LUMILEDS HPWA-MXOO

application brief AB20-5
replaces AN1149-5
Secondary Optics Design
Considerations for SuperFlux LEDs
Secondary optics are those optics which exist outside of the LED package, such as reflector
cavities, Fresnel lenses, and pillow lenses. Secondary optics are used to create the desired
appearance and beam pattern of the LED signal lamp.
The following section details the optical characteristics and optical model creation for Lumileds
SuperFlux LEDs. In addition, simple techniques to aid in the design of collimating reflectors,
collimating lenses, and pillow lenses are discussed.
Optical Characteristics of SuperFlux LEDs
LED Light Output
SuperFlux LED Radiation Patterns
Optical Modeling of SuperFlux LEDs
Point Source Optical Model
Detailed Optical Models
Secondary Optics
Pillow Lens Design
Design Case—Pillow Design for an LED CHMSL
Non-symmetric Pillow Lenses
Selecting the Size of the Pillow Optic
Recommended Pillow Lens Prescriptions
Other Diverging Optics
Reflector Design
Design Case—Reflector for a CHMSL Application
Reflector Cavities with Linear Profiles
Reflector Cavities with Square and Rectangular Exit Apertures
Other Reflector Design Techniques
Collimating Lens Design
Fresnel Lens Design
Design Case—Collimator Lens
Other Lens Design Options
Appendix 5A
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2
2
3
3
4
5
9
9
11
11
12
13
14
14
15
15
16
17
18
19
19
21
Optical Characteristics of
SuperFlux LEDs
LED Light Output
The light output of an LED is typically described
Solid angle is used to describe the amount of
by two photometric measurements, flux and
angular space subtended. Angular space is
intensity.
described in terms of area on a sphere. If a solid
angle ω, with its apex at the center of a sphere of
In simple terms, flux describes the rate at which
radius r, subtends an area A on the surface of
light energy is emitted from the LED. Total flux
that sphere, then ω = A/r2. The units for solid
from an LED is the sum of the flux radiated in all
angle are steradians (sr).
directions. If the LED is placed at the center of a
sphere, the total flux can be described as the
To put some of these concepts into perspective,
sum of the light incident over the entire inside
consider the simple example of a candle. A
surface of the sphere. The symbol for
candle has an intensity of approximately one
photometric for flux is Φv, and the unit of
candela. A candle placed in the center of a
measurement is the lumen (lm).
sphere radiates light in a fairly uniform manner
over the entire inner surface (ω = A/ r2 = 4π r2/ r2 =
In simple terms, intensity describes the flux
4π steradians). With this information, the flux from
density at a position in space. Intensity is the
a candle can be calculated as shown below:
flux per unit solid angle radiating from the LED
source. The symbol for photometric intensity is
Iv, and the unit of measurement is the candela
(cd).
SuperFlux LED Radiation Patterns
The radiation pattern of an LED describes
intensity, the radiation pattern becomes a
how the flux is distributed in space. This is
description of how the flux is distributed,
accomplished by defining the intensity of the
independent of the amount of flux produced.
LED as a function of angle from the optical axis.
Figure 5.1 shows a graph of the radiation pattern
for an HPWA-Mx00 LED.
Since the radiation pattern of most LEDs is
rotationally symmetric about the optical axis, it
An attribute of the radiation pattern that is of
can be described by a simple, two-axis graph of
common interest is known as the full-width, half-
intensity versus angle from the optical axis.
max, or 2θ1/2. This attribute describes the full
Intensity is normalized in order to describe the
angular width of the radiation pattern at the half
relative intensity at any angle. By normalizing
power, or half maximum intensity point. Looking
at Figure 5.1, the 2θ1/2 of the HPWA-Mx00 LED
Looking at Figure 5.2, the total included angle is
is approximately 90°.
approximately 95°. This implies that 90% of the
flux produced by an HPWA-Mx00 LED is emitted
Another attribute that is of common interest is
within a 95° cone centered on the optical axis.
the total included angle, or θv 0.9. This attribute
describes the cone angle within which 90% of
the total flux is radiated. Using Figure 5.1, the
percent of total flux versus included angle can
be calculated and graphed. (The derivation of
this graph is shown in Appendix 5A.) This graph
is included in the data sheet of SuperFlux LEDs
and is shown in Figure 5.2 for the HPWA-Mx00
Figure 5.1 Graph of the radiation pattern for an
HPWA-MxOO LED.
LED.
Optical Modeling of SuperFlux LEDs
An optical model of the LED is useful when
unacceptable when lenses or reflectors are
designing secondary optic elements such as
placed within 25 mm of the SuperFlux LED. A
reflector cavities and pillow lenses. The optical
more accurate technique involves using an
output of an LED can be approximated as a
optical model, which takes into account the
point source of light passing through an
extended source size of the LED.
aperture, but modeling errors may be
Point Source Optical Model
The internal structure of a SuperFlux LED is
shown in Figure 5.3. Light is produced in the
LED chip. A portion of this light goes directly
from the chip and is refracted by the epoxy
dome (refracted-only light). The remainder of
the light is reflected by the reflector cup and
then refracted by the epoxy dome (reflectedrefracted light).
Figure 5.2 Percent total flux vs. included angle for
an HPWA-MxOO LED.
The light that is refracted appears to come from
and is not a point source, the refracted-only light
a certain location within the LED, while the light
does not appear to come from a single location,
which is reflected and refracted appears to
but a range of locations or a focal smear. This is
come from a different location. In addition,
true for the reflected-refracted light as well.
because the LED chip itself has physical size
3
These focal smears overlap, creating an
points source; and the aperture size should be
elongated focal smear as shown in Figure 5.4.
equal to that of the epoxy dome at its base as
shown in Figure 5.5.
To create the best approximation using a point
source model, the center point of the focal
The optimal position of the point source for each
smears should be chosen as the location of the
SuperFlux LED is shown in Table 5.1.
Figure 5.3 Internal structure of a SuperFlux
LED.
Figure 5.4 Focal smear produced by reflected
and reflected-refracted light.
Detailed Optical Models
Detailed optical models of LEDs include all
surface, and the epoxy encapsulant must be
the internal optical structures within the LED
known. The process usually involves a tedious
including the chip, the reflector, and the dome.
trial and error technique of changing parameters
In order to accurately construct such a model,
in the model until empirical measurements are
detailed information about the chip, the reflector
matched.
Table 5.1
Position of Point Source for SuperFlux LEDs
SuperFlux LED
Position of Point Source
Part Number
“Z” (mm)
HPWA-MxOO
HPWA-Dx00
HPWT-Mx00
HPWT-DxOO
1.03
1.13
0.99
1.17
Due to the complexity of this process, Lumileds
can be used by many optical-modeling software
Lighting provides customers with rayset files for
packages. Contact your local Lumileds
SuperFlux LEDs. The raysets contain spacial
and angular information on a set of rays exiting
copies of the raysets.
the device at the dome surface. These raysets
4
Secondary Optics
This section contains practical design tools for
optics), and those that gather the incoming light
secondary optic design. More accurate and
into a collimated beam (collimating optics).
sophisticated techniques exist which are beyond
the scope of this application note. The design
The most common type of diverging optic used
methods discussed here are proven, but no
in automotive signal lamp applications is the
analytical technique can completely replace
pillow lens. The pillow lens spreads the incoming
empirical testing. Designs should always be
light into a more divergent beam pattern, and it
prototyped and tested as early in the design
breaks up the appearance of the source
process as possible.
resulting in a more uniform appearance. A cross
section of an LED signal lamp with a pillow lens
Secondary optics are used to modify the output
is shown in Figure 5.6.
beam of the LED such that the output beam of
the finished signal lamp will efficiently meet the
desired photometric specification. In addition,
secondary optics serve an aesthetic purpose by
determining the lit and unlit appearance of the
signal lamp. The primary optic is included in the
LED package, and the secondary optics are part
of the finished signal lamp. There are two
primary categories of secondary optics used,
those that spread the incoming light (diverging
Figure 5.5 Point source model of a SuperFlux
LED.
Figure 5.6 Cross section of an LED signal
lamp with a pillow lens.
Figure 5.7 Cross section of an LED
signal lamp with a reflector cavity and
pillow lens.
5
Figure 5.8 Cross section of an LED signal
lamp with Fresnel and pillow lenses.
As the spacing between the pillow and the
LED signal lamp with a Fresnel lens and a pillow
LEDs is increased, each LED will illuminate a
lens is shown in Figure 5.8.
larger area of the pillow lens. As the spot
illuminated by each LED grows and as the
In general, designs that use collimating
adjacent spots begin to overlap, the lens will
secondary optics are more efficient, and produce
appear more evenly illuminated. The trade-off
a more uniform lit appearance than designs
between lamp depth and lit uniformity is a
utilizing only pillow or other non-collimating
common consideration in LED design, where
optics. Fresnel lenses are a good choice for thin
both unique appearance and space-saving
lamp designs and produce a very uniform lit
packages are desired.
appearance. Reflectors are a good choice for
thicker lamp designs and are more efficient than
Collimating optics come in two main varieties:
Fresnel lenses at illuminating non-circular areas.
reflecting and refracting. Reflecting elements are
This is because reflectors gather all of the light,
typically metalized cavities with a straight or
which is emitted as a circular pattern for most
parabolic profile. A cross section of an LED
SuperFlux LEDs, and redirect it into the desired
signal lamp with a reflector cavity and a pillow
shape. In addition, reflectors can be used to
lens is shown in Figure 5.7.
create a unique, “jeweled” appearance in both
the on and off states.
Refracting, collimating optics typically used in
LED signal lamp applications include plano-
The dependency of reflector height on reflector
convex, dualconvex, and collapsed plano-
efficiency will be covered later in this section.
convex (Fresnel) lenses. A cross section of an
Figure 5.9 Half-angle subtended by an individual
pillow (A) for convex (upper) and concave (lower)
pillow lenses.
6
Figure 5.10 Half-angle divergence of the
input beam (B).
Figure 5.11 Ideal radiation pattern
produced by a pillow optic where
A(n-1) > B.
Figure 5.12 Ideal radiation pattern
produced by a pillow optic where
A(n-1) < B.
Figure 5.13 Ideal input beam with halfangle divergence B.
7
Figure 5.14 Common form of the input
beam with half-angle divergence B.
Figure 5.15 Ideal vs. actual radiation
patterns from a pillow lens.
Table 5.2
CHMSL INTENSITY SPECIFICATION
Vertical Test Points
(degrees)
10 U
5U
H
5D
Horizontal Test Points
(degrees)
Minimum Luminous Intensity
(cd)
8
16
8
16
25
25
25
16
16
25
25
25
16
16
25
25
25
16
10 L
8
5L
V
5R
10 R
Pillow Lens Design
Consider a pillow lens where the half-angle
The ideal radiation patterns shown in Figures
subtended by and individual pillow is A as
5.11 and 5.12 assume that the input beam has
shown in Figure 5.9, and the input beam has
a box-like radiation pattern as shown in Figure
a half-angle divergence B as shown in Figure
5.13.
5.10.
However, in actual cases the input beam will
The ideal radiation pattern generated would be
have the characteristics of the Cosine form of
as shown in Figure 5.11, where n is the index of
the Lambertian as shown in Figure 5.14.
refraction of the pillow lens material. It should be
noted that Figure 5.11 is applicable when B is
The differences between the ideal, box-like input
smaller than A(n-1). This assumption is true for
beam, and the more common Lambertian input
most LED applications using a collimating
beam result in changes to the final radiation
secondary optic.
pattern as shown in Figure 5.15. The magnitude
of this deviation in the radiation pattern can be
In cases where B is larger than A(n-1), which is
estimated by evaluating the magnitude of the
often the case when the LED is used without a
input beam’s deviation from the ideal. This
collimating optic, the ideal radiation pattern
deviation from the ideal should be considered
would be as shown in Figure 5.12.
in the design of the pillow lens.
Design Case—Pillow Design for an LED CHMSL
Consider the case where a collimating secondary optic is
used producing a beam divergence of B = 5° (B < A(n-1))
and similar to that shown in Figure 5.14. The pillow lens
material is Polycarbonate which has an index of refraction of
1.59 (n = 1.59). The ideal CHMSL radiation pattern is shown
in Figure 5.17 such that all the extreme points of the
specification are satisfied. Figure 5.17 shows the predicted
Using a Center High Mounted Stop Lamp (CHMSL) as an
example, we can see how the design techniques discussed
previously can be used to determine an optimum value of A.
The minimum intensity values for a CHMSL are shown in
Table 5.2.
As a conservative estimate, we can treat this pattern as
symmetric about the most extreme points. The extreme
points are those with the highest specified intensity values
at the largest angular displacements from the center of the
pattern. These points are shown in italics in Table 5.2. The
angular displacement of a point from the center is found by
taking the square root of the sum of the squares of the
angular displacements in the vertical and horizontal
directions. A point at 10R and 5U would have an angular
displacement from the center of:
From Figure 5.17, we can see that A(n-1)-B = 8°?and
A(n-1)+B = 18°; therefore, A = 22°. The value of A selected
will determine how much spread the pillow optic adds to the
input beam.
These points are charted on an intensity versus angle plot in
Figure 5.16.
9
Figure 5.16 Extreme points on the CHMSL
specification.
Figure 5.17 Ideal and actual
radiation patterns satisfying the
extreme points of the CHMSL
specifications.
Figure 5.18 Toroidal pillow
geometry.
10
Figure 5.19 Radiation pattern
produced by a toroidal pillow
(determine AV < Ah)
Non-symmetric Pillow Lenses
performance, provided the individual pillows are
In our previous example, the CHMSL radiation
small relative to the area illuminated by the light
pattern was treated as if it were symmetric
source. For incandescent designs, this is not an
about its center. In this case, the radii of the
issue and aesthetic considerations dictate the
pillow were the same along the horizontal and
pillow size. However, for LED designs, the light
vertical axes, resulting in a spherical pillow.
source is an array of individual LEDs. The pillow
lens pitch must be small relative to the area
In some signal lamps, the desired output beam
illuminated by a single LED or the pillow will not
is much wider along the horizontal axis than
behave as designed. For this reason, pillows
along the vertical axis. In these cases, the
designed for LED applications typically have a
optimum value of A will be larger for the
pitch of 1 to 5 mm; where those designed for
horizontal axis (Ah) than the vertical axis (Av).
incandescents can be as large as 10 mm.
The resulting geometry would be that of a
circular toroid, which can be visualized as a
Figure 5.20 shows a top view of a single pillow
rectangular piece cut from a doughnut as
with the pitches along both the horizontal, Ph ,
shown in Figure 5.18.
and vertical, Pv, axes. In addition, the crosssection geometry through the center of the
For non-symmetric pillow designs, an exercise
primary axes is shown.
similar to that performed for the CHMSL
example must be performed for both the
After Ah and Av have been calculated, and the
vertical and horizontal axes in order to
pitch has been chosen along one axis; the radii,
determine Av and Ah. The resulting isocandela
R, and pitch along the other axis can be
plot of the radiation pattern will appear as
determined by using the following equations:
shown in Figure 5.19.
(Note: Ph was chosen as a known value for this
example.)
Selecting the Size of the Pillow Optic
After determining A for both axes, the next step
is to determine the size, or pitch of the pillows.
The pitch of the pillow typically does not effect
11
Recommended Pillow Lens Prescriptions
case of the CHMSL, the desired output beam is
Table 5.3 lists recommended pillow
the same in the vertical and horizontal. In
prescriptions (Ah & Av) for different signal lamp
addition, for applications where no collimating
applications. The pitch can be changed to suit
secondary optic is used, the function of the
by varying R as described in the previous
pillow is to break up the appearance of the
section.
sources rather than spread the output beam.
In these cases, a weak, symmetric prescription
Examining Table 5.3, we observe that for
pillow was chosen.
CHMSL designs, a symmetric pillow
prescription was chosen (Ah = Av). However, for
The technique described above provides some
the rear combination lamp/front turn signal
practical tools for designing pillow lenses. If
(RCL/FTS) application utilizing a collimating
optical modeling software is available, along with
optic, a non-symmetric pillow prescription was
an accurate model of the LED source, these
used (Ah > Av). The desired output beam pattern
tools should be utilized to aid in the design
for the RCL/FTS applications is twice as wide in
process and provide more accurate models of
the horizontal than in the vertical; whereas in the
the final output beam.
Table 5.3
RECOMMENDED PILLOW LENS PRESCRIPTIONS
Application
CHMSL
LED Type
HPWA-MHOO
CHMSL
HPWT-DHOO
RCL/FTS
HPWT-MxOO
RCL/FTS
HPWT-MxOO
Collimating
Optic
Ah
(deg)
Av
(deg)
Rh
(mm)
Ph
(mm)
Rv
(mm)
Pv
(mm)
Fresnel Lens
(B = 5°)
None
(B = 20°)
Fresnel Lens
(B = 7°)
Reflector
Cavity
(B = 20°)
22
22
5.3
4
5.3
4
5
5
17
3
17
3
30
20
4.0
4
8.9
5.7
5
5
17
3
17
3
Figure 5.20 Geometry of a single pillow.
12
Figure 5.21 Cross-section geometry of a
desired reflector cavity.
Other Diverging Optics
Pillow lenses are the most popular diverging
example, diffuse lenses produce a uniform lit
optic used in automotive signal lamps, however,
appearance and a cloudy unlit appearance. Pillow
other types exist which produce similar effects
lenses can be diffused by bead-blasting the pillow
but have different appearances. Alternate types
lens surface on the mold tool resulting in a less
of diverging optics include: diffuse lenses,
efficient optic, but one that is more uniform in
faceted lenses, rod lenses, and many others
appearance when lit.
including combinations of the above. For
Figure 5.22 Geometry of a parabola.
Figure 5.23 LED position relative to the
parabola.
Figure 5.24 Design of parabolic reflector
with f = 0.66 mm.
13
Reflector Design
Reflector cavities serve two main purposes: to
the reflector. Once the parabola has been
redirect the light from the LED into a useful
designed, a cavity with a profile comprised of
beam pattern, and to provide a unique
multiple linear sections that closely approximates
appearance for the finished lamp. Often the look
the form of the parabola may be used depending
sought after is not achievable by the most
on the look desired.
optically efficient design. As a result, there is a
trade-off required between optical efficiency
In order to accommodate the SuperFlux LED
and lit appearance to arrive at an acceptable
dome, the bottom aperture of the reflector must
design.
be greater than three-millimeters in diameter.
Considering the tolerances of the molded
As discussed in the previous section Point
reflector, the LED, the LED alignment to the PCB,
Source Optical Model, a parabola is designed
and the alignment of the reflector to the PCB, the
to collimate the light from the point source. For
bottom reflector aperture should be a minimum of
the design technique discussed here, the LED is
3.5 mm in diameter. The focal length of the
treated as a point source. This treatment is very
reflector must be greater than 0.5 mm to produce
accurate for larger parabolas where the size of
a bottom aperture of greater than 3.5 mm.
the dome is small relative to the exit aperture of
Design Case—Reflector for a CHMSL Application
Consider the case where a reflector cavity will be used to
collimate the light from an HPWT-MH00 source, and a
pillow optic cover lens will be used to form the final radiation
pattern. Vacuum-metalized ABS plastic will be used as the
reflector material. The reflector cavity can be a maximum of
20 mm in height and should have a minimum opening for
the LED dome of diameter 3.75mm to accommodate piecepart misalignment and tolerances. The LED spacing is 15
mm, and each cell must illuminate a 15 mm x 15 mm patch
on the pillow lens. Figure 5.21 shows a cross-section of the
lamp described above. The geometry of a parabola, in polar
coordinates, is described by the following equation:
Table 5.4 describes the profiles of three different parabolas
(f = 0.9 mm, 0.7 mm, 0.66 mm).
An efficient, practical collimator design for a CHMSL
application should collimate all the light beyond 20°?from on
axis (φ ≤ 20°). More efficient reflectors can be designed which
collimate more of the light, but they are typically too deep to be
of practical value.
The ideal reflector for this application will have the following
characteristics:
Height constraint: 0.99 ≤ z ≤ 20 mm
Figure 5.22 shows how the terms in this equation are
applied.
From Table 5.1, we find that the optimum point source
location for the HPWT-MH00 LED is at Z = 0.99 mm.
Placing the point source of the LED at the focus of the
parabola will result in an LED position as shown in Figure
5.23.
Fit of LED dome into bottom aperture:x (z = 0.99 mm) ≥?1.875
mm
15 mm pitch: x (Φ = 20°) ≅?7.5 mm
Looking at Table 5.4, we find that the parabola with f = 0.66
mm most closely meets these requirements. Figure 5.24 gives
the geometry of the parabolic reflector chosen.
Since the base of the LED dome is above the location of the
parabola’s focus, this implies that 2f < 1/2 base aperture =
3.75 mm/2 = 1.875 mm (f < 0.94 mm). This information will
give us a starting point to begin searching for the optimum
parabola.
14
Figure 5.25 shows the profiles of several
practical reflector geometries (f = 0.5 to 1.0
Reflector Cavities with Square
mm). It should be noted that in order to
and Rectangular Exit Apertures
produce a reflector with a cutoff angle less than
The previous sections dealt with reflector cavities
20°, the height must increase radically. For this
that are rotationally symmetric about the optical
reason, reflectors with a high degree of
axis, which result in round entrance and exit
collimation (<20°) are often impractical.
apertures. In some designs, it may be desirable to
Therefore, Fresnel lenses are the preferred
have a square or rectangular exit aperture in order
method to produce highly collimated beams. In
to more evenly illuminate a square or rectangular
addition, it can be seen that reflectors with
section of the cover lens. In this type of design,
smaller focal lengths can produce a greater
each axis of the reflector cavity must be analyzed
degree of collimation in a shorter height,
separately, using the techniques described in the
however, the exit aperture also becomes
previous section.
smaller.
It should be noted that these reflector cavities will
Reflector Cavities with Linear Profiles
produce beam patterns that are similar in shape
After designing the appropriate parabolic
to their exit aperture. Figure 5.27 compares the
reflector, this form can be closely approximated
beam patterns of the rotationally-symmetric
by a few linear sections. Reflectors with linear
parabolic reflector designed in the previous
profiles require simpler mold tools and are
example Design Case—Reflector for a CHMSL
easier to measure and verify the accuracy of the
Application to that of a reflector cavity with a
form. Usually two linear sections are sufficient
square exit aperture having the same wall profile.
depending on the efficiency needed and the
In this case, each side of the square exit aperture
appearance that is sought. Figure 5.26 shows
is equal in length to the diameter of the circular
an approximation of the parabolic reflector from
exit aperture of the parabolic design.
the previous section, designed by a best fit of
two linear sections.
_
Figure 5.25 Comparison of Practical
Parabolic Reflector Profiles.
15
Other Reflector Design Techniques
rotationally symmetric reflectors by mapping the
Many other methods exist to design reflectors
flux contained within the source beam into the
for LED sources.
desired output beam. This method breaks the
input beam into angular sections, each containing
Nonimaging techniques focus on extracting light
a known percentage of the total flux. It is then
from the LED source and redirecting it such that
determined at what angle each of these flux
the exit beam has the desired divergence. The
packets should be reflected to produce the
most common form of a Nonimaging reflector
desired output beam. The profile of the final
used for LED applications is a truncated,
reflector will consist of a series of straight
compound parabolic collector (CPC). Several
sections. As the number of flux packets
publications explaining the principles of
considered is increased, the number of steps in
Nonimaging optics exist. One such text is High
the reflector increases, until a smooth curve is
Collection Nonimaging Optics by Welford &
approximated.
Winston, 1989.
Detailed information on the reflector design
Other reflector design techniques have been
principles developed by William Elmer can be
developed by William B. Elmer. One concept of
found in The Optical Design of Reflectors by
particular interest is a method for designing
William Elmer, 1989.
Figure 5.27 Isocandela plots of a circular vs.
square reflector design.
Figure 5.26 Linear profile approximation of a
parabolic reflector (f = 0.66 mm).
16
Table 5.4
PROFILE GEOMETRY OF PARABOLAS (f = 0.9 mm, 0.7 mm, 0.66mm)
f
(mm)
0.9
0.70
0.66
Φ
(deg.)
Φ
r
(mm)
x
(mm)
(mm)
20
22
25
30
35
40
45
50
55
60
65
70
20
22
25
30
35
40
45
50
55
60
65
70
20
22
25
30
35
40
45
50
55
60
65
70
0.35
0.38
0.44
0.52
0.61
0.70
0.79
0.87
0.96
1.05
1.13
1.22
0.35
0.38
0.44
0.52
0.61
0.70
0.79
0.87
0.96
1.05
1.13
1.22
0.35
0.38
0.44
0.52
0.61
0.70
0.79
0.87
0.96
1.05
1.13
1.22
29.85
24.72
19.21
13.44
9.95
7.69
6.15
5.04
4.22
3.60
3.12
2.74
23.21
19.23
14.94
10.45
7.74
5.98
4.78
3.92
3.28
2.80
2.42
2.13
21.89
18.13
14.09
9.85
7.30
5.64
4.51
3.70
3.10
2.64
2.29
2.01
10.21
9.26
8.12
6.72
5.71
4.95
4.35
3.86
3.46
3.12
2.83
2.57
7.94
7.20
6.31
5.22
4.44
3.85
3.38
3.00
2.69
2.42
2.20
2.00
7.49
6.79
5.95
4.93
4.19
3.63
3.19
2.83
2.54
2.29
2.07
1.89
28.05
22.92
17.41
11.64
8.15
5.89
4.35
3.24
2.42
1.80
1.32
0.94
21.81
17.83
13.54
9.05
6.34
4.58
3.38
2.52
1.88
1.40
1.02
0.73
20.57
16.81
12.77
8.53
5.98
4.32
3.19
2.38
1.78
1.32
0.97
0.69
z
Collimating Lens Design
In this section we will deal with spherical lenses
Where:
and geometrical optics design techniques,
f = focal length of the lens
treating the LED as a point source of light. More
n = index of refraction of the lens material
sophisticated and accurate methods exist, but
R1= radius of lens surface nearest the LED
are beyond the scope of this application note.
R2= radius of other lens surface
T = thickness of the lens
An LED signal lamp with a dual-convex,
collimator lens is shown in Figure 5.28. The
If T is less than one sixth of the diameter of the
“lensmaker’s” formula for this arrangement
lens, then this equation simplifies to:
is shown below:
17
For thin lenses, it is a good approximation to
A cross-section through the center of a plano-
measure f from the center of the lens.
convex lens, and its Fresnel counterpart are
shown in Figure 5.32.
For thin, plano-convex lenses (R1 = ∞), the
equation further simplifies to:
The thickness of the Fresnel lens is reduced as
the number of steps is increased. Typically Fresnel
lenses are designed with the minimum number of
The above equations assume all rays arrive at
steps needed to achieve the desired thickness,
shallow angles with respect to the optical axis
because additional light losses may occur at the
(paraxial assumption). However, for SuperFlux
internal faces and joining vertices. However, for
LED applications, where much of the flux is
plastic lenses, a thin design is desirable where
contained at angles far from the optical axis,
excessive lens thickness will result in sink
this is not the case. As a result, rays which are
distortions. Therefore, the performance and
not close to the optical axis will be bent at too
moldability of a lens are traded-off when choosing
great an angle, a condition known as spherical
the optimal number of steps.
aberration. A correction factor, C, can be added
to the above equations to compensate for this
effect as shown below:
For most LED collimator designs, a correction
factor of C ≅ 1.35 will produce the best results.
The value of f chosen can be checked by
tracing a ray from the source to the outer edge
of the collimator lens (edge ray). If the edge ray
is under collimated, the value of C used is too
Figure 5.28 Cross-section of an LED signal
lamp using a dual-convex, collimator lens.
large. If the edge ray is over collimated, the
value of C used is too small. Figure 5.29
graphically depicts the edge ray method for
checking f.
Fresnel Lens Design
A Fresnel lens can be visualized as a thick
convex lens which has been collapsed about a
series of circular, stepped setbacks. This type
of lens takes on the properties of a much
thicker lens and eliminates the difficulties
involved with the manufacture of thick lenses.
Figure 5.29 Edge ray method for checking f.
18
Design Case—Collimator Lens
Consider the case where a lens will be used to collimate the
light from an HPWT-DH00 source, and a pillow optic cover
lens will be used to form the final radiation pattern. Clear
PMMA (n = 1.49) will be used as the lens material. The LED
spacing is 20 mm and the spacing from the top of the PCB
to the top surface of the lens must be less than 25 mm.
The total included angle of the HPWT-DH00 is 70°,
therefore, to capture 90% of the light from the LED, the lens
must span 35°?from the optical axis, and fill a 20 mm X 20
mm area. The combination of included angle, lamp depth,
and LED spacing define the necessary items to determine f.
Figure 5.30 shows a cross-section of the lamp described
above.
Examining the geometry shown in Figure 5.30, the desired
focal length, f, is approximately 15.3mm. A lens of this
power will be a dual-convex, and R1 and R2 can now be
calculated using the following equation:
To optimize collection efficiency, R1 must be greater than R2.
By placing the flatter surface closer to the LED, the ray
bending is more equally shared between the two lens surfaces.
However, if R2 becomes too small, the lens will be too thick
and difficult to manufacture. A good compromise between
these two competing factors is R1 = 24 mm, and R2 = 18 mm.
Figure 5.31 shows a cross-section of an LED signal lamp with
this dual-convex lens design.
Consider a case with a plano-convex lens (R =
efficient than spherical forms. However, the
19mm) where an aperture diameter of 25 mm
design of these types of lenses is more complex
is desired for use as a collimating lens. This lens
and generally requires optical modeling software
will be too thick to properly injection mold
and accurate optical models of the LED.
(greater than 6 mm), so a Fresnel design will be
used with a maximum height of 4 mm. The
Another class of lens exists which couple the
resulting design will have three steps, as shown
principles of refraction and total internal reflection
in Figure 5.32.
(TIR). These lenses are commonly referred to as
reflective/refractive, or catadioptric lenses. Lenses
Convex-Fresnel lenses can be designed in
designed by Fresnel over 100 years ago for light
which a large radius (low curvature) lens is used
houses contained such TIR faces for improved
on the LED side, and a Fresnel-type lens with a
efficiency. An example of a catadioptric lens is
smaller radius (more curvature) is used on the
shown in Figure 5.34.
other side as shown in Figure 5.33.
This type of lens is useful when refractive lens
Other Lens Design Options
designs cannot efficiently bend the light rays at
In this section we have discussed only spherical
the required angle. By combining reflection and
lens designs. Spherical lenses are easily
refraction into a single optical element, a very
designed, specified, and checked; but may not
powerful and efficient lens can be designed. TIR
be the most efficient collimator due to spherical
is most efficient when incident rays are nearly
aberrations. Other lens designs, such as
tangential, where as refraction is most efficient
hyperbolic-planar, sphero-elliptic, and free-form
when the rays are close to the normal.
lenses can be designed which may be more
19
Figure 5.30 Cross-section of the
desired LED lamp configuration.
Figure 5.31 Cross-section of
an LED signal lamp with a dual convex
lens (R1 = 24mm, R2 = 18mm).
Figure 5.32 Cross-section of a planoconvex lens and its Fresnel equivalent.
Figure 5.33 Convex-Fresnel lens used as an LED
collimator.
Figure 5.34 Cross-section of a catadioptric lens
used as an LED collimator.
20
Appendix 5A
Flux Integration of Rotationally Symetric Radiation Patterns
The cummulative flux as a function of angle
Substituting Iv(θ) into (6) we get:
from the optical axis (Figure 5.2) can be
Φv(θ)
calculated from the radiation pattern (Figure
5.1). This calculation is simple for rotationally
∫
= 2 π cosθ sinθ dθ
= π sin2 θ
(7)
symetric radiation patterns and is shown below:
Intensity is defined as the flux per unit solid
angle, or
This equation can be rearranged to solve
for flux.
Φv = Iv ω
Φ v=
(2)
∫ Iv d ω
(3)
Figure 5A.1 Graphic explanation of flux integration
technique.
Solid angle, ω, as a function of θ can be
determined with the aid of Figure 5A.1.
dω(θ) = 2 πτ sinθ dθ
(4)
Assigning a value of r=1, this equation becomes
dω(θ) = 2 π sinθ dθ
(4)
and substituting (5) into (3) we can solve for
Φv(θ).
Φv(θ) = 2 π
∫ Iv (θ)sinθ dθ
(6)
Figure 5A.2 Rotationally symmetric, lambertian
Consider the case where the LED has a
rotationally symetric, lambertian radiation
pattern as shown in the Figure 5A.2.
21
The plot for equation (7) is shown in
Figure 5A.3.
By normalizing the Y-axis to 100% at 90°, this
graph becomes that which is typically shown in
the LED data sheets (Figure 5A.4). It should be
noted that the data sheet refers to the X-axis as
“Total Included Angle” which is equal to 2θ (see
Figure 5A.1).
Figure 5A.4 Percent cummulative flux vs. total
included angle.
For rotationally symetric radiation patterns that
cannot be easily represented with functions,
Simpson’s rule can be applied to approximate
the integral. For example, the HPWT-MH00
radiation pattern cannot be easily described by
a function. In such a case, the radiation pattern
can be divided into a finite number of elements
each with an angular width, dθ, as shown in
Figure 5A.5.
The smaller the dθ chosen, the larger n will
become and the more accurate the
approximation of the integral becomes.
Applying Simpsons rule, we can approximate
(6) by the following summation
Figure 5A.5 Approximation of the HPWT-MH00
As before, (8) can be plotted as shown in Figure
5A.6.
Figure 5A.3 Graphic representation of
Equation (7).
Figure 5A.6 Graphic representation of
equation (8).
22
Company Information
Lumileds is a world-class supplier of Light Emitting Diodes (LEDs) producing
billions of LEDs annually. Lumileds is a fully integrated supplier, producing
core LED material in all three base colors (Red, Green, Blue)
and White. Lumileds has R&D development centers in San Jose,
California and Best, The Netherlands. Production capabilities in
San Jose, California and Malaysia.
Lumileds is pioneering the high-flux LED technology and bridging the gap
between solid state LED technology and the lighting world. Lumileds is
absolutely dedicated to bringing the best and brightest LED technology to
enable new applications and markets in the Lighting world.
LUMILEDS
www.luxeon.com
www.lumileds.com
For technical assistance or the
location of your nearest Lumileds
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2002 Lumileds Lighting. All rights reserved. Lumileds Lighting is a joint venture between Agilent Technologies and Philips
Lighting. Luxeon is a trademark of Lumileds Lighting, Inc. Product specifications are subject to change without notice.
Publication No. AB20-5 (Sept2002)
23
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San Jose, CA 95131