Modeling of three-dimensional camera imaging in a tokamak torusP. H. Edmonds and S. S. Medley Citation: Review of Scientific Instruments 68, 918 (1997); doi: 10.1063/1.1147769 View online: http://dx.doi.org/10.1063/1.1147769 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/68/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Upgrade of the infrared camera diagnostics for the JET ITER-like wall divertora) Rev. Sci. Instrum. 83, 10D530 (2012); 10.1063/1.4740523 Three-dimensional confocal thermal imaging using anti-Stokes luminescence Appl. Phys. Lett. 87, 023901 (2005); 10.1063/1.1993761 High definition imaging in the Mega Amp Spherical Torus spherical tokamak from soft x rays to infrared (invited) Rev. Sci. Instrum. 75, 4069 (2004); 10.1063/1.1789583 Infrared camera diagnostic for heat flux measurements on the National Spherical Torus Experiment Rev. Sci. Instrum. 74, 5090 (2003); 10.1063/1.1623625 Three-dimensional visualization for everyone Comput. Phys. 12, 346 (1998); 10.1063/1.168694

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Modeling of three-dimensional camera imaging in a tokamak torusP. H. EdmondsFusion Research Center, University of Texas at Austin, Austin, Texas 08543

S. S. MedleyPrinceton Plasma Physics Laboratory, Princeton, New Jersey 08543

~Presented on 15 May 1996!

A procedure is described for precision modeling of the views for imaging diagnostics monitoringtokamak internal components, particularly high heat flux divertor components. Such modeling isrequired to enable predictions of resolution and viewing angle for the available viewing locations.Since oblique views are typically expected for tokamak divertors, fully three-dimensional~3D!perspective imaging is required. A suite of matched 3D CAD, graphics and animation applicationsare used to provide a fast and flexible technique for reproducing these views. An analytic calculationof the resolution and viewing incidence angle is developed to validate the results of the modelingprocedures. The tokamak physics experiment~TPX! diagnostics1 for infrared viewing are used as anexample to demonstrate the implementation of the tools. As is generally the case in tokamakexperiments, the available diagnostic locations for TPX are severely constrained by accesslimitations and the resulting images can be marginal in both resolution and viewing incidence angle.The procedures described here provide a complete design tool for in-vessel viewing, both forcamera location and for identification of viewed surfaces. Additionally, these same tools can be usedfor the interpretation of the actual images obtained by the diagnostic cameras. ©1997 AmericanInstitute of Physics.@S0034-6748~97!64301-4#

I. INTRODUCTION

In divertor tokamaks, the high heat loads on the divertortargets require continuous temperature monitoring to antici-pate and correct for any damaging fault conditions.2,3 Thismonitoring is often done using infrared cameras opticallycoupled to imaging elements located inside the vacuum sys-tem and viewing through penetrations in the plasma facingcomponents. An important requirement is that the cameras beoptimally located in order to allow as complete view of thedivertor structure as possible, with sufficient resolution thatthe various fault conditions can be distinguished. Viewingangles are usually limited by the divertor structure itself andother internal structures.

A procedure for generating images showing both theviews accessible for arbitrary camera locations and for quali-tatively estimating the appropriate viewing resolution andincidence angles using commonly available DOS base three-dimensional~3D! computer aided design, graphics, and ani-mation applications is described. A detailed user guide to thesoftware programs used in this article is available in an ex-panded report.4

II. OVERVIEW

The aim of this work is to provide a convenient tech-nique for displaying camera views of in-vessel components,particularly divertors, and to determine the expected resolu-tion and viewing angles for the various surfaces. The proce-dure is to import a 3D model of the relevant tokamak struc-tures into a 3D modeling application. In the application, a‘‘spotlight’’ is positioned at the camera location and thisspotlight projects a pattern which exactly represents the cam-era field of view. Projections more or less perpendicular tothe divertor surface are generated using viewing tools from

the application. The views of these projected images thenshow the areas that are visible from the various camera lo-cations and identify the achievable resolution and imagequality. A simplified drawing of the TPX vacuum vessel,ports, limiter, and divertor structures was made usingAutoCad.5 This drawing was used as the starting point forthe study. The divertor and limiter outlines were lofted into3D shapes. The drawing is shown in Fig. 1 which includesthe poloidal location of the imaging optics used in this study.

This drawing was imported into the graphics and anima-tion application, 3D Studio.6 The procedure used in thisstudy is to represent the imaging systems in the experimentwith spotlights which project either a checkerboard or anannular pattern. A typical view, from the spotlight location,of a checkerboard pattern is shown in Fig. 2. If a diagnosticcamera was located at the same place as the spotlight in themodel, there is an exact correlation between the location,shape, and size of the pattern and the camera image, assum-ing that the field of view is the same in both cases. Forinstance, if the pattern is 32 squares on a side and the cameradiode array is 512 pixels square, then each pattern squarecorresponds to 16 pixels.

The images in 3D Studio are obtained by appropriatelygenerating a view, defined in the application by a ‘‘camera’’and then rendering the resulting image. The images correctlyindicate both perspective and shadows and the projected im-age of the spotlight represents the image that would beviewed by a real camera in the experiment. To indicate ex-pected viewing areas and resolutions, the 3D Studio camerawas placed so as to view normal to the relevant divertorsurface. Scale was indicated in the original 3D model byappropriate markers. In order to view the inner divertor, thecamera needs to be located outside the divertor structure andhas to see through the outboard divertor. In 3D Studio, a

918 Rev. Sci. Instrum. 68 (1), January 1997 0034-6748/97/68(1)/918/4/$10.00 © 1997 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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surface can be constructed that is transparent to viewing butprojects shadows. Multiple spotlights can be installed so thatthe projected patterns which represent the areas visible forcameras are located at the corresponding positions. In addi-tion, spotlights can be added at different toroidal locations toindicate the extent of toroidal coverage.

III. MEASUREMENT OF IMAGE RESOLUTION ANDVIEWING INCIDENCE ANGLE

In order to further quantify the image resolution, thesquare checkerboard projector pattern was replaced with anarray, 64 on a side, of annuli. As an example, the upper panelin Fig. 3 shows the rendered image obtained with spotlightNo. 2. The 3D Studio camera is located at the same verticalelevation as the divertor and the camera views from insideoutward. The image projected onto the outboard divertor cy-lindrical plate is limited to a toroidal angle of less than be-tween 150° and 140° by the self-shadowing and tangency ofthe divertor viewing line. The view from about 120° to 100°is gradually shadowed by the inner baffle and is cut off atabout 100° by the inner divertor and limiter shadow.

For analysis, the length of the long and short axis of eachpattern were measured and, assuming the individual patternsto be ellipses, the individual pattern centers, axis lengths, andaspect ratios calculated. Taking the length of the long axis ofeach ellipse,l, as the appropriate dimension, the resolution,r, is defined asr5l3Ncheck/Npixel , whereNcheck is the num-ber of patterns on one side of the checkerboard,Npixel is thenumber of pixels along one side of the camera imaging array,and the field of view of the projected pattern matches that ofthe camera.

The angle of incidence is defined asu, where cosu5hand h is the aspect ratio of the ellipse, always taking thevalue less than unity. For normal incidence,u50° and fortangential incidence,u590°.

In order to calculate the resolution and the viewingangle, the coordinates of the ends of each axis of the pro-jected ellipse were hand digitized from the GraphicConvertordisplay and entered into an EXCEL spreadsheet. The coordi-nates of each pattern center, the length of each axis and theresolution and normal incidence angle for each pattern werethen calculated. The coordinates of each pattern center wereincluded in a scale AutoCad drawing of the panoramic imageand the resolution and incidence angle entered at each coor-dinate point. The set of contour plots obtained are shown inFig. 3 for the resolution~center panel! and for the incidenceangle~lower panel!. Units of resolution are inches. For muchof the toroidal range of view, only one or two annuli arecomplete and only a single data point is available. For theselocations, the contour lines are clipped short and do not nec-essarily indicate a direction. The accuracy is estimated atabout 25%. The bold outline represents the boundary of theprojected pattern. This boundary extends from about 100° to145°, although the bottom of the view is clipped between100° and 120°.

FIG. 1. Developed 3D drawing showing locations of the IR cameras prior toloading into the 3D Studio graphics application.

FIG. 2. View of spotlight No. 2 showing the projected image of a 32332square checkerboard.

FIG. 3. Mosaic reconstruction of a panoramic view of the outer limiter withspotlight No. 2 and a 64 element annular projector image~top panel!. Con-tour plots of the resolution~center panel! and incidence angle~lower panel!corresponding to this image.

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IV. ANALYTIC CALCULATION OF RESOLUTION

In order to validate the resolution and viewing incidenceangle results, an analytical calculation of the image was de-veloped. The calculation projects the divertor surface coor-dinates onto the imaging plane and is applicable to any casewhere an array describing the divertor surface can be con-structed. The calculation is applied to the case described inSec. III.

Consider the geometry shown in Fig. 4. If the angle be-tween ther pixel sight line ~coordinatesv,u on the imageplane, viewing the pointn on the divertor surface! and thecamera sight line isf, then for an elemental angle about thissight line,df, the ellipse projected onto the image plane hasa long axis of length given by

a5F3df3A11tan2 g cos2 f

11tan2 g,

whereF is the distance from the camera lens to the imageplane andg is the angle between the surface normal at thedivertor (np) and the line from the camera axis to the pixelr , ~or! projected along the camera sight line (op).

In order to avoid the complication of calculating theangleg, which requires a description of the camera orienta-tion, the radical will be ignored. This at most underestimatesthe resolution for a corner pixel by about 10% for the camerafield of view of C542° described here. Similarly, if theangle between the sight line and the normal to the divertorviewing point is u, the larger axis of the ellipse projectedonto the divertor surface by this elemental angle isb5L3df/cos~u!, whereL is the distance from the camera pointto the viewing point on the divertor (n). Then the ratio of theimage to pixel size,b/a5L/~F3cosu!. Assume a squareimage array 23N pixels on a side. Then the length of asingle pixel is l p5F3tan~C/2!/N. And finally, the resolu-tion, r, which is defined as the image of a single pixel pro-jected onto the divertor, is given by

r5L3tan~C/2!

N3cosu.

A program was written to calculate the values ofr, u,andf for an equally spaced grid on the surface of the outer

divertor for the same conditions used for the resolution cal-culation described in Sec. III. The analytic calculation givesno information on the viewed image and the array limitswere taken from Fig. 3. The results of the calculation areshown in the contour plots in Fig. 5 for the resolution and forthe viewing angle. The contours are essentially straight orslowly curving lines. The structure or meanders are a conse-quence of the spline fits used by the contour generating pro-gram and should be disregarded. These figures should becompared with Fig. 3. For most of the range, the agreementis excellent for both the resolution and for the angle of inci-dence. The procedure described above can readily be ex-tended to include the resolution expected for any surfacegeometry. This calculation combined with the ability of the3D visualization procedure to indicate the range of view pro-vides a complete solution to the camera view problem.

V. CONCLUSIONS

The procedures described here provide a fast and flexibletechnique for developing detailed images of 3D cameraviews of the tokamak interior. From these images, reason-ably accurate estimates of image resolution and viewingangles of incidence may be obtained. The corresponding ex-perimental problem of interpreting the camera views cansimilarly be solved by this technique.

An analytic solution was developed for interpretingviews of more complex surfaces and for higher precisionmeasurements. The results of this calculation were comparedwith one set of results from the imaging technique and werein good agreement.

The combination of the 3D view generated by these pro-cedures and the analytical resolution and viewing incidenceangle obtained from the analytic calculation provide a com-plete solution to the viewing diagnostic design requirement.

FIG. 4. Geometry details for calculation of image resolution and viewingangle.

FIG. 5. Contour plots of the resolution~upper panel! and the viewing inci-dence angle~lower panel! for a camera located at position No. 2 with a fieldof view of 42°.

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ACKNOWLEDGMENTS

This work was performed for the TPX project and wassupported by the U.S. Department of Energy under ContractNo. DE-AC02-76CH03073. The authors would like to thankEmilia Solano and Bill Craven, University of Texas FusionResearch Center, and Thorsten Lemke, author of GraphicConverter for their help in this study. The assistance Z. Sim-pson and B. Garland, Austin, Texas in applying the 3D Stu-dio software in this study is gratefully acknowledged.

1S. S. Medley, Rev. Sci. Instrum.66, 297 ~1995!.2R. C. Davidson, R. J. Goldston, G. H. Neilson, and K. I. Thomassen, Phys.Plasmas2, 9 ~1995!.

3P. H. Edmonds, S. S. Medley, K. M. Young, G. H. Neilson, R. J. Goldston,M. G. Bell, D. W. Johnson, F. M. Levinton, G. Renda, G. Gettelfinger, N.L. Bretz, and S. J. Zwelben, Proceedings of the 22nd European PhysicalSociety Conference on Controlled Fusion and Plasma Physics,Bournemouth, United Kingdom, 3–7 July 1995~unpublished!, Vol. 19C,p, III-397.

4P. H. Edmonds and S. S. Medley, PPPL-3187, May, 1996~unpublished!,p. 23.

5AutoCad Version 12, Autodesk Inc.63D Studio release 4c1, Autodesk Inc.

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