Bernshtejn, L I

Kharitonov, V M

Klevalin, V A

Petrakov, A V

CERN Document Server

CERN LIBRARIES, GENEVA CM-P00100730 EREVAN PHYSICS INSTITUTE SCIENTIFIC REPORT EFI-18(73) EXPERIMENTAL DETERMINATION AND ANALYSIS OF THE GEOMETRICAL DISTORTIONS IN THE PICK-UP TUBE OF A TELEVISION SYSTEM FOR MEASURING TRACK CO-ORDINATES IN A SPARK CHAMBER L . I . Bernsh te jn , V.A. K leva l in , A.V. Petrakov and V.M. Kharitonov Erevan 1973 Trans l a t ed a t CERN by R. Luther ( O r i g i n a l : Russian) Not r ev i s ed by t h e T r a n s l a t i o n Service (CERN Trans . 73-5) Geneva June 1973 - 1 -UDK 5 3 9 . 1 . 0 7 4 . 2 7 : 5 3 . 0 8 7 . 4 / 9 S c i e n t i f i c Repor t EF1-18(73) Au tho r s and t i t l e a s o v e r l e a f . The e f f e c t of s p e c i f i c d i s t o r t i o n s on t h e t r a j e c t o r y of a v i d i c o n ' s s c a n n i n g beam i s i n v e s t i g a t e d . E x p e r i m e n t a l d a t a , o b t a i n e d by m e a s u r i n g t h e c o - o r d i n a t e s of a p r e c i s i o n t e s t c h a r t w i t h t h e t e l e v i s i o n sy s t em, a r e used t o d e t e r m i n e n o t on ly t h e s y s t e m a t i c e r r o r and t h e g e o m e t r i c a l d i s t o r t i o n s of t h e r a s t e r b u t a l s o t h e o r d e r of t h e a p p r o x i m a t i n g po lynomia l and t h e r e q u i r e d f r e q u e n c y f o r r e - c a l i b r a t i n g t h e t e l e v i s i o n s y s t e m . Erevan P h y s i c s I n s t i t u t e Erevan 1 9 7 3 . Owing to a number of distortions, the vidicon beam shifts irregularly across the target: depending on the shift, components of t h e s econd , t h i r d o r h i g h e r o r d e r s o c c u r . T h i s g i v e s r i s e t o a s y s t e m a t i c e r r o r which must be t a k e n i n t o a c c o u n t i f c o - o r d i n a t e s a r e t o be measured w i t h t h e n e c e s s a r y a c c u r a c y by t h e t e l e v i s i o n s y s t e m . Among t h e most s i g n i f i c a n t c a u s e s of d i s t o r t i o n a r e t h e following: 1 . n o n - l i n e a r i t y of t h e d e f l e c t i o n c u r r e n t ; 2 . t a r g e t s which a r e n o n - s p h e r i c a l and n o t p e r p e n d i c u l a r t o t h e a x i s of t h e p i c k - u p t u b e ; 3. p o t e n t i a l f i e l d of t h e unscanned p a r t of t h e t a r g e t a t t h e edges of t h e r a s t e r ; 4. non-uniformity of the deflecting magnetic field, misalignment of the tube, focussing and deflection system, optics, etc. - 2 -L e t us c o n s i d e r t h e e f f e c t of t h e above f a c t o r s and t h e methods f o r d e t e r m i n i n g and ta lc ing i n t o a c c o u n t g e o m e t r i c a l d i s t o r t i o n . 1 . D e f l e c t i o n c u r r e n t i n t h e d e f l e c t i o n c o i l of t h e p i c k - u p t u b e . The t i m e - b a s e g e n e r a t o r n o r m a l l y c o n s i s t s of a s a w - t o o t h v o l t a g e g e n e r a t o r and an o u t p u t s t a g e c o m p r i s i n g a power a m p l i f i e r o p e r a t i n g on the deflection coil. There is no problem in building a saw-tooth voltage generator with low non-linearity (hundredths of a per cent)/1/ and it is therefore assumed that asaw-tooth trapezoidal voltage is supplied to the deflection coil (we shall ignore the distortions i n t h e o u t p u t s t a g e ) . In t h i s c a s e , as was shown i n / 2 / , t h e c u r r e n t / 2 / e q u a t i o n may be e x p r e s s e d as f o l l o w s ; where K = Im T P i s t h e r a t e of v a r i a t i o n of t h e c u r r e n t , τa = RCk i s t h e t ime c o n s t a n t , Ck i s t h e c a p a c i t a n c e of t h e d e f l e c t i o n c o i l , R comprises the core loss resistance and the shunt resistance, Im is the maximum deflection current and Tp i s t h e scan p e r i o d . I n t h i s c a s e t h e beam ' s v e l o c i t y a c r o s s t h e t a r g e t w i l l be where Ro i s t h e r a d i u s of d e f l e c t i o n , α i s t h e a n g l e of d e f l e c t i o n and ω i s t h e beam ' s a n g u l a r v e l o c i t y . - 3 -I t may be seen ( f i g . 1) t h a t , due to the ex i s t ence of a considerable s e l f - c a p a c i t a n c e i n the c o i l and to the l im i t ed power capabilities of the saw-tooth voltage generator, the current may be substantially non-linear as it contains components of the second or h igher o rde r s . The maximum d i s t o r t i o n s occur a t the i n i t i a l s tage of the curve and are caused by t r a n s i e n t processes in the d e f l e c t i o n c o i l . The dura t ion of a t r a n s i e n t process i s determined by the parameters of the d e f l e c t i o n c o i l and t3 ≈ 3 τa. In the case of the widely-used focussing and d e f l e c t i o n system FOS-35, Ck = 150 picofarad and R = 20 kohm. Therefore, τa =3 µ sec and t3 = 9 µsec. In practice, the fly-back time is normally designed to be s e v e r a l t imes g r e a t e r than t3 so t ha t the maximum d i s t o r t i o n s occur dur ing f ly -back . The e r r o r due to n o n - l i n e a r i t y of the d e f l e c t i o n cur ren t was investigated by several authors/3-5/ and depends on the position of the object in the raster. In the case of exponential scanning with the object symmetrical ly placed i n r e l a t ion to the cen t re of the l i n e , the e r r o r ranges from 1.5 to 5 - 7 % / 3 / . 2 . Targets which are non- sphe r i ca l and not pe rpendicu la r to the ax i s of the v id i con . If the v id icon t a r g e t i s n o n - s p h e r i c a l , the beam's v e l o c i t y i s g r e a t e r a t the edges of the t a r g e t than a t the c e n t r e , thus causing the appearance of a t h i r d - o r d e r component. If the t a r g e t i s not pe rpend icu la r (up to 1 ° / 3 / ) , a second-order component i s produced. The v e l o c i t y of the beam across the t a r g e t w i l l be where α is the angle of deflection, and α0 is the non-perpendicularity of the target. By substituting the current value into this expression, we obtain: where β i s a cons t an t . - 4 -F i g . 2 shows t h e v a r i a t i o n of t h e beam's v e l o c i t y a c r o s s t h e t a r g e t u s i n g t h e above d e p e n d e n c e . I t may be s een t h a t t h e v e l o c i t y a t t h e edges i n c r e a s e s , c a u s i n g p i n - c u s h i o n d i s t o r t i o n of t h e r a s t e r , and the graph is asymmetrical in relation to the centre of the vidicon due to the non-perpendicularity. When the target slopes in the v e r t i c a l p l a n e , t h e g r a p h i l l u s t r a t i n g t h e v a r i a t i o n i n v e l o c i t y a c r o s s t h e l i n e w i l l be s y m m e t r i c a l b u t t h e v e l o c i t y a t t h e v a r i o u s l i n e s w i l l be d i f f e r e n t , t h u s c a u s i n g k e y s t o n e d i s t o r t i o n . An e r r o r of ~ 0 . 2 5 % i s c aused by t h e t a r g e t ' s n o n - s p h e r i c i t y , and ~ 1 .5% by ~ 1° n o n - p e r p e n d i c u l a r i t y / 3 / . 3 . P o t e n t i a l f i e l d of t h e v i d i c o n t a r g e t . When the target is triggered by slow electrons travelling at low speeds near the target, the electron trajectories may be distorted by the surface field. The authors of/6/observed that t h e e l e c t r o n beam was d e f l e c t e d by t h e p o t e n t i a l d rop be tween t h e r a s t e r and t h e unscanned p a r t of t h e t a r g e t . The a u t h o r s of/4/ p o i n t e d ou t t h e d i f f e r e n c e i n s p a t i a l l e n g t h be tween t h e c u r r e n t r i s e and decay p r o c e s s e s a t t h e l e a d i n g and t r a i l i n g e d g e s of t h e v i d e o p u l s e s from o b j e c t s , i n d i c a t i n g t h a t the e l e c t r o n beam i s d e f l e c t e d by t h e f i e l d d i f f e r e n c e of t h e " b l a c k and w h i t e " p a r t s of t h e t a r g e t . When t h e h e i g h t of the r a s t e r i s i n c r e a s e d ( i s o l a t e d l i n e mode ) , some of t h e beam ' s e l e c t r o n t r a j e c t o r i e s a r e d e f l e c t e d from t h e c e n t r e of t h e l i n e where t h e p o t e n t i a l i s low t o t h e s e c t i o n be tween t h e l i n e s where t h e p o t e n t i a l i s h i g h e r / 7 / . C o n s e q u e n t l y , t h e e l e c t r o n t r a j e c t o r i e s a r e d e f l e c t e d by t h e c h a r g e p a t t e r n f i e l d t o such an e x t e n t t h a t t h e r a s t e r i s g e o m e t r i c a l l y d i s t o r t e d , and t h e t u b e ' s r e s o l v i n g power d e t e r i o r a t e s . A p o t e n t i a l w e l l forms a t t h e t a r g e t and i t s edges a r e cha rged w i t h r e s p e c t to t h e s canned p a r t up t o t h e s i g n a l p l a t e v o l t a g e . Immed ia t e ly n e x t t o t h e edges an a d d i t i o n a l f o r c e a c t s on t h e beam, d i s t o r t i n g i t s t r a j e c t o r y ( f i g . 3 / 8 / ) and c a u s i n g a f u r t h e r e r r o r (up t o 1.5%) i n measu remen t . Apar t from t h e above f a c t o r s , n o n - u n i f o r m i t y of t h e d e f l e c t i n g magnet f i e l d , m i s a l i g n m e n t of t h e t u b e , f o c u s s i n g and d e f l e c t i o n - 5 -system and optics, hysteresis of the focussing and deflection system, and chromatic and spherical aberrations (distortions) at deflection also cause pin-cushion or barrel distortion of the raster. The maximum error due to these factors in LI-415 vidicons is 2.5%/9/. It is clear that the geometrical distortions are complex (table 1) and it is, therefore, generally difficult (or impossible) to show how systematic error is related to the total number of distortions present, especially as many of them depend on the specific type of television pick-up tube or deflection coil used, on the way in which they are inter-connected etc. It is, therefore, easier to determine the systematic error by experiment. The vidicon simply reads out the co-ordinates of a precision test chart with vertical and oblique reference lines, and the necessary parameters of the system are determined by mathematically processing the experimental data. We shall describe below the method for determining the geometrical distortions in the pick-up tube of a television system used with spark chambers. The television system read out the co-ordinates of eighteen vertical lines on a test chart and the data was fed into a Razdan-2 computer which was connected on-line to the system/11/ during operation in the raster mode with 45 data lines per frame. Using these data, a straight line was plotted by the least squares' method and its slope (K) and displacement (B) were found for each reference line. Fig. 4 shows the dip angles of the reference lines and it may be seen that all the lines are parallel with an accuracy of ± 2.10-3 rad and that the average dip angle for all the lines is 1.1 ± 0.11°. This confirms the data in Fig. 5 which shows that all the points lie on parallel straight lines (three test charts each with 6 reference lines). The graph in Fig. 6 shows the variation of the beam's velocity along the line obtained by approximating the experimental data for a fifth-order curve. The beam's velocity when scanning the second reference line is 1.3% slower than when scanning the first line and it increases afterwards. It may be assumed that the beam velocity is higher when scanning the - 6 -f i r s t co -o rd ina te owing to the n o n - s p h e r i c i t y of the t a r g e t and i t s non -pe rpend icu l a r i t y to the v i d i c o n ' s a x i s . In f a c t , i t may be seen from Table 1 t h a t the t o t a l v e l o c i t y graph, a l lowing fo r nonlinearity of the deflection current, non-sphericity and non-perpendicularity (at α0 ≠ 0) of the target, gives a higher value at the beginning of scanning which then drops and again increases to wards the end of the line. The s igna l p l a t e ' s p o t e n t i a l f i e l d has l i t t l e e f f e c t i n t h i s c a s e . This i s because the beam's f ly-back time i s s h o r t e r than normal (8% i n s t e a d of 12%) on the t ransmiss ion s ide and longer than normal ( ~ 25%) on the r ecep t ion s i d e . This l eads to an inc rease i n the scanned a rea and a r educ t ion i n the e f f e c t i v e a rea of the t a r g e t . The e f f e c t i v e a rea i s a cons iderab le d i s t ance away from the edges where t h e r e i s v i r t u a l l y no e f fec t from the p o t e n t i a l f i e l d 11. In order to determine the va lue of the geomet r ica l d i s t o r t i o n s , the exper imental da ta (F ig . 7a) were approximated by means of the maximum l i k e l i h o o d method in terms of s ix re fe rence l i n e s of a t h i r d - o r d e r curve where Xi is the co-ordinate of the i line in mm ti is the co-ordinate of the i line in sec and ak a re the scanning parameters . By f ind ing ak from the above express ion and i n s e r t i n g f ixed t i va lues in i t , we obta in the value of the X co -o rd ina te along the l i n e and r a s t e r . The r e s u l t s a re given in F i g . 7b from which i t i s easy to f ind the geometr ica l d i s t o r t i o n value u s ing formula 13 which g ives ~ 2.0% in our c a se . The i n i t i a l da t a are s e t out i n Table 2 . - 7 -In order to determine the systematic error, the maximum likelihood method was used to approximate the experimental data of a second-and third-order curve in terms of six co-ordinates, and the parameters ak and value x were calculated. The results are shown in Table 3. As the test chart was 57.5 mm long, the relative r.m.s. error in measuring a co-ordinate was 5.2.10-4 and 3.1.10-4 for second-and third-order curves respectively. When the system is calibrated, the co-ordinates of the calibration grid are fed into the computer which corrects the results of the experiment where necessary. The frequency of calibration is determined by the stability of the system. With this in view, the test chart's reference lines were measured at set intervals and the corresponding parameters of the approximating function were computed. Fig. 8 shows the time dependences of the scanning parameters when the experimental data of the third-order curve were approximated. These functions were then linearized and the value of the X co-ordinate at set intervals was determined (Fig. 9). Hence the rate at which the system is to be re-calibrated is ~ 30 minutes when the measurement accuracy is 5.10-4 (30 m per test chart), and ~ 1 hour when the accuracy is 10-3. - 8 -- 9 -Table 2. No. of l i n e s Co-ordinates of re fe rence l i n e s in channels 1 l i n e 2 l i n e 3 l i n e 4 l i n e 5 l i n e 6 l i n e 5 181 358 532 703 871 1041 9 178 355 529 701 870 1038 13 177 354 526 701 868 1035 17 174 352 526 699 866 1034 21 169 347 523 700 864 1032 25 166 346 521 698 861 1029 29 164 344 519 692 859 1028 33 162 343 517 688 858 1028 NOTE : When the graph in F i g . 7a was p l o t t e d , the number of channels was divided i n t o 4 (one channel equals 0.25 μsec) and was sh i f t ed 150 μsec to the l e f t . - 10 -CONCLUSIONS 1. Owing to the complexity of the var ious geomet r ica l distortions and to t h e i r dependence on p a r t i c u l a r types of v id icon , i t i s d i f f i c u l t to e s t a b l i s h a l i n k between sys temat ic e r r o r , time and the d i f f e r e n t types of d i s t o r t i o n by means of theory . By determining the co -o rd ina t e s of a t e s t cha r t by experiment and mathematical ly p rocess ing the da t a , the parameters of a s p e c i f i c v id icon may be found and the geometr ica l d i s t o r t i o n s , sys temat ic e r r o r e t c . def ined. 2 . The geomet r ica l d i s t o r t i o n s p resen t in the type of v id icon used with spark chambers are such t h a t scanning may by adequately approximated using a t h i r d - o r d e r polynomial, and f ive t e s t - c h a r t r e f e rence l i n e s are s u f f i c i e n t fo r c a l i b r a t i o n when the measurement accuracy i s 5 . 1 0 - 4 . 3 . At t h i s accuracy, the system should be r e - c a l i b r a t e d every 0.5 hour . 4 . By using t h i s technique f o r determining and t ak ing i n t o account sys temat ic e r r o r , des igners of h i g h - p r e c i s i o n t e l e v i s i o n equipment need no longer worry about minimizing n o n - l i n e a r i t y of scanning. For the type of system i n ques t ion , i t i s more important to ensure high s t a b i l i t y , and n o n - l i n e a r i t y may be taken i n t o account by a s i n g l e c a l i b r a t i o n system. - 11 -BIBLIOGRAPHY 1. A.E.Model ' , G.N.Shishkov. Radiotekhnika, 20 No. 9, 45, (1965). 2. Edited by Yu.M.Kazarinov. Raschet elementov impul'snykh radiotekhnicheskikh ustrojstv, GEI, M-L,(l963). 3 . V.S.Polonik. Voprosy r a d i o e l e k t r o n i k i , Tekhnika televideniya,vyp. 1,44 , (1965) . 4 . K.V.Mikhalkov. Osnovy t e l e v i z i o n n o j av tomat ik i , Energiya, L.1967. 5. V.V.Aprelikov, V.A.Granovskij . Voprosy r a d i o e l e k t r o n i k i , Tekhnika t e l e v i d e n i y a , Vyp.5, 62 (1967) 6. S.B.Gurevich, R.E.Bykov. Radiotekhnika i e l e k t r o n i k a , No.4, 638, (1960). 7 . A.E.Gershberg, N.N.Mikhajlov-Teplov. Elektronnaya tekhnika , s e r . 4 , No. 1, 17, (1968). 8. A.V.Petrakov. TKiT, No. 6 ,60, (1972) . 9. B.E.Bonshtedt, M.G.Markovich. Fokusirovka i otklonenie puchkov v elektronno-luchevykh priborakh. Sov. radio M. (1967). 10. V.A.Klevalin, E.S.Belyakov, L.I.Bernshtejn, B.A.Lebedev, A.V. Petrakov. Izv. AN Arm SSR, Fizika, 7, 219, (1971). 1 1 . A.A.Varbanski j . Televis ionnaya tekhnika , 1969. 12. M.I .Krivosheev. Osnovy t e l ev i s ionnykh i z m e r e n i j , Svyaz' 1964. The manuscript was rece ived on 28 September 1972. F i g . 1 . Dependence of beam v e l o c i t y on t h e nonlinearity of t h e d e f l e c t i o n c u r r e n t . F i g . 2 . E f f e c t of t a r g e t n o n - s p h e r i c i t y and nonperpendicularity on beam v e l o c i t y . Fig. 3. Effect of signal plate's potential on beam velocity. F i g . 4 . Dependence of d i p a n g l e on t e s t -c h a r t l i n e number. F i g . 5. Dependence of d i s p l a c e m e n t ( B ) on l i n e number. F i g . 6 . Dependence of beam v e l o c i t y a l o n g t h e l i n e a l l o w i n g f o r t o t a l distortion. F i g . 7 . G e o m e t r i c a l d i s t o r t i o n s of r a s t e r . a ) e x p e r i m e n t a l d a t a ; b) c a l c u l a t e d d a t a . F i g . 8 . Dependence of t h e approx ima ted p o l y n o m i a l ' s p a r a m e t e r s on t h e s y s t e m ' s o p e r a t i n g t i m e . F i g . 9 . Dependence of t h e s h i f t of t h e test-chart c o - o r d i n a t e on t h e s y s t e m ' s o p e r a t i n g t i m e . 

Experimental determination and analysis of the geometrical distortions in the pick-up tube of a television system for measuring track co-ordinates in a spark chamber

Experimental determination and analysis of the geometrical distortions in the pick-up tube of a television system for measuring track co-ordinates in a spark chamber

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