A spot-focusing Čerenkov detector

N U C L E A R I N S T R U M E N T S AND METHODS

165 (1979) 4 3 9 - 4 6 1 ,

(~) N O R T H - H O L L A N D P U B L I S H I N G CO

A SPOT-FOCUSING CERENKOV DETECTOR M BENOT, J C BERTRAND, A MAURER and R MEUNIER*

CERN, Geneva, Swttzerland Recewed 18 June 1979 Tests on a new type of Cerenkov counter have been carrted out at CERN m a 50 GeV c - t positive beam This detector can be seen as a nng-focusmg counter m which a subtracUon of a fixed angle 00 has been performed opucally on the (~erenkov angle 0 For a parttcular value 70 of the relattvlsUc factor of the panicle detected, the (~erenkov angle 0 is equal to 0e, and all the t~erenkov hght ~s focused on a spot, which gives ~ts name to the detector For all other values of 7 the spot degenerates into a small ring, much smaller than ~t would have been m a conventional focusing counter The radms of the nng provides a determmatton of the velocity of the parttcle, and the position of the centre is related to Its d~recuon Th,s counter can be used for the detection of mult~-parttcle events A descnptton of the detector and ~ts basic design pnnctples are given Results concermng the velocity resolution and hght y~eld are also presented and compared wtth computed pred~cUons

1. Introduction

It has been shown m a prewous paper 1) that It is possible to design a (~erenkov detector to provide simultaneously the direction and velocity of a charged particle coming from a small target or from a focused beam Such a detector is based on an optical transformation of the (~erenkov hght phasespace coordinates onto a two-dimensional hghtsenslUve array Thin t~erenkov detector uses conical optics to focus the t~erenkov hght from a particle w~th a Lorentz factor 7o into a small spot image For a particle with 7 ~ 7o a ring image is produced, the radms of which is related to the value of 7, and the poslUon of the centre yields reformation on the angular coordinates of the particle For a gwen focal length of the system, the radms of the rmg is much smaller than In the usual ringfocusing detectors but the resolution AB is of the same order, due m particular to the minimization of the optical aberraUons and because of the compensation of the chromatic dispersion of the (~erenkov hght Such a detector is as fast as the ring focusing detectors For various reasons which are explained below, the prototype described here and which has been tested at the CERN Super Proton Synchrotron (SPS) is somewhat different from the one studied m ref 1

This prototype is of relatively short length, 3 8 m (to reduce its cost), and m order to keep the hght yield to a reasonable level the nominal (~erenkov angle has been set to 35 mrad instead of 20 mrad, as quoted in the first studies l) * Visitor from the Centre d'Etudes Nuclealres, Saclay, France

For purely economical reasons the angular acceptance of this prototype has been hmtted to ___4 5 mrad but could easdy be increased The light ~s detected by an 11 × 11 matrix of 14 mm diameter R760 Hamamatsu phototubes The equivalent focal length of the system is ~ 20 m, making it optically equivalent (from the resoluUon point of view) to a DISC counter producing rings of about 1 4 m dmmeter Th~s prototype has been tested in a 50 GeV c -~ posttlve beam, allowing the detecuon of 7r, K, p, and d The tuning value 70 at which one could observe the spot-focusing effect could be chosen m the range 20 < 7 < oo by adjustment of the pressure of the mtrogen used to fill the counter The refractwe index was monitored with a d~gltal mterferometer-refractometer ~mmersed m the counter vessel ttself 2. General description

According to the pnnctples already descrlbed~), a spherical mirror produces an ~mage of the target posmon at a place where one must put a corneal lens (axlcon) In this case the spots or rings of (~erenkov hght produced by this axlcon are in the focal plane of the mirror and are wrtual All the performances simulated by computer in ref 1 were analysed for thts purely theoreUcal condlt~on of v~rtual focus It was assumed that m pracUce th~s virtual image would be focused as a real ~mage m the plane of a hght-detectmg matrix by a suitable focusing system In the present prototype (fig 1) the (~erenkov hght hits the first main spherical m~rror M~ of 2 m

440

M BENOTet al P M MATRIX FIELD LENSES SECOND FOCUS

OPTICAL WINDOW AND FIELD LENS

\

/ /

TRANSFER LENS MAIN MIRROR M~

r...~..l.~T L SCANNER

PARTICLE ~ANE

MIRROR MAIN MIRROR FOCAL PLANE RING FOCUS

i

lm

/AXICON DOUBLET "~ASPHERIC MIRROR M2

Fig 1 Spot-focusing detector

focal length and is sent on to a second mirror M2 (sphencal to first order) after a 90 °C deflection by a plane mirror Mp and refraction in the axlconlc lens After further reflection the hght crosses the axlcon a second time, passes through a hole m Mp, and is focused on a fused-sdica optical window W of 55 mm dmmeter This part of the optics defines a "first stage" producing a pnmary real image (referred to in the rest of this paper as the "primary image") and has an equivalent focal length of 1 m The exact pOSltlOn of this pnmary image plane can be adjusted to coincide with the plane of the photocathode of a multmnode phototube or image intensifier of about 40 mm useful dmmeter In fact, the mult]channel multmnode phototube available to us was not suffioently rehable and we had to use an alternative techmque 2) We have instead used a matnx of phototubes as mentioned above, which, when provision Is made for their individual mumetal shielding, can be arranged on a 16 mm pitch matrix Th~s phototube matrix ~s too large and ~ts p~xel (p~cture element) size too coarse to ]nstall it at the first focus We therefore had to project this pnmary image onto a matrix of square field lenses by means of a specml-purpose transfer lens TL Finally, the hght ~s detected by the matrix of phototubes, the pos]t~on of which is such that the exit pupd of the transfer lens is focused by each field

lens on the photocathode of the corresponding phototube The ~mage produced by the transfer lens ~s called here the "secondary ~mage" It should be noted that the system used, namely an axlcon and focusing mirror, Is optically equivalent to an axicon of twice the bending angle, followed by a focusing optics equivalent to the mirror M2 The detector described in the previous paper ~) was restncted to a sphencal mirror M~ and an ax]con doublet only The ~mage produced by such a configuraUon Is vtrtual and is situated m the focal plane of M1 Here the role of M2 is to produce a primary real image, and the transfer lens TL allows us to accommodate large-size detectors hke our matnx of photomultiphers The mechanical design of the field lenses and phototube support and the optical charactenst]cs of the transfer lens are such that the global eqmvalent focal length of the counter can be adjusted to 10, 20, 30 or 40 m Increasing the equivalent focal length of the counter would improve the velocity resoluUon A/3 of the detector, but would reduce the angular acceptance of the counter by increasing the angular range beyond which the Cerenkov hght falls outside the matnx At the pnmary focus, on the optical window W where the equwalent focal length of the system is 1 m, the angular acceptance is +__20mrad

A SPOT-FOCUSSING

(~ERENKOV

The particles emitted in this cone cross the counter window and the main spherical mirror, the thickness of which is reduced to 10 m m in the central zone crossed by these particles The counter windows are made of mylar sheets (or 2 m m AI when high pressure is needed) The counter ~s designed to work with nitrogen, helium, or a mixture of the two at pressures of up to 15 atm

3. The axiconic objective 3 1 BASICDESIGNPRINCIPLE The axlcon is the main optical element which characterizes a spot-focusing detector (SFD) and distinguishes it from a conventional-focusing ~erenkov counter An axlcon with a straight meridian, 1 e limited by a conical surface, is not the only possible shape for the corrector This optical element can be generated by an arc o f a c~rcle, in which case it can be more exactly referred to as a torold In the thin-lens approximation a torold is eqmvalent to the combination o f an axlcon and a spherical lens, which may also be an interesting solution, since a focusing element must be combined with the axlcon to produce real images at the primary focus For this counter we have chosen to use an ax~con doublet and an aspherlcal m~rror to focus a real image on the optical window o f the detector It has been shown in ref 1 that an axlcon doublet is needed to fulfil s~multaneously the conditions o f spot focusing and o f correction o f the chromatic dispersion o f the (~erenkov hght A cemented doublet ~s preferable not only because it improves the hght transmission but also because it places less stringent requirements on the surface accuracy at the interface In fact, ~t can be seen that an error/lot of the axlcon angle at, m a gwen region o f the surface crossed by a merldmn ray, introduces an error 6d m the dwmtlon such that

441

DETECTOR

have a plane face, which means, for a cemented doublet, that their apex angle is o f equal magnitude and opposite sign For the required design the basic relations are ~)

(~g-1),-,~-~+(1-flo)~-~Ii+o-~ol,

(1)

where n8 is the refractive index o f the gas, for the average wavelength of the useful spectrum ~,, 00 Is the (~erenkov angle at this wavelength, Y0 is the nominal y value for which one wants spot focusing The chromatic dispersion ~s F /l A0o ~ 02 °Vg

+ Y-~ol '

(2)

where v~ is the Abbe n u m b e r of the gas ~- 1 v~ = n~(21) - n~(22)'

(3)

,;q and 22 are the two achromatlzatlon wavelengths of the useful spectrum, and r~(;h), r~(22) the corresponding values o f the gas Index o f refraction Our optical design follows the classical concept of achromatlsm for two selected wavelengths because of its s~mphclty and usefulness, but we should not overlook the necessity of a careful secondary spectrum optimization The angular deviation dUO o f a light ray by a symmetric axlcon doublet of refractive radices n 1 and n2 is given by d(2) ~ ct {In x( 2 ) - 1] - [ n 2 ( 2 ) - 13}

(4)

In the present case, where the target is positioned at the centre o f curvature of the first mlrror~), the condition for spot focusing ~s d(2) = 0 o(2)

(5)

Moreover, since the chromatic dispersion must be cancelled, this can be written d(2,) - d(22) = AOo

(6)

6d/6o: ~ A n l 2 ,

Combining eqs (1) to (6), it is found that

where An~2 ~s the difference between the Indices on each side of the interface W h e n one o f the media ~s a gas, this quantity is three to four t~mes larger than at an optically cemented surface In general, making such a doublet lmphes the grinding and polishing o f at least three conical surfaces, as the fourth one can always be a plane one However, the making of such surfaces is a rather delicate and expenswe task and ~t ~s therefore useful to see whether the two axlcons could both

02 = #Ang,

(7)

with =

(nl - -

(8)

R2)/(An~ - An2),

where An, = n,(21) - n,(22) , Then 0t ~ 0o/(n 1 - n2) Eq (7) can be rewritten

o~ ~ ~(n~- O/v,

~, = n,(,~) (9)

0o)

442

M BENOT et al

In our case from formulae (1) and (10) we have

TABLE 1 Gas index and chromatic dispersion as a function of )'0 Yo

It follows that once 0o and ~ have been fixed, ff it ~s necessary to tune the counter m order to have spot focusing for various possible values of 7o, ~t must be done by proper setting of (rig- 1) according to (1), but also the vg of the gas must be adjusted each Ume In order to saUsfy (10) This can be done by varying the gas composition and its pressure In practice there is a ltmlted choice of matermls which can be used for the axtcomc lens, as they have to be sufficiently transparent m the useful wavelength range considered, ~e about 250 n m to 5 0 0 n m , where we have chosen the following design values achromatlzatlon [ ;q = 440 nm wavelength [ 22 250 nm mean wavelength

I

= 350 nm

Fused silica Is the most c o n v e m e n t m e d m m because ~t is not b~refrmgent, it is avadable m p~eces o f sufficient s~ze and at a reasonable price, and ~t can be ground and pohshed almost a s easily as glass Monocrystals of NaC1 are also adequate and have m fact been used m the construcUon of h~ghperformance DISC counters 3,4) where the chromatic d~sperslon correction ~s made adjustable according to the 7 of the selected parttdles However, the pecuharit~es of the present design have led us to consider the use of water and fused silica Water ts mdeed a rather good and convenient m e d m m which has been used here for the design of both the ax~conlc objectwe and the transfer lens T h e / ~ value for the doublet H20-SIO2 ts ~ = 36 597,

(13)

and the nominal value chosen for 0o (see section 1) IS

0o = 35 mrad (14) In fact, as seen in fig 1, the hght crosses the axtcon doublet twice It ~s thus designed for a deviation of 00/2 Th~s solutton, based on the use of a second m~rror M2 to produce on the optical window a real ~mage of the desired s~ze, offers the ~mportant advantage of ~mplymg a shallower shape and therefore a thmner lens The apex angle oc of the fused-sdma axlcon has been set to 137 0 mrad, which ~s very close to the first-order value obtained from formula (9) The

10 20 40 50 80 100 200 500

( n g - 1)x 106 5612 1862 925 812 690 662 625 614 612

50 50 60 98 99 85 32 81 81

Vg 167 67 55 64 a 27 63 24 27 20 63 b 19 79 18 67 18 36 18 30

a Pure He b Pure N 2

exact value o f thts angle is not ~mportalat, as the ray-tracmg program provides the exact value of 00 for which the detector ~s tuned The outer diameter of the objectwe is 300 mm, and this is stdl a reasonable size The mirror M2 haS a focal length of 1 333 m, and the design has been optimized by ray-tracing (see section 3 2) to include in particular a plane-parallel S102 plate, the tuner face of which is used as the plane interface with the ax~con water lens The chromatic d~sperslon o f a mixture of gases [such as CH4, v = 15 4, air, v = 20 66 (or N2), SF6, v = 35 53, He, v = 54 52] m fact matches the chromatic correction o f the objectwe qmte well over quite a large range of 7 values Table 1 shows the values of ( n g - 1 ) for spot focusing and of vg as a function of Y0 for SIO2-H20 and with 00 = 35 mrad It can be seen by interpolation that mr, at atmospheric pressure, allows a tuning value Y0of 79 6, with (ns - 1) = 281 35 × 10 -6 and vg = 20 66 It is interesting to look at the a m o u n t of residual primary chromatic d~spers~on introduced when working w~th N2 at various pressures m order to achieve the spot-focusing condition for d~fferent values of 70 If the counter ~s correctly compensated for 70 = 80, for example, the residual primary dtspersmn for 70 is g~ven by ~chr -- 2Vg00 In the present case th~s relatton becomes 6chr = [(692 25/y 2) -- 0 108] mrad

(16)

This residual chromatic error is not neghglble, the gas comp'osltlon must be adjusted to Y0, although

443

A S P O T - F O C U S S I N G (~ERENKOV D E T E C T O R

this ts not very critical For the present test we have used only N2 The extremely small variation of the ratio of the refractive indices of SIO2 and H20 in our range of interest (from 1 09398 to 1 09512) explains the achromatic properties of this doublet In fact the secondary spectrum is, In the present case, about five times smaller than it would be with a StO2-NaCI combination It is only when the bendlng angle ts about comparable to the (~erenkov angle that the chromatic dispersion of the Cerenkov light can be corrected by such a combination This IS not the case, for example, tn a D I S C 3'4) where the corrector is a zero deviation element and requires a strongly dispersive combination such as S102-NaC1, although the secondary spectrum and the inconvenience of using NaC1 make this combination less favourable In the present case, the losses due to reflection at the interface, as given by the Fresnel relation, are particularly small

L~ + n2J

= =

xlo-

3 2 OPTIMIZATION OF THE DESIGN The design of the axlconlc objective has been optimized by direct ray-tracing using a simulation program which generates (~erenkov light along the particle trajectories with the three wavelengths defined m eq (12) The optimization for a particle is done along the optical axis, N2 and He havmg been chosen for the mixture, the angle ~z is also given, as well as the ~0 value The program then works out the Cerenkov angle 00 and the exact proportion of gas needed to produce the desired conditions of spot-focusing and chromatic angular dispersion compensation The exact position of the axlcon and of Its associated mirror, and the geometric aberrations, are optimized by studying the size of the spot produced in the primary image plane The position of this plane is found by the program The spherical aberration has been minimized by slightly "aspherlzlng" the mirror of the axlconlc objective The assumed shape of the mirror is defined by a meridian of the type

H2

l+eH4

X =TR + ~-r

l+e'

+ 1--g-~- H 6 ,

(18)

where H is measured perpendicularly to the optical axis and R is the radius of curvature at the apex of the surface (A perfect sphere in the nelghbourhood

TABLE 2 Spot-focussing detector opUcal spec~ficatlons Surface

Sph mirror Piano Piano Comcal Piano Asph mirror Piano Comcal Piano Piano

Medium

Gas Gas SIO2 H20 StO2 Gas Gas SIO2 H20 StO2 A~r

Posmon (mm) 4000 45 30 39 10 39 10 2 71 -540 2 71 39 10 39 10 45 30

R curvature or angle (ram) (mrad) -4000 137 0

-1333 a 137 0

a E = 0 6 , e ' = - 2 4 , see section 3 2

of the apex would be represented in the above development by making e = e ' = 0 ) The optimization process consists, then, in finding the values of e and e' for which the sperhlcal aberration is minimized Thin gives a raised-edge-shaped mirror, and the maximum departure from a sphere is 8 5 wavelengths at points a 100 mm from the optical axis Table 2 gives the optical specifications of the SFD We have demonstrated ~) and, indeed, observed by simulation, that for particles which are not emitted from the centre of the target, l e with a nonneghglble impact parameter, the light rays in the image lie on fourth-order curves The departure of these curves from a spot, or a circle, is larger as the rays are emitted nearer to the target These rays cross the axlcon near the apex It is therefore necessary, in order to reduce such aberrations, to create a dead region ahead of the target where no useful light can be emitted In practice, in our tests, we have introduced a gap between the focus of the beam of particles and the counter body itself In any case, when the counter is used in an experiment a space is required between the target and the counter for the installation of apparatus such as magnets, a vertex detector, scintillation counters, wire chambers, etc Such a dead space is optically matched with the central hole m the axlcon defining the forbidden region for the hght In the present case this corresponds to a reduction of the radiator length, and therefore of the hght produced, of ~ 20% The length of thin region has been fixed by ray-tracing simulation It is also by means of this simulation that the size of the central hole in the plane mirror M r (fig

444

M

B E N O T et al

1) has been determined This central hole is particularly crltacal as at acts twice as a diaphragm on the light path There must be a good match between the angular acceptance of the counter as defined by the first mirror, by the hole m the plane mirror, and by the axlconlc objective Indeed, vignettlng du6 to the plane mirror starts for particles with a divergence > 15 mrad, and the vlgnettlng amounts to N2096 at 20 mrad However, owing to the hmlted size of the photodetectlon matrix (see section 4) chosen for the tests presented here, the actual acceptance of the counter, which is ___4 5 mrad, is not affected by this problem Because of the relatively small number of optical components used in this objective and because of the various constraints we have introduced, at is not possible to further reduce the remaining aberrations an the primary image The main aberration here is coma, which could have been reduced by changing the angle which the surfaces of the axlcon doublet faces make with the axis, and this is precisely what we did not want to do, m order to have plane external faces 4. The transfer lens 4 1 GENERALCHARACTERISTICS OF THE TRANSFER LENS

The (~erenkov light flux finally transmitted to the photomultlplIers is proportional to the radiator length It is then particularly important to transmit as much as possible of the light produced to the phototubes in order to keep the counter length to a minimum compatible wath an acceptable photoelectron yaeld The transfer lens must therefore be free of vlgnettmg, it must have the required numerical aperture, and have a good transparency m the range considered here [see eq (12)] A field lens in optical contact with the optical window W (fig 1) IS used to image, without hght losses, the axicon objective on the entrance pupil of the transfer lens For practacal reasons the focal distance has been fixed to be about 100 ram, and the numerical aperture needed, depending slightly on the exact equivalent focal length of the lens, was 3 5 The achromatic correction had to lie an the same range as for the first stage of the optics (see section 3 1), l e m the near UV Such a lens is not readily available commercially and had to be specially designed by us

As in the future we do not expect to enlarge the detector matrix to more than 500 to 1000 ptxels, the field m the object space does not need to be larger than 30 mm diameter This relatively modest field size was of considerable help for the design The medl~, chosen for this design were S102 and H20, as for the axlconic objective Such a combination has good optical transmission characteristics over the wavelength range of interest, and it reduces the number of lenses which have to be made Moreover, if one manages, as is the case here, to have no air gaps between lenses, it makes antlreflectlon coating unnecessary except on the two external faces, with, however, an extremely favourable Fresnel factor at the interfaces [see eq (17)] The main drawbacks of such a combination are the small refractive index differences leading to large geometric aberrations, and the large temperature coefficient of the refractive index of water, but the temperature variations in the experimental hall were acceptable for our apphcation 4 2 TRANSFER LENS DESIGN We started the design wath a basic system chromatically corrected and aplanatlc for a combination point-infinity, thanks to an asphenc surface (Descartes oval) and an aplanatlc spherical interface SIO2-alr on the short conjugate side The other SIO2-aIr interface was plane Such a basic system could be symmetrlzed in order to make it a relay lens with twice the original power Such a starting design cannot entirely satisfy the conditions of achromatism and aplanatlsm, as these two conditions demand slightly different radn for the SlO2-alr interfaces Since we did not want to use asphenc surfaces, we tried to replace them by strongly curved spherical surfacesS), which finally became thin menisci having a common centre of curvature Reduction of the spherical aberration was only possible by sphttlng the central lenses The optlmlzataon process was based on a ray-tracing program using 20 rays and 3 wavelengths One of the difficulties encountered was the lmposslbflaty of using a diaphragm to reduce some aberrations, because of the undesirable vlgnettmg effect which it could introduce When an acceptable solution had been found, we evaluated the effect of small variations of thackness and curvature of each element on the vanous optical aberrations The choice of the final values was determined by reqmrlng that all rays fall inside a

445

A SPOT-FOCUSSING CERENKOV DETECTOR

TABLE 3 Transfer lens optical spec=ficattons

Medmm Anr SiO2 H20 SiO2 H20 SnO2 H20 SnO2 H20 S~O2 H20 S102 H20 S102 H20 SnO2 Anr

f

500P.m

Posnt~on (mm)

R curvature (mm)

0 4 4 5 85 13 85 23 85 23 85 33 85 33 85 43 85 43 85 53 85 61 85 63 7 63 7 70 7

374

f

67"-Y

- 58 65 - 50 87 28 57 26 72 72 35 -72 35 72 35 -72 35 72 35 -72 35 72 35 -72 35 -26 72 -28 57 50 87 583 0

I-,,

0

I

1

I

5o

100

150

Field a n g l e mnad

Fig 2 Transfer lens spot size (dmmeter of circle containing

10096 of the hght)

the transfer lens, but the correction o f the ast~gmatlsm whnch dominates the field curvature [although th~s system presents a favourable Petzval radius o f curvature (R = 2 8 9 × e q m v a l e n t focal length] reqmres the use of components with relatively large separatnons along the optical axns Therefore a compromise had to be reached which partially satlsties these contradictory reqmrements

EFL (= equivalent focal length) = 94 24 mm BFL(= back focal length) = 85 22 mm

c~rcular region corresponding to the spot s~ze produced at the primary focus by the first-stage 4 3 PERFORMANCES AND CONSTRUCTION OF THE TRANSFER LENS optics (table 3) The discrete and coarse character of Thns lens accepts nearly the full aperture up to our detection matrix, and the need for the h~ghest possnble resolutnon for the counter, d~ctates th~s the maxnmum necessary field angle o f ~ 150"mrad, condtt~on It is preferable to have a sharply defined ~t ~s also a nearly symmetrical system optimized for spot, even if it ~s large, than a bright spot accom- lnfimte conjugate (figs 2 and 3) Fig 2 shows that the spot snze of the transfer lens is a good match to the pained by flares As could be expected, the final design o f the first-stage optics up to a field angle of 150 mrad transfer lens shows appreciable residual errors The corresponding to a particle dwergence z = 15 mrad The various components were mounted in a low refractwe radices and their small dnfferences lead to very strong curvatures, and hngh-order aber- stainless-steel barrel passlvated with hot nitric acnd rations sharply hm~t the maxzmum aperture of the and then filled with b~dlstdled water under v a c u u m lens In fact we have extended it shghtly more than Only the external faces were ant~reflectlon coated would have been the case in a conventional lens m for 350 n m with a 2 / 4 layer of MgF2 Tests o f this order to accept all the Cerenkov hght This is clear- lens on the optical bench have shown good agreely wslble in fig 2 when one compares the spot size ment between the computed performances and the Its eqmvalent focal length ~s for different F numbers Most o f the spot size ns measurements accounted for by the lateral colour, which could be 94 24 m m and the numencal aperture ns F / 3 45 It attenuated only by reducing the total thickness of has been set up w~th a magmficaUon of × 20 for SI Oz

H2 0

X~L=~/IF- m

F~g 3 Transfer lens

~-~

L-.

~m "

%'=-I

,~

446

M BENOT et al

this test run Although, as shown In fig 3, this lens as composed of 16 surfaces, the measured transmissaon indicated in table 4 as better above 405 nm than the transmission of a single uncoated S102 lens 4 4

TRANSFER LENS FOR FUTURE S F D

These studies can be used as a starting point for the design of an axicon + focusing lens which would replace the double-pass axicon + aspheric marror of the present desagn In this case the equwalent focal length of the optics as large enough to darectly accommodate a phototube matrix placed at the primary focus, with a consaderable improvement in the light transmission The F number of this focusing lens, of about F/6, wall allow much better optical correctaons

5. Construction and adjustment of optical elements The shghtly aspherlc mirror M2 (fig 1) made of Zerodur*, chosen for its ease of shaping and testrag, was first pohshed spherical and then figured in the required regaon between the centre and the outer edge Tests were done by interferometrlc measurements of the gap between the marror profile and a spherical convex test plate, whach had been desagned to touch at the centre and the outer edge of the mirror simultaneously The fringe pattern produced was compared to a template on whach was shown the expected radial dastribuUon of eaght fringes corresponding to the desired profile of the marror The SaO2 axicon and the flat window needed to make the H20 axlcon (fig 2) are made of Spectrosd B~ The conical face was first generated at CERN on a mdhng machine using a bell-shaped dtamond grinding tool 80 mm In dmmeter At this stage arregularitles along a generator were found to be less than 1 ~m Difficulttes occurred during the polishing stage, and some astagmatasm was observed making necessary a second grinding operatton before final pohshang* During pohshmg, tests were made by observation of the fringe pattern produced between the contcal surface and a reference glass cylinder Manufactured by Jenaer Glaswerk Schott und Gen, Mamz, Germany ~ Manufactured by Thermal Syndicate, Ltd, Wallsend, Northumberland, England ÷ All the precision optical surfaces have been pohshed at Optical Surfaces, Ltd, Kenley, Surrey, England

TABLE 4 Measured transmission of the transfer lens

Wavelength (nm)

Transmtsslon (96)

334 365 405 436 546

87 5 90 93 5 95 96

After polishing it was found that radial and circumferentml errors on the cone were less than 2/2 except for a turned-down outer edge (on a N 2 - 3 mm wide annular zone) and a carcumferentml error of N ;t close to the inner edge Laboratory tests were performed with the complete axaconIc objectwe mounted on a bench, by observation of the circle produced by a point source, using the objective in the reverse optical path mode The point source was produced with a laser and a microscope objective With this method mhomogeneatles were found in an annular zone, about 3 cm wide, near the outer edge of the axacon Local reflection errors have been measured using a perforated screen Local errors of irregular aspect, amounting to an error of N 0 1 mrad on the deflection, have been observed over areas the total of whach as less than 10% of the total useful area of the lens They are dastrlbuted m the mhomogeneous annular zone mentioned above, and there may be a relation between these two defects The external faces of the axlcon doublet have been anUreflectlon-coated under vacuum below 10 -7 Torr with a 2/4 layer of MgF2, matched to a wavelength of 350 nm The reflecting surfaces have been flash-coated with a 500 A thack alummium coating and coated lmmedmtely afterwards with a 2/2 MgF2 layer, and then soaked in pure O2 for 5 man These elements are mounted m steel barrels The marrors M~ and M2 (fig 1) are each held against three lead inserts, and they are spring loaded at the back They are also centred m thear barrel by teflon stubs pressed against the mirror side Tests on mirror M~ using the kmfe-edge method have shown that, when mounted mats barrel, there are no appreciable distortions as these are well within the 2/8 tolerance The plane mirror Mp cut m an available stock of 12 mm thick glass shows some evtdence of sagging

447

A SPOT-FOCUSSING (~ERENKOV DETECTOR

under ats own weaght Thas was certainly the reason for the shght astagmatasm found m the well-focused amage of a spot during our tests The dafferent optical elements have been aligned and centred in the counter with the help of a H e - N e laser, and the secondary focus was adjusted by autocolhmatlon To this end a 130 mm dmmeter plane mirror was inserted at the focal plane of marror M1 and carefully ahgned perpendicularly to the axis on which the centre of curvature of M~ had already been adjusted The focusing at the first focus was performed with the red laser hght, and also with the green light of a hght-emlttmg &ode (LED) It is an easy matter to ahgn the counter m the experamental hall an a beam line Only the target posatlon, l e the centre of curvature of the mare mirror, needs to be put on this line Thas is achaeved by removing the front than pressure window and by finding the position of a pro-point obJect which is imaged on atself by M~

6. The photodetectors The number of detected photoelectrons, when the detector is set for spot focusing, is given by N = A L 02 ,

(19)

which in our case, where the radiator length L is 360 cm and 8o = 35 mrad, becomes N = 0441 x A , where A is a figure of merat which characterizes the photodetector efficaency and the hght transmlssaon efficaency of the optics The present design was based on the mtenUon to use a multlanode photomultapher (MPM) wath a macrochannel plate A prototype (MPM 5 × 5)* was tested at CERN 2) The anode of such a detector was made of a square matrix of 5 × 5 elements, 2 5 × 2 5 mm 2 each We had hoped, at that tame, that a tube of about 40 × 40 mm with the same paxel size could be obtained, which would have been placed at the position of the primary Image, and these considerations led us to choose an effective focal length of 1 m for the first stage Had such a solution been satasfactory, the second stage, consastlng of the transfer lens and the field lens matrix, would not of course have been necessary The prototype tested, which had a glass window and a blalkah photocathode, exhibited very inter* Made by LEP, Pans, France

estmg features, an particular for the detecUon of single photoelectrons2), and we had hoped that for a larger tube we would have 50 < A < 100 cmwith therefore 22 < N < 44 photoelectrons Unfortunately, during these tests it turned out that the cathode was rapadly destroyed by lOmC bombardment, and the llfetame of the tube was therefore considered to short The alternative solutaon, which has been adopted, is the use of a matrix of Hamamatsu R760, 14 mm diameter fused-slhca window phototubes with a bmlkah photocathode Extenswe tests made on these tubes 2) have shown anterestlng performances The relative quantum efficiency of our sample of tubes is shown m fig 4 Such a solutlon reqmres a magmficatlon of the primary image, which covers a field of 55 mm, in order to match it to the physical size of the phototubes and associated magnetac shielding tubes, l e 1 6 m m diameter A matrix of 11×11 of such phototubes has been used for the tests reported here, and the primary image is focused by the transfer lens onto a matrix of 11×11 square lenses Each of these lenses, acting as a field lens, images the exit pupil of the transfer lens onto a phototube The sides of these lenses are not chamfered, and as they are pressed one against the other there is no dead space between them Therefore all the light received by each of them as collected on the 9 mm diameter photocathode, except for the transmission losses, which have been minimized by the use of the same antlreflectlon coating treatment

18

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53 57 61 65 RELATIVE EFFICIENCY Fig 4 Distribution of the relatwe efficiency of the photomultlphers

448

M BENOT et ai

as was used for the other opucal elements of the counter These fused-sihca lenses have a focal length of 100 mm and reqmre well-polished but not hlgh-precmlon surfaces

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reduce the angular dwergence of the particles (see section 8) The base of each phototube (fig 5) consisted of a voltage dwlder, designed by the manufacturer and modified according to our reqmrements (essentially an increase m the potential between photocathode and first dynode m order to ~mprove the quantum efficiency2)) The high voltage on each phototube was adjusted with a potent~ometer so that all phototubes were operating at the same point on the plateau of the characteristic curve The adjustments were made using a Xe flash tube and a Wratten optical filter selectmg the 360nm Hg hne The mare high voltage was set to 1400 V for most of the tests The power dlsstpated is ~0 45 W in each base The phototubes were connected through 50 I2 R6U cables, 50 ns long, to the input of a LeCroy ADC 2249A The trigger signal produced by the coincidence S1 × $2 was used to gate each event The ADCs were read through CAMAC by a PDP-11 PI

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7. Experimental conditions 7 1 SET-UP The counter was tested m a 50 GeV c -1 posltwe beam at the CERN SPS, containing 65% n + , 32% p, ~4% K ÷, and N002% d Slmphclty and cost considerations led us to fill the counter w~th N2, although for a better chromattc correction a Ho-N2 mixture would have been better The gas refractive index was momtored by a fully ~mmersed mterferometer-refractometer with a digital read-out and a least-count value of 5 × 10 -7 The gas pressure could be adjusted to tune the counter to the spot-focusing condmon for different values of ~'0 corresponding to n, K, p, or d However, the chromatic correction, which depends on ~'0, was not changed as this would have implied the mconvemence of a modification of the gas composition F~g 5 shows how the radms of the ring vanes w~th the gas refractwe index for n, K, and P The beam was magnetically focused onto a small region w~th a 5 × 5 mm 2 cross-sect~on located at the centre of curvature T of the first mirror M~ (where the target would normally be situated) Two scmtdlators (S~ and $2) along the counter axis, 4 5 m apart and hawng a cross-section of 3 ~3 mm 2, were used to define particle trajectories w~th an impact parameter a ~<15mm and a dwergence of 0 6 7 m r a d maximum Another set of smaller sclntdlators was added during a second phase of the run m order to

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7 2 DATA RECORDING Three types of data recordings and displays could be obtained 1) A pattern showing which phototubes were fired by a single event (figs 6, 7 and 8) In these figures, as in the following, F represents the experimental refractometer reading of the index of refraction of the gas and n - 1 = F × 5 × 1 0 -7 ii) A pattern produced by the accumulation of many events where, on the display, each cell 1001

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is represented by a square, the sine of whmh ~s proportional to the number of times it has been hit by at least one photoelectron (hit pattern) in) A pattern produced by the accumulation of many events, as above, but the square s~ze ~s proportional to the sum of the pulse amplitudes measured by the corresponding ADC (pulse pattern) A recording of these data on tape could also be obtained on request PI

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A few examples of such patterns are shown in figs 9 and 10 It was also possible to do a d~rect image analysis by a remotely controlled translation of the field lens in a d~rection parallel to the symmetry plane of the system This movement produces a scanning or the phototube array by the image By selecting a row of three phototubes along a d~rectlon perpendicular to the displacement, the s~tuatlon was the same as if the Image was scanned through a slit 4 8 cm long and 1 6 cm wide, corresponding to an angular definition of 2 4 and 0 8 mrad, respectively The intensity profile produced by an accumulation of events was determined by recording the total number of hits in this " s h t " as a function of the transfer lens posmon Such a method has also been used to focus the ~mage produced on the matrix by the transfer lens Thin is achieved when the intensity profile is the sharpest (fig 11) 8. Resolution of the detector Distinctions must be made between the various factors affecting the velocity and angular resolution of this detector (a) The opttcal resolutton The performance of the optics hmited by the residual aberrations, and the quahty of the optical elements, are ultimately the factors hmitmg the resolution of the detector and will be discussed in detail (see section 8 1) Co) The matroc resolution Discrete and relatively large phototubes limit the resolution if the equivalent focal length of the system is not sufficiently large For a given matrix it is always possible to

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trade matrix resolution against the angular acceptance of the detector simply by changing the magnification of the transfer lens If instead of phototubes a high-resolution, ]0- to 20-hne pairs/ mm image intensifier was used at the primary image plane, all the information given by the optics would be resolved (c) The beam divergence The beam divergence has a very small effect in the present case~), and we have checked (fig 12) that no effect is visible when the particle divergence is increased in steps up to the 3 2 mrad limit set by our restricted matrix size (d) The target size It has been demonstrated (refs 1 and 6) and is shown here (fig 13) that for particles emitted from a point at a small distance from the axis, the image produced departs from a sharp spot or a true circle We know that the light rays fall on fourth-order curves in the image plane An appropriate fit through the image could in such cases 422: ME

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8 1 CALCULATEDOPTICALRESOLUTION Our ray=traclng simulator has given the spot size for 70 = oo and the ring widths at ), = 50, evaluated at the primary= and secondary-image planes produced by the first stage and the complete optical system, respectively Tables 5 and 6 give the aberration data for the two cases of interest, i e the spot focusing and the rlng focusing Aberrations at the first focus and at the second focus after the transfer lens are given, with the corresponding velocity reso= lutlon of the SFD

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provide not only the 7 and the divergence angle of the particle but also its azimuthal angle and its impact parameter, as can be seen from the equations of the image ~) These fits are possible only on individual events and with a precision depending on the number of recorded photoelectrons For this test run we have not tned to achieve such a degree of sophistication, but we observe that with the target size considered here and for an accumulation of events this effect was similar to that of a 0 22 mrad beam divergence corresponding to the acceptance when counters S, and $2 were of 1 mm diameter (e) The multiple scattermg of the particle In the gas radiator At 50 GeV c -1 and with N2 as a radiator the gas pressure is about 2 2 atm, and the multiple scattering angle calculated for these conditions amounts to (A02) i - O 0 7 m r a d and is negligible compared to the other factors affecting the precision

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D I R E C T TESTS ON THE OPTICAL RESOLUTION OF THE FIRST-STAGE OPTICS

Direct observation of the image of a monochromatic point object produced by the optical system tested by autocolhmatlon on a bench has shown a

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F~g 13 Pattern o f particles passing through a target o f 3 m m dtameter, the target bem[[ displaced from the SFD axts by (a) = 0 ram, (b) = 2 5 m m , (c) = 5 rnm, (d) = 5 7 m m F = 1485, Rp = 0 The proton spot is degraded according to the SFD theory by the impact parameter, into a small circle which is not uniformly dlummated

spot s~ze < 0 3 mm diameter, w~th some flares Moreover, the transfer lens scanning method has also shown some astigmatism m the image We believe that th~s ~s due to a shght sagging of the lnchned plane mirror ~ (see section 5). 8 3

BEAM TESTS ON THE OPTICAL RESOLUTION OF THE COMPLETE OPTICAL SYSTEM

Wsth N2 as a filhng gas for the counter, we know that spot focusing and chromatic compensation are obtained simultaneously for ~'0= 79 6 (see section 2 1) When working at a momentum of 50 GeV c -t and adjustmg the pressure to obtain spot focusing for protons (~,0= 53), kaons (~,0= 101), or p,ons (~'0 = 360), the chromatic dispersion ts never correctly compensated (fig 14) For example, when ~'0 = 53, the system ~s under-compensated, and th~s

gives rtse to an angular chromattc spread of the tmage of ~ 0 14 mrad according to eq (17) When Y0= 360, the system is over-compensated and the angular spread ts then - 0 1 mrad The optical resolution may be studied using the transfer lens scanning method Fig 11 shows an example of the intensity profile obtained w~th accumulated events The central peak is produced by the spot image of protons, whereas the two other peaks correspond to the accumulated rings produced by plons A deconvoluUon of the intensity profile exploration by the "phototube sht" is made s~mply by measuring the slope of the d~stnbut~on. It ts then necessary to dtstmgulsh, ,n the result, the component due to the particle dwergence m order to find the angular spread of the linage produced by the opUcal aberrations alone We have taken the

A S P O T - F O C U S S I N G (~ERENKOV D E T E C T O R

453

TABLE 5 Spot-focusmg detector aberraUon data (SFD tuned for spot, 3'o = ~,, full angular stze m mrad) 1st focus, SFD alone d/3//~

Radial Gum) 0 5 10 15 20 25

0152 0156 0 170 0 215 0295 0285

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R

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pessimistic assumption and have added these two components quadrattcally We have considered the results of the analysts on the secondary ~mage and scaled them to the pnmary tmage plane where 211 ME

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454

M BENOT et al

the optical aberraUon, by a differentmtton of the basic Cerenkov relauon

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In our case tg #0 - 00 = 35 mrad and z/8~<0 32 mrad for a ring ~mage The spot tmage ~s not symmetric and ts probably overesUmated, counter S~ not being set properly at the target posmon m the verUcal plane We have then Afloptlc s _~< 11 2x 10 - 6 (21)

(24)

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We find that the hmlt on the velocity resolution as set by the matrix structure (w,th a magnification factor of x20 for the transfer lens and a global equwalent focal length of 20 m for the detector) is about half the over-all opUcal resoluuon that we had deduced from the transfer lens scanning It ~s also possible to have a direct determination of the velocity selecuon of the SFD from the dstnbutton of ring rad. of fitted single events by the least-squares-fit method apphed to all the hits of the pattern In this case the dwergence of each parUcle does not play any role This method suffers from a serious defect The patterns which contain one or more h~ts uncorrelated with the Cerenkov ring can be badly fitted, leading to large tads m the hstograms Clearly a more sophisticated data handhng ~s reqmred An effecuve nng radms resoluUon of N05_+01 plxel (figs 15, 16, and 17) was found The observed velocity resoluuon for fitted single events ~s then

However, it has been found 3) that a good separaUon is obtained when the velocity d~fference between parucles ~s at least three umes the resoluUon In this case A/3opt,.-34×10 -6, and the maximum momentum for rr-K separation wdl be - 8 0 GeV c -t and for zc-p separaUon ~ 160GeVc -t In the present case, however, one must also take into account the effect of the matrix resolution on these performances It has been found by Monte Carlo simulation that a perfect c~rcle can be determined w~th an error of _ 0 09 plxel on the radms (when the radms is larger than one p~xel) It ~s then possible to esUmate the error introduced m the velocity determmaUon by the matrix resoluuon Aflmatr,x/fl ~ 0 18 x tg0 o x AOa, (22)

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This s h o w s - a fatrly good agreement between the two methods of m e a s u r e m e n t (" sht analysts" and pattern analysis),

- a fairly good agreement also with our theoretical predictions, - a justtficatlon for the choice of 20 m for the equivalent focal length, because the resolution is

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limited mostly by the optical aberratmns, and to some extent by the m a t n x structure F~gure 18 shows the fitted radn o f plons, kaons and protons of 50 G e V c -1, for different values of the index of refraction of the gas The relatlWStlC factor y of a particle can be deduced from the index of refraction o f the nng radius in plxels by the approximate formula = [2(n - 1) - (0o 4- RAOa)2] - 1/2

the expected values derived by computation Our m e t h o d is based on the fact that there ~s a close relation between the n u m b e r of cells triggered by an event, the radms o f the nng, and the number of R=oo

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T h e most important charactensttcs of this detector, and mdeed the mare reason for our tests m a beam, is probably the actual average n u m b e r N o f detected photoelectrons per single event It is possible to be confident enough m the opttcal computations and In the lens-making techniques to predict w~th a high accuracy the opUcal resolutton o f a spot-focusing detector, but the usefulness of such a detector is directly linked to the n u m b e r o f bits of reformation obtained per event, l e the n u m b e r of photoelectrons detected by the complete system, electromcs included It ts of great interest to evaluate experimentally the average n u m b e r N o f photoelectrons produced per singly charged particle, and to compare it with

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Fig 19 Number of hits versus N for dtfferent R

A SPOT-FOCUSS|NG

CERENKOV DETECTOR

photoelectrons produced A Monte Carlo simulation has shown how these parameters are related (fig 19) If for a sample of events we know the average radius and the average n u m b e r of cells hit, it is then possible to derive the average n u m b e r N of photoelectrons produced per event, and therefore the average value o f A for the R760 phototubes, when the optical transmlss,on T of the optics is known This study, carried out on two samples of plons obtained with two different refractive index settings, is shown in table 7 There is an independent experimental determination of the light y,eld obtained by the transfer lens scan across a ring image W h e n the gas refractive index is set at ( n - I ) = 748 5 × 10 -6, the plons in the beam with 7 = 360 produce a ring image of 4 3 plxels radius The photoelectrons are spread along the 27-plxel-long circumference Therefore a phototube along this c,rcumference, when hit, receives an average signal corresponding to one photoelectron for this event W h e n scanning with the transfer lens and looking at the signal of the central phototube (PM0) of the matrix, it is found that the efficiency of the triple coincidence

457

tlon o f the phototube efficlencles, this one is 1 14 times more efficient Therefore we can estimate that the matrix receives, on the average, for the average-quahty phototube, N = 28 4___6 photoelectrons/event Taking the average of the two different measurements, we obtain ~7= 24 6___3 6 with admittedly large uncertainties This value is very slmdar to the one used m the DISC design 3) W e know that the ring radius o f a particle with a y value different from the tuning value ~'0 depends only on the quantity I~'-~'01, and we have studied rings of the same radius produced by particles with ~'1 > Y0 and with ~2 < ~'0 but such that (~1-~,0)=(~,0-~,2) W e have found that in such cases there is 30% difference in the ,g/value This fact may provide a way of removing ambiguities m the determination of the 7 of the particles

10. Optical transmission and figure of merit of the phototubes 10 1 OPTICAL TRANSMISSION OF THE SFD The optical transmission losses through the system are far from negligible, as the •erenkov light Is reflected by three mirrors and is transmitted through 10 interfaces between SIO2 and gas, and 14 PM o x $1 x S 2 r/ = $1 x $2 (28) interfaces between SIO2 and H20 Moreover, the average path lengths In SIO2 and in H20 are differs appreciably from 1 and is only 0 70_+0 05 150 m m and 33 m m , respectively when PM0 is set on the ring image for pions But it W e have measured the transmission o f the becomes - 1 on the central spot, produced by system at the 365 n m H g line, which is an approxprotons (~, = 53) We do not know the exact ratio o f imation to the effective Cerenkov spectrum peak of protons to plons in the beam, but we can measure 350 n m as detected by the phototubes For the firstit, as well as the average n u m b e r of photoelectrons stage optics alone, which would be the only part ~V produced by the plons, by repeating the scan required if a multlanode phototube or an image with the " p h o t o t u b e slit" (see section 8 3) In this intensifier was used, T~ is >~0 405 Practical difficulcase the efficiency reaches nearly 1 on the plon ties in this measurement, taken over an 8 m light ring F r o m a comparison o f these two efficiencles path, are such that we can quote only a lower and knowing that n = ( 1 - e - ~ ) , we can deduce that limit we have a s~gnal on the central phototube of for the transfer lens T2 = 0 90 1 2___0 2 photoelectron per event However, we for the field lenses cannot consider this value as typmal for all the in front of the phototubes T3= 0 946 phototubes, since we tested t h e m (fig 4) and The total measured transmtss~on of the system installed the best ones at the centre of the matrix as ~t was used during our test is therefore Compared with the average value o f the distribu- T = T~×T2 × T3~>0 345 It is interesting to check the consistency of these TABLE7 measurements Experimental evaluation of the photoelectron yield For the transfer lens the transmission is given by the product of three terms One is the transmission Average radms Average number N photoelectrons m plxels of hits (from the graph) of a fused-slhca lens coated on both sides, like the field lenses, T3 = 0 946 This transmission is about 3 131___1 1 205___35 1% smaller than that found by computation The 43 15 7 ± 2 3 21 ± 5 second term is the transmission of 14 SIO2-H20

458

M BENOT et al

interfaces, T4= 0 972, and the third term the transmission of 16 mm of H20, T5= 0 995 Therefore we expect that T2= 0 91, whtch is m good agreement with the measured value For the first-stage optics alone we have three mirrors For each of these we have measured a reflection coefficient of 0 83, and six SIO2 gas interfaces (equivalent to three coated SIO2 lenses) and two SiO2-H20 interfaces We therefore expect T~= 0 48 leading to T = 0 41 The agreement between the measured value and the computed one is considered to be rather good if we take into account the practical difficulties that have to be faced for such delicate measurements

this requires that the N photoelectrons produced in a cluster be efficiently recogmzed over the inherent noise of the photodetector, and that spurious triggers occur only at a negligible rate We have tested this possibility in searching for deuterons in the beam Figs. 20 and 21 indicate haw these particles have been detected and could easily have been used as trigger particles The detector can be also used m another mode when the particles of interest do not necessarily 304

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It ~s interesting, notwithstanding the limited accuracy of these measurements, to evaluate the figure of merit A* of the R760 photomultlpher from eq (19) A* = NI(T x L x 0o2)

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7

11. Utilization of a spot-focusing detector The detector can be run in two modes One mode is the spot focusing for at least one particle emitted m an interaction at a given ?0 The electromcs recognizes the presence of a spot extending over very few adjacent pixels and containing N photoelectrons The posmon of the spot on the matrix is a measurement of the angle of emission, and the mere presence of a bright spot is the proof that the particle has ?0 for its relatwiStlC factor If the momentum p of the particle ~s known from its magnetic rigidity, these three parameters define the mass M, the longitudmal momentum PL and the transverse momentum Pr of the particle These data provide a very useful indicator whmh could be used to trigger the data acqmsmon of the event Clearly

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Fig 20 Spot focusing of deuterons, F = 2467 Deuterons form only 2 × 1 0 - 4 of the beam For tMs pattern, data have been accumulated at a beam intensity of 3 x 106 per second The computer hm~ted the data-taking rate to 20 events s - I The tngger selectton with two threshold (~erenkov counters reduced the rate to only about 3 x 104 s -1 Therefore only one part:cle m 50 tnggers can be a deuteron The pattern shows five deuterons focused on the centre of the matnx, as can be seen from the comparison between the h~t and pulse pattern For this run the pulse pattern was recorded wtth a pedestal raised to 16 umts Many spurious s~gnals appear at certain locations m the matrix This effect ~s repeated for different runs, and is connected with home at the input of the ADC

A SPOT-FOCUSSING

459

CERENKOV DETECTOR

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produce a spot but a ctrcle The pattern recogmtmn and reconstrucUon of these c~rcles, which may be too slow for trigger purposes, call for a sufficiently large number N of photoelectrons per event However, th~s number does not need to be so large as to produce a hit on nearly all the plxels which correspond to the c~rcle It can even be stud that such an abundance of photoelectrons rather than improving the reconstructmn would only make the analys~s of multiparticle events more complicated Experience wdl tell us the suitable values for N, but ~t can be guessed that for a sat,sfactory performance ~t wdl he between 10 and 30 However, we do not underestimate the dzfficult~es we wdl find m multipart,cle events when more than one c~rcle per event has to be recogmzed and reconstructed Thzs ~s a wide subject that we cannot

Fig 23 matrix

H,t pattern of the same event on the field lens

discuss m this arUcle, which IS devoted to the performance of the detector rather than to the way m which the results should be exploited Such a question can only be tackled when enough expenence has been gained in the practical use of the detector We will limit ourselves to dlustratmg the problem, using one parUcular example We have tested the poss~bd~ty of disentanghng multlparUcle events such as the one shown in figs 22 and 23 Using an inversion, we transform the circle of the h~t pattern into an easily recognized straight hne when the pole is on a circle F,g 24 shows the reverted pattern and fig 25 the ~dentified circles They correspond to particles of }, = 47.8 or y = oo, and y = 48.4 or ~,= oo The four umdent~fied h,ts m the c~rcles can correspond to a c~rcle of about 1 5 ptxel m radius

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460

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M

B E N O T et al

1

F~g 25 C~rclesobtained from the strmght hne fit to the reverted

pattern If they are the s~gnature of a beam proton, a pulse-height analysis could prove that th~s is due to the concentration of the hght on a few p~xels Tentattvely we can interpret th~s event as two electrons produced by a beam proton 12. Conclusions All these results show that a spot-focusing detector, as described m the onginal art~clet), can indeed be built, and ~ts measured performances agree closely w~th the design data The mare reason for the optical complexity of the present device hes m the uncertainty which extsted at the design stage concermng the photodetect~on system Moreover, the actual performances, part~culady the hm~ted angular acceptance, are the result of a dehberate decision to build a test instrument and to minimize ~ts cost However, this detector, as ~t ~s, can be used as a convement beam partacle ~dentlfier, since we have shown that it can tag three different types of particles s~multaneously m a nonparallel beam, unhke a DISC counter 3'4) which reqmres a parallel beam, and this feature may save beam transport lenses and space An SFD has the same advantages as a DISC very short output pulses (a few nanoseconds), very high counting rate capabdlty (~> 10 7 S-l), lmmumty to low-velocity background particles, and highvelocity resolution (10 -6 can be achieved) It has also specafic advantages over a DISC 100% detection efficaency thanks to ats average of ~25 photoelectrons per event, which do not have to be collected through a narrow daaphragm as m a DISC (In the latter a certain fractaon of them are lost owing to the spread of the rmg ~mage, and thas spread as larger than the dmphragm, whose wadth as

fixed by the tolerance on the velocity and the divergence of the particle ) Moreover, the present SFD has multiparticle detectaon abdlty and very good spatml resolution It as an interesting forward detector which can produce a trigger on the passage of a particle w~th a preset 7 value, at a gaven angle A new project would of course use single-stage opUcs, instead of two, w~th a purely refractwe axlconlc objective giving, m one step, the final equivalent focal length In this case th~s objectwe gwlng, m one step, the final eqmvalent focal length In this case this objective would be crossed only once by the hght, and there would be no need for a transfer lens The total hght transmission coeffictent could be raised to at least 0 62 One could even make use of an axacomc lens ~dentacal to the present one In thas case the nominal (~erenkov angle would be twice as small, a e 17 5 mrad, gwmg a better veloctty resolutaon, and therefore such a counter could work in the range 100-300 GeV c -1 The length of thas counter could then be doubled in order to produce nearly the same global hght yaeld The design could also include a larger free space between the target and the counter body so as to allow for the mstallataon of a vertex detector and a magnet Working at about atmospheric pressure with a gas maxture such as He and N2 and the refractwe index being measured wath an internal anterferometer-refractometer, such a detector would introduce a minimal amount of materml in the partacle path We thank that an SFD can be the best t~erenkov detector for most of the cases where the lnteract~on region ~s a target of limited s~ze such as an external target m secondary particle beams, or the antersectmg region of storage rings where topological problems assocrated wath the presence of vacuum tubes wdl hmat the detection capabdltaes along the beams ax~s This SFD project has been made possible by the support of P Falk-Valrant, E Gabathuler and E Plcasso, of the CERN Experimental Physics Dwtslon, and P Zanella of the Data-Handhng Dwlslon, A Muller, from CEN Saclay, and many other people have contributed to ats success Drs E Lesquoy and S Zylberajch have been responsable for the data acqmsmon and the data analys~s Thear contrtbutlon merits our apprecmtaon We would lake to acknowledge the skill and the patience of J Mortleman and J Thomson (from Optical Surfaces, Ltd) who polashed the axacon and the asphencal marror We want also to thank C Nichols and' has

A S P O T - F O C U S S I N G (~ERENKOV D E T E C T O R

staff for the careful grinding and the ant~reflect~on coating of the optical elements Drs Brian Powell and JayanU Dharma Teja are especially thanked for their careful readmg of the manuscript and their constructwe remarks References 1) M Benot, J M Howle, J Litt and R Meumer, Nucl Instr and Meth 111 (1973) 397

461

2) R Meumer and A Maurer, 1EEE Trans Nucl Scl NS-25 N1 (1978) 528 3) M Benot, J Lttt and R Meunter, Nucl Instr and Meth 105 (1972) 431 4) j Lltt and R Meumer, Ann Rev Nucl Scl 23 (1973) 1 5) A Bouwers, A c h t e v e m e n t s m opttcs (Elsevier, New York, 1950) p 16 6) M Benot and J M Howle, CERN Data-Handhng Divtslon Report DD/73/I (Feb 1973) unpubhshed