SOURCE: Agilent Technologies
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A light guide is a device designed
to transport light from a light
source to a point at some distance
with minimal loss. Light is
transmitted through a light guide
by means of total internal
reflection. Light guides are usually
made of optical grade materials
such as acrylic resin,
polycarbonate, epoxies, and glass.
A light guide can be used to
transmit light from an LED lamp
on a pc board to a front panel for
use as status indication, can be
used to collect and direct light to
backlight an LCD display or
legend, and can be used as the
means to illuminate a grid pattern
on a see through window. This
Application Brief discusses the
basics of simple light guide design
for these and other possible uses.
Snell’s Law: When light rays are
incident to a boundary between
two mediums, i.e. plastic and air,
the light rays are refracted when
they cross the boundary as
illustrated in Figure 1. The angle at
which the light rays are incident to
the boundary is called the angle of
incidence, φi, and the angle at
which the light rays leave the
boundary is called the angle of
Figure 1. Refracted Light Ray.
refraction, φf,. Snell’s law states:
the index of refraction of the first
medium, ni, multiplied by the sine
of the angle of incidence at the
boundary, φi, is equal to the index
of refraction of the second
medium, nr, multiplied by the sine
of the angle of refraction at the
Specular reflection is defined
when the angle of incidence
equals the angle of reflection as
shown in Figure 2. Specular
reflected light rays are reflected
When light rays cross the
boundary from one medium to
another, there is a loss due to
reflection at the boundary as
shown in Figure 2. This is called
Fresnel loss and is calculated with
the following expression:
For plastic to air and glass to air
interface boundaries, the Fresnel
loss is 4%.
for plastic (glass) to air interfaces.
When light rays cross a boundary
into a more dense medium, the
angle φf is less than the angle φi.
Conversely, when light rays cross
a boundary into a less dense
medium, the angle φf is greater
than the angle φi. This is illustrated
in Figure 3 for light rays passing
through a parallel plastic (glass)
plate. The light rays are incident
to the plate top surface at an angle
φi, are refracted within the plate at
the angle φf, are incident to the
Figure 2. Specular Reflected Light Ray at Mirror Smooth Boundary.
Figure 3. Light Ray Passing Through Nondiffused Plastic (Glass) Parallel Plate.
Figure 4. Definition of Critical Angle for Total Internal Reflection.
plate bottom surface of the plate at
the angle φ’i, and then are refracted
in the air at the angle φ’f. The angle
of refraction within the plastic
plate φf is smaller than the angle of
refraction in air φ’f since the plastic
is a more dense medium than air.
The exit rays are parallel to the
incident rays because the internal
angle of refraction φf and the
internal angle of incidence φ’i are
equal, and because the external
angle of incidence φi and the
external angle of refraction φ’f are
When the angle of refraction is 90°
the incident light ray is refracted
along the boundary, as shown in
Figure 4. The sin φf (90°) = 1.0, and
Equation 1 for Snell’s law reduces
to: ni sin φi = nf. This expression
can be rewritten to define the
critical incident angle for total
internal reflection, φc:
Critical Angle Definition:
Setting nf = 1.0 in Equation 3, the
index of refraction value for air,
the critical angle for a light guide
can be quickly determined when
the material index of refraction is
known. For most plastics and
glass, the index of refraction is
approximately 1.50. Thus, the
critical angle for total internal
reflection for most light guide
materials is approximately 42°.
Internal specular reflection within
a light guide at the guide surface to
air boundary is utilized to help
transmit light through the light
φc = 42° approximate value for
plastics and glass.
Light rays internal to a light guide
incident to guide surface to air
boundary are total internally
reflected when the angle of
incidence is 42° or greater. Having
the critical angle being slightly less
than 45° for most light guide
materials is very convenient
because it allows the use of 45°
reflecting prism surfaces in light
Ray tracing is a technique used to
predict the path of light rays into,
through, and out of a light guide.
The principles of Snell’s law,
Fresnel loss, and specular
reflection are applied at each guide
surface to air interface to
determine the direction of the light
ray. Ray tracing is used in this
Application Brief to illustrate the
performance of light guide designs.
There are three design issues to be
examined when designing a light
1) effective flux coupling to get the light
from an LED lamp into the light guide
with minimal loss,
2) transmitting the light through the
guide to the exit surface, and
3) allowing the light to escape through
the exit surface with minimal loss.
Flux from an LED lamp must be
effectively coupled to the entrance
end of a light guide to permit light
capture (light to enter the light
guide) with minimal loss before it
can be effectively transmitted and
utilized. Flux coupling and capture
are usually ineffective when the
LED lamp is external to the
envelope of the light guide surface
to air boundary, and conversely are
effective when the lamp is located
inside the light guide surface to air
With the LED lamp external to the
light guide, as shown in Figure 5,
effective flux coupling and light
capture occur only when the LED
lamp radiation pattern angle
matches the acceptance pattern
angle of the light guide. Thus,
effective flux coupling may be very
difficult to accomplish and most of
the flux from the LED lamp may be
lost. Less than 10% of the available
flux is typically captured by a light
guide with this configuration.
A lens may be used for flux
coupling to focus the flux from an
LED lamp onto the entrance end of
a light guide, as shown in Figure 6.
The focused flux should just fill
the entrance end of the light guide.
Light capture can be up to 80%
effective, but does require
availability of physical distance to
accommodate the focal length of
Figure 5. LED Lamp External to Light Guide.
Figure 6. Using a Lens to Focus LED Light Onto Light Guide.
the lens. The cost of the focusing
lens must be added to the cost of
the light pipe design.
The best design for most effective
flux coupling is to have the LED
lamp located inside the envelope of
the light guide surface to air
boundary. This concept is
illustrated in Figure 7a. In this
configuration, the LED lamp is
embedded into the light guide and
all light rays emanating from the
LED lamp are captured by the light
guide. The light capture
effectiveness is 92%, taking into
account the Fresnel losses across
the air gap. This design concept is
recommended for use with dome
LED package devices such as
T-1 3/4, T-1, and subminiature LED
Figure 7a. LED Lamp Located Inside a Light Guide for Best Flux Coupling.
Figure 7b. LED Lamp Epoxied into a Light Guide to Eliminate Fresnel Loss.
When the LED lamp package is
glued into the light guide with an
optical grade epoxy, as shown in
Figure 7b, the epoxy package of
the lamp optically disappears due
to the elimination of Fresnel
losses, and the flux capture is
essentially 100%. In most light
guide applications, using epoxy to
glue the LED lamp to the light
guide to eliminate air gap Fresnel
loss is neither practical nor
necessary. All of the suggested
light guide designs presented in
this Application Brief assume there
is an air gap between the LED
lamp and the light guide.
Physical Attributes of a Light Guide
The exterior surface finishes of a
light guide are important to assure
proper operation, as shown in
Figure 8. The sides parallel to the
direction of light travel should be
smooth, like a mirror, to affect
total internal reflection. They may
be painted with a white light
reflecting paint to reflect those
diagonal rays less than the critical
angle that may otherwise escape.
The entrance end should be
smooth, contoured to match the
LED lamp device for effective light
capture, allowing light rays to
enter the light guide with minimal
reflection and scatter. The exit end
should be diffused. A diffused exit
end has random critical angles
its surface providing a high
probability light rays can escape,
and also scatters the light rays
producing a wide radiation
Light guides may be made in any
desired shape, cylindrical (oval),
rectangular (square), conical
Figure 8. The Basic Attributes of a Light Guide, shown with a change in shape from Circular to Rectangular along its Length.
(increasing in size from entrance
end to exit end), or any special
shape (arrow, star shaped, quarter
moon, etc.). For rectangular and
special shapes, the corners should
have a radius greater than 0.5 mm
(0.020 in.), not sharp, to assure
illumination in the corners. The
shape of the light guide may
gradually change along its length,
i.e. from circular at the entrance
end to accommodate the lamp, to
square at the exit end, as shown in
For effective flux coupling and
light capture, the light entrance
end of a light guide should be
smooth and flat or concave
contoured to match the light
output radiation pattern and
package configuration of the
mating LED lamp device.
For SMT LED lamp devices that
have a light emitting area that is a
flat surface, the entrance end of the
light guide should be a smooth flat
surface. The entrance end of the
light guide should be placed over
and in close proximity to the light
emitting surface of the SMT LED
lamp for effective flux coupling
and light capture, as illustrated in…
Figure 9. The entrance end of the
light guide needs to be slightly
larger than the emitting surface of
the LED lamp to assure 92% flux
capture, taking into account the
Fresnel losses across the air gap.
Figure 9. Light Guide with a Smooth
Flat Entrance End positioned over an
SMT LED Lamp.
SMT Chip LED lamp packages are
cubic in shape, diffused, allowing
light to emit from the sides as well
as the top. Only about 40% of the
total available flux is emitted from
the top. The other 60% is emitted
from the side. Thus, only 40% of
the light from an SMT Chip LED
lamp would be captured by a light
guide with a flat surface entrance
end, the remaining flux is lost. A
light guide with a smooth concave
entrance end to fit over the SMT
Chip LED lamp is effective in
increasing flux capture, as shown
in Figure 10. The smooth concave
surface enhances flux coupling
and light capture by reducing the
possibility of a light ray
intersecting the light guide at the
critical angle and being reflected.
With the concave entrance end,
about 70% to 80% of the available
emitted flux from an SMT Chip
LED is captured by the light guide,
and the light loss is reduced to 20%
This concave contoured entrance
end technique may be used with
any light guide/LED lamp
Figure 10. A Light Guide with a Smooth Concave Entrance End increases Flux
Coupling and Light Capture from an SMT Chip LED Lamp.
combination to enhance flux
coupling and light capture. In
Figure 11, a “Yoke” lead SMT
subminiature lamp is used to
illuminate a light guide located at
the back side of a pc board. The
lamp is located in a through hole
and surface mounted on the
component side of the board. The
smooth concave surface entrance
end of the light guide captures
more of the radiated flux from the
Figure 11. The Concave End of a Light
Guide Enhances Flux Coupling and
Light Capture From an Inverted
Surface Mounted “Yoke” Lead SMT
Subminiature LED Lamp.
LED lamp than does a flat surface.
As a minimum insertion distance
for positive flux coupling and light
capture, standard T-1 3/4 untinted,
nondiffused LED lamps should be
inserted into the entrance end of a
light guide up to the LED reflector
cup, located within the lamp
package, as shown in Figure 12.
This assures 92% flux capture,
taking into account the Fresnel
loss across the air gap between the
lamp dome and light guide. For
best performance, insertion to the
base flange on the lamp package is
Figure 12. Insertion of T-1 3/4 and T-1 Untinted, Nondiffused LED Lamps into the Entrance End of a Light Guide for Effective Flux Coupling.
recommended. For T-1 3/4 LED
lamps, the lamp acceptance hole
should be 5.33 mm (0.210 in.) to
5.59 mm (0.220 in.) in diameter.
The end of the hole should be a
smooth spherical dome radius. The
hole should be at least 5.33
mm (0.210 in.) in depth for
minimum length insertion, and 8.31
mm (0.327 in.) minimum in depth
for full length insertion. For T-1
LED lamps, the lamp acceptance
hole diameter should be 3.30 mm
(0.130 in.) to 3.43 mm (0.135 in.) in
diameter. Only full length insertion
to the lamp base flange is
recommended for T-1 lamps to
achieve effective flux coupling and
capture, with a minimum hole
depth of 2.165 mm (0.085 in.).
LED light bars may also be used as
light sources for light guides.
These devices that have a light
emitting area that is a large flat
surface. Therefore, for effective
flux coupling and light capture the
entrance end of the light guide
should be a smooth flat surface,
placed over and in close proximity
to the light emitting surface of
the LED light bar, as illustrated in
Figure 13. The entrance end of the
light guide needs to be slightly
larger than the emitting surface of
the light bar to assure 92% flux
capture, taking into account the
Fresnel losses across the air gap.
A diffused exit end presents
random critical angles to internal
light rays, assuring the probability
Figure 13. Light Guide with a Smooth Flat Entrance End Positioned Over an LED Light Bar for Best Flux Coupling.
of light escaping from a light guide.
This may also be viewed as the
diffused exit end having random
indices of refraction. The exiting
light rays are disbursed at random
angles into a wide radiation pattern
of light, as shown in Figure 14.
Figure 14. Diffused Exit End Enhances the Probability of Light Escaping from a Light Guide.
Figure 15. Light Guide with a 90° Bend. Light Rays are Scattered by Diffused Exit End.
Light guides may be bent to go around corners. The bend radius should be equal to or greater than two thicknesses or twice the diameter of the light guide to minimize light loss. The light ray reflections follow the smooth contour of the radius bend without loss, as shown in Figure 15. Sharp right angle direction changes may be achieved by using a reflective prism design in the light guide at the 90° bend location, as shown in Figure 16.
Figure 16. Light Guide with Built in 45° Prism Reflector.
Wedge shaped light guides may be
used to achieve backlighting
effects. Two basic kinds are shown
in Figure 17, the planar surface
wedge which gives a uniform
distribution of light and the curved
surface wedge which gives a light
distribution somewhat logarithmic
in nature. The planar surface
wedge is typically used to
backlight transreflective LCD
Transreflective LCD displays may
be backlighted with LED lamps
using either a simple flat planar
light guide or a wedge light guide.
For small area LCD displays, 1 to 2
inches high by 2 to 4 inches wide, a
simple flat planar light guide may
be used, as shown in Figure 18.
The top surface of the light guide is
diffused to permit light to
escape. The edges and backside
are smooth. The back surface is
coated with white light reflecting
paint. Two surface mount pc board
assemblies are mounted to the
sides of the transparent plate for
even illumination. Optional
grooves are cut into the plate to
provide alignment of the pc board
assembly with the plate. The
number of SMT LED lamps,
spaced on 1/4 to 1/2 inch centers,
depends upon the size of the
transparent plate and the required
A planar wedge light guide may be
used with SMT LED lamps for
backlighting a medium size
transreflective LCD display, i.e. 2
to 3 inches high by 3 to 6 inches
wide. A diffusing film interlayer
between the LCD and the wedge
guide may be used to diffuse the
light, as shown in Figure 19. The
SMT LED lamps are spaced on 1/4
to 1/2 inch spacing to achieve even
Figure 17. Wedge Light Guides, Planar Surface and Curved Surface.
Figure 18. A Transreflective LCD Display Backlighted with SMT LED Lamps, Surface Mounted on Small PC Boards, Using a Simple Flat Planar Light Guide.
illumination. The SMT LED lamps are electrically connected in series on the pc board assembly.
Figure 19. A Planar Wedge Light Guide used with SMT LED Lamps for Backlighting a Medium Size Transreflective LCD Display.
A right angle planar wedge light guide may be used with SMT LED lamps to backlight a medium sized transreflective LCD display that is mounted parallel to a surface mount pc board assembly, as shown in Figure 20a. The SMT LED lamps are spaced on 1/4 to 1/2 inch spacing to achieve even illumination. The SMT LED lamps are electrically connected in series on the pc board assembly. The ray tracing is shown in Figure 20b.
Figure 20a. A Right Angle Planar Wedge Light Guide used with SMT LED Lamps for Backlighting a Medium Size Transreflective LCD Display.
Figure 20b. Ray Tracing Pattern for A Right Angle Planar Wedge Light Guide used for Backlighting a Medium Size Transreflective LCD Display.
Untinted, nondiffused T-1 3/4 or T-1
LED lamps can also be used with a
right angle planar wedge light
guide as shown in Figure 21. The
spacing for these lamps is between
adjacent placement and 3/4 inches
centers, depending upon the
A dual right angle planar wedge
light guide may be used with SMT
LED lamps to backlight a mediumlarge
size transreflective LCD
display, 4 to 6 inches high by 6 to 9
inches wide, that is mounted
parallel to a surface mount pc
board assembly, as shown in
Figure 22. The SMT LED lamps are
spaced on 1/4 to 1/2 inch centers for
both light pipe wedges to achieve
even illumination. This technique
also provides sufficient
illumination for bright ambient
lighting conditions. The SMT LED
lamps are electrically connected in
series-parallel on the pc board
assembly, one series string for
each side of the light guide.
Diffusing films are made with
particles that internally reflect
incident light rays so that exit light
rays are scattered at random
angles, as illustrated in Figure 23.
Diffusing films are lossy as some of
the incidant flux, Ev(0)(lm/m2), is
reflected and some of the flux is
absorbed. The remaining flux exits
the diffusing film over a wide
radiation pattern that can be
described by three parameters:
1) Iv(0)(cd), the luminous intensity
perpendicular to the surface of the
2) θ 1/2 , the off-axis angle where the
luminous intensity is 1/2 the on-axis
3) Lv(0)(cd/m2), the surface luminance.
Figure 21. A T-1 3/4 or T-1 Untinted, Nondiffused LED lamp Used as the Light Source for a Right Angle Planar Wedge Light Guide.
Figure 22. A Dual Right Angle Planar Wedge Light Guide used with SMT LED Lamps for Backlighting a Medium-Large Size Transreflective LCD Display.
Figure 23. Properties and Figures of Merit of a Diffusing Film.
A diffusing film with a Lambertian
radiation pattern has a θ 1/2 value of
60 degrees, and is the maximum
viewing angle performance that
can be achieved with a diffuser.
Figures of merit for comparing one
diffusing film with another are:
• Lv(0)(cd/m2)/Ev(0)(lm/m2) = The
ratio of on-axis luminance to incidant
Where: Lv(0)(cd/m2) =
A(m2) = a selected area of the
diffusing film surface.
• 2θ 1/2 = The viewing cone angle.
Using these figure of merit
parameters, a trade-off between
output luminance and radiation
pattern must then be made in
selecting a diffusing film in order
to achieve desired overall
illumination performance in
combination with a light guide. The
higher the value of the Lv(0)/Ev(0)
ratio, the brighter is the output
luminance through the diffusing
film for illuminating an LCD
display. Also, the wider is the 2θ 1/2
angle, the better will be the output
radiation pattern (viewing cone
angle) from the diffusing film,
reducing the chance of an LCD
display appearing brighter in the
center than at the outer edges. The
following companies supply
3M Safety and Security Systems
Division, 3M Center, Building 225-
St. Paul, MN 55144-10000
Type 100, 5 mils, 2q 1/2 = 26°.
Type 070, 10 mils, 2q 1/2 = 32°.
Type 050, 16 mils, 2q 1/2 = 36°.
Type 040, 20 mils, 2q 1/2 = 40°
Mobay Road, Bldg. 8
Pittsburgh, PA 15205-9741
(412) 777-2000 FAX: (412) 777-2021
Makrofol BL 6-2:
a pigment filled polycarbonate
film, 8 and 16 mil thicknesses,
2θ 1/2 = 18° and 36°.
Makrofol LT 6-4:
a glass fiber
filled polycarbonate film, 16 to 20
mil thicknesses, 2θ 1/2 = 16°.
Physical Optics Corporation
20600 Gramercy Place Bldg. 100
Torrance, CA 90501
(310) 320-3088 Fax: (310) 320-8067
Products: Beam Homogenizing
Light Shaping Diffusing Films.
Luminous intensity variations, as
measured across the exit surface
of a light guide or a light guide/
diffusing film combination,
determine the evenness of
illumination. The ideal would be to
have a perfect rectangularly
shaped illumination pattern so that
the luminous intensity is the same
at all points across the surface, the
edges, the corners, and the center
all be at the same luminance. An
approximation to this ideal is
shown in Figure 24a, where the
illumination is flat across the
surface, falling off smoothly at the
edges. However, in a good design
there are typically minor luminous
intensity variations across the
surface as shown in Figure 24b.
These variations should not
exceed 20% of the luminous
intensity at the center.
Figures 24c – 24f show various
luminous intensity patterns that
produce unacceptable illumination
variations across the face of an
LCD display and should be
avoided. Careful optical design of
the light guide and selection of the
proper diffusing film to reduce
luminous intensity variations
should produce an acceptable
illumination pattern equivalent to
Figure 24a or 24b.
Flat plate light guides, wedge light
guides, and right angle and dual
right angle wedge light guides, with
either SMT LED or standard T-1 3/4
and T-1 LED lamps, are ideal for
illuminating flat surface
annunciator panels. The techniques
shown in Figures 18 through 24
directly apply to annunciators that
are the same size as the LCD
modules. Typically, annunciators
are made by silk-screening opaque
letters and symbols on the surface
of a diffusing film, leaving open a
background area for illumination.
The most effective approach is to
silk-screen the message on the
backside surface so it cannot be
damaged. The diffusing film is
placed directly onto the light
emitting surface of the light guide
to form the annunciator unit. In the
“off” condition, the background
surrounding the message is dark
and without color. When
illuminated, the bright color of the
LED light readily signifies to an
observer the “on” condition of the
annunciator. The opaque letters
and symbols forming the message
are easy to read against the