1. 3280 East Foothill Boulevard Pasadena, California 91107 USA (626) 795-9101 Fax (626) 795-0184 e-mail: service@opticalres.com World Wide Web: http://www.opticalres.com Copyright © 2007 Optical Research Associates Angular Apodization (Source Modeling)

2. Source Angular Apodization, Slide 5-2Overview Angular apodization basics Coordinate systems File format Selecting the angular range and the source surface(s) Data orientation and effect of binning Examples – Rotationally symmetric example – IES Import example

3. Source Angular Apodization, Slide 5-3 What is Apodization? The default emission patterns of LightTools source models are either Uniform or Lambertian. Apodization allows you to change the default distribution to match the distribution of real sources Apodization data is defined using an input data file The data is usually from measured intensity data for a given source – Real sources are not always Uniform or Lambertian

4. Source Angular Apodization, Slide 5-4 When to Use Angular Apodization? When the intensity distribution of the source is different from Uniform and Lambertian You have the measured angular intensity data (usually obtained from a datasheet supplied by the source manufacturer), such as an IES file Measured Intensity Distribution for K2 LED from Philips

5. Source Angular Apodization, Slide 5-5 A Closer Look Angular apodization ONLY defines the distribution at far field. This means that all rays generated from the source in a given direction will have the same “flux” (or magnitude) – Angular apodization alone may not have a complete source definition A simple ray generation example from a surface source. (a) all rays from the source in a given direction have equal magnitude and (b) rays have different magnitude. Both will produce the same intensity. (a) (b)

6. Source Angular Apodization, Slide 5-6 Apodization File Format Data is applied to the source using a data file or by direct entry in the grid – File format is ASCII text – Header line must contain the word MESH: n m, SPHEREMESH: n m, or POLARMESH: n m, where n x m is the size of the text file – U and V directions correspond to X, Y for spatial apodization and Longitude, Latitude for angular apodization MESH: n m a11 a12 a13... a1n a21 a22 a23... a2n... am1 am2 am3... amn Example File U - Direction V - Direction

7. Source Angular Apodization, Slide 5-7 Angular Apodization Coordinate System [Longitude 0, Latitude 90] [Longitude 90, Latitude 90] [Latitude 180] [Longitude 180, Latitude 90] [Longitude 270, Latitude 90] [Latitude 0] Latitudes  0 to 180 0 Longitudes  0 to 360 0 Coordinate system shown can be “global” or “local” (to the surface)

8. Source Angular Apodization, Slide 5-8 Coordinate Systems Two coordinate systems can be used for apodization Source – Allows you to use the “global” coordinate system for apodization Surface – Allows you to use the coordinate system of the emitting surface For example, if the distribution is rotationally symmetric then it is convenient to use the “surface” coordinate system Global Coordinate System Local Coordinate System

9. Source Angular Apodization, Slide 5-9 Source/Surface Options “Surface” option is always the best when you have rotational symmetry “Source” option works better when the data is asymmetric Rotationally symmetric – “Surface” option is convenient [Longitude 0- 360], [Latitude 0-90] Rotationally asymmetric – “Source” option is convenient [Longitude 90- 270], [Latitude 0-180]

10. Source Angular Apodization, Slide 5-10 Selecting the Convenient Coordinate Range “Surface” coordinate system is usually a hemisphere. The coordinate space is a “Polar” grid. Rotational symmetry is easy to define but asymmetry is harder to define “Source” coordinate system is closer to a “Cartesian” system around the equator. In this region asymmetry is easier to define but symmetry is harder to define

11. Source Angular Apodization, Slide 5-11 Selecting the Surface (for Asymmetric Data) “FrontSurface” gives the range [Longitude 0- 180], [Latitude 0-180]. Latitudes 50- 180 are shown in the picture “TopSurface” gives the range [Longitude 90- 270], [Latitude 0-180]. Latitudes 50- 180 are shown in the picture “BackSurface” gives the range [Longitude 180- 360], [Latitude 0-180]. Latitudes 50- 180 are shown in the picture All coordinate values shown are with respect to the “global” (or “source”) coordinate system Latitude 50 Latitude 130

12. Source Angular Apodization, Slide 5-12 Coordinate System Example An apodization file with angular bounds [Latitude 0-90], [Longitude 0-360]. No rotational symmetry Cartesian and Polar illustration of the data; variation in Latitude and Longitude directions. Green cells in the table shows the “center coordinates of each bin”.

13. Source Angular Apodization, Slide 5-13 Data Orientation Data is aligned with the local coordinate system of the surface Latitude = 0 Longitude = 270 Longitude 180 Longitude = 0 Longitude = 90 Latitude = 90

14. Source Angular Apodization, Slide 5-14 Bin Size Latitude = 0 Longitude = 270 Longitude 180 Longitude = 0 Longitude = 90 Latitude = 90 First “column” (Latitudes) located at 2.37 0 First “row” (Longitudes) located at 16.36 0

15. Source Angular Apodization, Slide 5-15 Example 1 LED example: HP HSMx-C650 Surface Mount LED – Rotational symmetry – Any surface of a source is easier to use

16. Source Angular Apodization, Slide 5-16 Example 1 – Data Input File Note that the LED intensity distribution is rotationally symmetric. Therefore, only one column of data is required to specify the variation in Latitude Max Value Min Latitude (“North Pole”) Min Value, Max Latitude (“South Pole”) 100 degrees latitude

17. Source Angular Apodization, Slide 5-17 Example 1 – Data Orientation Resulting intensity distribution using the 3D Raster Chart and a Polar Line Grid in the 3D View. Latitude bins=19, Longitude buns=29 Data is rotationally symmetric. Latitude values are duplicated (interpolation) around longitude angles. Picture above is only for illustrative purposes +Y +X

18. Source Angular Apodization, Slide 5-18 Example 2 Importing angular data from an IES file (hypothetical data is shown) – Use the IES Read utility to create an apodization file Polar wire grid illustration of the IES data using the “Source” (or global) coordinate system

19. Source Angular Apodization, Slide 5-19 Apodization Data This particular IES file has 171 horizontal angles and 171 vertical angles Note: The IES utility shown here is the latest version. Please request a copy if you like to try it.

20. Source Angular Apodization, Slide 5-20 Example 2 – Data Orientation Resulting intensity distribution using the 3D Raster Chart and a Polar Line Grid in the 3D View. Latitude bins=41, Longitude buns=41

21. Source Angular Apodization, Slide 5-21Conclusion Angular apodization provides you a flexible and fast method to create a wide variety of source models using their measured (or known) intensity distribution in LightTools Thanks you for your valuable time and support for ORA products!