AN1149-5_技术文档

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.

Table of Contents

Optical Characteristics of SuperFlux LEDs

LED Light Output

2

SuperFlux LED Radiation Patterns

Optical Modeling of SuperFlux LEDs

Point Source Optical Model

2

3

Detailed Optical Models

4

Secondary Optics

5

Pillow Lens Design

9

Design Case—Pillow Design for an LED CHMSL

9

Non-symmetric Pillow Lenses

11

12

13

14

15

16

17

18

19

21

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

Optical Characteristics of

SuperFlux LEDs

LED Light Output

The light output of an LED is typically described

by two photometric measurements, flux and

intensity.

Solid angle is used to describe the amount of

angular space subtended. Angular space is

described in terms of area on a sphere. If a solid

angle w, with its apex at the center of a sphere of

radius r, subtends an area A on the surface of

In simple terms, flux describes the rate at which

light energy is emitted from the LED. Total flux

from an LED is the sum of the flux radiated in all

directions. If the LED is placed at the center of a

sphere, the total flux can be described as the

sum of the light incident over the entire inside

surface of the sphere. The symbol for

2

that sphere, then w = A/r . The units for solid

angle are steradians (sr).

To put some of these concepts into perspective,

consider the simple example of a candle. A

candle has an intensity of approximately one

candela. A candle placed in the center of a

sphere radiates light in a fairly uniform manner

photometric for flux is F v, and the unit of

measurement is the lumen (lm).

2

over the entire inner surface (w = A/ r = 4p r / r =

4p steradians). With this information, the flux from

a candle can be calculated as shown below:

In simple terms, intensity describes the flux

density at a position in space. Intensity is the

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

how the flux is distributed in space. This is

accomplished by defining the intensity of the

LED as a function of angle from the optical axis.

intensity, the radiation pattern becomes a

description of how the flux is distributed,

independent of the amount of flux produced.

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

can be described by a simple, two-axis graph of

intensity versus angle from the optical axis.

Intensity is normalized in order to describe the

relative intensity at any angle. By normalizing

An attribute of the radiation pattern that is of

common interest is known as the full-width, half-

max, or 2q¹/2. This attribute describes the full

angular width of the radiation pattern at the half

power, or half maximum intensity point. Looking

at Figure 5.1, the 2q¹/2 of the HPWA-Mx00 LED

is approximately 90°.

Looking at Figure 5.2, the total included angle is

approximately 95°. This implies that 90% of the

flux produced by an HPWA-Mx00 LED is emitted

within a 95° cone centered on the optical axis.

Another attribute that is of common interest is

the total included angle, or q_{v 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

LED.

Figure 5.1 Graph of the radiation pattern for an

HPWA-MxOO LED.

Optical Modeling of SuperFlux LEDs

An optical model of the LED is useful when

designing secondary optic elements such as

reflector cavities and pillow lenses. The optical

output of an LED can be approximated as a

point source of light passing through an

aperture, but modeling errors may be

unacceptable when lenses or reflectors are

placed within 25 mm of the SuperFlux LED. A

more accurate technique involves using an

optical model, which takes into account the

extended source size of the LED.

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 (reflected-

refracted light).

Figure 5.2 Percent total flux vs. included angle for

an HPWA-MxOO LED.

The light that is refracted appears to come from

a certain location within the LED, while the light

which is reflected and refracted appears to

come from a different location. In addition,

because the LED chip itself has physical size

and is not a point source, the refracted-only light

does not appear to come from a single location,

but a range of locations or a focal smear. This is

true for the reflected-refracted light as well.

3

These focal smears overlap, creating an

points source; and the aperture size should be

equal to that of the epoxy dome at its base as

shown in Figure 5.5.

elongated focal smear as shown in Figure 5.4.

To create the best approximation using a point

source model, the center point of the focal

smears should be chosen as the location of the

The optimal position of the point source for each

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

the internal optical structures within the LED

including the chip, the reflector, and the dome.

In order to accurately construct such a model,

detailed information about the chip, the reflector

surface, and the epoxy encapsulant must be

known. The process usually involves a tedious

trial and error technique of changing parameters

in the model until empirical measurements are

matched.

Table 5.1

Position of Point Source for SuperFlux LEDs

SuperFlux LED

Part Number

Position of Point Source

“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

Lighting provides customers with rayset files for

SuperFlux LEDs. The raysets contain spacial

and angular information on a set of rays exiting

the device at the dome surface. These raysets

can be used by many optical-modeling software

packages. Contact your local Lumileds

Applications Engineer for more information and

copies of the raysets.

4

Secondary Optics

This section contains practical design tools for

secondary optic design. More accurate and

sophisticated techniques exist which are beyond

the scope of this application note. The design

methods discussed here are proven, but no

analytical technique can completely replace

empirical testing. Designs should always be

prototyped and tested as early in the design

process as possible.

optics), and those that gather the incoming light

into a collimated beam (collimating optics).

The most common type of diverging optic used

in automotive signal lamp applications is the

pillow lens. The pillow lens spreads the incoming

light into a more divergent beam pattern, and it

breaks up the appearance of the source

resulting in a more uniform appearance. A cross

section of an LED signal lamp with a pillow lens

is shown in Figure 5.6.

Secondary optics are used to modify the output

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

LEDs is increased, each LED will illuminate a

larger area of the pillow lens. As the spot

illuminated by each LED grows and as the

adjacent spots begin to overlap, the lens will

appear more evenly illuminated. The trade-off

between lamp depth and lit uniformity is a

common consideration in LED design, where

both unique appearance and space-saving

packages are desired.

LED signal lamp with a Fresnel lens and a pillow

lens is shown in Figure 5.8.

In general, designs that use collimating

secondary optics are more efficient, and produce

a more uniform lit appearance than designs

utilizing only pillow or other non-collimating

optics. Fresnel lenses are a good choice for thin

lamp designs and produce a very uniform lit

appearance. Reflectors are a good choice for

thicker lamp designs and are more efficient than

Fresnel lenses at illuminating non-circular areas.

This is because reflectors gather all of the light,

which is emitted as a circular pattern for most

SuperFlux LEDs, and redirect it into the desired

shape. In addition, reflectors can be used to

create a unique, “jeweled” appearance in both

the on and off states.

Collimating optics come in two main varieties:

reflecting and refracting. Reflecting elements are

typically metalized cavities with a straight or

parabolic profile. A cross section of an LED

signal lamp with a reflector cavity and a pillow

lens is shown in Figure 5.7.

Refracting, collimating optics typically used in

LED signal lamp applications include plano-

convex, dualconvex, and collapsed plano-

convex (Fresnel) lenses. A cross section of an

The dependency of reflector height on reflector

efficiency will be covered later in this section.

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 half-

angle 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

Minimum Luminous Intensity

(degrees)

(cd)

16

25

10 U

5 U

H

5 D

8

16

25

16

Horizontal Test Points

(degrees)

10 L

5 L

V

5 R

10 R

8

Pillow Lens Design

Consider a pillow lens where the half-angle

subtended by and individual pillow is A as

shown in Figure 5.9, and the input beam has

a half-angle divergence B as shown in Figure

5.10.

The ideal radiation patterns shown in Figures

5.11 and 5.12 assume that the input beam has

a box-like radiation pattern as shown in Figure

5.13.

However, in actual cases the input beam will

have the characteristics of the Cosine form of

the Lambertian as shown in Figure 5.14.

The ideal radiation pattern generated would be

as shown in Figure 5.11, where n is the index of

refraction of the pillow lens material. It should be

noted that Figure 5.11 is applicable when B is

smaller than A(n-1). This assumption is true for

most LED applications using a collimating

secondary optic.

The differences between the ideal, box-like input

beam, and the more common Lambertian input

beam result in changes to the final radiation

pattern as shown in Figure 5.15. The magnitude

of this deviation in the radiation pattern can be

estimated by evaluating the magnitude of the

input beam’s deviation from the ideal. This

deviation from the ideal should be considered

in the design of the pillow lens.

In cases where B is larger than A(n-1), which is

often the case when the LED is used without a

collimating optic, the ideal radiation pattern

would be as shown in Figure 5.12.

Design Case—Pillow Design for an LED CHMSL

Consider the case where a collimating secondary optic is

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.

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

actual radiation pattern.

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 A_V< A_h)

Non-symmetric Pillow Lenses

performance, provided the individual pillows are

small relative to the area illuminated by the light

source. For incandescent designs, this is not an

issue and aesthetic considerations dictate the

pillow size. However, for LED designs, the light

source is an array of individual LEDs. The pillow

lens pitch must be small relative to the area

illuminated by a single LED or the pillow will not

behave as designed. For this reason, pillows

designed for LED applications typically have a

pitch of 1 to 5 mm; where those designed for

incandescents can be as large as 10 mm.

In our previous example, the CHMSL radiation

pattern was treated as if it were symmetric

about its center. In this case, the radii of the

pillow were the same along the horizontal and

vertical axes, resulting in a spherical pillow.

In some signal lamps, the desired output beam

is much wider along the horizontal axis than

along the vertical axis. In these cases, the

optimum value of A will be larger for the

horizontal axis (A_h) than the vertical axis (A_v).

The resulting geometry would be that of a

circular toroid, which can be visualized as a

rectangular piece cut from a doughnut as

shown in Figure 5.18.

Figure 5.20 shows a top view of a single pillow

with the pitches along both the horizontal, P_h,

and vertical, P_v, axes. In addition, the cross-

section geometry through the center of the

primary axes is shown.

For non-symmetric pillow designs, an exercise

similar to that performed for the CHMSL

example must be performed for both the

vertical and horizontal axes in order to

determine A_vand A_h. The resulting isocandela

plot of the radiation pattern will appear as

shown in Figure 5.19.

After A_hand A_vhave been calculated, and the

pitch has been chosen along one axis; the radii,

R, and pitch along the other axis can be

determined by using the following equations:

(Note: P_hwas 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

Table 5.3 lists recommended pillow

prescriptions (A_h& A_v) for different signal lamp

applications. The pitch can be changed to suit

by varying R as described in the previous

section.

case of the CHMSL, the desired output beam is

the same in the vertical and horizontal. In

addition, for applications where no collimating

secondary optic is used, the function of the

pillow is to break up the appearance of the

sources rather than spread the output beam.

In these cases, a weak, symmetric prescription

pillow was chosen.

Examining Table 5.3, we observe that for

CHMSL designs, a symmetric pillow

prescription was chosen (A_h= A_v). However, for

the rear combination lamp/front turn signal

(RCL/FTS) application utilizing a collimating

optic, a non-symmetric pillow prescription was

used (A_h> A_v). The desired output beam pattern

for the RCL/FTS applications is twice as wide in

the horizontal than in the vertical; whereas in the

The technique described above provides some

practical tools for designing pillow lenses. If

optical modeling software is available, along with

an accurate model of the LED source, these

tools should be utilized to aid in the design

process and provide more accurate models of

the final output beam.

Table 5.3

RECOMMENDED PILLOW LENS PRESCRIPTIONS

Collimating

Optic

A_h

(deg)

22

A_v

(deg)

22

R_h

(mm)

5.3

P_h

(mm)

4

R_v

(mm)

5.3

P_v

(mm)

4

Application

CHMSL

LED Type

HPWA-MHOO

Fresnel Lens

(B = 5°)

CHMSL

RCL/FTS

HPWT-DHOO

HPWT-MxOO

None

5

30

5

20

5

17

4.0

17

3

4

3

17

8.9

17

3

5.7

3

(B = 20°)

Fresnel Lens

(B = 7°)

Reflector

Cavity

(B = 20°)

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

optic used in automotive signal lamps, however,

other types exist which produce similar effects

but have different appearances. Alternate types

of diverging optics include: diffuse lenses,

faceted lenses, rod lenses, and many others

including combinations of the above. For

example, diffuse lenses produce a uniform lit

appearance and a cloudy unlit appearance. Pillow

lenses can be diffused by bead-blasting the pillow

lens surface on the mold tool resulting in a less

efficient optic, but one that is more uniform in

appearance when lit.

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

redirect the light from the LED into a useful

beam pattern, and to provide a unique

appearance for the finished lamp. Often the look

sought after is not achievable by the most

optically efficient design. As a result, there is a

trade-off required between optical efficiency

and lit appearance to arrive at an acceptable

design.

the reflector. Once the parabola has been

designed, a cavity with a profile comprised of

multiple linear sections that closely approximates

the form of the parabola may be used depending

on the look desired.

In order to accommodate the SuperFlux LED

dome, the bottom aperture of the reflector must

be greater than three-millimeters in diameter.

Considering the tolerances of the molded

As discussed in the previous section Point

Source Optical Model, a parabola is designed

to collimate the light from the point source. For

reflector, the LED, the LED alignment to the PCB,

and the alignment of the reflector to the PCB, the

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

accurate for larger parabolas where the size of

the dome is small relative to the exit aperture of

reflector must be greater than 0.5 mm to produce

a bottom aperture of greater than 3.5 mm.

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 piece-

part 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 (f £ 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

Fit of LED dome into bottom aperture:x (z = 0.99 mm) ³ ?1.875

mm

Figure 5.22 shows how the terms in this equation are

applied.

15 mm pitch: x (F = 20°) @?7.5 mm

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.

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

mm). It should be noted that in order to

produce a reflector with a cutoff angle less than

20°, the height must increase radically. For this

reason, reflectors with a high degree of

collimation (<20°) are often impractical.

Therefore, Fresnel lenses are the preferred

method to produce highly collimated beams. In

addition, it can be seen that reflectors with

smaller focal lengths can produce a greater

degree of collimation in a shorter height,

however, the exit aperture also becomes

smaller.

Reflector Cavities with Square

and Rectangular Exit Apertures

The previous sections dealt with reflector cavities

that are rotationally symmetric about the optical

axis, which result in round entrance and exit

apertures. In some designs, it may be desirable to

have a square or rectangular exit aperture in order

to more evenly illuminate a square or rectangular

section of the cover lens. In this type of design,

each axis of the reflector cavity must be analyzed

separately, using the techniques described in the

previous section.

It should be noted that these reflector cavities will

produce beam patterns that are similar in shape

to their exit aperture. Figure 5.27 compares the

beam patterns of the rotationally-symmetric

parabolic reflector designed in the previous

example Design Case—Reflector for a CHMSL

Application to that of a reflector cavity with a

square exit aperture having the same wall profile.

In this case, each side of the square exit aperture

is equal in length to the diameter of the circular

exit aperture of the parabolic design.

Reflector Cavities with Linear Profiles

After designing the appropriate parabolic

reflector, this form can be closely approximated

by a few linear sections. Reflectors with linear

profiles require simpler mold tools and are

easier to measure and verify the accuracy of the

form. Usually two linear sections are sufficient

depending on the efficiency needed and the

appearance that is sought. Figure 5.26 shows

an approximation of the parabolic reflector from

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

Many other methods exist to design reflectors

for LED sources.

rotationally symmetric reflectors by mapping the

flux contained within the source beam into the

desired output beam. This method breaks the

input beam into angular sections, each containing

a known percentage of the total flux. It is then

determined at what angle each of these flux

packets should be reflected to produce the

desired output beam. The profile of the final

reflector will consist of a series of straight

sections. As the number of flux packets

considered is increased, the number of steps in

the reflector increases, until a smooth curve is

approximated.

Nonimaging techniques focus on extracting light

from the LED source and redirecting it such that

the exit beam has the desired divergence. The

most common form of a Nonimaging reflector

used for LED applications is a truncated,

compound parabolic collector (CPC). Several

publications explaining the principles of

Nonimaging optics exist. One such text is High

Collection Nonimaging Optics by Welford &

Winston, 1989.

Detailed information on the reflector design

principles developed by William Elmer can be

found in The Optical Design of Reflectors by

William Elmer, 1989.

Other reflector design techniques have been

developed by William B. Elmer. One concept of

particular interest is a method for designing

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

r

x

z

F

(deg.)

F

(rad.)

(mm)

0.9

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

0.70

0.66

Collimating Lens Design

In this section we will deal with spherical lenses

and geometrical optics design techniques,

treating the LED as a point source of light. More

sophisticated and accurate methods exist, but

are beyond the scope of this application note.

Where:

f = focal length of the lens

n = index of refraction of the lens material

R₁= radius of lens surface nearest the LED

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

“lensmaker’s” formula for this arrangement

is shown below:

If T is less than one sixth of the diameter of the

lens, then this equation simplifies to:

17

For thin lenses, it is a good approximation to

A cross-section through the center of a plano-

convex lens, and its Fresnel counterpart are

shown in Figure 5.32.

measure f from the center of the lens.

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

steps needed to achieve the desired thickness,

because additional light losses may occur at the

internal faces and joining vertices. However, for

plastic lenses, a thin design is desirable where

excessive lens thickness will result in sink

distortions. Therefore, the performance and

moldability of a lens are traded-off when choosing

the optimal number of steps.

The above equations assume all rays arrive at

shallow angles with respect to the optical axis

(paraxial assumption). However, for SuperFlux

LED applications, where much of the flux is

contained at angles far from the optical axis,

this is not the case. As a result, rays which are

not close to the optical axis will be bent at too

great an angle, a condition known as spherical

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

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.

Figure 5.28 Cross-section of an LED signal

lamp using a dual-convex, collimator lens.

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.

To optimize collection efficiency, R₁must 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 R₂becomes 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.

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 R₁and R₂can now be

calculated using the following equation:

Consider a case with a plano-convex lens (R =

19mm) where an aperture diameter of 25 mm

is desired for use as a collimating lens. This lens

will be too thick to properly injection mold

(greater than 6 mm), so a Fresnel design will be

used with a maximum height of 4 mm. The

resulting design will have three steps, as shown

in Figure 5.32.

efficient than spherical forms. However, the

design of these types of lenses is more complex

and generally requires optical modeling software

and accurate optical models of the LED.

Another class of lens exists which couple the

principles of refraction and total internal reflection

(TIR). These lenses are commonly referred to as

reflective/refractive, or catadioptric lenses. Lenses

designed by Fresnel over 100 years ago for light

houses contained such TIR faces for improved

efficiency. An example of a catadioptric lens is

shown in Figure 5.34.

Convex-Fresnel lenses can be designed in

which a large radius (low curvature) lens is used

on the LED side, and a Fresnel-type lens with a

smaller radius (more curvature) is used on the

other side as shown in Figure 5.33.

This type of lens is useful when refractive lens

designs cannot efficiently bend the light rays at

the required angle. By combining reflection and

refraction into a single optical element, a very

powerful and efficient lens can be designed. TIR

is most efficient when incident rays are nearly

tangential, where as refraction is most efficient

when the rays are close to the normal.

Other Lens Design Options

In this section we have discussed only spherical

lens designs. Spherical lenses are easily

designed, specified, and checked; but may not

be the most efficient collimator due to spherical

aberrations. Other lens designs, such as

hyperbolic-planar, sphero-elliptic, and free-form

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 plano-

convex 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

Substituting Iv(q) into (6) we get:

F v(q) = 2 p cosq sinq dq

The cummulative flux as a function of angle

from the optical axis (Figure 5.2) can be

ò

(7)

= p sin²q

calculated from the radiation pattern (Figure

5.1). This calculation is simple for rotationally

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.

F v = Iv w

(2)

(3)

F v = ò Iv d w

Figure 5A.1 Graphic explanation of flux integration

technique.

Solid angle, w, as a function of q can be

determined with the aid of Figure 5A.1.

dw(q) = 2 pt sinq dq

Assigning a value of r=1, this equation becomes

dw(q) = 2 p sinq dq (4)

(4)

and substituting (5) into (3) we can solve for

F v(q).

F v(q) = 2 p òIv (q)sinq dq

(6)

Figure 5A.2 Rotationally symmetric, lambertian

radiation pattern.

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 2q (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, dq, as shown in

Figure 5A.5.

The smaller the dq 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

radiation pattern.

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


型号：	AN1149-5
厂家：	LUMILEDS LIGHTING COMPANY
描述：	Secondary Optics Design Considerations for SuperFlux LEDs 二次光学设计考虑食人鱼LED灯
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