LED Source Modeling for Optical Design Workbook Davis 2004

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  • Light Emitting Diode Source Modeling for Optical Design

    Co-Instructor:Art Davis

    Reflexite Display OpticsPhone: 585-647-1609x137

    Email: Art.Davis@Reflexite.comwww.display-optics.com

  • 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

  • October 20, 2004Arthur 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 tendue

    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 Sllner 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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    1. Photometry Flux ()

    Photometric Power Lumen (lm)

    Illuminance (E=d /dA) Flux Density (or exitance) Flux per Unit Area lm/m2 (lux)

    Luminous Intensity (I=d /d) Flux per Unit Solid Angle lm/sr (candela or cd)

    Luminance (L=d2 /[dAd]) Flux Radiance Flux per Unit Area per Unit Solid Angle lm/sr/m2 or cd/m2 (nit)

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    1.1 Photometry Right Handed Spherical Coordinate System

    Zenith is Azimuth is For the full sphere

    For the hemisphere

    In radiansFor the full sphere

    For the hemisphere

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    1.2 Spherical Differential Differential Area and Solid Angle

    For the full sphere

    For the hemisphere

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    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.

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    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.

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    1.5 Conservation of Luminance

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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    1.6 Lambertian Emitter

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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    1.7 Illuminance of Disk Lambertian Source

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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    1.8 tendue 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

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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    2. Optical Specifications of LEDs

    CIE ColorCoordinates

    x=0.31y=0.72

    x=0.29y=0.70

    x=0.27y=0.68

    IF=50mATa=25C

    x, yGreenColor

    degrees (deg)9021/2ViewingAngle

    millicandela(mcd)768064005120

    IF=50mATa=25C

    IvLuminousIntensity

    LambertianRadiationPattern

    nanometers(nm)301/2

    SpectralHalf-Width

    Lumens (lm)0.420.350.28IF=50mATa=25CvLuminousFlux

    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.

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    2.1 Luminous Flux

    CIE ColorCoordinates

    x=0.31y=0.72

    x=0.29y=0.70

    x=0.27y=0.68

    IF=50mATa=25C

    x, yGreenColor

    degrees (deg)9021/2ViewingAngle

    millicandela(mcd)768064005120

    IF=50mATa=25C

    IvLuminousIntensity

    LambertianRadiationPattern

    nanometers(nm)301/2

    SpectralHalf-Width

    Lumens (lm)0.420.350.28IF=50mATa=25CvLuminousFlux

    UnitMax.Typ.Min.ConditionSymbol

    B A

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    2.1 Luminous Flux

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

    Result is a single value = v

    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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    2.2 Luminous Intensity

    CIE ColorCoordinates

    x=0.31y=0.72

    x=0.29y=0.70

    x=0.27y=0.68

    IF=50mATa=25C

    x, yGreenColor

    degrees (deg)9021/2ViewingAngle

    millicandela(mcd)768064005120

    IF=50mATa=25C

    IvLuminousIntensity

    LambertianRadiationPattern

    nanometers(nm)301/2

    SpectralHalf-Width

    Lumens (lm)0.420.350.28IF=50mATa=25CvLuminousFlux

    UnitMax.Typ.Min.ConditionSymbol

    B A

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    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, 2004Arthur 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

    Polar Intensity Plot polar axis (spokes) equals zenith angles

    Polar Intensity Plot radial axis (rings) equals intensity magnitude

    0

    22.5

    45

    67.590

  • October 20, 2004Arthur 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, 2004Arthur 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, 2004Arthur Davis, Reflexite Display Optics

    2.2.6 Sllner 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, 2004Arthur 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, 2004Arthur Davis, Reflexite Display Optics

    2.2.8 3D Intensity Plot

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

  • October 20, 2004Arthur Davis, Reflexite Display Optics

    2.3 Viewing Angle

    CIE ColorCoordinates

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