Optimization of the Refractive Index of a Gap Material Used for the 4-layer DOI Detector

$: Optimization of the Refractive Index of a Gap Material Used for the 4-layer DOI Detector$
1066 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 61, NO. 3, JUNE 2014

Optimization of the Refractive Index of a GapMaterial Used for the 4-layer DOI Detector

Fumihiko Nishikido, Naoko Inadama, Eiji Yoshida, Hideo Murayama, and Taiga Yamaya, Member, IEEE

Abstract—We have developed a 4-layer depth-of-interaction(DOI) detector which consists of four layers of scintillation crystalarrays and a position sensitive photomultiplier tube (PS-PMT). Tocontrol the behavior of scintillation light in each DOI crystal array,some reflectors between crystals are removed so that all crystalresponses in the four layers are expressed in one two-dimensional(2D) position histogram by implementing an Anger-type calcula-tion of the PS-PMT signals. Since the method utilizes spread ofscintillation light through the boundary of the crystals with noreflectors, positioning performance in the 2D position histogramdepends on the crystal dimensions, the crystal surface finish, andgap materials. In this work, we propose an adjustment methodfor crystal identification performance of the 4-layer DOI detectorby selecting the optimal refractive index for the gap materialsbetween the crystals in which the reflectors are removed. We fab-ricated single-layer detectors and 4-layer detectors using LYSOscintillators and evaluated the crystal identification performance,while varying the refractive index of the gap materials (by usingdifferent optical cements). As a result, we found the 2D positionhistogram changes as a function of the refractive index of theoptical cement between crystals and the optimal refractive indicescan be determined for the detector using the LYSO crystals. Weconcluded that the crystal response of the 2D position histogramscan be adjusted and crystal identification performance can beoptimized by changing the refractive index of the gap materials.

Index Terms—Depth of interaction, gamma ray detectors,positron emission tomography, scintillation detectors.

I. INTRODUCTION

T HE depth-of-interaction (DOI) encoding method is animportant technique used in PET detectors to achieve

a high imaging performance. Generally, spatial resolution ofreconstructed images is degraded in the peripheral field-of-viewwithout the DOI technique due to the parallax error.Many research groups have reported on various types of

DOI-PET detectors. For example, DOI information can be ob-tained by stacking single-layer crystal arrays [1]–[3], detectingscintillation photons at two opposite sides of the continuouscrystals (dual-end readout detector) [4], [5], using pulse shapediscrimination (phoswich detectors) [6], [7], and using stag-gered dual-layer crystal arrays [8].

Manuscript received August 12, 2013; revised December 26, 2013; acceptedFebruary 03, 2014. Date of publication April 28, 2014; date of current versionJune 12, 2014.The authors are with the National Institute of Radiological Sciences,

Chiba 263-8555, Japan (e-mail: [email protected]; [email protected];[email protected]; [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TNS.2014.2305170

The 4-layer DOI detector we previously developed was de-signed to promote the development of an advanced PET systemwhich has high spatial resolution and low parallax error [9]. Itis a 4-layer DOI detector composed of a single kind of crystalelements and has photo-detectors mounted on only one side ofthe crystal block. The crystals are arranged in a 4-layer DOIcrystal array and coupled to a position sensitive photomultipliertube (PS-PMT). All crystals in the layers of the 4-layer DOI de-tector can be identified on one two-dimensional (2D) positionhistogram which is obtained by implementing an Anger-typecalculation of the PS-PMT signals; this identification is madepossible by the controlling of the scintillation light path using asuitable reflector arrangement in the DOI crystal array.The principle is illustrated in Figs. 1 and 2. Each crystal ele-

ment produces responses on the 2D position histogramwhen theradiation interacts with the scintillator. As shown in Fig. 1(a), re-flectors of a conventional non-DOI PET detector are inserted inall spaces between crystals. Since scintillation light cannot passthough the reflectors and enter in adjacent crystals, the crystalresponses on the 2D position histogram are placed at equal dis-tance as shown in Fig. 1(b). On the other hand, some reflec-tors are removed in the 4-layer DOI detector of Fig. 1(c). Sincethe scintillation light originating in a crystal passes through theboundary and spreads to the adjacent crystals where the reflec-tors are removed, the light distribution on the PS-PMT changes.As a result, the responses corresponding to the four crystalswithout the reflectors between them become closer to each otheron the 2D position histogram as shown in Fig. 1(d). By stackingthe crystal arrays with the different reflector arrangements indi-cated in Fig. 2(a), all crystal responses of the 4-layer DOI de-tector (Fig. 2(b)) appear without overlap in one 2D position his-togram (Fig. 2(c)).The 4-layer DOI encoding method has some advantages over

other DOI encoding methods. The presented method realizes4-layer encoding with a single kind of scintillator while thephoswich detector needs to use scintillators with slow decaytime to get pulse shape discrimination. One-side readout andAnger-type calculation with a register chain circuit can reducethe number of photo-detectors and the amount of readout elec-tronics needed, compared with the stacking detectors and thedual-ended readout detectors. In addition, the method identifiesthe 4-layer crystal with only one 2D position histogram whilethe phoswich detectors and stacking detectors need the samenumber of 2D histograms as the number of their layers.In this method, however, the crystal responses may overlap

under some detector conditions such as inappropriate crystal di-mensions, the type of crystal surface finish or the position rela-tionship between the crystals and the PS-PMT [10]. As indicated

0018-9499 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

NISHIKIDO et al.: OPTIMIZATION OF THE REFRACTIVE INDEX OF A GAP MATERIAL USED FOR THE 4-LAYER DOI DETECTOR 1067

Fig. 1. (a) Reflector arrangement and (b) corresponding 2D positionhistograms for a typical PET detector. (c) Reflector arrangement and (d) corre-sponding 2D position histograms for the 4-layer DOI detector. In the 4-layerDOI detector, some reflectors are removed and responses corresponding to thetwo crystals without any reflector between them become closer to each otheron the 2D position histogram.

Fig. 2. (a) Reflector arrangement patterns of each layer and 2D position his-tograms in the 4-layer DOI detector. (b) Schematic of the 4-layer DOI detectorand (c) its 2D position histogram.

in Fig. 3(a), when the four crystal responses in each layer moveaway from each other due to an inappropriate crystal condition,the crystal responses between different layers overlap and thecrystals cannot be distinguished. Then we should adjust the lo-cation of the crystal responses so all responses can be discrimi-nated as indicated in Fig. 3(b).Nevertheless, crystal dimensions are ordinarily determined

by targets of PET scanners and scintillator materials in orderto achieve sufficient spatial resolution and sensitivity. In addi-tion, surface finish is mainly determined by selecting the op-timum machining process for each scintillation crystal. In thiswork, we focused on the material between the scintillation crys-tals when the reflectors are not inserted in order to adjust the

Fig. 3. (a) Example of an overlapped 2D position histogram for the 2-layer DOIdetector. In this case, the corresponding crystals cannot be identified. (b) 2Dposition histogram of the ideal 2-layer DOI detector.

crystal responses at the optimal positions on the 2D positionhistogram. We proposed an adjustment method for the 4-layerDOI detector performance and conducted experiments to eval-uate its suitability.

II. MATERIALS AND METHODS

A. Adjustment Method of the 2D Position Histogram

The amount of scintillation light passing through theboundary between crystals determines the fraction of scintilla-tion light incident on each PS-PMT anode. The fraction of thescintillation light determines the location of crystal responseson the 2D position histogram. It should be noted that thereflector removal does not allow all scintillation light to passto an adjacent crystal because of material in the gap betweenthe crystals. The scintillation light which has a certain incidentangle undergoes total reflection at the boundary because ofthe refractive index difference between the crystal and air.This means that the fraction of incident light for all PS-PMTanodes change as the refractive index changes. It also meansthat we can adjust the 2D position histogram by selecting theappropriate refractive index.The refractive index can be controlled by choosing the mate-

rial used in the gap between crystals. Fig. 4 shows the relation-ship between the 2D position histogram and refractive index ofthe gap material between crystals. Fig. 4(a) shows a crystalarray surrounded by reflectors and Fig. 4(b) shows 2D posi-tion histograms for gap materials that have various refractiveindices. As the refractive index of the gap material approachesthe refractive index of the crystal, more light spreads to the ad-jacent crystals because the critical angle becomes larger. Thecorresponding crystal responses accordingly become closer toeach other as shown in the center drawing of Fig. 4(b). In theextreme case of the material having the same refractive indexas the crystal, the scintillation light spreads inside the four crys-tals as if it is in one large crystal. This makes only one crystalresponse on the 2D position histogram.


Fig. 4. Relationship between 2D position histogram and refractive index of amaterial between crystals. (a) Four crsytals surrounded by the reflector. Reflec-tors between each crystal are removed and these spaces are filled with certainmaterials. (b) The 2D position histograms using the gap materials which havevarious refractive indices.

B. Optical Cements with Various Refractive Indices

In order to study the effect of refractive index of materials onthe positioning of the crystal responses, we compared the 2Dposition histograms obtained with materials of different refrac-tive indices in the gaps between the crystals. We used a series ofoptical cements produced by NTT Advance Technology Corpo-ration (Japan). The different refractive indices of the optical ce-ments are the result of using different amounts of an additive sothat the series members have similar characteristics other thantheir refractive index. Refractive index can be adjusted from1.32 to 1.70 in 0.005 increments. In this work, we used fourtypes of optical cements with refractive indices of 1.40, 1.50,1.60 and 1.70. The optical cements are UV-adhesive and liquidsbefore hardening; they do not come unstuck after hardening.They are also transparent before and after hardening.

C. Experiment

Two types of crystal arrays were used in measurements. Thefirst was an single-layer crystal array whose reflectors wereinserted as the first layer reflector arrangement before stackingas shown in Fig. 2(a). For the single-layer detector, we used

(LYSO, Proteus Inc. USA) with dimensionsof mm mm mm and refractive index of 1.82.All their surfaces were mechanically polished. The reflector wasa multilayer polymer mirror (Sumitomo 3M, Ltd., Japan) of0.065 mm thickness and 98% reflectivity. The second crystalarray was a 4-layer DOI crystal array composed by stacking four

LYSO arrays. The crystal array in the first layer was thesame as the single-layer crystal array described above. Crystalarrays in the other layers had the reflector arrangement indicatedin Fig. 2(a).We prepared five crystal arrays with a different optical

boundary condition between crystals for each array type. Inthe first four arrays, the four adjacent crystals surrounding thereflector were bonded to each other by four types of opticalcements with refractive indices of 1.40, 1.50, 1.60 and 1.70between the crystals. The fifth array was fabricated without anyoptical cement between crystals and remained as an air gap.

Fig. 5. A block diagram for the experiment.

A 256-channel flat panel position sensitive photomultipliertube (256ch FP-PMT, H9500, Hamamatsu Photonics K.K.Japan) was used as the photo detector. Although the FP-PMThas a channel (ch) anode with 3.08 mm pitch, onlych were used in experiments. Fig. 5 shows a block diagram of ameasurement system. The individual 64ch signals were fed intoshaping amplifiers and finally recorded with analog-to-digitalconverters (ADCs) of a CAMAC system. A dynode signal wasfed to a photomultiplier amplifier and triggered by a constantfaction discriminator. Finally, CFD output signals were fed toa gate and delay generator to generate the gate pulse for theADCs. 662 keV gamma-rays from a point source wereirradiated onto the crystal arrays before and after stacking thearrays.

D. Monte Carlo Simulation

We conducted a detector simulation with a previously de-veloped Monte Carlo simulator [11] in order to theoreticallyconfirm our presented method. The simulator traces interactionof the annihilation photons in a scintillation crystal array andscintillation photon tracks from the interacted point to a pho-tocathode of a PMT. A single-layer crystal array wasassumed which consists of mm mm mmlutetium oxyorthosilicate crystals. Reflectors were inserted asthe first layer reflector arrangement before stacking, the sameas for the single-layer crystal array used in the experiment. Thegap thickness between the crystals, absorption in the gap mate-rial, energy resolution of the scintillator, variation in light yieldof each crystal element and non-uniformity of anode gain of thePMT were not assumed. Refractive index of the gap materialwas only changed at 1.00, 1.40, 1.50, 1.60 and 1.70. Other sim-ulation parameters and detector geometry were given the samevalue as the detector used in the experiment.

III. RESULTS

A. Simulation Results

Figs. 6 and 7 show 2D position histograms and the profilesobtained by the Monte Carlo simulation. In the simulation, thesingle-layer detectors using no optical cement (air gap) andusing the optical cements of different refractive indices wereassumed. Peak-to-valley ratio for the detectors of the refractiveindices of 1.00, 1.40, 1.50 and 1.60 are , ,

and , respectively. The peak-to-valley ratio of


Fig. 6. 2D position histograms obtained by the Monte Carlo simulations forsingle-layer detectors: (a) using air in the spaces between crystals and (b) to(e) using different optical cements.

Fig. 7. Profiles of the 2D position histograms obtained by the Monte Carlosimulations for single-layer LYSO detectors of various refractive indices.

the refractive index of 1.70 cannot be calculated since the peaksof the profile are completely overlapping. As another figure ofmerit, the peak distance is defined as the distance between peakpositions of the two crystal responses for crystals bonded by the

Fig. 8. 2D position histograms of the LYSO single-layer detector: (a) usingnothing in the spaces between crystals and (b) to (e) using different optical ce-ments.

optical cement. The peak positions were obtained by observingpeak pixels of the profiles shown in Fig. 7. The average peakdistance for the refractive indices of 1.00, 1.40, 1.50 and 1.60are , , and , respectively.The peaks of the crystals surrounded by the reflector becomeclose with increasing refractive index value and finally the peakdistance cannot be calculated for the refractive index of 1.70 asthe expectation (see the right figure in Fig. 4(b)).

B. Experimental Results

Figs. 8 and 9 show 2D position histograms and the profiles ofthe LYSO single-layer DOI detectors without the optical cement(air gap) and with the optical cements of different refractive in-dices. The 2D position histogram for refractive index of 1.00was obtained with the air gap crystal array (Figs. 8(a) and 9(a)).Four responses in the green squares correspond to the crystalswith air or optical cement gap, and which are surrounded by thereflectors. The four responses of the bonded crystals becomecloser to each other as the refractive index of the optical ce-ment approaches that of the scintillation crystals and finally theresponses overlap as a single cluster in the case of the LYSOscintillation crystal. Peak-to-valley ratio for the detectors of therefractive indices of 1.00, 1.40, 1.50, 1.60 and 1.70 are ,

, , and , respectively. Theratio also shows that peak separations between the crystals sur-rounded by the reflectors are dramatically degraded in the caseof the refractive indices of 1.60 and 1.70.Fig. 10 shows average peak distances of the crystal responses

for each refractive index. The peak distance of the crystal re-sponses gradually becomes smaller as the refractive index be-comes larger. We expect that the peak distance will approachzero, as if the four crystals behave as a single crystal, when theoptical cement with refractive index of 1.82 is used. The solidcurve shows the extrapolation of the curve as the peak distanceapproaches zero around the refractive indices of LYSO. In thecalculation of the peak distance, the peak positions were simply


Fig. 9. Profiles of the 2D position histograms for single-layer LYSO detectorswithout the optical cement (air gap) and with the optical cements of differentrefractive indices.

Fig. 10. Relationship between refractive index and average of each layer peakdistance for the single-layer LYSO array.

observed at positions of the peaks in the profiles. The crystal re-sponses are largely overlapping as shown in Figs. 9(e) and peakpositions of the overlapping crystal response are closer than theactual peak position due to simple observation of the peak posi-tions. As a result, the peak distances for the refractive index areestimated as smaller, and then the point for the refractive indexof 1.7 is not on the extrapolated curves.

Fig. 11. 2D position histograms of the LYSO 4-layer detector: (a) using nothingin the spaces between crystals and (b) to (e) using different optical cements.

Fig. 12. Profiles of 1st and 2nd layers obtained from the 2D position histogramsof the 4-layer LYSO detectors without the optical cement (air gap) and with theoptical cements of different refractive indices.

Figs. 11 and 12 show 2D position histograms and the pro-files of 4-layer DOI detectors using no optical cement (air gap)and using the optical cements of different refractive indices. Thefour responses surrounded by the green squares correspond to


Fig. 13. Relationship between refractive index and the average peak distanceof each layer for the single-layer LYSO array.

Fig. 14. Energy spectra for 662 keV gamma rays of single-crystal elements ineach layer of the crystal array using the optical cements with the refractive indexof 1.40.

the first layer crystals bonded by the optical cement. We seethat the four responses of the bonded crystals become closerto each other as the refractive index of the optical cement ap-proaches that of the crystal. In the case of a material of low re-fractive index such as air, two peaks corresponding to the samelayer crystals are at a distance and overlap the peak of anotherlayer crystal on the opposite side. As the refractive index ofthe material becomes higher, the overlap of peaks decreases;however, the refractive index becomes too high such as in thecase of refractive index where overlap is observed be-tween peaks of the same layer crystals. Fig. 13 plots the averagepeak distance of crystal responses in the same layer. It showsthat peak distances become smaller as the refractive index ap-proaches that of the crystal the same as with the results of thesingle-layer detector.Fig. 14 shows energy spectra for 662 keV gamma rays of

single-crystal elements in each layer of the crystal array usingthe optical cements with the refractive index of 1.40. The fourthlayer crystals are in bottom of the crystal array and directlycoupled to the PS-PMT. Therefore, photo-peak position of thefourth layer crystal is the highest and the photo-peak moves tolower positions in the case of the upper layer crystals. Peaksaround 50ch of the third and fourth layers and tails in higherchannels than the photo-peaks for the first and second layer are

Fig. 15. Average energy resolutions for four single-crystal elements in eachlayer of the 4-layer DOI detectors using the optical cements with various re-fractive indices.

caused by misidentification of the crystal elements since thepeak responses representing different layer crystals appear atthe adjacent position on the 2D position histograms.Table I and Fig. 15 show energy resolutions measured for 16

crystal elements sampled from each layer of the 4-layer DOIdetectors with various refractive indices. Sufficient energy res-olutions for use as PET detectors are obtained for the detectorsusing the optical cements with the refractive indices of 1.40,1.50 and 1.60. The energy resolution is degraded over 17% inthe case of the detectors using the air gap ( ) and theoptical cement with the refractive index of 1.70.Table II shows photo-peak positions measured for 16 crystal

elements sampled from each layer of the 4-layer DOI detectorswith various refractive indices. These crystal elements are thesame crystals used in the analysis of the energy resolution. Inthe measurement, the crystal arrays were not at precisely thesame position on the FP-PMT. The difference of the photo-peakpositions includes position dependence of anode gains and dif-ference of the light yield of the crystal elements. Therefore, in-fluence of the optical cements on the light output cannot be di-rectly estimated from the table. In order to estimate decrease ofthe scintillation light, relative light output defined as ratios of thephoto-peak positions to that for fourth layer crystals were cal-culated as shown in Fig. 16. The light outputs of the upper layercrystals decrease for all refractive indices due to absorption inthe LYSO crystal itself and the gaps between crystals. The de-creases of the average light outputs for the crystal elements inthe first layer from the fourth layer in the detectors of the re-fractive indices of 1.00, 1.40, 1.50, 1.60 and 1.70 are 20.5%,29.7%, 26.1%, 29.2% and 34.5%, respectively. The data indi-cate that the absorption of the scintillation photons in the opticalcements is larger than that in the air gap.

IV. DISCUSSION

As seen in Figs. 10 and 13, the distance of the crystal responsefor the 4-layer DOI detector can be controlled by changing therefractive index of the gap material. The simulation data alsoshow a similar tendency as the experimental data as seen inFig. 6 and 7. There are differences between the simulation and


TABLE IENERGY RESOLUTIONS FOR FOUR SINGLE-CRYSTAL ELEMENTS IN EACH LAYER OF THE 4-LAYER DOI DETECTORS USING THE OPTICAL CEMENTS WITH

VARIOUS REFRACTIVE INDICES

TABLE IIPHOTO-PEAK POSITIONS FOR FOUR SINGLE-CRYSTAL ELEMENTS IN EACH LAYER OF THE 4-LAYER DOI DETECTORS USING THE OPTICAL CEMENTS WITH

VARIOUS REFRACTIVE INDICES

Fig. 16. Relative outputs of crystals in each layer of the 4-layer DOI detectorsusing the optical cements with various refractive indices and the air gap.

experiment due to the simplification of the simulation describedin II-D. The tendency of the simulation and experimental data,however, theoretically support suitability of the presentedmethod to optimize the position of the crystal responses.If an optimal refractive index exists in the desired range, we

can obtain the best crystal identification performance by con-trolling the positions of the crystal responses. We applied thefollowing method to determine optimal refractive indices foreach detector. We define the distance of the crystal responsescorresponding to the adjacent crystals without a reflector be-tween the crystals as “A”, and with the reflector as “B” as shownin Fig. 17(a). The material with the optimal refractive index pro-duces evenly spaced crystal responses on the 2D position his-togram. Then the peak distance ratio defined as the ratio of A to( ) is close to 0.25 in the optimal condition.Figs. 17(b) and (c) show the peak distance ratio as a function

of the refractive index of the gap material for the single-layerdetector and 4-layer DOI detector, respectively. As Figs. 17(b)and (c) show, the best refractive indices for the single-layer de-tector and 4-layer detector of the LYSO scintillators are around1.45 and 1.50, respectively. Stacking of the 4-layer crystal ar-rays causes little difference in the best value of the refractiveindex because the scintillation light can enter into the upper

Fig. 17. (a) Ideal peak distance, . (b) Relationship betweenrefractive index and ratio of peak distance in the single-layer detectors. (c) Rela-tionship between refractive index and ratio of peak distance in the 4-layer DOIdetector.


layer and spread to adjacent clusters of the four crystals beyondthe reflector.In addition, the best value of the energy resolution can be

obtained around the refractive index of 1.50. The degradationof the energy resolution for the detector using the optical ce-ment with the refractive index of 1.70 can be explained by com-mingling of the same layer events. As shown in Fig. 11(e), thecrystal responses of the same layer are close and overlapping onthe 2D position histogram. The different light yields of the over-lapping crystals lead to degradation of the energy resolutions.On the other hands, in the case of the air gap, the peak responsesof each layer are apart from each other, and then overlappingon the crystal responses of other layers as shown in Fig. 11(a).Since the differences of the light yield between the crystals ofdifferent layers are larger than that of the same layer, the degra-dation of the energy resolution for the detector with the refrac-tive index of 1.00 becomes larger than that of the detector withrefractive index of 1.70.These results confirm our previous work [12]. We used

the LYSO crystals with the same dimensions ( mmmm mm) in the previous work. RTV rubber

(refractive index ) was choose as the material of thegaps between the four crystals surrounded by the reflectors. As aresult, sufficient crystal identificationperformancewasobtained.The previous result was consistent with the above discussions.

V. CONCLUSIONS

We studied the optimization method of the 4-layer DOI de-tector by selecting the appropriate reflective index of the gapmaterials. We found that the crystal response of the 2D positionhistograms could be adjusted by changing the refractive indexof the optical cement and the optimal refractive indices couldbe determined for the LYSO crystal scintillators. In addition,the result confirmed that the RTV rubber we used previously asthe gap material for the 4-layer DOI detector had a refractiveindex that was close to the optimum choice.

ACKNOWLEDGMENT

The authors would like to thank Messers. A. Ohmura,Y. Yazaki and H. Osada for support during the experiments.

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Optimization of the Refractive Index of a Gap Material Used for the 4-layer DOI Detector

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