Light Emitting Diode Source
Modeling for Optical Design
Co-Instructor:
Art Davis
Reflexite Display Optics
Phone: 585-647-1609x137
Email: Art.Davis@Reflexite.com
www.display-optics.com
Introduction
“in optics it is easy to do something roughly but very difficult to do it well.”
--Rudolf Kingslake
•
•
•
•
Photometry Background
Understanding Optical Specifications for LEDs
Methods for Computations
Fresnel Lenses
• Attendee Introductions and Interests?
• Several Sample Problems Included
• Interrupt with Questions Freely
October 20, 2004
Arthur Davis, Reflexite Display Optics
Table of Contents
1. Photometry
1.1 Photometry Spherical Coordinate System
1.2 Spherical Differential
1.3 Solid Angle Subtended by a Right Circular Cone
1.4 Point Source Illumination
1.5 Conservation of Luminance
1.6 Lambertian Emitter
1.7 Illuminance of Disk Lambertian Source
1.8 Étendue
2. Optical Specifications of LEDs
2.1 Luminous Flux
2.2 Luminous Intensity
2.2.1 Understanding Intensity Plots
2.2.2 Polar Intensity Contour Plot
2.2.3 Polar Intensity Plot
2.2.4 Rectangular Intensity Plot
2.2.5 Rectangular/Polar Intensity Plot
2.2.6 Söllner Plot
2.2.7 Rectangular Intensity Contour Plot
2.2.8 3D Intensity Plot
2.3 Viewing Angle
2.4 Radiation Pattern
2.5 Color
2.6 Spectral Half-Width
2.7 Scaling Using K-factors
October 20, 2004
Arthur Davis, Reflexite Display Optics
3. Source Modeling of LEDs
3.1 Importing Radiant Imaging Source
4. Optics for use with LEDs
4.1 Suitability of Optics
4.2 Design Methods
4.3 Flux Approximating Calculation
4.4 F/#, NA and Ray Angle
4.5 Calculation of Transmission Efficiency
4.6 Reflectors
4.7.1 “Thin Lens” Newtonian Real Image
4.7.2 “Thin Lens” Newtonian Virtual Image
4.7.3 Embedded Source Virtual Image
4.7.4 Embedded Source Virtual Image Example
5. Fresnel Lens
5.1 Types of Fresnels
5.1.1 Refractive Fresnel Lens
5.1.2 TIR Fresnel Lens
5.1.3 TIR Fresnel Lens
5.1.4 Fresnel Lens Hybrid1
5.1.5 Fresnel Lens Hybrid2
5.1.6 Domed Fresnel Lens
1. Photometry
•
Flux (Φ)
– Photometric Power
– Lumen (lm)
•
Illuminance (E=dΦ /dA)
– Flux Density (or exitance)
– Flux per Unit Area
– lm/m2 (lux)
•
Luminous Intensity (I=dΦ /dΩ)
– Flux per Unit Solid Angle
– lm/sr (candela or cd)
•
Luminance (L=d2Φ /[dAdΩ])
– Flux Radiance
– Flux per Unit Area per Unit Solid Angle
– lm/sr/m2 or cd/m2 (nit)
October 20, 2004
Arthur Davis, Reflexite Display Optics
1.1 Photometry Right Handed Spherical
Coordinate System
• Zenith is θ
• Azimuth is φ
• For the full sphere
• For the hemisphere
In radians
For the full sphere
For the hemisphere
October 20, 2004
Arthur Davis, Reflexite Display Optics
1.2 Spherical Differential
October 20, 2004
Arthur Davis, Reflexite Display Optics
•
Differential Area and Solid Angle
•
For the full sphere
•
For the hemisphere
1.3 Solid Angle Subtended by a Right
Circular Cone
From previous slide:
Then:
Calculate Solid Angle by
precisely encompassing
the right cone by a
section of a sphere.
October 20, 2004
Arthur Davis, Reflexite Display Optics
Use trig identity:
1.4 Point Source Illumination
The projected area is
perpendicular to the
angle of observation
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Radiometry and the Detection of Optical Radiation, R. W. Boyd, 1983, Wiley.
1.5 Conservation of Luminance
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Radiometry and the Detection of Optical Radiation, R. W. Boyd, 1983, Wiley.
1.6 Lambertian Emitter
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Radiometry and the Detection of Optical Radiation, R. W. Boyd, 1983, Wiley.
1.7 Illuminance of Disk Lambertian Source
Reference: Radiometry and the Detection of Optical Radiation,
R. W. Boyd, Wiley, 1983.
October 20, 2004
Arthur Davis, Reflexite Display Optics
1.8 Étendue
•
Characterize the optical system independently of the flux content.
Start with:
Small Source
with wide angle
radiation pattern
October 20, 2004
Arthur Davis, Reflexite Display Optics
Maps to:
Large Image
with narrow angle
radiation pattern
Reference: Radiometry and the Detection of Optical Radiation, R. W. Boyd, 1983, Wiley.
2. Optical Specifications of LEDs
Symbol
Condition
Min.
Typ.
Max.
Unit
Luminous
Flux
Φv
IF=50mA
Ta=25°C
0.28
0.35
0.42
Lumens (lm)
Luminous
Intensity
Iv
IF=50mA
Ta=25°C
5120
6400
7680
millicandela
(mcd)
Viewing
Angle
2θ1/2
Radiation
Pattern
Lambertian
Color
Green
Spectral
Half-Width
x, y
90°
IF=50mA
Ta=25°C
x=0.27
y=0.68
∆λ1/2
x=0.29
y=0.70
30
degrees (deg)
x=0.31
y=0.72
CIE Color
Coordinates
nanometers
(nm)
•
Conditions
– IF is Forward Current
• Verify drive current
• Take note of Pulse Width Modulation
– Ta is ambient temperature
• Consider realistic operating temperatures
•
Current and temperature effects the optical specifications. Refer to the data charts for
the specified LED to see how.
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.1 Luminous Flux
B
Symbol
Condition
Min.
Typ.
Max.
Unit
Luminous
Flux
Φv
IF=50mA
Ta=25°C
0.28
0.35
0.42
Lumens (lm)
Luminous
Intensity
Iv
IF=50mA
Ta=25°C
5120
6400
7680
millicandela
(mcd)
Viewing
Angle
2θ1/2
Radiation
Pattern
Lambertian
Color
Green
Spectral
Half-Width
October 20, 2004
Arthur Davis, Reflexite Display Optics
x, y
∆λ1/2
90°
IF=50mA
Ta=25°C
x=0.27
y=0.68
x=0.29
y=0.70
30
degrees (deg)
x=0.31
y=0.72
CIE Color
Coordinates
nanometers
(nm)
A
2.1 Luminous Flux
• Flux measurement
integrates the
entirety of the flux
(lumens) from the
LED.
• Result is a single
value = Φv
October 20, 2004
Arthur Davis, Reflexite Display Optics
References:
• “Recent Activity in LED Measurement Standards with CIE and CORM”,
K. Murray, INPHORA, Intertech LED 2003
• CIE publication 127-197
• Council for Optical Radiation Measurement: www.corm.org
• “Standardization of LED Measurements”, C.C. Miller and Y. Ohno, NIST,
Sept. 2004, Photonics Spectra
2.2 Luminous Intensity
B
Symbol
Condition
Min.
Typ.
Max.
Unit
Luminous
Flux
Φv
IF=50mA
Ta=25°C
0.28
0.35
0.42
Lumens (lm)
Luminous
Intensity
Iv
IF=50mA
Ta=25°C
5120
6400
7680
millicandela
(mcd)
Viewing
Angle
2θ1/2
Radiation
Pattern
Lambertian
Color
Green
Spectral
Half-Width
October 20, 2004
Arthur Davis, Reflexite Display Optics
x, y
∆λ1/2
90°
IF=50mA
Ta=25°C
x=0.27
y=0.68
x=0.29
y=0.70
30
degrees (deg)
x=0.31
y=0.72
CIE Color
Coordinates
nanometers
(nm)
A
2.2 Luminous Intensity
•
•
October 20, 2004
Arthur Davis, Reflexite Display Optics
CIE Standard condition for
the measurement of the
Averaged LED Intensity
– “Condition A”: d=0.316 m
– “Condition B”: d=0.100 m
Result is a single value = Iv
References:
• “Recent Activity in LED Measurement Standards with CIE and CORM”,
K. Murray, INPHORA, Intertech LED 2003
• CIE publication 127-197
• Council for Optical Radiation Measurement: www.corm.org
• “Standardization of LED Measurements”, C.C. Miller and Y. Ohno, NIST,
Sept. 2004, Photonics Spectra
2.2.1 Understanding Intensity Plots
• 3D Mesh of Intensity
Distribution
• Magnitude of luminous
intensity is plotted in
three dimensional
coordinates
• Distribution shown
here (batwing) is used
for the next several
figures
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Lumileds Lighting, Dataset for LXHL-MW1A, www.lumileds.com
2.2.2 Polar Intensity Contour Plot
• Contour colormap values assigned according to
magnitude of luminous intensity
• Polar axis (spokes) of the plot are the azimuth angles
• Radial axis (rings) of the plot are the zenith angles
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.2.3 Polar Intensity Plot
• Slices through contour for
constant azimuth angle
– Example:
0°,22.5°,45°,67.5°,90°
0°
22.5°
45°
67.5°
90°
• Polar Intensity Plot polar
axis (spokes) equals
zenith angles
• Polar Intensity Plot radial
axis (rings) equals
intensity magnitude
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.2.4 Rectangular Intensity Plot
• The polar slices can
also be plotted on
rectangular axes
– x-axis is zenith angles
– y-axis is intensity
magnitude
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.2.5 Rectangular/Polar Intensity Plot
• When symmetry is assumed, sometimes the rectangular
and polar plots are split in half and combined into a
single graph.
• Also known as a Directivity Plot
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.2.6 Söllner Plot
• Typically used for
Lighting Specifications
• Usually plotted in
Luminance but intensity
is also possible
• x-axis is photometric
magnitude
• y-axis is zenith angles
• Useful for quickly
determining adherence
to specification
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.2.7 Rectangular Intensity Contour Plot
•
•
•
•
“Unroll” a polar contour plot
x-axis is azimuth angles
y-axis is zenith angles
Colormap values assigned according to magnitude of luminous
intensity
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.2.8 3D Intensity Plot
• Plot of the 3D surface for the Rectangular Intensity
Contour Plot
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.3 Viewing Angle
B
Symbol
Condition
Min.
Typ.
Max.
Unit
Luminous
Flux
Φv
IF=50mA
Ta=25°C
0.28
0.35
0.42
Lumens (lm)
Luminous
Intensity
Iv
IF=50mA
Ta=25°C
5120
6400
7680
millicandela
(mcd)
Viewing
Angle
2θ1/2
Radiation
Pattern
Lambertian
Color
Green
Spectral
Half-Width
October 20, 2004
Arthur Davis, Reflexite Display Optics
x, y
∆λ1/2
90°
IF=50mA
Ta=25°C
x=0.27
y=0.68
x=0.29
y=0.70
30
degrees (deg)
x=0.31
y=0.72
CIE Color
Coordinates
nanometers
(nm)
A
2.3 Viewing Angle
• 2θ½ refers to cone of
luminous intensity
defined by ±θ½
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.4 Radiation Pattern
B
Symbol
Condition
Min.
Typ.
Max.
Unit
Luminous
Flux
Φv
IF=50mA
Ta=25°C
0.28
0.35
0.42
Lumens (lm)
Luminous
Intensity
Iv
IF=50mA
Ta=25°C
5120
6400
7680
millicandela
(mcd)
Viewing
Angle
2θ1/2
Radiation
Pattern
Lambertian
Color
Green
Spectral
Half-Width
October 20, 2004
Arthur Davis, Reflexite Display Optics
90°
degrees (deg)
A
x, y
∆λ1/2
IF=50mA
Ta=25°C
x=0.27
y=0.68
x=0.29
y=0.70
30
x=0.31
y=0.72
CIE Color
Coordinates
nanometers
(nm)
2.4 Radiation Patterns
Lambertian
______________
1.
Batwing
______________
2.
Side Emitter
______________
3.
Narrow Angle
______________
4.
October 20, 2004
Arthur Davis, Reflexite Display Optics
2.5 Color
B
Symbol
Condition
Min.
Typ.
Max.
Unit
Luminous
Flux
Φv
IF=50mA
Ta=25°C
0.28
0.35
0.42
Lumens (lm)
Luminous
Intensity
Iv
IF=50mA
Ta=25°C
5120
6400
7680
millicandela
(mcd)
Viewing
Angle
2θ1/2
Radiation
Pattern
Lambertian
Color
Green
Spectral
Half-Width
October 20, 2004
Arthur Davis, Reflexite Display Optics
x, y
∆λ1/2
90°
IF=50mA
Ta=25°C
x=0.27
y=0.68
x=0.29
y=0.70
30
degrees (deg)
x=0.31
y=0.72
CIE Color
Coordinates
nanometers
(nm)
A
2.5 Color
520nm
510nm
400nm
Arthur Davis, Reflexite Display Optics
1,500K
2,000K
490nm
10,000K
6,500K
4,500K
3,500K
2,800K
570nm
500nm
October 20, 2004
• Color coordinates of
LED define a range
within which lies the
dominant wavelength
540nm
600nm
700nm
• Similar can be done
for white LED’s
defining a range in
which the CCT can lie
References:
• Principles of Color Technology, 2nd ed., F.W. Billmeyer, M. Saltzman, 1981, Wiley.
• efg’s Computer Lab, www.efg2.com
• Blackbody coordinates downloaded from: www.imagingscience.com
2.6 Spectral Half-Width
B
Symbol
Condition
Min.
Typ.
Max.
Unit
Luminous
Flux
Φv
IF=50mA
Ta=25°C
0.28
0.35
0.42
Lumens (lm)
Luminous
Intensity
Iv
IF=50mA
Ta=25°C
5120
6400
7680
millicandela
(mcd)
Viewing
Angle
2θ1/2
Radiation
Pattern
Lambertian
Color
Green
Spectral
Half-Width
October 20, 2004
Arthur Davis, Reflexite Display Optics
x, y
∆λ1/2
90°
IF=50mA
Ta=25°C
x=0.27
y=0.68
x=0.29
y=0.70
30
degrees (deg)
x=0.31
y=0.72
CIE Color
Coordinates
nanometers
(nm)
A
2.6 Spectral Half-Width
October 20, 2004
Arthur Davis, Reflexite Display Optics
•
∆λ0.5 Full Width at Half
Maximum (FWHM)
•
∆λ0.1 Full Width at 10%
height
•
∆λ0.5m Center Wavelength
of Half Intensity Bandwidth
•
∆λc Centroid Wavelength
Reference: CIE publication 127-197
2.7 Scaling Using K-factors
• Optical data is reported at
fixed average forward
current
• Scale Luminous Flux by
the k-factor of the actual
drive current to be used
• The k-factor at specified
driving current is equal to
1.0
Example 1:
Say drive current is 30mA (instead of 50mA).
Find the typical luminous intensity.
Example 2:
Say drive current is 30mA and source distribution was recorded
at 80 mA. Find the appropriate scaling factor to apply.
Answer:
The K-factor reads at 0.64.
Typical luminous intensity will be = 0.64 x 6400 mcd = 4096 mcd
Answer:
The K-factor reads at 1.5 for 80mA. Normalize the source distribution
by dividing by this factor. Then multiply by 0.64 to scale it to 30mA
ÖScale Factor = 0.64/1.5 = 0.43
October 20, 2004
Arthur Davis, Reflexite Display Optics
3. Source Modeling of LEDs
•
•
Eight types described in D. Kreysar’s presentation
Geometric Model
– Accurate CAD model of source
– Optical properties need to be precisely characterized and included (refractive index,
scattering, absorption, etc.)
– Perturbable for tolerance analysis
– Difficult to get real world convergence
•
Angularly/Spatially Measured Model
–
–
–
–
•
Radiant Imaging
Very close to real world performance
Does not account for variation between sources
Easy to use for inclusion in raytrace software
Combined Geometric/Measured Model
– Most accurate
– Most difficult
– Especially useful for return light incident on the geometry (detailed in D. Kreysar’s
presentation)
October 20, 2004
Arthur Davis, Reflexite Display Optics
References:
• Light Source Modeling, W. Cassarly, ORA, Aug. 2004, SPIE SC345
• Optical Modeling of UHP Lamps, H. Moench, Jul. 2002, SPIE Vol. 4775, pp. 36-45.
• Advanced Topics in Source Modeling, M.S. Kaminski et al,Jul. 2002, SPIE Vol. 4775, pp. 46-57.
• Accurate Illumination System Predictions Using Measured Spatial Luminance Distributions, W.J.
Cassarly, D.R. Jenkins, H. Mönch, Jul. 2002, SPIE Vol. 4775, pp. 78-85.
• Radiant Imaging: www.radimg.com
3.1 Importing Radiant Imaging Source
• Generate Rays
• Scale the Flux
• Align Origins
• Import Rays
• Remove LED
• Encompass with absorbing shell
• Trace Rays
• Reverse vectors
October 20, 2004
Arthur Davis, Reflexite Display Optics
• Import absorbing LED geometry
• Trace Rays again
• Reverse Vectors
• Remove spurious rays of choice
• Incremental Propagation
• Export to Rayfile
• Optionally import accurate LED model
• Raytrace system
Reference: Microstructured Optics for LED Applications, A. Davis, Reflexite Display
Optics, Intertech LED 2002, http://www.display-optics.com/pdf/tech_papers_oct2002.pdf
4. Optics for use with LEDs
• Refractive
– Continuous Surface
• Conventional lens
– Microstructured
• Linear Prism
• Fresnel Lens
• Reflective
– Continuous
• Parabolic Reflector
– Facetted
• Headlamp reflector
• Diffractive
– Surface Relief Diffuser
– Diffraction Grating
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.1 Suitability of Optics
• Conventional Lens
– Ubiquitously available
– Outperformed by tailored nonimaging optics
• Fresnel Lens
– Small volume of space with short conjugates
– Drafts can incur transmission loss
• Reflectors
– Full spherical area flux collection possible
– Consumes large area of space
• Diffractive
– Small volume of space
– Color separation
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.2 Design Methods
•
Manual Calculation
–
–
–
•
Computer Program
–
–
–
–
•
Handy built in optimizer
Fast raytraces
Does not account for non-sequential ray paths
Built in imaging tolerance analysis
Nonsequential Raytracer
–
–
–
•
Extension of manual calculation
Well suited to iterative solution searching
Preliminary design solution
Full design optimization
Sequential Raytracer
–
–
–
–
•
Photometry Integrals
Efficiency Approximations
Newtonian Lens Equations
Most accurate optical simulation
Compatibility with CAD models
Tolerancing/Optimization possible, requires manual detuning and merit definitions and is
much slower
Prototyping
–
–
Test the design output from any of the previously listed methods by making a custom optic
Get any and every optic you can and just try it to see if it works for you: Plug and Pray
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Using Computers to Design Nonimaging Illumination Systems, D. Jenkins,
M. Kaminski, Jul. 1997, SPIE Vol. 3130 pp. 196-203
4.3.1 Flux Approximating Calculation (Lorentzian)
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.3.2 Flux Approximating Calculation (Lorentzian)
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.3.3 Flux Approximating Calculation (Cosine)
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.3.4 Flux Approximating Calculation (Cosine)
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.3.5 Flux Approximating Calculation (Cosine)
For flux integration of Lambertian emitter and
application of Simpsons rule to arbitrary intensity
profile, refer to: Secondary Optics Design
Considerations For SuperFlux LEDs, Lumileds
Application Brief: AB20-5.
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.4 F-number, Numerical Aperture and
Ray Angle
• Lens f/# defined by the
extent of the lens and
its focal length
• Ray f/# is on a “per-ray”
basis and defined by
that ray’s angle
• Speed of a lens refers
to its f/#
– Fast = Low f/#
– Slow = High f/#
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.5.1 Calculation of Transmission Efficiency
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.5.2 Calculation of Transmission Efficiency
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Optics, 2nd ed., E. Hecht, 1990, Addison Wesley
4.5.3 Calculation of Transmission Efficiency
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.5.4 Refractive Transmission Efficiency
• “Correct orientation”
directs the plano side of
the lens face towards the
short conjugate
• Example chart is for
Acrylic: n=1.494
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.5.5 Total Transmission Efficiency
• Average value of total
efficiency of “correct
orientation” on previous
slide
• Data is “idealized”, real
world factors will
decrease the efficiency
– Precision
– Fidelity
– Scatter/Absorption
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.6 Reflectors
• Parabolic
– Source at focus point, far field collimated
• Elliptic
– Source at first focal point, image at second focal point
• Compound Parabolic Concentrator (CPC)
– All light from designated source plane is redirected into defined
output half angle
– Dielectric design possible
• Facetted
– One to one mapping
– Superposition
• Die cup
October 20, 2004
Arthur Davis, Reflexite Display Optics
References:
• Design of Efficient Illumination Systems, W. Cassarly, ORA, Aug. 2004 SPIE SC011
• Selected Papers on Nonimaging Optics, R. Winston ed., SPIE Vol. MS 106
4.7.1 “Thin Lens” Newtonian Real
Image
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.7.2 “Thin Lens” Newtonian Virtual
Image
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.7.3 Embedded Source Virtual Image
Typical application is in air so n’=1
θ’s in radians
The focal point f is defined as the
value of s1 when s2 goes to infinity
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Modern Optical Engineering, 2nd ed., W.J. Smith, 1990, McGraw Hill.
4.7.4 Embedded Source Virtual Image
Example
• An LED die is encapsulated by a 5mm diameter dome of
epoxy with an index of refraction of 1.5 and a radius of
curvature of 4mm. The die to dome distance is 8mm. Find the
virtual image location, the magnification and the effective
focal length of the dome lens.
• Ö R=4.0mm, n=1.5 and s1=8.0mm.
• Ö s2=16.0mm, m=3.0 and f =12.0mm
October 20, 2004
Arthur Davis, Reflexite Display Optics
4.7.4 Embedded Source Virtual Image
Example (continued)
•
•
Knowing the die to dome distance (s1) and the LED diameter (d), calculate
the output cone half-angle (θ2).
From the geometry:
•
•
d=5.0mm, s1=8.0mm Ö θ1=17.35°
Recalling that:
•
•
n=1.5, m=3.0 Ö θ2=8.88 °
Output beam half-angle is ≈ ±9°
October 20, 2004
Arthur Davis, Reflexite Display Optics
Using Radians:
5. Fresnel Lens
• “Collapse out” the
unused volume
• Optionally, flatten out
the curved facets
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Use of Fresnel Lenses in Optical Systems: Some Advantages and
Limitations, J.R. Egger, Aug. 1979, SPIE Vol. 193, pp. 63-68.
5.1 Types of Fresnels
•
•
•
•
Refractive
Total Internal Reflective
Hybrid
Domed
October 20, 2004
Arthur Davis, Reflexite Display Optics
5.1.1 Refractive Fresnel Lens
•
•
References:
•Thin Sheet Plastic Fresnel Lenses of High Aperture, O.E. Miller, J.H.
McLeod, W.T. Sherwood, Nov. 1951, JOSA v.41 n.11, pp.807-815.
• Manufacturing Methods for Large Microstructured Optical
Components for Non-imaging Applications, J.R. Egger, Oct. 1995,
SPIE Vol. 2600, pp. 28-33.
October 20, 2004
Arthur Davis, Reflexite Display Optics
•
Refraction at plano interface
followed by refraction at Slope
facet.
Short LED to lens conjugate
distance.
Orientation: Facets face long
conjugate (improved
transmission and minimized
draft loss)
5.1.2 TIR Fresnel Lens
Rays misbehaving
Rays behaving
Refracted ray
misses
TIR surface
Ray incident
on Slope
(wrong) facet
• Refraction at Draft facet,
followed by TIR at Slope
facet, followed by
refraction at plano
interface.
• Orientation: Facets face
source (design
requirement)
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: The Converging TIR Lens for Non-Imaging Concentration of Light from Compact
Incoherent Sources, W.A. Parkyn, P. Gleckman, D.G. Pelka, Jul. 1993, SPIE Vol. 2016, pp. 78-86.
5.1.3 TIR Fresnel Lens
• Extremely short LED to lens
conjugate distance.
October 20, 2004
Arthur Davis, Reflexite Display Optics
5.1.4 Fresnel Lens Hybrid1
• Central region refractive
facets, outer region TIR
design
• Improved efficiency for
low angle and high angle
light zones
October 20, 2004
Arthur Davis, Reflexite Display Optics
Reference: Uniform LED illuminator for miniature displays, V. Medvedev, D. Pelka, B.
Parkyn, Jul. 1998, SPIE Vol. 3428, pp. 142-153.
5.1.5 Fresnel Lens Hybrid2
• Further improved
transmission efficiency at
refractive surface
October 20, 2004
Arthur Davis, Reflexite Display Optics
5.1.6 Domed Fresnel Lens
• Any of the previous outlined Fresnel types can be “bent”
into a dome shape.
• Improved hemispherical light collection.
October 20, 2004
Arthur Davis, Reflexite Display Optics
References:
• Nonimaging Fresnel Lenses, R. Leutz, A. Suzuki, 2001, Springer.
• TIR lenses for fluorescent lamps, W.A. Parkyn, D.G. Pelka, Jul. 1995,
SPIE Vol. 2538, pp. 93-103.
Closing Remarks
•
•
•
•
October 20, 2004
Arthur Davis, Reflexite Display Optics
•
If it’s too hard to design and
or make a Fresnel lens for
yourself, hire an expert.*
* For example, Reflexite Display Optics. (585) 647-1609, www.display-optics.com
Glossary
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pticsReflexipticsReflexipticsReflexiticsReeflexticsReeeflexticsReeeflexticsReeef
ay OpticsRefay OpticsRefay OpticsRefay OticcsRfayy OticcsRfayy OticcsRfayy Oticc
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Azimuth: Angle around polar axis (φ ). Also called the polar angle
or Longitude.
BotE: Back of the Envelope. A quick (or not-so-quick) manual
calculation.
BSOD: The windows Blue Screen of Death indicating your
computer has crashed… hard. This is a highly dreadful event if it
occurs during a presentation.
CA: Clear Aperture or diameter of a lens.
Conjugate: A source or an image location relative to an optical
surface. An infinite conjugate implies the source or image is rather
far away.
Drafts: The typically unused components of Fresnel Lens facets
which returns the optical surface (slopes) back to a plane.
f: Focal length of a lens. Essentially the distance from the lens to the
point at which collimated rays intercept the optical axis.
f/#: F-number ≡ f /CA
Far Field: The condition where the distance from the source is
relatively large with respect to the source size so the source may be
treated as a point emitter.
GI GO: Garbage In equals Garbage Out.
Lambertian Emitter: A source whose luminance is independent of
the view angle.
October 20, 2004
Arthur Davis, Reflexite Display Optics
LED SMOD: The title of this talk, “Light Emitting Diode Source
Modeling for Optical Design”.
Near Field: The condition under which the distance from the source
is relatively short compared to the extent of the source so the source
must be treated as an extended area and not a point.
NA: Numerical Aperture ≈1/2f/#
Paraxial approximation: Small angle approximation in which
Sinθ ≈ Tanθ ≈ θ (θ in radians).
Plug’n’Pray: Drop any old optic in to your system, cross your
fingers and test it. (chance of success) ∝ (1/importance)
Radians: A measure of angle. To convert radians to degrees
multiply by (180°/π )
Slopes: The optical power components of Fresnel Lens facets which
approximate the aspheric surface of a conventional lens.
TIR: Total Internal Reflection. The reflection of light within a
media which occurs because the angle of incidence exceeds the
critical angle.
Virtual Prototyping: Making an accurate optical simulation in
order that the “Pray” component of “Plug’n’Pray” is mitigated.
Zenith: Angle from polar axis (θ). Also called Latitude.