of which has a pattern of
recesses complementary to the desired element shape. In some
processes, the second roller die has projections that mate with the
recesses of the first roller die. The combination of pressure and
heat impresses the element pattern into the polymer sheet.
[0072] Following fabrication, the array is joined (e.g., adhesively
bonded) to an array of light-emitting elements such that each of
the elements is at least partially aligned with (i.e., centered
over) one of the optical elements. As explained below, some
misalignment may be tolerable or, depending on the desired output
profile, intentional.
EXAMPLES
[0073] Several exemplary embodiments of lenses are presented
herein. In general, they comprise a planar array 100 of
light-emitting elements as shown in FIG. 4. Each light-emitting
element 110 comprises a bare InGaN light-emitting diode die coated
with a phosphor layer measuring, for example, 1.0 mm wide by 1.0 mm
by 0.15 mm thick; the phosphor particles within the layer, which
are conventional, absorb a portion of the blue light emitted by the
LED die 110 and re-emit it at longer wavelengths to produce, in
combination with the blue light emission, white light. The
light-emitting elements are mounted in a rectangular array on a
substrate 120 such as, for example, multi-cellular polyethylene
terephthalate (MCPET). In an embodiment, the spacing between
adjacent light-emitting elements 110 is 7.0 mm and the substrate
120 measures 100 mm wide by 300 mm long.
[0074] A layer of transparent material 130 such as, for example,
polymethyl methacrylate (PMMA) or polydimethylsiloxane (PDMS), is
optically bonded to the substrate 120 using an optically
transparent adhesive 140, such as, for example, Norland Optical
Adhesive manufactured by Norland Products, Cranbury, N.J. In an
embodiment, the transparent material 130 has a thickness of 4.0 mm.
The transparent material has optical elements 150 molded or
embossed into its exposed face. Each optical element 150
corresponds to, and is substantially centered over, a single
light-emitting element 110.
1. Cubic Lens Profile
[0075] In a first exemplary embodiment, each optical element has a
rotationally symmetric profile, measured from the opposite face
(i.e., looking "up" from substrate 120), embossed into PMMA. The
aspherical profile is analytically described by the cubic equation
z=-0.02a.sup.3+b between a=0.0 and a=5.0, and where b=4.0. This is
illustrated in FIG. 5, in which the ordinate axis represents lens
thickness (height) and the abscissa corresponds to distance from
the lens center (at the origin). The vertical offset b, the height
z, and the width a are measured in millimeters. A
computer-generated rendering of the corresponding optical elements
is shown in FIG. 6.
[0076] The quadrilaterally symmetric luminous intensity
distribution generated by this example is shown in FIGS. 7A
(horizontal view) and 7B (nadir view). The quadrilateral
distribution is due to both the square light-emitting element 110
and the square optical element 150. The quadrilateral luminous
intensity distribution of FIGS. 7A and 7B generate a desirably
square illuminance distribution. Since the majority of office
spaces are rectangular, such a distribution delivers luminous flux
precisely where it is needed. This capability is not possible with
conventional linear fluorescent luminaires.
[0077] The vertical positioning tolerance with respect to the
phosphor emitter influences the luminous intensity distribution.
For example, FIG. 8 shows the luminous intensity for the same
example except with a vertical offset of b=3.7 mm. Similarly, FIG.
9 shows the luminous intensity for the same example except with a
vertical offset of b=4.3 mm. The cutoff angle changes somewhat, but
the desirable constant illuminance feature remains essentially
unchanged.
[0078] The horizontal positioning tolerance with respect to the
alignment of the center of the light-emitting element 110 and the
axis of rotation for the optical element also influences the
luminous intensity distribution. For example, FIG. 10 shows the
luminous intensity of the same example except with a horizontal
offset of 0.3 mm. This is desirable in that it allows the lenslet
array to be tilted about a horizontal axis while still producing a
substantially constant illuminance distribution on the workplane or
ceiling.
[0079] The luminous intensity distribution is minimally influenced
by the thickness of the phosphor emitter. FIG. 11A shows the
luminous intensity for the same example with a phosphor emitter
thickness 0.15 mm, while FIG. 11B shows the luminous intensity
distributions for the example with a phosphor emitter thickness
0.35 mm. As can be seen, the distributions are substantially
identical.
2. Cubic Fresnel Lens Profile 1
[0080] In a second example embodiment, the above rotationally
symmetric lens with a cubic profile can be approximated by a
Fresnel lens with 0.5 mm wide segments, as shown in FIG. 12. The
profile of each segment is described analytically by the cubic
equation z=-0.02a.sup.3+b+c.sub.seg between a=0.0 and a=5.0 mm,
b=4.0 mm and c.sub.seg is a vertical offset chosen to ensure that
the inner edge of each segment has height b and a maximum embossing
depth of 0.7 mm; as illustrated in FIG. 13, this maximum depth
occurs at the outer edge of the lens. More generally, the parameter
c.sub.seg is a vertical offset that ensures that the inner edge of
each Fresnel segment has height b; accordingly, for each segment i,
c.sub.seg=0.02a.sub.i0.sup.3, where a.sub.i0 is the horizontal
distance from the center to the inner edge of the segment.
[0081] The edges of the Fresnel lens segments result in some stray
light, as shown in the luminous intensity distribution shown in
FIG. 14A (horizontal view) and FIG. 14B (nadir view). The advantage
is that the 0.7 mm embossing depth of the PMMA sheet (compared to
the 2.5 mm depth used in the cubic lens design) improves its
manufacturability.
3. Cubic Fresnel Lens Profile 2
[0082] In a third exemplary embodiment, the above rotationally
symmetric lens with a cubic profile is approximated by a Fresnel
lens with variable width segments. The profile of each segment is
described analytically by the cubic equation
z=-0.02a.sup.3+b+c.sub.seg between a=0.0 and a=3.5 mm, and where
b=4.0 mm and c.sub.seg is chosen such that the inner edge of each
segment has height b and an approximately constant depth of 0.05 mm
(as shown in FIG. 15). Given that the lenses are spaced 7.0 mm on
center, the embossed pattern is circular with flat areas beyond a
radius of 3.5 mm; this is illustrated in FIG. 16. The luminous
intensity distribution for this lens profile is shown in FIG. 17.
An embossing mold for fabricating the illustrated lens is typically
diamond-machined, as the radius of the peaks and valleys of the
lens profile shown in FIG. 15 should not exceed approximately 0.002
mm. It is also possible to fabricate an embossing mold for the lens
profile shown in FIG. 15 using a 3D laser printer that writes the
mold pattern into a liquid photopolymer. Assuming a laser beam with
a full-width half-maximum (FWHM) beam width of 0.006 mm at the
point of focus, the resulting lens profile will be approximately as
shown in FIG. 18. The relatively large radius of the peaks and
valleys will tend to scatter the incident light, resulting in the
luminous intensity distribution shown in FIG. 19.
4. Cubic Linear Lens Profile
[0083] A fourth exemplary embodiment is a linear lens as
illustrated in FIG. 20. The lens has a profile described
analytically by the cubic equation z=0.03a.sup.3+b between a=-3.5
mm and a=0.0 mm, and z=-0.03a.sup.3+b between a=-3.5 mm and a=0.0
mm, with a maximum value of b=3.7; the resulting profile is
illustrated in FIG. 21. This lens produces the bilaterally
symmetric luminous intensity distribution shown in FIGS. 22A
(lateral view), 22B (longitudinal view), and 22C (nadir view).
5. Hyperbolic Lens Profile
[0084] In a fifth exemplary embodiment, a hyperbolic lens as
illustrated in FIG. 23 produces a highly focused spotlight
distribution that may be useful, for example, in theatrical and
entertainment lighting applications. The radially symmetric lens
profile is described analytically by the quadratic equation
z=b-2a.sup.2/(1+4a) between a=0.0 mm and a=5.0, where b=4.0; the
lens profile is shown in FIG. 24. This lens produces the radially
symmetric luminous intensity distribution shown in FIGS. 25A
(horizontal view) and 25B (nadir view). Offsetting the LED die
horizontally by 1.5 mm results in the radially symmetric luminous
intensity distribution shown in FIGS. 26A (horizontal view) and 26B
(nadir view).
6. Conic Lens Profile
[0085] In a sixth exemplary embodiment, a radially symmetric lens
with a linear profile (i.e., a conic lens) also produces a highly
focused spotlight distribution that may be useful for theatrical
and entertainment lighting applications. The radially symmetric
lens profile is described analytically by the linear equation
z=-0.4762a+b z=-0.4762*a+b between a=0.0 mm and a=5.0, where b=4.0,
and is depicted in FIG. 27. This lens produces the radially
symmetric luminous intensity distribution shown in FIG. 28A
(horizontal view) and FIG. 28B (nadir view). This distribution is
quite similar to the hyperbolic lens, which highlights the
sensitivity of the luminous intensity distribution to small changes
in the lens profile for such a focused optic.
7. Conic Fresnel Lens Profile
[0086] In a seventh exemplary embodiment, the above-described
rotationally symmetric lens with a linear profile can be
approximated by a Fresnel lens with 0.5 mm wide segments as
illustrated in FIG. 29. The radially symmetric lens profile is
described analytically by the linear equation
z=-0.4762a+b+c.sub.seg between a=0.0 mm and a=5.0, where b=4.0 mm
and c.sub.seg is chosen such that the inner edge of each segment
has height b; the resulting profile is illustrated in FIG. 30. This
lens produces the radially symmetric luminous intensity
distribution shown in FIGS. 31A (horizontal view) and 31B (nadir
view). Finally, the exposed surface of the optical element may be
patterned or roughened to further diffuse the emitted light and
obscure the direct view of the light-emitting element 110 through
the transparent substrate 130.
8. Cubic Lens Profile 2
[0087] In an eighth exemplary embodiment, each optical element has
a rotationally symmetric profile, measured from the opposite face,
embossed into PMMA. The aspherical profile is analytically
described by the cubic equations z=b-(a-2.5).sup.2.times.0.1
z=-0.02*a.sup.2+b between a=0.0 and a=2.5, and
z=b-(a-2.5).sup.2.times.0.2 z=-0.02*a.sup.2+b between a=2.5 and
a=5.0, where b=3.0; the resulting profile is shown in FIG. 32. The
vertical offset b, the height z, and the width a are measured in
millimeters. The resultant batwing distribution, which may be
employed for indirect ceiling illumination, is shown in FIG. 33A
(horizontal view) and FIG. 33B (nadir view).
9. Working Example 1
[0088] An optic was designed and manufactured according to the
first exemplary embodiment to produce a bat-wing distribution,
similar to that shown in FIG. 7A. The optic, a rectilinear array of
lenses, was formed from PMMA. The lens array size was about 287 mm
by about 98 mm by about 4 mm thick. The optic was attached to an
array of white-light-emitting LEDs using an index-matched epoxy.
FIG. 34A shows a simulation of the light-distribution pattern while
FIG. 34B shows the measured light-distribution pattern. As can be
seen, this optic produces a well-formed bat-wing distribution
pattern.
10. Working Example 2
[0089] An optic was designed and manufactured according to the
fifth exemplary embodiment to produce a substantially collimated
beam, similar to that shown in FIG. 25A. As the term is used
herein, a "substantially collimated" beam has a beam angle less
than 15.degree.. The optic, comprising a hexagonal array of lenses,
was formed from PMMA. The array diameter was about 107 mm and had a
thickness of about 3.5 mm. The optic was attached to an array of
white light emitting LEDs using UV-cured epoxy with an index of
1.586. FIG. 35 shows a simulation of the light-distribution pattern
and the measured light-distribution pattern. As can be seen, this
optic produces a highly collimated beam pattern. The same optic was
also intentionally misaligned with the optical axis of the white
light emitting LEDs in the array by about 1 mm. As shown in the
simulation of FIG. 36, this was predicted to produce an asymmetric
collimated beam pattern, which is observed in the measured beam
profile also shown in FIG. 36.
[0090] It should be noted that different LED phosphor package
shapes can be used to obtain bilaterally symmetric, quadrilaterally
symmetric, or asymmetric luminous intensity distributions. In
effect, phosphor package shape becomes another free variable for
the evolutionary algorithm to optimize.
TABLE-US-00001 Representative Algorithmic Implementation c = 2.0 //
Multiplication constant inertia_step = 0.005 // Inertia step
max_velocity = 0.05 // Maximum velocity min_inertia = 0.01 //
Minimum inertia step_count = 0 // Step counter DO IF step_count ==
0 Initialize candidate equations with random values w = 1.0
velocity_scale = 1000.0 ENDIF // Decrease velocity with each step
IF velocity_scale > 0.01 velocity_scale = velocity_scale -
step_count * 0.001 ENDIF FOR each candidate // Ignore best
candidate IF best candidate CONTINUE ENDIF Calculate uniform
distribution random vector r // Update new candidate velocity
v.sub.inertia = w * v.sub.candidate v.sub.social = c * r *
(x.sub.best - x.sub.candidate) v.sub.cognitive = c * r *
(x.sub.global.sub.--.sub.best - x.sub.candidate) v.sub.candidate =
velocity_scale * (v.sub.inertia + v.sub.social + v.sub.cognitive)
// Clamp candidate velocity to maximum FOR each dimension j IF
v.sub.candidate(j) > max_velocity v.sub.candidate(j) =
v.sub.candidate(j) * r(j) * max_velocity ENDIF ENDFOR // Update new
candidate position x.sub.candidate = x.sub.candidate +
v.sub.candidate ENDFOR FOR each candidate Calculate candidate
intensity distribution Compare candidate and target distributions
IF candidate better than best candidate Replace best candidate with
current candidate ENDIF ENDFOR // Decrease inertia IF w >
min_inertia w = w - inertia_step ENDIF step_count = step_count + 1
// Reset step count if maximum IF step_count == 1000 step_count = 0
ENDIF UNTIL best candidate matches target
[0091] While the description above has been mainly with reference
to visible light, this is not a limitation of the present invention
and in other embodiments the structures and methods described
herein may be applied to radiation outside of the visible spectrum,
for example in the infrared and ultraviolet radiation ranges.
[0092] The terms and expressions employed herein are used as terms
and expressions of description and not of limitation, and there is
no intention, in the use of such terms and expressions, of
excluding any equivalents of the features shown and described or
portions thereof. In addition, having described certain embodiments
of the invention, it will be apparent to those of ordinary skill in
the art that other embodiments incorporating the concepts disclosed
herein may be used without departing from the spirit and scope of
the invention. Accordingly, the described embodiments are to be
considered in all respects as only illustrative and not
restrictive.
* * * * *