Advanced Topics in Source Modelingmodeling of the source parameters in order to have the fabricated system agree with the design results. These These characteristics include the radiance

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Advanced Topics in Source Modeling

Mark S. Kaminski, Kevin J. Garcia, Michael A. Stevenson, Michael Frate, and R. John Koshel* Breault Research Organization, Inc.

Copyright 2002 Society of Photo-Optical Instrumentation Engineers. This paper will be published in the proceedings from the July 2002 SPIE Annual Conference and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of

the content of the paper are prohibited.

ABSTRACT Techniques to improve source modeling are presented: filament flux weighing, depositions on the arc envelope interior, and electrode degradation. Filament sources provide more light from the center in comparison to the ends. Additionally, the helix interior is hotter due to increased absorption, and thus the flux emission is greatest here. These effects for linear filaments are modeled in software with the ancillary use of camera images of lit appearance. The result is that the source luminance is more accurately modeled. This technique, called flux weighting, is described and software examples using reflectors are presented and compared to those that do not use flux weighting. Software models of arc sources that employ camera images of the arc provide accurate representations of the source radiance. However, these models do not include arc source aging. Aging effects include degradation of the electrodes and the depositions on the interior of the envelope. These phenomena lead to a decrease typically in the luminance from the source. Camera images of the lit and unlit appearance of arc sources are presented and their effect on the arc output is discussed. Additionally, software examples using reflectors are presented and compared to those that do not use these techniques. Keywords: Source Modeling, mathematical methods, incandescent sources, arc sources

1. INTRODUCTION Illumination systems depend greatly on the source characteristics, in fact, design of such systems requires accurate modeling of the source parameters in order to have the fabricated system agree with the design results. These characteristics include the radiance from the source, color output, geometry, and so forth. Depending on the design parameters and the source being used, neglecting any of these items can lead to output illumination distribution errors approaching 75% for the illumination system design.† These distribution errors affect, to name a few, the uniformity, transfer efficiency, and color at the target plane. Two examples are: filament-based sources and arc sources. Note that the errors listed before are for illumination system designs, not the source by itself. Radiance measurements for a source not included with other optical components are accurate, just being limited by the sampling of the radiance distribution.1 Such measurements that are included in an optical design do not account for source and optic interactions, which ultimately leads to errors. To study these errors, Advanced Systems Analysis Program (ASAP ) is used herein.2 Experience has shown that using a generic helical emitter for a filament-based source can lead to a 50% error when included in the optical system design. Including the geometry of the source can bring this error down to 15%. By making measurements of the radiance distribution with a goniometer setup, without inclusion of the source geometry in the illumination design, experience has shown upwards of a 25% error. Including both the geometry and luminance measurement the error can be reduced to a maximum of 5%. Of course, more careful modeling and measurements of the source emission leads to better accuracy. For an arc source, a generic cone, surface tube, or so forth can be used to model the emission. However, arc sources tend to have a “bowed” emission region (often called an “arc banana”), so the generic source model is a rather poor representation of an arc source. Depending on the actual characteristics of the arc, especially arc gap, pulse width, orientation, fill pressure, electrical characteristics; and the generic source parameters, one can obtain up to a 75% error

* [email protected]; phone: 1 520-721-0500; fax 1 520-721-9630; http://www.breault.com; Breault Research Organization, Inc., 6400 East Grant Road, Suite 350, Tucson, AZ USA 85715. † The errors quoted within this first section are derived from experience on proprietary projects not owned by BRO but modeled or designed by BRO. This leads to a limited body of actual references besides private communication that can be cited. These private communications will not be cited herein, but when possible actual references will be cited.


for the illumination system design. Including the radiance measurement leads to a reduction of the error to upwards of 25%, which agrees with the filament-based sources. Including solely the geometry of the arc source with a generic emitter will reduce the maximum error to 50%.3 As with incandescent sources, inclusion of both the radiance measurements and the geometry of the source will lead to a maximum error of 10%. The increase in error for arc sources in comparison to incandescent sources in our experience is due to the nature of the arcs – they tend to have less tolerance-to-fabrication error and operation and aging characteristics can dramatically affect performance. Analogous to filament sources, the error can be reduced with more careful modeling and measurements of the source emission. Thus, in order to model effectively an illumination system with optical design software, the most crucial parameter is the source model. Without accurate modeling of the source, the comparison between the design and actual may be lacking. Maximum errors of 5% with incandescent sources and 10% with arc sources may prove adequate (i.e., when the designer includes both the radiance measurement and the source geometry), but there are several applications where this maximum error will not prove satisfactory. Such applications include transportation external lighting, scanners, and precise uniform illumination (e.g., photo resist application). In these cases more accurate modeling of the source is required such that the source is not the limiting factor, but rather manufacturing tolerances. The same two examples discussed previously are used herein to highlight how improved modeling of the source leads to better modeling of the illumination system. Essentially, this paper is subdivided into two separate topics: modeling of filament-based sources and modeling of arc-based sources. Both lead to the same result – improved accuracy. In the next two sections, incandescent sources are described. The first describes how to model the source better, while the second shows examples of how the improved modeling increases accuracy. In order to better model the source a radiance measurement technique called flux weighting is described. Flux weighting removes the need for a suite of images of the filament emission, but rather a single image capture and knowledge about the emission can reduce the time to model but retain accuracy. The two sections following those describe arc source modeling. Once again, the first describes how to model the arc better, while the second provides examples. For arc sources two model improvements are discussed: inclusion of the interior deposits and aging affects. Both affect the radiance distribution, especially over the lifetime of the source. In both cases, the examples are compared to with and without the improvement of the modeling, and, then the affect of aging. Both are done with the inclusion of a parabolic reflector. The parabolic reflector is arbitrary, but it does display the interaction of the source with the optics. Finally, this paper ends with conclusions and a discussion of future improvements that can be done.

2. MODELING OF FILAMENT-BASED SOURCES The steps required to model a filament-based source such that the accuracy is maximized are: develop a geometrical model of the source, assign optical properties to the objects that comprise the source, experimentally measure the radiance (or luminance), and assign rays based upon the measurements. Fig. 1 shows a rendering of an HB3 bulb from the automotive headlamp industry. In this figure one can see the level of detail included in the model. The source can then be included in an illumination system design with one of two options: develop the ray set from the radiance measurement or apply the results from the radiance measurement to the developed emitter. In the former case, a series of images capture the radiance distribution of the source such that rays can be located in space due to the results of the measurements. These rays will be located with propagation directions also based on the measurements. The geometry of the source is not included in this first step since it has already been accounted for in the image captures. Upon tracing the rays out to their next intercept (e.g., reflector, target, etc.), the geometry is then included and the ray trace is completed. In the latter option, a single image capture of the filament allows the emitted flux from the filament to be weighted across its length and radius. The single image capture uses an assumed characteristic that angular emission from the emitter, even when weighted, is Lambertian in nature. If this property is not true for a source, then one must use the first method to determine the radiance distribution. This image capture is used to assign the flux emission of the already generated rays as a function of position. The assigned rays are then traced through the optical system. Typically a ray set is saved on the exterior of the bulb in order to speed up future ray traces. These saved ray sets can be called up upon demand, such that the initial complex and tedious ray trace through the bulb is only done once. The number of rays that is incident once again on the bulb is typically less than the size of the original ray set. Fig. 2 shows the ray trace from the filament, while Fig. 3 shows the ray trace through the entire bulb.


Fig. 1: Rendering of the HB3 automotive headlamp bulb.

Fig. 2: Ray trace from the filament. Fig. 3: Ray trace from the filament through the HB3 bulb.


There are numerous methods that one can assign the flux to the filament: uniform weighting, weighting along the length, weighting as a function of transverse direction (i.e., a radial distance from the axis of the filament), and combination of the above methods. Uniform weighting leads to the problems already discussed, especially non-uniformity at the target plane or, rather, a disagreement between the model and measurements. Flux weighting along the length of the source shows that the flux emission peak is located near the center of the filament. Thus an incandescent source better represents a point source than first anticipated. As a function of radius, the source emission for a given length is highest in the interior of the helical filament. The reason is that the source absorbs light emitted from regions within the helical coils. This absorption leads to a hotter filament in its interior, so the blackbody temperature is highest in this region. Finally, the last option means that the designer can include flux weighting along its length and as a function of radial position. Fig. 4 shows the single-image captures of the filament of the HB3 bulb when it is (a) unlit and (b) lit, and Fig. 5 shows the respective representations in software. In Fig. 5b it is evident that along the length of the filament that the center has a higher irradiance. Additionally, the interior emits more flux than the exterior. The image data is then used to assign the flux to the rays shown in Figs. 2 and 3. In this next section comparisons using flux weighting and not using it are made.

Fig. 4: Image captures of the (a) unlit and (b) lit filaments.

Fig. 5: Imports of the image captures of Fig. 4 into the ray-trace software for the (a) unlit and (b) lit HB3 filaments.

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(b)

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3. EXAMPLES WITH FILAMENT-BASED SOURCES 3.1 Comparison of the HB3 bulb with and without flux weighting In the first example, the assigned rays are traced from the filament with the rest of the bulb objects in position. Two cases are done: with and without the flux weighting described in the previous section. Without flux weighting the emission is uniform and Lambertian from the filament. With flux weighting the spatial emission is based on the measurements from Fig. 5b and the angular emission is Lambertian. The intensity distribution for the bulb is then determined. Fig. 6a shows the intensity distribution in direction cosine space for the case with no flux weighting, while Fig. 6b shows the intensity distribution in direction cosine space for the case with flux weighting. Fig. 7 shows relative difference between the two cases, such that the difference is ratio to the value of the flux-weighted case. Therefore, Fig. 7 has the units of percentage difference. Note that most of the flux is at higher angles (due to the filament orientation), but the difference is about 50%, while the peak error is just over 185% (toward the center of the intensity distribution). This error leads to inaccurate modeling of the source – flux weighting is required to model accurately the source.

(a) (b)

Fig. 6: Intensity distributions in direction cosine space (a) without flux weighting and (b) with flux weighting.

Fig. 7: Relative difference between the two intensity distributions shown in Figs. 6a and 6b. It is plotted in direction cosine space with the units being percentage difference relative to that of Fig. 6b.


3.2 Comparison of the HB3 bulb within a parabolic reflector with and without flux weighting The next step is to place the modeled HB3 bulb, with and without flux weighting, into an arbitrary parabolic reflector and determine the intensity distribution. The center of the HB3 filament is placed at the focus of the parabolic reflector and 1.1 million rays are traced. Fig. 8a shows the intensity distribution in direction cosine space when there is no flux weighting, while Fig. 8b shows the same when flux weighting is included. Note that the distributions appear to be the same, with the peak value being about 21% less in the case with flux weighting. Additionally, the flux-weighted case shows less flux at the perimeter of the intensity distribution. In other words, the flux-weighted case has a lower peak value but it has a more compact distribution. Fig. 9 shows the relative difference between the two cases shown in Fig. 8, where the difference is plotted relative to the flux-weighted case. Note that the error is upwards of 21% at the center of the distribution, while much greater errors exist in the aforementioned low-flux halo region. This amount of error means that non-flux-weighted designs will provide unsatisfactory representation of actual performance.

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Fig. 8: Intensity distributions in direction cosine space (a) without flux weighting and (b) with flux weighting.

Fig. 9: Relative difference between the two intensity distributions shown in Figs. 8a and 8b. It is plotted in direction cosine space with the units being percentage difference relative to that of Fig. 8b.


4. MODELING OF ARC-BASED SOURCES Improvements in arc source modeling are required due to their increased use in commercial sectors, for example automotive headlamps. Headlamps require a fair degree of accuracy (on the order of ±0.25 degrees for the intensity distribution) in order to meet governmental standards (e.g., SAE, ECE, and FVMSS). Failure to meet standards means the headlamps are not legal for road use; therefore, accuracy is a driving factor in headlamp design. The methods of Ref. [1] have been used effectively within the headlamp design community, but interaction between the source and the optics means that a geometrical model is imperative for the design process. The process to develop an accurate model of an arc source is the same as described in Section 2 in regards to filament-based source. First, a geometrical model of the source is developed. Second, optical properties to the objects within the model are assigned. These properties include, but are not limited to index of refraction, reflection, transmission, absorption, and scattering. Fig. 10 shows the rendering of the D2S automotive headlamp bulb used in this study. Next, the radiance measurement is made. Two techniques have been developed for this measurement. The first is the goniometer method of Ref. [1]. A series of images capture the spatial and angular emission characteristics of the source. These images are then stitched together to assign rays to the measured distribution. The second method uses a single-image capture while assuming rotational symmetry along a piecewise sampling of the emission distribution. In this case the Inverse Abel method, as described in Ref. [3] is used to generate the ray set. Fig. 11 shows the wireframe of the geometrical model of the D2S bulb and the resulting vertical segments that comprise the source emission when developed into a ray set. The vertical segments result due to the need to model the bowing of the arc as shown in Fig. 12. The bowing is a result of the various forces within the bulb when it is in operation. Each one of the disc segments (often denoted as “hockey pucks”) is symmetric around the local centroid of the emission pattern. Therefore, since a single image capture is being used to model this asymmetric distribution, one must capture this image such that the asymmetry is fully accounted. Thus one must capture a full view of the bowing of the arc. If there are additional asymmetries not in direct view of this image capture, then methods employing several image captures need to be developed. Finally, rays are assigned due to the measurement, as shown in Figs. 11 and 12. Note that some rays are generated directly outside the emission region (see Fig. 12 for the best visualization). These rays are due to reflection and scattering within the bulb, but they must be included in all modeling since they represent part of the actual radiance of the source. It is important to note that with either of the radiance measurement methods, one must not include all of the geometrical aspects of the bulb for the initial step of the ray trace. Optical properties such as reflection, transmission, and scattering for the entire bulb have already been captured in the image(s). The rays are then traced till they intercept the next object, and then the geometry of the bulb is inserted into the model. This method ensures that bulb interactions are included if light is re-incident upon it. Additionally, unrealistic rays must be removed from the models. Unrealistic rays are those generated within the electrodes or the like. In both radiance measurement methods such rays can be generated. This removal of rays is typically accomplished by inserting absorbing surfaces for the electrodes and similar constructs. Their optical properties are then altered upon completion of the first step of the ray trace. The next step is to model the deposits on the inside of the bulb and the effects of operation on the arc formation.

Fig. 10: Rendering of the D2S automotive arc lamp used within this study.


Fig. 11: The D2S bulb and the generated rays developed with the Inverse Abel method by sampling the source emission from a single image. Each one of the segments (often denoted as “hockey pucks”) is comprised of a set of rays generated uniformly around the local centroid of the emission. See Fig. 12 for a magnified view of the emission region.

Fig. 12: Magnified view of the D2S emission region. Note the segments in which rays are generated using the Inverse Abel method. Of special note is the bowed shape of the peak arc emission. The arc bow (often called “arc banana” is due to forces (e.g., convection) within the envelope when in operation.

5. EXAMPLES WITH ARC-BASED SOURCES

5.1 Modeling of the sodium deposits within the D2S arc source In Section 4 the basic model of the bulb is described in detail. It has been noted that such models still do not match experimental observations. Several reasons exist: poor modeling of the optical properties, inaccurate ray generation, and the lack of modeling all characteristics of the bulb. One immediate noted omission in the model is the presence of the salt lake, getter, or simply the deposits on the interior envelope of the bulb. One can observe its presence in Fig. 12 by noting the hemispherical area in the emission region where no ray generation is evident (i.e., beneath the bow, on the perimeter of the envelope as shown in Fig. 12). Such deposits exist in one form or another within an arc source. They block some light from passing through this region, so one must effectively model it to get accurate results. Fig. 13 shows a rendering of the salt lake for the D2S bulb. The inclusion of these objects and the assignation of optical properties are done by direct observation of the bulb and its emission characteristics and also by comparing the results using the Inverse Abel method to those obtainable from Ref. [1].


Fig. 13: Rendering of the emission region of the D2S bulb showing the inclusion of the deposit on the interior envelope of the bulb. Next, the intensity distribution for this bulb when inserted into a parabolic reflector was investigated. The center of the arc bow was positioned at the focus of the same parabolic reflector used in Section 3, and one million rays were traced. Fig. 14a shows the intensity distribution in direction cosine space for the case where the salt lake was not present, while Fig. 14b shows the analogous case when the modeled salt lake is present. Note that the peak intensity is in the negative-B direction, which is due to the presence of the salt lake and the standoff. A relative difference plot is shown in Fig. 15, whereby the percentage difference is shown relative to the model in Fig. 14b. The maximum error in directions showing useful flux is about 10%.

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Fig. 14: Intensity distributions in direction cosine space for the D2S bulb located at the focus of a parabolic reflector with (a) no sodium deposit present and (b) a sodium deposit present.


Fig. 15: Relative difference between Figs. 14a and 14b, whereby the percentage difference is plotted relative to that of Fig. 14b.

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Fig. 16: Images of the D2S emission region in an unlit state for (a) 0 hours and (b) 639 hours of operation. 5.2 Modeling of the aging of the D2S arc source It was noted during this process that the electrodes and interior surface of the bulb envelope changed over the duration of operation. Therefore, the bulb was left lit over 26.6 days (639 hours). It was only turned off in order to capture images of the bulb in an unlit state on approximately a daily basis. Additionally, the lit appearance of the arc was also captured on these occasions such that the Inverse Abel method of Section 4 could be implemented as required. Fig. 16a shows the unlit appearance of the bulb at 0 hours, while Fig. 16b shows the same at 639 hours. Note that the electrodes have degraded noticeably and that there appears to be a haze on the interior surface of the bulb envelope. Figs. 17a to 17d show the arc at 0 hours, 196 hours, 400 hours, and 639 hours respectively. There are subtle variations in the arc emission distribution between these four images. In order to better understand the impact of these subtle variations, the D2S bulb at 0 hours and 639 hours is included at the focus of the previously used parabolic reflector. Once again the center of each arc is placed at the focus of the parabolic reflector since it is evident that there is a slight jitter of the placement of the arc. This slight repositioning mirrors the ability of a user of such a system to dynamically adjust the illumination characteristics of the system. Upon completion of a one million ray trace, the intensity distributions for the cases shown in Figs. 17a and 17b were determined. Fig. 18a shows such in direction cosine space for Fig. 17a, while Fig. 18b shows likewise for Fig. 17d. Note that the distributions at first appear to be unchanged; however, there are substantial variations that are manifesting. Of note, the


on-axis value at 639 hours is reduced by 19%, the central spot is a bit smaller in subtense, and the peak has shifted more in the negative-B direction (i.e., in the negative vertical direction). Fig. 19 shows the relative difference plot between Figs. 18a and 18b, whereby the percentage difference is plotted relative to that of 0 hours of operation. The peak intensity region is around 40% less than in the 639 hour case. These changes are due to the size of the deposit increasing, a general hazing of the interior surface of the bulb envelope from electrode degradation, and a smoothing of the emission profile of the arc.

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(c) (d)

Fig. 17: Lit appearance of the arc at (a) 0 hours, (b) 196 hours, (c) 400 hours, and (d) 639 hours.

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Fig. 18: Intensity distributions in direction cosine space for the D2S bulb located at the focus of a parabolic reflector at (a) 0 hours and (b) 639 hours of operation.


Fig. 19: Relative difference between Figs. 18a and 18b, whereby the percentage difference is plotted relative to that of Fig. 18a.

6. CONCLUSIONS AND FUTURE IMPROVEMENTS The presented advanced topics in source modeling provide more accurate source representations. Flux weighting of incandescent sources offers in concert with a geometrical model a reduction of the error by from 25% to less than 5% (as determined herein: 3%). The website noted in Ref. [2] contains these flux-weighted source models. The arc source improvements including modeling of the interior deposit and the aging of the bulb show increased accuracy of 10% and 40% respectively. Once again it is the connection between the experimental measurement and the geometrical model that increases the accuracy. Also, the website noted in Ref. [2] contains these sources with modeled deposits. The increase in model performance is due in large part to the use of a single image capture. There is no need for expensive setups that require a number of images. One can use the known symmetries of the system and knowledge of the emission properties to reduce the overhead requirements. Finally, all cases involving the parabolic reflector are arbitrary, but similar results are expected for other reflector shapes. Future improvements will include flux weighting on toleranced filaments, color modeling of the emission, and modifications as required in the optical characteristics of the various objects.

REFERENCES

1. Radiant Imaging, 26425 NE Allen St., Suite 203, Duvall, WA 98019; www.radimg.com. 2. Advanced Systems Analysis Program (ASAP) is a trademark of Breault Research Organization, Inc., 6400 East

Grant Road, Suite 350, Tucson, AZ 85715; www.breault.com. 3. M. A. Stevenson, M. Cote, C. J. Campillo, D. G. Jenkins, “Computer simulation of asymmetric arc lamp volume

emitters,” Proc. Of Optical Design and Analysis Software, Ed. R. C. Juergens, Vol. 3780, pp. 93-102, SPIE, Bellingham, WA, 1999.

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Advanced Topics in Source Modelingmodeling of the source parameters in order to have the fabricated system agree with the design results. These These characteristics include the radiance