Optical Properties of the Quartz Bars for the TOP Counteryhorii.nagoya/belle... · Optical Properties of the Quartz Bars for the TOP Counter Belle II Note 13, Version 0.3, 25th November

Optical Properties of the Quartz Bars

for the TOP Counter

Belle II Note 13, Version 0.3, 25th November 2011

Y. Horii1, Y. Koga2, N. Kiribe2, K. Inami2, and T. Iijima1

1Kobayashi-Maskawa Institute, Nagoya University2Graduate School of Science, Nagoya University

Abstract

A time-of-propagation detector named TOP is a hadronic particle identification systemfor the Belle II experiment. In this note, we report optical properties of the quartz-bar radiator. We measure bulk transmittance, internal surface reflectance, and possibleeffect of striae for two prototype bars of Suprasil-P710 and Corning 7980 0D polished byOkamoto and Zygo, respectively. Both bars seem to have enough qualities for the particleidentification at the Belle II experiment.

Contents

1 Introduction 2

2 Photon paths and requirements for optical properties 3

3 Quartz bars 6

4 Equipments 74.1 Optical table and aluminum plates . . . . . . . . . . . . . . . . . . . . . . 74.2 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 PD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.4 CCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5 Bulk transmittance 115.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Internal surface reflectance 146.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

7 Possible effect of striae 177.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

8 Conclusions 24

1

Chapter 1

Introduction

A time-of-propagation detector named TOP is a hadronic particle identification systemfor the Belle II experiment [1]. Cherenkov light propagating in a 2.6-meter-long quartzbar is detected by an array of micro-channel-plate photomultiplier tubes (MCP-PMTs),and the angle of the Cherenkov light is reconstructed. The quartz bars must transmitthe light over long optical length with a number of internal reflections. Therefore, highbulk transmittance and surface reflectance are required. The bars should be opticallyuniform, and then the level of striae must be low. In this note, we measure the bulktransmittance and the surface reflectance using laser and photodiodes (PDs). We alsoestimate a possible effect of striae by using laser and a CCD. The measurements areperformed for two prototypes which have quite similar specifications to the one designedfor the TOP. Most of measurements are done referring the reports in Ref. [2], while themeasurements using CCD are newly developed.

In Chapter 2, we show typical photon paths and requirements for the optical propertiesof the radiator. In Chapter 3, we show the specifications of the two bars tested in thisreport. In Chapter 4, we show the equipments used for the measurements. In Chapter 5–7,we show the methods and the results for bulk transmittance, internal surface reflectance,and possible effect of striae, respectively. In Chapter 8, we conclude the report.

2

Chapter 2

Photon paths and requirements foroptical properties

In Figure 2.1, examples of typical simulated paths of photons generated by a chargedparticle passing through a bar are shown. Since we do not have images for the designedbar for the TOP of Belle II, we show the paths for the bar used for the beam test in 2010.1

The quartz bars must transmit the photons over long optical length with a number ofinternal reflections.

For the quartz bar designed for the TOP, a typical photon-path length is 5 m anda typical number of internal reflections is 100. Resolution of Cherenkov angle naivelydepends on square root of the number of detected photons. We set the requirement forthe photon retainment after a bulk transmittance of 5 m and a number of reflections of100 to 80%. The retainment of 80% photons corresponds to a resolution of Cherenkovangle of 90%.

Non-uniformity of the refractive index, or striae, in the bar could effect on the photonpaths. At a momentum 3.5 GeV/c2, which is a typical maximum momentum of chargedkaons and pions for the Belle II experiment in the system of experimental room, thedifference of Cherenkov angles between charged kaon and pion is 5.6 mrad. We set therequirement of angle variation due to the striae to be 0.5 mrad. This precision correspondsto more than 10σ of K/π separation power for momentum range of interest. In Figure 2.2,effects of photon-path shift of 1 mrad of 1 meter-long bar are schematically shown. Ourrequirement is safely better than the specification of the MCP-PMT, which has timeresolution of about 30 psec and channel size of 5 mm2. We note that the effective size ofchannel in y direction is 12.5 mm, since the thickness is extended by an extension blockat the end of the bar from 2 cm to 5 cm.

1The bar used for the beam test in 2010 has smaller size than the design for the Belle II. The lengthis 1.85 m and the width is 0.40 m, where the ones for the Belle II are 2.6 m and 0.45 m. The thicknessis the same as the design and is 0.02 m.

3

(a) Examples of photon paths for a charged pion having β = 1 and cos θ = 60◦. Weshow two paths, while a charged particle typically generate 15–20 photons.

(b) Projections of photon paths in y-z and x-z planes for several incident chargedparticles. Mirror images of the bar are implied for the x and y axes.

Figure 2.1: Photon paths in the quartz-bar radiator used for the beam test in 2010.

4

Figure 2.2: Effect of photon-path shift of 1 mrad for a 1 meter-long bar. We show zdirection in the horizontal and x or y direction in the vertical. Mirror images of the barare implied for the x or y direction as in Figure 2.1 (b).

5

Chapter 3

Quartz bars

In this report, we measure the optical properties of two prototypes. One is Suprasil-P710bar of Shin-Etsu Quartz Product Co.1 polished by Okamoto Optics Co.,2 and the otheris Corning 7980 0D bar of Corning Co.3 polished by Zygo Co.4

1http://www.sqp.co.jp/e/.2http://www.okamoto-optics.com/.3http://www.corning.com/.4http://www.zygo.com/.

6

Chapter 4

Equipments

In this chapter, we describe equipments used in our measurements.

4.1 Optical table and aluminum plates

Quartz bar is placed on polyacetal balls put on an aluminum plate on an optical table asin Figure 4.1. The positions of the polyacetal balls are kept in the holes on a vinyl-chlorideplate, which also plays a role of avoiding quartz-aluminum contact. The heights of thealuminum plate is adjustable by using micrometerheads, and the flatness of the plate is±50 µm. Since polyacetal balls are soft, the flatness of the quartz bar is better and ±10µm. The flatnesses are measured by autocollimator 6D of Nikon Co.1

Figure 4.1: Quartz bar is placed on polyacetal balls put on an aluminum plate on anoptical table.

1http://www.nikon.com/

7

4.2 Laser

We use a diode laser of LDU33-405-3.5 provided by Sigma Koki Co.2 The wavelength ofthe laser is 405 nm, which is a typical wavelength of interest for the TOP. The power is3.5 mW. Beam diameter is about 2 × 1 mm2, while the beam divergence is < 1 mrad.Aspherical collimator lens integrated with the laser diode enables adjustment of the focalposition. Since the intensity of the laser fluctuates continuously, we divide the laser usingprism into two, one of which is taken as a reference to calibrate the fluctuations. For theprism, we employ a polarizing beamsplitter PBS-10-4050 of Sigma Koki Co. By polarizingthe beam, calculations of reflections at air-quartz boundaries become easier. The laserand the prism is set to motorized stages of SGSP46-500 and SGSP33-200 of Sigma KokiCo. for horizontal and vertical directions, respectively. The position accuracy is 25 µm(20 µm) and the positional repeatability is 6 µm for the former (latter). Figure 4.2 showsa schematic view and a picture of our setup.

Figure 4.2: Setup of the laser. Since the intensity of the laser fluctuates continuously, wedivide the laser using prism into two, one of which is taken as a reference to calibrate thefluctuations.

4.3 PD

For measuring the intensity of the laser, we use a PD of S3994-01 provided by HamamatsuPhotonics Co.3 Photo sensitivity for a wavelength of 400 nm at 25 ◦C is about 0.25 A/W.Figure 4.3 (a) shows a picture of this PD. The PD is attached to a movable stage as inFigure 4.3 (b).

The efficiency of the PD is measured for several incident points to check the effectivearea of the PD and the position dependence of its efficiency. In Figure 4.4, we showobtained values of the intensities relative to the reference. For each point, we measurethe intensity fifty times and take the average. The scan is performed for each 2 mm step.Effective area is obtained to be at least 6 × 6 mm2, which is larger than the standardwidth of our laser spot of ≤ 0.3 × 0.3 mm2.

2http://www.sigma-koki.com/3http://jp.hamamatsu.com/en/

8

(a) A picture of the PD. (b) The PD is attached toa movable stage.

Figure 4.3: PD.

Figure 4.4: Intensity of the laser relative to the reference for each 2 mm step on the PD.There are no important meanings in the absolute values but in the relative ones. In thecentral area of at least 6 × 6 mm2, the efficiency is stable within 1%.

9

4.4 CCD

For measuring the intensity of the laser dependent on the position, we use a CCD of STC-TC202USB-AT provided by Sensor Technologies Co.4 Figure 4.5 (a) shows a picture ofthis CCD. The pixel size is 4.40 × 4.40 µm2. The number of pixels is 1600 × 1200. TheCCD is set to motorized stages of SGSP46-300 and SGSP26-100 of Sigma Koki Co. forhorizontal and vertical directions, respectively, as in Figure 4.5 (b). The position accuracyis 25 µm (10 µm) and the positional repeatability is 6 µm (3 µm) for the former (latter).

(a) A picture of the CCD. (b) The CCD is attached to a movablestage.

Figure 4.5: CCD.

4http://www.sentech.co.jp/

10

Chapter 5

Bulk transmittance

Number of Cherenkov photons detected by the MCP-PMTs is crucial for the reconstruc-tion of the Cherenkov angle. Resolution of Cherenkov angle naively depends on squareroot of the number of detected photons. Since typical path length of Cherenkov pho-tons in the quartz bar is 5 m, bulk transmittance of 98%/m corresponds to the photonretainment of 90%, which satisfies our requirements.

5.1 Method

Figure 5.1 shows the overview of the setup for measuring the bulk transmittance. Thebulk transmittance τ is obtained from the equation

I0(1 − R0)τ(1 − R1) = I1, (5.1)

where I0 is the intensity of the incident light, I1 is the intensity after the transmission,and R0 and R1 are the reflectances at the air-to-bar and bar-to-air surfaces, respectively.

We use laser which has wavelength of 405 nm with incident angle of (0 ± 1) mrad.The intensities I0 and I1 are measured using PDs. Position of the PD is set so that theshown value of intensity becomes the largest. Since the intensity of the laser fluctuatescontinuously, we divide the laser using prism into two, one of which is taken as a referenceto calibrate the fluctuations (see Section 4.3). The intensity relative to the reference ismeasured fifty times, and the average is taken as the measured value. The reflectancesR0 and R1 are calculated by the Fresnel theorem, since the paths of reflected lights areclose to the one of the incident light and PD cannot be put. The validity of using Fresneltheorem is checked independently by setting the incident angle to be 3, 5, and 10 degrees,where the polarization of the laser is correspondingly taken into account.

To check the position dependence of the bulk transmittance, we test several incidentpositions. As shown in Figure 5.2, we define the axes x and y so that the x and ycoordinates indicate the incident positions in depth and width directions, respectively. Wemeasure the bulk transmittance for all combinations of x = (25, 125, 225, 325, 425) mmand y = (3, 5, 7, 9, 11, 13, 15, 17) mm.

11

Figure 5.1: Overview of the setup for measuring the bulk transmittance. The intensitiesI0 and I1 are measured by PD, while the reflectances R0 and R1 are calculated by Fresneltheorem. The bulk transmittance is calculated from obtained I0, I1, R0, and R1.

Figure 5.2: A rough drawing of the incident points used for checking the position depen-dence of bulk transmittance. The view is from the incident direction.

12

5.2 Result

Measured value of the bulk transmittance at each incident point is shown for the two barsin Table 5.1 and 5.2. We estimate the error of I0 and I1 by measuring hundred times theintensity of the laser not through the quartz bar but through only the air. Obtained valueis +0.04

−0.17%/m. Then the error of bulk transmittance is estimated to be ±0.17%/m. Nosignificant position dependence is observed. The averages of the bulk transmittance are99.44%/m and 99.35%/m for the Suprasil-P710 and Corning 7980 0D bars, respectively.Both Suprasil-P710 and Corning 7890 0D have enough bulk transmittance.

HHHHHHyx

25 mm 125 mm 225 mm 325 mm 425 mm

16 mm 99.47 99.49 99.39 99.47 99.5314 mm 99.53 99.49 99.40 99.49 99.5712 mm 99.28 99.38 99.39 99.43 99.5510 mm 99.49 99.30 99.37 99.40 99.548 mm 99.31 99.44 99.52 99.38 99.536 mm 99.31 99.27 99.49 99.47 99.484 mm 99.41 99.45 99.40 99.42 99.51

Table 5.1: Bulk transmittance in %/m for the Suprasil-P710 bar.

HHHHHHyx

25 mm 125 mm 225 mm 325 mm 425 mm

16 mm 99.34 99.32 99.28 99.38 99.4514 mm 99.39 99.32 99.27 99.35 99.3612 mm 99.39 99.36 99.41 99.39 99.4310 mm 99.36 99.31 99.41 99.38 99.298 mm 99.43 99.37 99.35 99.46 99.416 mm 99.39 99.40 99.44 99.50 99.384 mm 99.29 99.44 99.43 99.49 99.25

Table 5.2: Bulk transmittance in %/m for the Corning 7980 0D bar.

13

Chapter 6

Internal surface reflectance

Possible reduction of the number of Cherenkov photons arises from the internal surfacereflections. The number of internal surface reflections for a typical Cherenkov light is 100according to a MC simulation. Then 99.9% of internal reflectance corresponds to photonloss of about 10%, which satisfies our requirements.

6.1 Method

Figure 6.1 shows the overview of the setup for measuring the internal surface reflectance.The internal surface reflectance α is obtained from the equation

I0(1 − R0)αNe

−LΛ

√1+( bN

L )2

(1 − R1) = I1, (6.1)

where I0 is the intensity of the incident light, I1 is the intensity after the transmission andreflections, and R0 and R1 are the reflectances at the air-to-bar and bar-to-air surfaces,respectively. The N is the number of bounces, the Λ is the attenuation length defined asthe path length in the bulk region corresponding to the photon retainment of 1/e, andL and b are the length and the thickness of the bar, respectively. The exponential factorindicates the photon loss due to the bulk transmission.

We use the same laser and PD as for the measurement of bulk transmittance. Thevalues of I0 and I1 are measured in a similar way, where the angle of PD surface is setperpendicular to the light axis. The R0 and R1 are calculated by the Fresnel theorem.The N is obtained easily by counting bounces by our eyes. The Λ is obtained from thebulk transmittance τ measured in the previous chapter.

To check the angular dependence of the surface reflectance, we test the incident anglesof 56, 50, 45, 39, 35, and 30 degrees, which correspond to the angles of internal surfacereflections of 56, 59, 61, 65, 67, and 70 degrees, respectively. These angles are selectedso that the coming light does not go down but go up to practically put the PD on ouroptical table. Since the surface reflectance is related to the surface roughness, we extractaveraged surface roughness from measured reflectances.

6.2 Result

Measured values of internal surface reflectances are shown for the two bars in Table 6.1and 6.2. For both bars, obtained value is higher than 99.9% for each angle, indicating no

14

Figure 6.1: Overview of the setup for measuring the internal surface reflectance.

significant reduction of the performance of the particle identification. In Figure 6.2, weshow the surface reflectance depending on the angle of reflection. The data are fitted byan equation of scalar scattering theory

f(x) = 1 − (4πδ cos θ/λ)2, (6.2)

where δ is the root mean square of surface roughness, θ is the angle of reflection, andλ is the wavelength of the laser. We obtain the surface roughnesses of (12 ± 4) A and(17 ± 4) A for the bars polished by Okamoto and Zygo, respectively. The roughnessobtained by the vendor using interferences of photons is < 5 A for each bar (see Tables ??and ??). Dusts on the surfaces are a possible reason of this discrepancy, but we do nothave a conclusion. However, it is at least safe for the performance of particle identificationif we require ∼ 5 A in the stage of the production.

Angle of incidence (◦) Angle of reflection (◦) Number of bounces Reflectance (%)

56 56 45 99.95 ± 0.0150 59 39 99.96+0.02

−0.01

45 61 35 99.97+0.02−0.01

39 65 31 99.92+0.02−0.01

35 67 27 99.96+0.02−0.01

30 70 23 99.98+0.02−0.01

Table 6.1: Result for internal surface reflectance for the bar polished by Okamoto.

Angle of incidence (◦) Angle of reflection (◦) Number of bounces Reflectance (%)

56 56 45 99.92 ± 0.000150 59 39 99.93 ± 0.000145 61 35 99.93 ± 0.000139 65 31 99.93 ± 0.000135 67 27 99.93 ± 0.000130 70 23 99.97+0.02

−0.01

Table 6.2: Result for internal surface reflectance for the bar polished by Zygo.

15

(a) Result for the bar polished by Okamoto. (b) Result for the bar polished by Zygo.

Figure 6.2: Internal surface reflectance depending on the angle of reflection. A fit isperformed by using a curve of scalar scattering theory.

16

Chapter 7

Possible effect of striae

Cherenkov light could curve due to the fluctuations of refractive index in the quartz bar.Especially, the striae, which would be made during the furnace deposition process, couldeffect on the photon path. The curve effects on the position and the time of photon arrivalat the MCP-PMTs. The difference of the Cherenkov angles between kaon and pion for 3.5GeV/c2 is 5.6 mrad, hence the mean of photon-path shift of 0.5 mrad is safe for achievingthe performance of particle identification for Belle II as described in Chapter 2. Differentcurves depending on the photon paths could produce interferences of photons, which leadto interference patterns at the MCP-PMTs. However, if the absolute position differenceof each photon arrival point is small enough, the periodicity of the interference pattern issmall enough not to affect the performance of particle identification. In this chapter, weestimate possible effect of striae using laser and CCD.

7.1 Method

Due to the method of the furnace deposition, the striae are most likely to make layersparallel to the largest surfaces. Then the photon close to parallel to the largest surfaceswould be affected by striae most significantly. The laser is incident from a smallest surface,and the transmitted photons are detected by the CCD. The laser and the CCD are seton individual motorized stages, while the positions can be simultaneously moved witha precision of O(µm). We scan the positions of the laser and the CCD, and check thespecifications of the spot detected by the CCD.

The measurement is based on three steps: 1) take data for all combinations of x = (25,125, 225, 325, 425) mm and y = (3, 5, 7, 9, 11, 13, 15, 17) mm, 2) transform the bluebitmap images to two-dimensional histograms, and 3) fit the two-dimensional histogramsby a probability density function made of two components corresponding to the signaland the background. The signal function is a product f1(x)f2(y) where f1(x) (f2(y)) is aGaussian for an axis x (y). The background function is a product g1(x)g2(y) where g1(x)(g2(y)) is a linear function for axis x (y). The mean and the width of the Gaussian couldbe affected by striae as well as non-flatness of the surface. The data for laser which doesnot pass through the quartz are also taken to compare the results.

The measurement is also done for an incident angle of 30◦ to estimate possible effectfrom different direction of striae. For this measurement, the laser after passing throughthe quartz should go up, since the CCD cannot be put below our optical table practically.Then the scanned region for y direction is limited, and we test with smaller steps to keep

17

number of scanned points higher. For the Corning 7980 0D bar, we additionally test they scan by 0.1 mm steps for incident angle of 0◦ to see possible effect of finer periodicstructure of striae parallel to the largest surfaces. Furthermore, we check for each datathat there are no lobes near the nominal peak, since it is reported that lobes could beseen for worse materials [2].

Figure 7.1: Overview of the setup for estimating possible effect of striae.

7.2 Result

Figure 7.2 shows a typical result of the data taken by the CCD. The projections in thefigure are obtained by integrating over whole data range. The data is well fitted with ourprobability density function. We also check the distributions in divided several regionsand find good qualities for all regions.

Figures 7.3 and 7.4 show the fit results for each point of laser incidence for the Suprasil-P710 and Corning 7980 0D bars. We show the mean and the width of fitted Gaussianfor x and y directions. The data for y < 20 mm corresponds to the laser passing throughthe quartz bar, while the data for y > 20 mm corresponds to the laser passing throughonly the air. For the region y < 20 mm, variations are seen especially for the mean andwidth in y direction. These variations correspond to photon-path shifts within ±0.15mrad and ±0.33 mrad for the Suprasil-P710 and Corning 7980 0D bars, respectively.These variations can be explained by only non-flatness of the surface. The angle of thesurface affects on the mean, while the differential of the angle of the surface could affecton the width. Note that the requirement for the non-flatness is worse for the Corning7980 0D bar (see Chapter 3), and the variations are slightly larger for the Corning 79800D bar. We conclude that the effect of striae is lower than the one of non-flatness at leastfor each measured point. We see gaps between the laser passing through the quartz andonly through the air, possible reason of which is a slight difference of the incident anglefrom zero. The stability for y > 20 mm indicates that our method using motorized stagesworks well.

Figures 7.5 and 7.6 show the results obtained by setting the incident angle to be 30◦.We obtain stable values of the means and the widths for both x and y directions. Whilethe scanned region is small, we see small variation for the Corning 7980 0D bar. Thisvariation can safely be explained by the non-flatness of the surface.

Figure 7.7 shows the result of the fine scan for the Corning 7980 0D bar. The step sizeof 0.1 mm is smaller than the spot size. Even if the periodic structure of the striae is finerthan the step size, the width could be affected by the striae. Obtained result is consistentwith the statement that the effect of striae is smaller than the one of non-flatness of thebars. We also scan in the x direction for several y points, and find no effects more thanthe ones of non-flatness.

18

(a) A typical bitmap imagetaken by CCD.

x0 500 1000 1500

Eve

nts

/ (

10 )

0

1000

2000

3000

4000

5000

6000

/NDF = 1.342χ

x0 500 1000 1500

Eve

nts

/ (

10 )

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y0 500 1000

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nts

/ (

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/NDF = 1.232χ

y0 500 1000

Eve

nts

/ (

10 )

0

500

1000

1500

2000

2500

3000

3500

4000

4500

(b) Typical projections obtained by a two-dimensional fit.

Figure 7.2: Typical result of the data taking with CCD.

Incident y position (mm)0 5 10 15 20 25 30

Y m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

3

3.5

4

4.5

5


Y w

idth

(m

m)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4


X m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

3

3.5

4

4.5

5


X w

idth

(m

m)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

Figure 7.3: Means and widths of the fitted two-dimensional Gaussian for the Suprasil-P710 bar. The data for y < 20 mm corresponds to the laser passing through the quartzbar, while the data for y > 20 mm corresponds to the laser passing through only the air.This figure shows the result for x = 225 mm while we obtain similar results for x = 25,125,325, and 425 mm.

19


Y m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

3

3.5

4

4.5

5


Y w

idth

(m

m)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4


X m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

3

3.5

4

4.5

5


X w

idth

(m

m)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

Figure 7.4: Means and widths of the fitted two-dimensional Gaussian for the Corning7980 0D bar. The data for y < 20 mm corresponds to the laser passing through thequartz bar, while the data for y > 20 mm corresponds to the laser passing through onlythe air. This figure shows the result for x = 225 mm while we obtain similar results forx = 25,125, 325, and 425 mm.

20

Incident relative y position (mm)0 0.5 1 1.5 2

Y m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

3

3.5

4

4.5

5


Y w

idth

(m

m)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2


X m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

3

3.5

4

4.5

5


X w

idth

(m

m)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Figure 7.5: Result of the scan at x = 225 mm with an incident angle of 30◦ for theSuprasil-P710 bar. In this figure, we use y coordinate relative to the starting point.

21

Incident relative y position (mm)0 0.2 0.4 0.6 0.8 1 1.2 1.4

Y m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

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Y w

idth

(m

m)

0

0.02

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0.12

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X m

ean

wit

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(m

m)

1.5

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X w

idth

(m

m)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Figure 7.6: Result of the scan at x = 225 mm with an incident angle of 30◦ for the Corning7980 0D bar. In this figure, we use y coordinate relative to the starting point.

22


Y m

ean

wit

h r

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ect

to C

CD

(m

m)

1.5

2

2.5

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Y w

idth

(m

m)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4


X m

ean

wit

h r

esp

ect

to C

CD

(m

m)

1.5

2

2.5

3

3.5

4

4.5

5


X w

idth

(m

m)

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

Figure 7.7: Result of the fine scan at x = 225 mm for the Corning 7980 0D bar. Highery widths are obtained for several incident positions, while these are safely small.

23

Chapter 8

Conclusions

In conclusion, we check optical properties of the Suprasil-P710 and Corning 7980 0D barspolished by Okamoto and Zygo, respectively, using laser, PD, and CCD. We measure thebulk transmittance to be 99.44%/m and 99.35%/m in average for the Suprasil-P710 andCorning 7980 0D bars, respectively. Relative photon loss due to a typical path lengthof 5 m is 3%, which is almost negligible when considering the performance of particleidentification. We also measure the internal surface reflectance to be larger than 99.92%in the range of angle of reflection larger than 56◦. Photon loss due to a typical bouncesof 100 times is less than 10%. Obtained surface reflectance corresponds to the surfaceroughness of (12 ± 4) A and (17 ± 4) A for the bars polished by Okamoto and Zygo,respectively, according to a scalar scattering theory. These surface roughnesses are worsethan the values of < 5 A measured by the vendors but at least the requirements of5 A to the vendors are secure. In addition, we estimate possible effect of striae by variousapproaches of different incident positions, different incident angles, and different stepsof the scan. The effect of striae is less than the one of non-flatness corresponding toabout < 0.3 mrad shift of photon path. This shift is smaller than the difference 5.6 mradof the Cherenkov angles between kaon and pion expected for a momentum 3.5 GeV/c.Finally, both of the prototype bars of Suprasil-P710 and Corning 7980 0D polished byOkamoto and Zygo, respectively, satisfy our requirements for bulk transmittance, surfacereflectance, surface non-flatness, and striae.

24

Bibliography

[1] T. Abe et al., “Belle II Technical Design Report,” KEK Report 2010–1,arXiv:1011.0352 (2010).

[2] J. Cohen-Tanugi et al., “Optical properties of the DIRC fused silica Cherenkov detec-tor,” Nucl. Instrum. Methods Phys. Res., Sect. A 515, 680 (2003).

25

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