IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 29, NO. 5, OCTOBER 2001 695

Computer-Aided Reconstruction of Cathode ImagesObtained by High Speed Photography of High

Current Vacuum ArcsVasiliy P. Afanas’ev, Alexey M.Chaly, Alexander A. Logatchev, Sergey M. Shkol’nik, and Konstantin K. Zabello

Abstract—The images of the cathode obtained by high-speedphotography are ellipsoidal because they are taken at a small angle(about 10 ) to the cathode surface. For this reason, it is very diffi-cult, if at all possible, to draw conclusions about the spatial distri-bution of cathode spots and current density over the cathode sur-face. One may perform inverse parallel projection, but previouslyit was necessary to free the image from the noise of the interelec-trode plasma radiation and other noise sources. In this paper, wepropose a method of image filtering based on contours of equal in-tensity evaluation, with subsequent determination of the cathodespots distribution.

Index Terms—Cathode spots, image processing, vacuum arcs.

I. INTRODUCTION

H IGH-SPEED photography (HSP) is a very powerful toolfor the investigation of temporal behavior of high current

vacuum arcs. In earlier works [1], [2], HSP had shown that dif-ferent modes of an arc can be studied, and the influence of anaxial magnetic field on the modes’ existence limits was investi-gated. In those papers the analysis was based on the visible sizeof the arc channel, i.e., the discussion was conducted in termsof current density averaged over this size.

In [3], it was shown that even in modes where no evident con-traction exists, the heat load on the anode is distributed inhomo-geneously, and there are areas of considerable local overheating.The results of [4] demonstrate that in a diffuse mode, the dis-tribution of emission centers on the cathode of a high-currentvacuum arc and the heat load of the anode are inhomogeneous.

It is well known that a shorting of the current between acold cathode and vacuum arc plasma is “pointwise”—throughso-called cathode spots (CS, brightly luminous objects of verysmall size)—ensuring sufficient emission of electrons andplasma generation from electrode material. The distribution ofcathode spots is directly connected to the distribution of currentdensity. By proper selection of the exposure time, HSP framesadequately mirror the CS distribution over the cathode surface.

Unfortunately, the discharge geometry forces us to takephotos at small angles to the cathode surface, and the imagesof the cathode surface with spots are ellipsoidal with an axisratio of about 0.1. CS are masked by a thick layer of a radiating

Manuscript received September 18, 2000; revised July 5, 2001.V. P. Afanas’ev, A. A. Logatchev, S. M. Shkolnik, and K. K. Zabello are with

the A.F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, St.Petersburg 194021, Russia (afan@atlant.ru).

A. M. Chaly is with the Tavrida Electric Ltd., Moscow 123298, Russia.Publisher Item Identifier S 0093-3813(01)09252-9.

Fig. 1. HSP of a high current vacuum arc (negative, exposure 75�s). The arcstabilized by a homogeneous axial magnetic fieldI = 15 kA, B = 0:27 T.CuCr electrodes, diameter 30 mm, electrode gap 4 mm.

plasma. One should first extract the CS images from interelec-trode plasma radiation, and afterwards make inverse parallelprojection before drawing any valuable conclusion about theparameters of spots distribution. Inverse parallel projection ispossible if the center of projection and the angle of observationare known. It is possible to derive these parameters fromelectrode images obtained by filming the electrodes without anarc.

There are many evaluation-ready digital filters available forimage filtering (MATLAB tools, for example), but the plasmaradiation is inhomogeneous and the spatial spectra of the signal(cathode spots image) and noise (interelectrode plasma inho-mogenity and film grains) are overlapping. For these reasonsour attempts to use standard filters did not lead to valuable andreproducible results. So, we were forced to devise an originaltechnique of image filtering, taking into account not only thesizes of luminous objects, but also their relative brightness. Inaddition, it was necessary to develop a method of approxima-tion of the cathode spots distribution.

II. CATHODE SURFACE IMAGE FILTERING

DETERMINING CS COORDINATES

An example of the HSP of the high-current vacuum arc is pre-sented in Fig. 1. The experiment is described in [5]. The originalnegative was scanned with a resolution of 1800 dpi. One can seethe cathode surface with spots at the bottom of the image. Theanode surface (invisible) is at the top of the image. One can alsosee the inhomogeneous plasma radiation, strongly masking thespots, in spite of the fact that the filming of an arc was executedwith a specially fitted glass filter. The goal is to remove plasmaradiation, to estimate the positions of cathode spots, and to makethe inverse parallel projection.

Fig. 2 shows the HSP frame with an ellipse superimposed,the latter being in accordance with the cathode surface. We ob-tain the ellipsoid parameters of the original image from inde-pendent measurements of the electrode without discharge. All

0093–3813/01$10.00 © 2001 IEEE

696 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 29, NO. 5, OCTOBER 2001

Fig. 2. HSP frame (negative, exposure 75�s) with an ellipse superimposed(axis labels are in pixels). The arc is stabilized by a homogeneous axial magneticfield I = 11:3 kA, B = 0:27 T. CuCr electrodes, diameter 30 mm, electrodegap 4 mm.

dimensions are expressed in pixels (one pixel on the map cor-responds to m on the cathode, in a direction of a largeaxis of the ellipse). Rotation of ellipsoid axis about-axis of theimage occurs in HSP and scanning processes. The size of a CSis m [6]. The resolving power of the HSP-camerais insufficient to record the object of such size without distortionduring filming of entire cathode with the size of several centime-ters. CS images can be considered as point objects distorted byan apparatus function of the HSP-camera.

As a first step of image processing, we build the equal inten-sity contours of the image. The procedure of evaluating equalintensity contours is of the interpolation type and, thus, con-tours are not bound to the integer values of coordinates. Ac-cordingly, perimeter of contours not necessarily expresses byintegers. Since the image is very inhomogeneous, the numberof contours to be constructed is very large—about 20 000. Thefiltering method is based on rejection or acceptance of each in-dividual contour in accordance with its length (perimeter forclosed contours). The low spatial frequency of plasma radiationproduces long and open contours, which we reject in the be-ginning. The middle and high spatial frequency parts of plasmaradiation produce, as a rule, contours having a few other con-tours within them, and the filtering also rejects such objects.

In other words, the image of the cathode surface can be con-ceived of as a map of a “mountainous country” with contourlines. The procedure is that we only deal with areas of rathergreat local height differences, independently of their absoluteheight, and we reject “mountains” that are too smooth.

It is assumed that every system of enclosed contours isassociated with one cathode spot. We define the perimeter ofthe largest contour in this system as the perimeter of the spot.“Spots” of very small perimeter are produced mainly by thegraininess of the photographic film, so they must be rejectedtoo. (For more details, see the following section.) The center ofthe smallest contour in the system is associated with the spotposition.

Figs. 3 and 4 illustrate the above-mentioned procedure. It ispractically impossible to map the outcome of a contouring, asthe full number of contours is very large and their structure iscomplex. Fig. 3(a) and (b) present the fragment of Fig. 2 be-fore and after filtering, respectively. The result of filtering ofthe overall cathode surface image (Fig. 2) is shown in Fig. 4.

For inverse parallel projection, we rotate the image to adjustthe major axis with the -direction, put the ellipsoid center intothe origin, and change the-coordinates of spots centers in ac-

Fig. 3. Equal intensity contours of the fragment of the image shown in Fig. 2Individual contours can be seen (axis labels are in pixels). (a) All contours(b) Accepted contours after filtering procedure.

Fig. 4. Accepted contours after filtering procedure of the image shownin Fig. 2.

cordance with major to minor ellipsoid axis ratio. The result ofinverse parallel projection of the image shown in Fig. 4 is pre-sented in Fig. 5. The positions of CS are marked by squares.

III. V ERIFICATION OF THEMETHOD

We have performed a series of test evaluations of images inorder to make sure that the presented method solves the image-processing task adequately. The optimal values for some param-eters in the contour treatment program were found, in particular,maximum length of an accepted contour is pixels. Thestability of the results with respect to these parameter variationswas verified.

For example, Fig. 6 illustrates the selection of the minimumsize of an object recognized as a cathode spot. The perimeterdistribution histogram of all detected objects (“spots”) obtained

AFANAS’EV et al.: COMPUTER-AIDED RECONSTRUCTION OF CATHODE IMAGES 697

Fig. 5. Reconstructed cathode spots positions.

Fig. 6. Histograms of “spot” perimeters (p-pixels). (a) “Spots” from 6 frames,(b) Objects from film veil (background).

as a result of treatment of six HSP frames is shown in Fig. 6(a).We see two reference groups of objects, dimensionedpixel and pixel, and uniformly distributed objects oflarger size. The rise of a histogram to the maximum value of theperimeter (20) is explained by underestimate of the largest spotssize as a result of removing long contours.

In Fig. 6(b), a similar histogram is obtained on the part offilm veil (background, where there are no spot images). Thishistogram was obtained at substantially smaller splitting step ofan image intensity and allows us to judge the specific sizes ofheterogeneity of photographic density caused by the grains offilm. On this histogram, we see two groups of objects also, withperimeter and pixel. On the basis of these his-tograms, we have defined that it is possible to consider objectswith a perimeter less than 7.5 pixels such as grains of a film,and larger such as CS. Thus, we are compelled to discard thesmall-sized CS, which cannot be separated from noise.

Fig. 7. Dependencies of the quantity of spotsNNN on frame numbernnn in thedeveloped discharges at the same conditions.

Fig. 7 illustrates the dependence of quantity of spotsin thedeveloped discharge on frame numbers. The features of theoptical scheme of high-speed photography explain the distinc-tion between even and odd frames. HSP-camera (“SFR-1”) ex-ecutes filming on a motionless film, the time sweep is made bya rotating mirror with the help of a system of diaphragms andlenses, which form a system of light shutters for each frame.The successive frames are located on the film in two rows-inone even, in the other odd-where the even and odd frames beingtaken at slightly different angles to the electrode surface. Wherethe angle is less, the image is stronger compressed, and, there-fore, it is more difficult to resolve the spots. The values obtainedfor the average current per spot (about 35A for CuCr) are in ac-cordance with known data.

The optimal scanner resolution and film processing regimeswere also determined. As the result, we claim now that wecan obtain the number of spots with an accuracy of approxi-mately 5%–10%, if the mean current density does not exceed

kA/cm .

IV. A PPROXIMATION OF THECS DISTRIBUTION

The CS distribution density may be estimated, for example,by counting the spot number in regions of equal area. However,this procedure gives only a very rough estimate. Therefore, wepropose to use a procedure that is based on Delaunay triangula-tion and Voronoi diagrams [7], [8]. For each CS, one can drawa boundary enclosing all the intermediate points lying closer tothis CS than to other spots. Such a boundary is called a Voronoipolygon, and the set of all Voronoi polygons for a given CS setis called a Voronoi diagram.

After building the Voronoi diagram (Fig. 8), for the cathodesurface, we can estimate the cathode spots distribution densityas a quantity that is inversely proportional to the area of respec-tive polygon. Since the camera delivers time-resolved data, wecan make a movie of the current density distribution, thus we areable to observe spot dynamics during the discharge evolution.

V. COMPARISON OF THERESULTS OFIMAGE PROCESSING

WITH THE PICTURES OFELECTRODEDAMAGE

In [4], the high-current vacuum arc on CuCr electrode undereffect of a homogeneous axial magnetic field was investigated.The correlation of the CS density distributed over the cathodebutt with the picture of erosion damage of electrodes is of in-terest. We used the above described image processing for HSPframes for the modes investigated in [4]. It is necessary to takeCS distribution averaged for sufficiently long-time period, as

698 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 29, NO. 5, OCTOBER 2001

Fig. 8. The Voronoi diagram for spots from one HSP frame.

Fig. 9. Arc stabilized by a homogeneous axial magnetic fieldI = 11:3 kA,B = 0:4 T. Electrodes: CuCr, diameter 30 mm, electrode gap 4 mm.(a) Cathode spots distribution density reconstruction averaged over 15 frames(� 1:1 ms). The hole in the center is an image of the triggering hole in thecenter of the cathode. (b) Photo of cathode erosion damages after arcing.

the electrodes accumulate the overall discharge pulse action. Anexample of the resulting cathode image is shown in Fig. 9(a),where the image is averaged over 15 sequential frames (1.1 ms).One can see that a CS distribution density on the cathode of ahigh-current vacuum arc in a rather strong axial magnetic fieldis essentially nonhomogeneous. The features, characteristic toelectrode erosion damage shown in Fig. 9(b), are visible in thereconstructed picture of cathode spots distribution density. Seealso Fig. 5 in [4].

VI. CONCLUSION

We consider that the proposed method of image filtering andprocessing allows us to estimate not only the mean value of thecurrent density in the arc channel, but also the cathode spot dis-tribution on the cathode. The obtained distributions of cathodespots are in good agreement with a picture of electrode erosiondamage.

REFERENCES

[1] J. V. R. Heberlein and J. G. Gorman, “The high current metal vapor arccolumn between separating electrodes,”IEEE Trans. Plasma Sci., vol.PS-8, pp. 283–288, Dec. 1980.

[2] M. B. Schulman, P. G. Slade, and J. V. R. Heberlein, “Effect of an axialmagnetic field upon the development of the vacuum arc between openingelectric contacts,”IEEE Trans. Plas. Sci., vol. 16, pp. 180–189, Apr.1993.

[3] K. Watanabe, E. Kaneco, and S. Yanabu, “Technological progress ofaxial magnetic field vacuum interrupters,”IEEE Trans. Plasma Sci., vol.25, pp. 609–616, Aug. 1997.

[4] A. M. Chaly, A. A. Logatchev, S. M. Shkol’nik, and K. K. Zabello, “Cur-rent density on the cathode of high current vacuum arc stabilized by axialmagnetic field,” inProc. 19th Inter. Symp. Discharges and Electrical In-sulation in Vacuum, vol. 1, Xi’an, China, 2000, pp. 286–289.

[5] A. M. Chaly, A. A. Logatchev, and S. M. Shkol’nik, “Cathode processesin free burning and stabilized by axial magnetic field vacuum arcs,”IEEE Trans. Plasma Sci., vol. 27, pp. 827–835, Aug. 1999.

[6] G. A. Mesyats,Cathode Phenomena in a Vacuum Discharge: The Break-down, the Spark and the Arc. Moscow, Russia: Nauka, 2000.

[7] J. O’Rourke,Computational Geometry in C. Cambridge, U.K.: Cam-bridge Univ. Press,, 1994.

[8] S. J. Fortune, “A sweepline algorithm for Voronoi diagrams,”Algorith-mica 2, pp. 153–174, 1987.

Vasiliy P. Afanas’ev was born in Likchoslavl,Russia, in 1946. He graduated from the PhysicalFaculty of Leningrad State University, and receivedthe Candidate of Physical-Mathematical Sciencesdegree from A. F. Ioffe Physical-Technical Institute,U.S.S.R. Academy of Sciences, Leningrad, U.S.S.R.,in 1970 and 1976, respectively.

Since 1970, he has been with the A. F. IoffePhysical-Technical Institute, Charged ParticlesOptics Group. He has been with the laboratory ofLow Temperature Plasma Physics since 1984. His

research interests include the study of various electron-optics devices, plasmadynamics, and nonequilibrium plasma thermodynamics in connection withhigh-current arcs.

Alexey M. Chaly graduated from the Institute of Industrial Devices, Sevastopol,Russia, and received the D.S.E. degree from the U.S.S.R. (now Russian) Elec-trotechnical Academy, in 1982 and 1997, respectively.

In 1982, he joined a scientific laboratory involved in the development ofvacuum circuit breakers and the investigation of switching phenomena. In 1990,he became the General Manager of Tavrida Electric, Moscow, U.S.S.R. (Russia),a company which specializes in the development and production of highly so-phisticated switching equipment.

Alexander A. Logatchev was born in Leningrad,U.S.S.R., in 1964. He graduated from the PhysicalFaculty of Leningrad State University in 1987. Hisspecialization was in optics and plasma physics.

Since 1987, he has been with the A. F. IoffePhysical-Technical Institute, Russian Academy ofSciences, Leningrad, U.S.S.R., in the Laboratoryof Low Temperature Plasma Physics. Currently, hisresearch interests include the physical investigationof high-current vacuum arc.

AFANAS’EV et al.: COMPUTER-AIDED RECONSTRUCTION OF CATHODE IMAGES 699

Sergey M. Shkol’nik was born in Leningrad,U.S.S.R., in 1946. He graduated from the PhysicalFaculty of Leningrad State University, and receivedthe Candidate of Physical-Mathematical Sciencesdegree from A. F. Ioffe Physical-Technical Institute,U.S.S.R. Academy of Sciences, Leningrad, U.S.S.R.,in 1970 and 1979, respectively.

Since 1970, he has been with the A. F. IoffePhysical-Technical Institute, Laboratory of “LowTemperature Plasma Physics.” He has been the Headof “Electrode Phenomena” group since 1985. His

research interests include the study of electrode phenomena in high-currentlow and atmospheric pressure discharges and vacuum arcs, with considerableattention given to the development of highly ionized dense plasma diagnosticsespecially by means of electric probes. In recent years, he has also taken partin the investigations of the discharge with liquid non-metallic electrodes in airat atmospheric pressure.

Konstantin K. Zabello was born in Leningrad,U.S.S.R., in 1976. He received the B.S. and M.S.degrees from the Radiophysics Faculty of St. Peters-burg State Technical University in 1997 and 1999,respectively. He is currently a postgraduate student atthe A. F. Ioffe Physical-Technical Institute, RussianAcademy of Sciences, St. Petersburg, Russia, in theLaboratory of Low Temperature Plasma Physics.

His research interests include the investigation ofhigh-current vacuum arc.