GETFOCOS for imaging atmospheric Cherenkov telescopes—A GEant4 tool for optimization and characterization of an optical system

Nuclear Instruments and Methods in Physics Research A 659 (2011) 282–288

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

GETFOCOS for imaging atmospheric Cherenkov telescopes—A GEant4 tool for optimization and characterization of an optical system L. Arruda n, P. Assis, F. Bara~ o, R. Pereira, M. Pimenta, B. Tome´ ´rio de Instrumentac- a~ o e Fı´sica Experimental de Partı´culas, Lisbon, Portugal LIP – Laborato

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 April 2011 Received in revised form 10 August 2011 Accepted 15 August 2011 Available online 22 August 2011

The aim of this article is to introduce a dedicated simulation package, named GETFOCOS, that combines Geant4 and ray-tracing algorithms that can be used on the characterization of the optics of a generic Imaging Atmospheric Cherenkov telescope as well as on the optimization of its focal plane geometry. The image spot size is evaluated for both cases in a large field-of-view observation scenario. This tool allows to perform fast but precise tests for different optical options. The specific case of a Fresnel lens, inspired by the concept developed for the GAW experiment, is analysed. However, this intends to be an universal and relevant tool for any kind of optical system. A complete characterization of the optics is presented together with a study for the optimization of the focal plane shape. & 2011 Elsevier B.V. All rights reserved.

Keywords: IACT VHE gamma rays Geant4

1. Introduction Imaging Atmospheric Cherenkov Telescopes (IACTs) detect the Cherenkov photons produced in the Earth’s atmosphere by charged, locally superluminal particles in atmospheric showers. The usage of this technique opened a window to the groundbased gamma-ray astronomy in the very high energy (VHE) range1 and a continuous effort is being done to improve the detection performance and the sensitivity. Examples of operating IACTs are CANGAROO III [2], HESS [3], MAGIC [4] and VERITAS [5]. Basically, an imaging atmospheric Cherenkov telescope consists of an optical system with a few degrees of field-of-view (lower than 51) and of a pixelized camera placed at its focus. Most IACTs have large diameter mirrors but their reduced field-of-view is a consequence both of the degradation of the image quality for off-axis observation angles and of the need of using small cameras at the focal plane to decrease the mirror obscuration. To cover larger sky areas, the usage of refractive optics with the camera located behind the lens has been considered. In particular, a Fresnel lens is a possible option due to its small weight and reduced thickness [6]. The GAW (Gamma Air Watch) telescope to be installed in the Calar Alto Observatory, in Spain brought forward this new approach [7]. The image quality of an IACT, measured by the rms of the focal point spread function (PSF) is aimed to be of the order of 0.11 within most of the field-of-view (FOV). A limit to the angular resolution arises predominantly from n

Corresponding author. Tel.: þ35 1217995022; fax: þ 35 1217934631. E-mail address: [email protected] (L. Arruda). 1 As a rule of thumb, gamma-rays are classified as VHE in the range with energies from 30 GeV up to 30 TeV [1]. 0168-9002/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2011.08.030

the air shower physics and from the limited collection efficiency of Cherenkov photons (including collection area and quantum efficiency of the photon detector). Independently of the chosen optical system for the light collection in a Cherenkov telescope, its design and complete characterization need to be done. In a first approach, qualitative and quantitative studies are performed for the most relevant wavelengths allowing to determine the main characteristics of the optics concerning the evaluation of the image quality. This can be done with commercial programs that take into account the correct geometry and the full description of the optical materials like CODE V [8] or OSLO [9]. However, these engineering packages are not included in the simulation programs of the experiments, where simplified ray-tracing methods and/or parameterization of the optical response (point spread function, stray light, aberrations) are used. More recently some experiments have been using the Geant4 toolkit [10,11], to simulate their optics [12–14]. Basically Geant4 receives the optical photons generated in the atmospheric cascade and transports them through the optical system to the detection matrix. However, detailed optical studies involving its characterization or optimization imply simulating a large number of photons and iterations on focal plane configuration, which can become too heavy and time consuming to handle. In this case, an algorithm combining the Geant4 simulation capabilities together with ray-tracing can be used without any loss of accuracy and will save a considerable amount of time. This article introduces the GETFOCOS tool, a G Eant4 Tool For Optimization and Characterization of an IACT Optical and detection Systems. The case study of the GAW telescope concept, but using a low performance lens design will be presented. The characterization of its optics and the optimization of configuration of the corresponding focal plane will be reported.

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2. Design of a wide field-of-view telescope To guarantee the success of an IACT, it is mandatory to deal with a relatively high optical resolution to efficiently select the rare gamma shower images from the few orders of magnitude more frequent images induced by background hadronic showers. Due to the smaller transverse momentum in electromagnetic interactions, a gamma-induced shower is much more compact than a hadronic initiated shower and consequently has a reduced and much more regular lateral distribution at the detection level for the same initial energy. Gamma showers produce spot images smaller in size compared to the hadron induced ones, however, such discrimination is not so easy because the distributions of the parameters used to describe the images have a huge overlap. For the TeV region these differences are in the range of (0.1–0.2)1 and they are a few times less for the region below 100 GeV [15]. Consequently, for an efficient image discrimination the telescope should have a point spread function with a rms of that order in each of the mentioned regimes. Ref. [16] introduces a very interesting review on the state of the art of the IACT solutions as well on the next generation of wide FOV atmospheric Cherenkov telescopes. Present IACTs have a tessellated reflector structure either with a parabolic shape or with a spherical mirror (Davies–Cotton design [17]). A reasonable rms for the point spread function (  0.11) and a moderate FOV ( o 51) are achieved. However, a significant drawback of the parabolic design is the existence of significant off-axis aberrations (coma). On the other hand, the spherical mirrors, provide compensation against coma. Nevertheless, global coma is dominant for photon images offset from the optical axis and has significant consequences for the design of a wide field-of-view telescope. The VHE gamma-ray community is concerned about increasing the IACTs field-of-view due to astrophysical reasons. A wider FOV is important to study extended emission regions in our galaxy, to allow surveys of the extragalactic sky, although limited, and to improve the probability of detecting a gamma-ray burst (GRB). Off-axis aberrations can be controlled by increasing the f-number [d=D, with d¼ focal length (distance to the detector plane) and D¼ reflector (or lens) diameter] since first order coma scales with 1=f 2 [18]. Current IACTs have f-numbers between 1.0 and 1.2 which is enough for a field-of-view of 51. A larger field-ofview can be achieved by increasing the f-number but it will imply to enlarge the detection matrix which brings higher costs. Unless a simplification is made on the requirements for pixelization, optical point spread function and consequently the d=D ratio, large FOV require larger cameras which bring significant obscuration. Another solution for a large FOV telescope consists of using a secondary mirror. Ref. [19] explores the idea of using two-mirror, aplanatic optical systems which are free from both coma and spherical aberrations. The Schwarzschild–Couder telescope is a specific example and was proposed for AGIS telescopes [20]. This design achieves an excellent point spread function across the wide FOV together with a considerably shorter focal length than traditional IACTs which allows low cost/pixel multi-anode photomultipliers (MAPMTs) to be used. On the other hand, the research on the use of Fresnel optics has taken off with the EUSO and JEM-EUSO missions [21] and GAW experiment [22]. The former uses two double-sided Fresnel lenses (15 mm thick) with 2.5 m external diameter. The FOV is of 301 from space. The latter uses a single Fresnel lens with a focal length of 2.58 m. The Fresnel lenses might be a real alternative to the mirror for IACTs with several advantages: they are more lightweight, they avoid the central obscuration due to the focal detection matrix and they maintain more imaging stability against deformation. In addition, refractive systems produce

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a tolerable signal spread in time. The isochronous distortion, which is the different light travel times from different parts of the optics, is  0:26 ns for each meter of the lens diameter. Although isochronous distortion is not directly related to the optical quality of the images, it is nevertheless intrinsic to the design and implies that longer integration times are necessary to capture an image. This introduces additional noise from night-sky, which does degrade the images. This is of major importance in the low energy regime where the night sky background (NSB) contamination is relevant. Since the optical system overall transmission is controlled ( 40:7) and the cost for large size is controlled, Fresnel lenses can be a worth choice for IACTs.

3. GETFOCOS description In the design and optimization of an optical system, several parameters must be considered namely the image accuracy, characterized by rms of the point spread function, the optical transmittance/reflectance and the detector FOV. The spot dimensions, coming from both the chromatic and coma aberrations, will depend on the observation angles. Keeping the spot size as low as possible is a key issue for having a good separation of gamma-ray events from hadron induced showers. The analysis of the lens focusing power relies on the measurement of the spot radius from the centroid containing 68% of encircled energy (EE) which corresponds to 68% of the number of detected photons. In a telescope the optical focal distance is normally optimized for on-axis photons. However, the spot size is not necessarily optimized for all the photon incident angles on the optical system. In large field-of-view telescopes, the detector distance is a key issue that should be optimized. The granularity of the detector plane can be explored to adjust the distance and the inclination of each cell to the optics. A dedicated procedure to study and characterize the optical performance and to optimize the geometry of the focal plane of an IACT was implemented and named GETFOCOS. This package derived from a general simulation and reconstruction framework (GAWsoft) developed for the GAW experiment. Fig. 1 illustrates the different software blocks integrated in GETFOCOS. This chain can handle simulated data, on an event-by-event basis. An external photon generator was developed, in a dedicated Cþþ class, to feed the package and is flexible enough to produce monochromatic or polychromatic photons following either a flat or a Cherenkov spectrum or even a source spectrum like star Vega. The direction of the photons can be generated uniformly or from a point-like source, while the impact position can be chosen to be fixed or uniformly distributed over the optical surface. Both the photon absorption in the atmosphere and the photon detection effects are taken into account by convolving the photon spectrum with the atmospheric absorption model and the photodetector’s efficiency curve. Afterwards, particles and optical photons generated according to the methods described before are propagated through the telescope detector geometry. Geant4 is used2 for the telescope simulation including the optical parts and the focal plane. Photon interactions include optical refractions and reflections and absorption by the media. The complete software chain is based on an Object Oriented design (written in Cþþ) which allows very high modularity making easier to use already implemented code, or to perform changes in certain blocks without significant interference on the entire code. The end-to-end simulation is controlled by user supplied data cards based on libconfig package [23] which 2

Geant 4.9.2 version.

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handles structured configuration files. Related data cards are grouped in different blocks. This strategy allows a high flexibility in running the program without recompiling it for example for different geometries under study. The output of the simulation is stored in a root tree structure. The simulation of photons in a given detector geometry described in Geant4, although accurate, is by nature a time consuming process. In addition, in order to obtain statistical

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4. Optimization of a large FOV telescope

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A promising way of building a large FOV telescope is to use a refractive optical system. The possibility of building large surface Fresnel lenses while keeping image distortions small together with their light weight makes them good candidates for the IACT optics. The GETFOCOS tool will be used both to characterize the optical system and to optimize the detector surface of a generic telescope setup made of a Fresnel lens and a matrix composed of planar and pixelized detection cells. The telescope lens size was chosen in order to cover the higher energy domain of the gammaray spectrum ( Z 1 TeV) [22]. A 1.2 f-number Fresnel lens with a diameter of 2.13 m, 3.2 mm thick and a groove density of 0.333/mm was simulated. For a more detailed description on the Geant4 lens geometry implementation see Ref. [12]. The light detection is ensured by an array of multi-anode photomultipliers with 8  8 pixels each. To overcome the photomultiplier’s dead space pyramidal frustum light guides made of UV-transparent plastic have been coupled on the top of it. The light guide unit is optically coupled to the active area of the phototube cathode through a 1 mm thick optical pad with the same refractive index as the light guide material in order to avoid photon losses from light guide medium transition to the photocathode. Therefore, the detection unit to be simulated is composed of a photomultiplier plus a light guide and an optical coupling layer. The dimension of the cell is 26.6  26.6 mm2 which corresponds to a readout pixel size of 3.325 mm and to a pixel FOV of 0.081. The PMT and the light guide can be grouped with similar detection cells which together with the corresponding read-out electronics constitute what is called a macrocell.

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significance for an optical characterization, thousands of photons have to be simulated. In this new approach a photon sample is simulated once in Geant4 for a specific setup and the corresponding results are stored. After, a ray-tracing method is applied to extrapolate the results for different focal plane distances and different inclinations of the detection cells. The spot sizes for each configuration are obtained. The modularity of the implemented scheme allows to simulate any telescope optics and photon detection geometry and makes the GETFOCOS package a flexible and user-friendly tool. Some of the results extracted in this study are introduced hereafter with the main purpose of illustrating the capabilities of the GETFOCOS simulation tool.

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4.1. Optimization of the detector plane geometry Let us assume the previously described case study. Fig. 2 shows the spots made by multiwavelength photons following the Cherenkov atmospheric spectrum impacting at the described telescope at three different incident angles: 0.41 (a), 51 (b) and 121 (c). The increase of the photon spot size is clearly visible for large incident angles. However, the spot size is not necessarily optimized for all the photon incidences on the optical system. To reach an optimal spot one can take advantage of the detection plane granularity defined by the detector cell dimensions. Both the distance from the cell to the light collector (focal distance) and the cell inclination can be adjusted. The maximum dimension of the same macrocell can also be estimated. A set of photons with wavelengths following the Cherenkov spectrum and incident angles ranging from 01 up to 121 were simulated. Fig. 3(a) shows photons impinging on the lens top with a polar angle y. The spot size, defined as the radius from the centroid containing 68% of the total number of detected photons, was calculated from photon intersections with virtual detector planes at different focal distances d and different orientations (a). The optimal spot was obtained by tracing the simulated event and finding the focal distance and cell orientation at which the spot radius was minimal. The main purpose of this procedure followed by the GETFOCOS package was to avoid an intensive use of the Geant4 simulation. Fig. 3(b) shows the spot size dimensions as function of the cell inclination (a) and of the focal distance (d) for 2.71 incident photons. The problem shows degeneracy in a and d parameters, therefore for sake of setup simplicity, the chosen configuration will have a ¼ 01. Fig. 4(a) shows the variation of the spot radius with the focal distance for each of the photon’s incident polar angle on the lens surface for photons with l ¼ 350 nm. The higher the incidence angle, the larger the spot size and the lower the optimal focal distance, as expected. The higher is the incidence angle the less

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sensitive one is to the optimal focal distance since wider curvatures are found for larger angles. Fig. 4(b) shows the evolution of the spot dimensions estimated for the optimized focal plane distances with the incidence photon angle on the lens surface for the monochromatic case (solid line) and for the Cherenkov-like spectrum (dashed line) obtained from the convolution of 1=l with the atmospheric absorption and with the quantum efficiency curve. In the former the image spot size ranges from 1.4 mm for 0.41 up to 19.5 mm for 121 while in the latter the image spot size ranges from 11.2 mm for 0.41 up to 23.0 mm for 121. The effect of introducing a pass-band optical filter from 285 nm to 420 nm was studied (dotted line). The spot size is clearly reduced especially for larger off-axis directions where both the monochromatic and filtered spot sizes get comparable. Fig. 5(a) shows the optimal relative displacements of the focal plane with respect to the optimal detection position for on-axis Cherenkov photons as function of the photon incident angle or to a similar variable which is the distance of the centre of the detection cell in study from the centre of the matrix. In all three cases (monochromatic, Cherenkov and Cherenkov with filter) the behaviour is similar: detection cells should require displacements up to  16 cm for angles ranging from 01 up to 121. The optimal distance from the lens where the centre of the inner photomultipliers should be placed is 2575.0 mm in the monochromatic case as shown in Fig. 4(a). For the Cherenkov case it should be 2637.8 mm and for the Cherenkov with filter 2592.1 mm. Mechanical assembling and the detection cells’ readout favor a detection matrix structure in macrocells where the Z-coordinate of the macrocell can be extracted from Fig. 5(a). Since the macrocell is not point-like, the variation of the focal distance (DZ), within the proper macrocell extension, with the photon source direction shown in Fig. 5(a) can determine a degradation on the spot image as it is presented in Fig. 5(b). For photon source directions above 51 and assuming as reasonable a spot image size variation of 1–2 mm, a focal distance variation of 10–20 mm can

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Fig. 4. (a) Radius of the spot containing 68% of the photons as a function of the focal distances (mm). Result extracted for photons with l ¼ 350 nm. (b) Spot radius (mm) that contains 68% of the encircled photons as function of the photon polar angle at the lens surface. Spots evaluated for each optimal focal plane distance.

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Fig. 5. (a) Curves with relative displacements of the focal plane with respect to the central PMT in the optimized matrix for the Cherenkov case as function of the photon polar angle at the lens surface, as well as, as function of the radial position from the centre of the matrix at which the PMT centre is located. Z-axis points downwards. (b) Spot size deviation from the optimal spot dimension as function of the cell positioning height deviation from the optimal height for different incident angles upon the lens surface.

be accommodated. Such variation on the focal distance can be translated on macrocell field of view or linear dimension, by using Fig. 5(a). A maximal variation of  711 on the field of view is obtained, for larger angles, corresponding to a dimension of 745 mm for the macrocell. Therefore, using a photodetector size of 26.6 mm, the detection plane can be organized in macrocells of 2  2 cells while keeping the spot size variation negligible.

4.2. Characterization and optimization of the optical system In this study, a telescope with a large diameter lens is being used. However, the side effect of using a large size lens to collect the atmospheric Cherenkov photons is the coma aberration. In addition the fact of dealing with a broadband Cherenkov spectrum after folding with the detection efficiency (atmosphere absorption

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Fig. 6. Fraction of encircled energy as function of the distance from the image barycentre, for sources at 350 nm (a) and for atmospheric Cherenkov photons (b). The different curves represent distinct off-axis sources ranging from 0.41 up to 121.

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Fig. 7. Spot radius as a function of the photon impact distance to the lens centre for different incident angles upon the lens surface. (a) Result extracted for photons at 350 nm. (b) Result extracted for Cherenkov spectrum convolved with atmospheric absorption and quantum efficiency.

included) from 300 nm to around 650 nm, implies the existence of chromatic aberration. Therefore, once the optical characteristics are provided by the manufacturer, this one can be simulated and characterized with the GETFOCOS tool. The Fresnel lens used on this simulation studies corresponds to a preliminary design done for the GAW experiment prototype. The lens characterization was performed for different sets of monochromatic photons corresponding to the maximal detection efficiency (  350 nm) and multiwavelength photons corresponding to the detected spectrum of the atmospheric Cherenkov photons. On-axis and off-axis photon directions uniformly distributed in the lens surface were simulated. Fig. 6 shows the fraction of encircled spot energy as function of the distance to the image barycentre for several source locations for the monochromatic case (a) and to the Cherenkov-like spectrum (b). The spot radius for on-axis photons, using the criterion of 68% of encircled energy, is less than 2 mm for monochromatic sources while it is around 11 mm for the Cherenkov case. For off-axis sources close to 121 the spot radius turns to be 20 mm and 24 mm, respectively. The lens focusing power was studied as a function of the photon distance to the lens centre. Fig. 7 presents the spot radius (68% EE) as a function of the photon off-centre distance for several pointsource directions, monochromatic (a) and Cherenkov-like (b). It is

clear that the more the photons are off-centre the bigger is the spot radius. Furthermore, the coma effect is dominant for source directions highly off-axis (\ 81) while chromaticity becomes dominant for lower off-axis source directions.

5. Summary and prospects A simulation package named GETFOCOS was developed to characterize a generic optical system chosen for an imaging atmospheric Cherenkov telescope as well as to be used as an optimization tool for the same focal plane geometry. This tool is composed by a Geant4-based simulation for the telescope and a ray-tracing algorithm. The modularity of this package makes it easy to interface a generic telescope design and to perform the optics characterization as well as to optimize the focal distance. The performance of a Fresnel lens design was simulated and studied for different off-axis point source locations. This package proved to be fast, flexible and accurate for the simulation of optical solutions for future IACTs. References [1] A. De Angelis, et al., Riv. Nuovo Cim. 31 (4) (2008) 187. [2] CANGAROO homepage, /http://icrhp9.icrr.u-tokyo.ac.jp/S.

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[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

L. Arruda et al. / Nuclear Instruments and Methods in Physics Research A 659 (2011) 282–288 HESS homepage, /http://www.mpi-hd.mpg.de/hfm/HESS/S. MAGIC homepage, /http://wwwmagic.mppmu.mpg.de/index.en.htmlS. VERITAS homepage, /http://veritas.sao.arizona.eduS. D. Lamb, et al., Design, Fabrication and Testing of Fresnel Lenses for Astrophysics Applications, Ph.D. Dissertation, Univ. Alabama, Huntsville, 1999. L. Arruda, in: Proceedings of the XLIVth Rencontres de Moriond on ‘‘Very High Energy Phenomena in the Universe’’, La Thuile, Italy, 2009, p. 185. /http://www.opticalres.com/cv/cvprodds_f.htmlS. Optics Software for Layout and Optimization (OSLO), LAMBDA Corporation. Available: /http://www.lambdares.comS. S. Agostinelli, et al., Nucl. Instr. and Meth. A 506 (2003) 250. J. Allison, et al., IEEE Trans. Nucl. Sci. NS-53 (2006) 270. J. Costa, et al., IEEE Trans. Nucl. Sci. NS-54 (2007) 313. C. Berat, et al., Astropart. Phys. 33 (2010) 221.

[14] P. Assis, et al., in: Proceedings of the 31st International Cosmic Ray Conference, Lo´dz´, Poland, 2009. [15] R. Mirzoyan, et al., Astropart. Phys. 31 (2009) 1. [16] F. Krennrich, New J. Phys. 11 (2009) 115008. [17] J.M. Davies, E.S. Cotton, J. Solar Energy Sci. Eng. 1 (1957) 16. [18] D.A. Lewis, Exp. Astron. 1 (1990) 213. [19] V. Vassiliev, et al., Astropart. Phys. 28 (2007) 10. [20] K.L. Byrum, et al., Bull. Am. Astron. Soc. 42 (2010) 720. [21] Y. Takizawa, et al., in: Proceedings of the 30th International Cosmic Ray Conference, Me´rida, Mexico, vol. 5, 2007, p. 1033. [22] GAW Collaboration, in: Proposal: GAW – Gamma Air Watch: A Very Large Field of View Imaging Atmospheric Cherenkov Telescope. Concept Design and Science Case. Available: /http://gaw.ifc.inaf.it/doc/GAW_proposal_v25.pdfS. [23] /http://www.hyperrealm.com/libconfigS.