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Light Emitting Diode Source Modeling for Optical Design

Co-Instructor:Art Davis

Reflexite Display OpticsPhone: 585-647-1609x137

Email: [email protected]

October 20, 2004Arthur Davis, Reflexite Display Optics

Introduction

• Photometry Background• Understanding Optical Specifications for LEDs• Methods for Computations• Fresnel Lenses

• Attendee Introductions and Interests?• Several Sample Problems Included• Interrupt with Questions Freely

“in optics it is easy to do something roughly but very difficult to do it well.”--Rudolf Kingslake


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

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)


1.1 Photometry Right Handed Spherical Coordinate System

• Zenith is θ• Azimuth is φ• For the full sphere

• For the hemisphere

In radiansFor the full sphere

For the hemisphere


1.2 Spherical Differential• Differential Area and Solid Angle

• For the full sphere

• For the hemisphere


1.3 Solid Angle Subtended by a Right Circular Cone

Use trig identity:

From previous slide:

Then:

Calculate Solid Angle byprecisely encompassing

the right cone by asection of a sphere.


1.4 Point Source Illumination

The projected area isperpendicular to theangle of observation

Reference: Radiometry and the Detection of Optical Radiation, R. W. Boyd, 1983, Wiley.


1.5 Conservation of Luminance



1.6 Lambertian Emitter



1.7 Illuminance of Disk Lambertian Source

Reference: Radiometry and the Detection of Optical Radiation, R. W. Boyd, Wiley, 1983.


1.8 Étendue• Characterize the optical system independently of the flux content.

Start with:Small Source

with wide angleradiation pattern

Maps to:Large Image

with narrow angleradiation pattern



2. Optical Specifications of LEDs

CIE ColorCoordinates

x=0.31y=0.72

x=0.29y=0.70

x=0.27y=0.68

IF=50mATa=25°Cx, yGreenColor

degrees (deg)90°2θ1/2ViewingAngle

millicandela(mcd)768064005120IF=50mA

Ta=25°CIvLuminousIntensity

LambertianRadiationPattern

nanometers(nm)30∆λ1/2

SpectralHalf-Width

Lumens (lm)0.420.350.28IF=50mATa=25°CΦv

LuminousFlux

UnitMax.Typ.Min.ConditionSymbol

• 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.


2.1 Luminous Flux


x=0.31y=0.72

x=0.29y=0.70

x=0.27y=0.68







SpectralHalf-Width


LuminousFlux



2.1 Luminous Flux

• Flux measurement integrates the entirety of the flux (lumens) from the LED.

• Result is a single value = Φv

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


x=0.31y=0.72

x=0.29y=0.70

x=0.27y=0.68







SpectralHalf-Width


LuminousFlux



2.2 Luminous Intensity

• 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

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


2.2.3 Polar Intensity Plot

• Slices through contour for constant azimuth angle– Example:

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

0°

22.5°

45°

67.5°90°


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


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


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


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


2.2.8 3D Intensity Plot

• Plot of the 3D surface for the Rectangular Intensity Contour Plot


2.3 Viewing Angle


x=0.31y=0.72

x=0.29y=0.70

x=0.27y=0.68







SpectralHalf-Width


LuminousFlux



2.3 Viewing Angle

• 2θ½ refers to cone of luminous intensity defined by ±θ½


2.4 Radiation Pattern


x=0.31y=0.72

x=0.29y=0.70

x=0.27y=0.68







SpectralHalf-Width


LuminousFlux



2.4 Radiation Patterns

______________1.

______________2.

______________3.

______________4.

Narrow Angle

Lambertian

Batwing

Side Emitter


2.5 Color


x=0.31y=0.72

x=0.29y=0.70

x=0.27y=0.68







SpectralHalf-Width


LuminousFlux



2.5 Color

• Color coordinates of LED define a range within which lies the dominant wavelength

• Similar can be done for white LED’s defining a range in which the CCT can lie

400nm

490nm

500nm

510nm

520nm

540nm

570nm

600nm

700nm

1,50

0K

2,80

0K3,

500K

4,50

0K

10,0

00K

2,00

0K

6,50

0K

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


x=0.31y=0.72

x=0.29y=0.70

x=0.27y=0.68







SpectralHalf-Width


LuminousFlux



2.6 Spectral Half-Width• ∆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 2:Say drive current is 30mA and source distribution was recordedat 80 mA. Find the appropriate scaling factor to apply.

Answer:The K-factor reads at 1.5 for 80mA. Normalize the source distributionby dividing by this factor. Then multiply by 0.64 to scale it to 30mA

Scale Factor = 0.64/1.5 = 0.43

Example 1:Say drive current is 30mA (instead of 50mA).Find the typical luminous intensity.

Answer:The K-factor reads at 0.64.Typical luminous intensity will be = 0.64 x 6400 mcd = 4096 mcd


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)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


• 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

• Generate Rays• Scale the Flux• Align Origins• Import Rays• Remove LED• Encompass with absorbing shell• Trace Rays• Reverse vectors

Reference: Microstructured Optics for LED Applications, A. Davis, Reflexite Display Optics, Intertech LED 2002, http://www.display-optics.com/pdf/tech_papers_oct2002.pdf

3.1 Importing Radiant Imaging Source


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


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


4.2 Design Methods• Manual Calculation

– Photometry Integrals– Efficiency Approximations– Newtonian Lens Equations

• Computer Program– Extension of manual calculation– Well suited to iterative solution searching– Preliminary design solution– Full design optimization

• Sequential Raytracer– Handy built in optimizer– Fast raytraces– Does not account for non-sequential ray paths– Built in imaging tolerance analysis

• Nonsequential Raytracer– 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

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)


4.3.2 Flux Approximating Calculation (Lorentzian)


4.3.3 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.


4.4 F-number, Numerical Aperture andRay 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/#


4.5.1 Calculation of Transmission Efficiency

October 20, 2004Arthur Davis, Reflexite Display Optics Reference: Optics, 2nd ed., E. Hecht, 1990, Addison Wesley



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


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


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

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


4.7.2 “Thin Lens” Newtonian Virtual Image


4.7.3 Embedded Source Virtual Image

Typical application is in air so n’=1

The focal point f is defined as thevalue of s1 when s2 goes to infinity

θ’s in radians

Reference: Modern Optical Engineering, 2nd ed., W.J. Smith, 1990, McGraw Hill.


• 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.

• R=4.0mm, n=1.5 and s1=8.0mm.

• s2=16.0mm, m=3.0 and f =12.0mm

4.7.4 Embedded Source Virtual Image Example


• 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 θ1=17.35°• Recalling that:

• n=1.5, m=3.0 θ2=8.88 °• Output beam half-angle is ≈ ±9°

4.7.4 Embedded Source Virtual Image Example (continued)

Using Radians:


• “Collapse out” the unused volume

• Optionally, flatten out the curved facets

Reference: Use of Fresnel Lenses in Optical Systems: Some Advantages and Limitations, J.R. Egger, Aug. 1979, SPIE Vol. 193, pp. 63-68.

5. Fresnel Lens


5.1 Types of Fresnels

• Refractive• Total Internal Reflective• Hybrid• Domed


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.

5.1.1 Refractive Fresnel Lens

• 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)


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.

5.1.2 TIR Fresnel Lens

• Refraction at Draft facet, followed by TIR at Slope facet, followed by refraction at plano interface.

• Orientation: Facets face source (design requirement)

Rays behaving

Refracted raymisses

TIR surface

Ray incidenton Slope

(wrong) facet

Rays misbehaving


5.1.3 TIR Fresnel Lens

• Extremely short LED to lens conjugate distance.


5.1.4 Fresnel Lens Hybrid1

• Central region refractive facets, outer region TIR design

• Improved efficiency for low angle and high angle light zones

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


5.1.6 Domed Fresnel Lens

• Any of the previous outlined Fresnel types can be “bent” into a dome shape.

• Improved hemispherical light collection.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

•

•

• If it’s too hard to design and or make a Fresnel lens foryourself, hire an expert.*

* For example, Reflexite Display Optics. (585) 647-1609, www.display-optics.com


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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.

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.

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