Spectral multiplexing using stacked VPHGs - Part I
MMNRAS , 1–12 (2017) Preprint 18 September 2018 Compiled using MNRAS L A TEX style file v3.0
Spectral multiplexing using stacked VPHGs - Part I
A. Zanutta (cid:63) & M. Landoni † , M. Riva , and A. Bianco INAF - Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate (LC), Italy
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Many focal-reducer spectrographs, currently available at state-of-the art telescopesfacilities, would benefit from a simple refurbishing that could increase both the res-olution and spectral range in order to cope with the progressively challenging scien-tific requirements but, in order to make this update appealing, it should minimizethe changes in the existing structure of the instrument. In the past, many authorsproposed solutions based on stacking subsequently layers of dispersive elements andrecord multiple spectra in one shot (multiplexing). Although this idea is promising,it brings several drawbacks and complexities that prevent the straightforward inte-gration of a such device in a spectrograph. Fortunately nowadays, the situation haschanged dramatically thanks to the successful experience achieved through photopoly-meric holographic films, used to fabricate common Volume Phase Holographic Grat-ings (VPHGs). Thanks to the various advantages made available by these materialsin this context, we propose an innovative solution to design a stacked multiplexedVPHGs that is able to secure efficiently different spectra in a single shot. This allowsto increase resolution and spectral range enabling astronomers to greatly economizetheir awarded time at the telescope. In this paper, we demonstrate the applicabilityof our solution, both in terms of expected performance and feasibility, supposing theupgrade of the Gran Telescopio CANARIAS (GTC) Optical System for Imaging andlow-Intermediate-Resolution Integrated Spectroscopy (OSIRIS).
Key words: instrumentation: spectrographs - techniques: spectroscopic - telescopes- methods: observational
The current state-of-the-art spectroscopic facilities could bedivided in two main groups depending on the resolution. Thefirst one is characterized by a low resolution (R < >> (cid:63) Contact e-mail: [email protected] † Contact e-mail: [email protected] to increase it as much as possible while maintaining a goodsignal-to-noise ratio (SNR) over a wide spectral range. Cur-rent focal reducer spectrographs, like the GTC-OSIRIS, al-ready provide diffraction gratings that allow to secure spec-tra with R ≥ > > © a r X i v : . [ a s t r o - ph . I M ] A p r A. Zanutta & M. Landoni et al. γ -rays by Extragalac-tic Background Light (EBL). In fact for example, Pita et al.(2014); Landoni et al. (2014) demonstrated that this prob-lem could be mitigated by securing spectra with high SNRand increased resolution to detect fainter spectral features,necessary to estimate the redshift (and thus the distance) ofthe source.As already pointed out, it is possible to collect spectraof astrophysical sources at high resolution (R > ∼ As highlighted in the introduction, being able to simultane-ously record multiple spectra of wavelength ranges, or alter-natively, to have a high resolution element that covers a verywide spectral range, brings a huge advantage to the astro-nomical community. In particular, depending on the opticallayout, a spectrograph would benefit of the possibility toincrease the resolution or the spectral range, maintainingthe same exposure times. Otherwise, a typical focal reducerimager, like FORS or OSIRIS, would benefit from the com-bination of very low dispersion gratings to acquire multiplesnapshots of the same field in different bands simultaneously,as depicted in the cartoon of Figure 1.In the present study we have tried to answer to theseneeds, testing the feasibility of a new type of dispersive ele-ment, that can result in a huge technological boost for thoseinstruments that are becoming obsolete and for the new onesthat are yet to be built.The general idea is to place multiple gratings (multi-plexed), stacked subsequently, in a way that they will pro-duce simultaneously spectra of different wavelength regions.
VPHG 1 VPHG 2 VPHG 3 − s t o r de r d i ff r a c t i on e ff i c i en cy wavelength [ μ m ] CAMERACOLLIMATOR
Figure 1.
Scheme of a possible application of a multiplexed de-vice in GRISM mode. Multiple and high dispersive VPHG layerscompose the multiplexed element which produces on the CCD,spectra of the slit in different spatial locations (one for each grat-ing layer). In the inset are reported the possible uncombined ef-ficiencies, peaked in different spectral ranges. Λ Λ filter glassVPHG 1 VPHG 2 xzy ε1 ε2 Figure 2.
Scheme of the layers composing a multiplexed grating.VPHG1 and VPHG2 may have different line density and orien-tation (clock) in order to separate the two spectra along the ydirection. Filter and glass are not mandatory elements and canbe replaced with other layers such as prisms.
The basic concept of a transmissive element is sketched inFigure 2.Each spectrum in the instrument’s detector is designedto cover a specific wavelength range, according to the scien-tific case that has to be studied. Consequently, the designphase is indeed a crucial part in the definition of the char-acteristics of the multiplexed dispersive element. Moreover,strategies to separate the spectra avoiding their overlappingshould be considered.In this particular configuration, since the grating layersare superimposed, the key idea is to apply a small rotationalong optical axis ( ε in Figure 2) between the layers, in or-der to separate (along the y direction) the different spectraappearing on the detector.Being able to secure multiple spectra with one exposure,the analyzed spectral range is extended (maintaining thesame resolution R) or the resolution of the system in thesame spectral range is significantly increased. This system istherefore suitable for upgrading an already built instrument, MNRAS000
The basic concept of a transmissive element is sketched inFigure 2.Each spectrum in the instrument’s detector is designedto cover a specific wavelength range, according to the scien-tific case that has to be studied. Consequently, the designphase is indeed a crucial part in the definition of the char-acteristics of the multiplexed dispersive element. Moreover,strategies to separate the spectra avoiding their overlappingshould be considered.In this particular configuration, since the grating layersare superimposed, the key idea is to apply a small rotationalong optical axis ( ε in Figure 2) between the layers, in or-der to separate (along the y direction) the different spectraappearing on the detector.Being able to secure multiple spectra with one exposure,the analyzed spectral range is extended (maintaining thesame resolution R) or the resolution of the system in thesame spectral range is significantly increased. This system istherefore suitable for upgrading an already built instrument, MNRAS000 , 1–12 (2017) pectral multiplexing using stacked VPHGs - Part I giving a great enhancement by a simple replacement of thedispersive element, which preserves all the existing abilities( e.g. the imaging in FOSC).The type of dispersive element that we have consideredin this study is the transmissive Volume Phase HolographicGrating, VPHG (Barden et al. 1998). They consist in a pe-riodic modulation of the refractive index ( ∆ n) in a thin layerof a photosensitive material. These elements represent todaythe most used dispersive elements in astronomy and yet theelement whose performances are most difficultly surpassedin both low and medium resolution spectrographs (Span`oet al. 2006; Baldry et al. 2004; Pazder & Clemens 2008).Since many different VPHGs are usually integrated in-side astronomical spectrographs and each of them is a cus-tom designed grating, each astronomical observation cantake advantage of specific dispersive elements with featurestailored for achieving the best performances. Accordingly,the design and manufacturing of highly efficient and reliableVPHGs require photosensitive materials where it is possibleto control both the refractive index modulation and the filmthickness d , in order to tune the device’s efficiency.Regarding the holographic materials, up to now Dichro-mated Gelatins (DCG) is considered the reference materialthanks to the very large modulation of the refractive indexthat can be stored (Liang-Wen et al. 1998; Bianco et al.2012), which turns into relative large bandwidth in highdispersion gratings. Unfortunately this material requires acomplex chemical developing process making it difficult forlarge scale and large size production. Moreover, the materialis sensitive to humidity, therefore, it is necessary to cover thegrating with a second substrate, burdening the control of thewavefront error.The availability of holographic materials with similarperformances, but with self-developing properties is desir-able, because they will not require any chemical post-processand moreover, the ∆ n formation could be monitored and setduring the writing step.Photopolymers are a promising class of holographic ma-terials and today, they are probably the best alternative toDCG, thanks to the improved features in terms of refractiveindex modulation, thickness control and dimension stability(Lawrence et al. 2001; Bruder et al. 2011; Ortu˜no et al. 2013;Fern´andez et al. 2015). A lot of studies have been carried outto understand deeply the behavior of this class of materials.Moreover, the formation of the refractive index modulationhas been recently studied (Gleeson & Sheridan 2009; Glee-son et al. 2011; Li et al. 2014a,b), through the developmentof models that predict the trends as function of the mate-rial properties and writing conditions (Kowalski & McLeod2016).We already demonstrated in other papers the useof photopolymers for making astronomical VPHGs withperformances comparable to those provided by VPHGs A GRISM is a combination of a prism and grating arranged sothat light at a chosen central wavelength passes straight through.The advantage of this arrangement is that the same camera canbe used both for imaging (without the grism) and spectroscopy(with the grism) without having to be moved. Grisms are in-serted into a camera beam that is already collimated. They thencreate a dispersed spectrum centered on the object’s location inthe camera’s field of view. based on DCGs and good aging performances (Zanuttaet al. 2014a), but with a much simpler production process(Zanutta et al. 2016b). Therefore, we think that the big ad-vantages of this novel holographic material could be the keypoint to realize the multiplexed dispersive element.The newly (Bruder & F¨acke 2010; Berneth et al. 2011,2013) developed photopolymer film technology (Bayfol HX (cid:114) film) evolved from efforts in holographic data storage (HDS)(Dhar et al. 2008) where any forms of post processing isunacceptable. These new instant developing recording me-dia open up new opportunities to create diffractive opticsand have proven to be able to record predictable and re-producible optical properties (Bruder et al. 2009). Depend-ing on the application requirements, the photopolymer layercan be designed towards e.g. (high or low) index modula-tion, transparency, wavelength sensitivity (monochromaticor RGB) and thickness to match the grating’s wavelengthand/or angular selectivity.Since the material consists in the holographic layer cou-pled with a polymeric substrate with a total thickness of ca.60 - 150 µ m, it can be laminated or deposited one on topof the other after having been recorded, making straightfor-ward the stacking realization.Clearly, another possibility is to holographically recordmultiple gratings inside the same layer but, as describedlater, in order to optimize the efficiency curves, usually verydifferent thicknesses are required for each grating, thereforethis strategy will not let us have the advantage to tune theresponse curves in the design process. As stated at the beginning of this section, the design con-cept consists in placing a set of transmission VPHGs stackedsubsequently (multiplexed) (see Figure 2). As highlighted inthe figures, this device will form one single optical elementwhose dimensions are comparable to standard VPHGs al-ready available in the target instrumentation.Some attempts have been made to explore this idea(Muslimov et al. 2016; Battey et al. 1996) but, althoughsteps have been made in the right direction, the proposedsolutions are limited by the necessity of a newly designedspectrograph, and do not take into consideration the cru-cial efficiency optimization that, without proper design, willmake the device ineffective.Hence, to preserve integration simplicity, one has to mixmaterials, design strategies and required performances, inorder to produce multiplexed dispersive elements that couldbe easily integrated in an available instrument. This gives toastronomers the possibility to enhance the resolution (andspectral coverage) by simply replacing the disperser alreadyinstalled in the optical path.Regarding the material, thanks to the crucial capabilityto finely tune the refractive index modulation ∆ n (Zanuttaet al. 2016a) and the slenderness of the film containing thegrating, Bayfol HX (cid:114) photopolymers by Covestro gave usthe possibility to design the multiplexing element to:(i) realize a compact and thin device that can be inte-grated as replacement in many already existing instruments(Landoni et al. 2016a; Zanutta et al. 2014b);(ii) tune the single stacked efficiency in such a precise way MNRAS , 1–12 (2017)
A. Zanutta & M. Landoni et al. that they will not interfere with each other and obviate toall the problems related to the realization of these devices;(iii) match the design requirements and obtain high effi-ciency;(iv) stack multiple layers of gratings in one single devicefor the simultaneous acquisition of multiple spectra with abroad wavelength band.In the multiplexed device, each layer will generate aportion of the spectrum that all together will compose thetotal dispersed range required. Such pieces, on the detector,will be disposed one on the top of each other, resulting in atotal spectral range that is far wider than the one obtainableusing a single grating with a comparable dispersion.
Although the stack of subsequent diffraction elements bringsmany advantages, some constraints and critical points ariseand should be discussed.The first one is purely a geometrical effect and is relatedto the propagation of the incoming beam throughout mul-tiple dispersing elements that must not interfere with eachother. For this reason, it has to be taken into account thatthe incoming beam is diffracted multiple times (since it en-counters two or more dispersive elements) according to thegrating equation m λ Λ = sin α + sin β (1)with m the number of the diffracted order, Λ the line densityof the VPHG and α , β the incidence and diffracted anglesrespectively.Fixing λ , different combinations of diffraction orderscan occur, resulting in light diffracted in different direc-tions. In particular let us consider for simplicity an exampleof two stacked multiplexed elements as shown in Figure 3.Each grating is optimized for dispersing efficiently a spe-cific wavelength range (labelled B for blue and R for red).Let’s suppose that the two possess the same line density. Ifa red monochromatic wavelength λ R (case i) enters the mul-tiplexed device, it will be firstly diffracted by the R gratingin all the possible orders, that will eventually enter the sec-ond grating. Each of these beams are in turn recursivelydiffracted by the B grating, but only few of them possessthe correct direction for further propagation (total internalreflection TIR can occur) to the detector.Otherwise, when a blue monochromatic beam λ B is con-sidered (case ii, for equal incidence angle) each diffractedorder will possess a smaller diffraction angle β (with respectof the previous case) due to the shorter wavelength, there-fore it is possible that some overlapping between blue andred orders would occur since more diffraction orders have adirection that can potentially enter the detector. In the design of VPHGs for an astronomical spectrograph,after having satisfied the dispersion and resolution require-ments, which fix parameters like the line density ( Λ ) of the λ R R B i) ii) λ B R B α β R Figure 3.
Monochromatic beam propagation in a two-multiplexed device (i - red wavelength case, ii - blue wavelengthcase). In the beam notation J.K, the number J is the diffractionorder of the first grating and K the one of the second grating. Ridentifies the grating layer designed for dispersing efficiently thered wavelengths, while B the blue ones. Bold lines are the ordersthat we want to exploit in the detector gratings and the incidence and diffraction angles ( α and β ),the optimization of the diffraction efficiency (both peak ef-ficiency and bandwidth) is necessary.To perform this task, the main parameters to be con-sidered are:(i) the refractive index modulation ∆ n;(ii) the active film thickness d ;(iii) the slanting angle φ (i.e. the angle between the nor-mal of the grating surface and the normal of the refractiveindex modulation plane).Considering a sinusoidal refractive index modulation,and working in the Bragg regime (the light is sent only inone diffraction order other than the zero), the well-knownKogelnik model can be used to compute the grating’s effi-ciency (Kogelnik 1969). For small angles, large diffractionefficiency is achieved when the product ∆ n · d is equal tohalf of the wavelength and this is the starting point in theoptimization process. As already stressed, during the VPHGdesign, not only the peak efficiency is important, but alsothe efficiency at the edges of the spectral range. Accordingto the Kogelnik model, the spectral bandwidth ( ∆ λ ) of thediffraction efficiency curve is proportional to (Barden et al.2000): ∆ λλ ∝ cot α Λ d (2)In this equation, α is the incidence angle, Λ is the linedensity of the grating and it is evident that the bandwidthis inversely proportional to Λ and the thickness of the grat-ing d . Hence, the optimization of the diffraction efficiencycurves, acting on the ∆ n and d , provides large differences inthe grating response.If a grating works in the Bragg regime, the largest peakefficiency and bandwidth is obtained for very thin films andlarge ∆ n. Undoubtedly, the ∆ n upper value is determined bythe performances of the holographic material. If the VPHGworks in the Raman-Nath regime (Moharam & Young 1978),it diffracts the light with a non-negligible efficiency in morethan one diffraction order and this is the case of low disper-sion gratings and should be considered to avoid the furtherexplained second order contamination (see Section 2.4).For such gratings, the light diffracted in high orders isproportional to ∆ n , ergo it is better to increase the film MNRAS000
Monochromatic beam propagation in a two-multiplexed device (i - red wavelength case, ii - blue wavelengthcase). In the beam notation J.K, the number J is the diffractionorder of the first grating and K the one of the second grating. Ridentifies the grating layer designed for dispersing efficiently thered wavelengths, while B the blue ones. Bold lines are the ordersthat we want to exploit in the detector gratings and the incidence and diffraction angles ( α and β ),the optimization of the diffraction efficiency (both peak ef-ficiency and bandwidth) is necessary.To perform this task, the main parameters to be con-sidered are:(i) the refractive index modulation ∆ n;(ii) the active film thickness d ;(iii) the slanting angle φ (i.e. the angle between the nor-mal of the grating surface and the normal of the refractiveindex modulation plane).Considering a sinusoidal refractive index modulation,and working in the Bragg regime (the light is sent only inone diffraction order other than the zero), the well-knownKogelnik model can be used to compute the grating’s effi-ciency (Kogelnik 1969). For small angles, large diffractionefficiency is achieved when the product ∆ n · d is equal tohalf of the wavelength and this is the starting point in theoptimization process. As already stressed, during the VPHGdesign, not only the peak efficiency is important, but alsothe efficiency at the edges of the spectral range. Accordingto the Kogelnik model, the spectral bandwidth ( ∆ λ ) of thediffraction efficiency curve is proportional to (Barden et al.2000): ∆ λλ ∝ cot α Λ d (2)In this equation, α is the incidence angle, Λ is the linedensity of the grating and it is evident that the bandwidthis inversely proportional to Λ and the thickness of the grat-ing d . Hence, the optimization of the diffraction efficiencycurves, acting on the ∆ n and d , provides large differences inthe grating response.If a grating works in the Bragg regime, the largest peakefficiency and bandwidth is obtained for very thin films andlarge ∆ n. Undoubtedly, the ∆ n upper value is determined bythe performances of the holographic material. If the VPHGworks in the Raman-Nath regime (Moharam & Young 1978),it diffracts the light with a non-negligible efficiency in morethan one diffraction order and this is the case of low disper-sion gratings and should be considered to avoid the furtherexplained second order contamination (see Section 2.4).For such gratings, the light diffracted in high orders isproportional to ∆ n , ergo it is better to increase the film MNRAS000 , 1–12 (2017) pectral multiplexing using stacked VPHGs - Part I thickness and reduce the ∆ n in order to achieve a large peakefficiency.The availability of an holographic material that can ex-ploit a precise ability to tune the ∆ n (Zanutta et al. 2014b,2016b), is therefore crucial for the design of multiplexed el-ements, in order to be able to adjust the efficiency responseof each dispersive layer.In the multipexing context, it is important to evaluatehow a grating with a certain efficiency affects the response ofthe following one. In order to give a feeling of the complexityof the problem, let us reconsider the two-multiplexing devicein Figure 3. The total multiplexed efficiency on the detectorwill not merely be the sum of the single layer efficiencies η B , st ( λ, α ) , η R , st ( λ, α ) , with λ the wavelength and α theinitial incidence angle.The notation ” st ” indicates the diffraction order atwhich the efficiency η refers to, meaning that the systemis aligned to work out the 1 st order.The spectrum generated by the R grating, before reach-ing the detector, has to pass through the B grating, and thiswill eventually diminish its intensity. To complicate that, weadd the fact that each wavelength of the R spectrum possessdifferent diffraction angles β R (which became the incidenceangles for the B grating) and therefore this varies the re-sponse from the second grating, according to the gratingequation (eq. 1). The resulting R efficiency η ∗ R , st ( λ, α ) willbe then: η ∗ R , st ( λ, α ) = η B , th ( λ, β R ) · η R , st ( λ, α ) (3)Moreover, the light that enters the second layer has al-ready been processed by the previous gratings, therefore, itsfinal efficiency will be the product of the leftover intensity,times the efficiency of the B grating: η ∗ B , st ( λ, α ) = η R , th ( λ, α ) · η B , st ( λ, α ) (4)Practically, the goal is to obtain gratings with negligibleoverlapping efficiencies. A critical point in spectroscopy is the contamination ofrecorded spectra, usually obtained through the first diffrac-tion order, by light coming from other diffraction orders,usually the second. Since signals of the different orders areoverlapped, there is no possibility to remove the unwantedlight a posteriori with data reduction. Therefore, dispersiveelements with spectral range greater than [ λ to λ ] will in-evitably suffer of this problem.This issue is well known in astronomy and it is usuallyavoided by placing order-sorting filters coupled with the dis-persing element or in a filter wheel in the optical path of theinstrument. The filters serve to block the light at lower wave-length that can overlap to the acquired spectrum. Anotherapproach is to reduce as much as possible the efficiency ofthe unwanted orders.Although in VPHGs, it is possible to mitigate theseeffect by varying parameters, such as thickness and ∆ n, in R a t i o be t w een t heo r e t i c a l s pe c t r u m and a c t ua l one Figure 4.
Ratio between contaminated and non-contaminatedspectrum (magenta line) for a source with a power law spectralenergy distribution at SNR of ∼ . Black lines correspond to thedetection limits dictated by SNR. The 2nd order contaminationappears as a recognizable peak surpassing the black lines whichcorresponds to the noise level. order to finely tune the efficiency curve, we decided to limitthe wavelength range of the multiplexed device, adopting aspectral band where no contamination occurs. However, wewill show another strategy that deals with the second ordersin the forthcoming ”Part II” of this work.In Figure 4 we report the effects of second order con-tamination with a multiplexed device designed to work inan extended wavelength range [4200 - 10000 ]. We have sim-ulated two different spectra: the first one contaminated withphotons coming from the second order, while the other oneconsidering only the contributions from the first order. Wealso assumed a SNR of about 100. The ratio between the twosignals (magenta line) is a rough estimation of how much un-wanted light appears as a bump in the collected data. In fact,according to this figure, the ratio between the two is withinthe noise level (solid black lines) up to λ (cid:39) , indicat-ing the two spectra are undistinguishable. Surpassing thiswavelength the ratio is higher than the noise level, meaningthat photons from the second order are superimposing inthe spectrum. In order to understand the spectral behavior of a multiplex-ing dispersive element, we choose to study the feasibilityof this system considering an astronomical instrument thatcould take advantage of the multiplexing technology.The resolving power of a spectrograph, R (or simplyresolution) is: R = m Λ λ W χ D T (5)where W is the length of the illuminated area on the gratingby the collimated beam, χ is the angular slit width (pro-jected on the sky) and D T is the diameter of the telescope. MNRAS , 1–12 (2017)
A. Zanutta & M. Landoni et al.
For a correct interpretation of the results, it has to be pon-dered that, the optical layout of the spectrograph (such asthe ratio of telescope diameter and the collimated beam inthe spectrograph) can be used as a rule of thumb to quantifythe advantage of this approach.In this paper we present the case of the focal reducerOSIRIS, installed at the 10 m telescope Gran Telescopio Ca-narias, as candidate facility for the on-sky commissioning ofthe multiplexed device. We have chosen to exploit two dif-ferent case studies, changing the number of elements in themultiplexed device. A two-stacked multiplexed device withan approximate resolution of R ∼ ∼ γ -ray BL Lacertae (BL Lac) objectS4 0954+258 (see Landoni et al. (2015a) and the next sec-tions) while the second one is intended to be compared withmedium-high state-of-the-art resolution spectrographs suchas ESO-XSHOOTER (Vernet et al. 2011; L´opez et al. 2016).In this section, we demonstrate the design and applicabilityof the two cases. For each of them, we present the analysisto determine the efficiency behavior, taking into account thedispersion and spectral range that each VPHG should showin relation to the instrument specifications. This activity iscarried out both through optical ray-tracing and RigorousCoupled Wave Analysis RCWA simulations (Moharam &Gaylord 1981). The outputs of this calculation are the mostsuitable efficiency curves for each stack that will guaranteethe higher overall diffraction efficiency and are computedvarying the key parameters described in Section 2.3.After the grating design, the subsequent step is to as-sess, through simulations, the expected on-sky performancesof each device. Thus, we build up syntethic simulated spec-tra (starting from powerlaw model, as in the case of BL Lac,or template spectrum as in the case of QSO) of the targetsaccording to the expected signal-to-noise ratio (SNR) in eachpixel defined as: SN = N ∗ (cid:113) N ∗ + N sky + n pix · RON (6)where N ∗ is the number of expected counts from the targetsource evaluated as: N ∗ = f ( λ ) · n (cid:214) i = · η i ( λ ) · A · t exp (7)where f ( λ ) is the input spectrum in ph sec − cm − ˚A − , Ais the collecting area of the telescope, η i are the efficienciesof atmosphere transmission, telescope, spectrograph, mul-tiplexed device and CCD (we consider a slit efficiency ofabout ∼ t exp is the total integration time.The quantity N sky is evaluated in the same way consideringa flat spectrum normalized in V o R band to a flux thatcorresponds to ∼
21 mag arcsec − , which is a typical valuefor the La Palma sky brightness. The read-out-noise (RON)of the detector is assumed equal to 7 e-/pix. For each sim-ulation, we consider a seeing of ∼ ∼ (cid:48)(cid:48) to be comparable with the current available in-strumentation specifications and performances (Cepa 2010).
400 nm 465 nm 550 nm675 nm 800 nm
550 nm
Figure 5.
Simulated spectra onto the OSIRIS detector with thetwo layers multiplexed grating.
The plate scale of the system is assumed to be ∼ This first case that we took into consideration is a twostacked multiplexed device, for OSIRIS and in GRISMmode, that can cover in one single exposure a spectral rangefrom 4000 to 8000 with a resolution of approximately 2000.In order to achieve that, the dispersive element splitsthe wavelength range in two parts, that are imaged onthe detector one on top of the other. The inter-spectra-separation depends on the tilt of the two gratings in thediffraction element. In this particular scenario, the minimumdistance between the two is approximately 2’ (projected an-gle on the sky), but merely because we have chose arbitrarilya tilt value of 2.5 ° (see Figure 5). The two dispersive elementsshare the same prisms and thus the same incidence angle.In Table 1 the specifications of the gratings that havebeen designed are reported, while in Figure 6 we presentedthe calculated efficiency curves of the layers that composethe device. With respect of this last figure, a long-pass filterat 4000 is installed in the device in order to avoid contam-ination from the second order. Moreover the VPHG, whichdisperses the light in the range 5500 - 8000 , has been de-signed to suppress as much as possible the contribution fromthe second order, which remains outside the spectral range.As highlighted in the previous sections, an importanteffect that has to be taken into account is that the diffractedintensity will be dimmed as light gradually passes throughthe VPHG layers but, in this configuration, thanks to theprecise design process, this effect is minimized. Indeed, foreach grating layer, a specific value of ∆ n, d and slanting angle φ was chosen in order to ensure the compatibility betweenthe efficiency curves.In the hypothesis that the sequence is first the REDgrating and second the BLUE grating, the wavelengths thatare diffracted by the RED grating (dotted green in Figure 6),are then transmitted through the BLUE layer with the re-sulting efficiency plotted in solid green. On the other hand,the wavelengths that have to be diffracted by the BLUEgrating, must firstly pass though the RED layer, with a re-sulting efficiency that is plotted in solid blue.After accounting for all of these effects, the obtainedefficiency curve for the multiplexed dispersive element is re- MNRAS000
The plate scale of the system is assumed to be ∼ This first case that we took into consideration is a twostacked multiplexed device, for OSIRIS and in GRISMmode, that can cover in one single exposure a spectral rangefrom 4000 to 8000 with a resolution of approximately 2000.In order to achieve that, the dispersive element splitsthe wavelength range in two parts, that are imaged onthe detector one on top of the other. The inter-spectra-separation depends on the tilt of the two gratings in thediffraction element. In this particular scenario, the minimumdistance between the two is approximately 2’ (projected an-gle on the sky), but merely because we have chose arbitrarilya tilt value of 2.5 ° (see Figure 5). The two dispersive elementsshare the same prisms and thus the same incidence angle.In Table 1 the specifications of the gratings that havebeen designed are reported, while in Figure 6 we presentedthe calculated efficiency curves of the layers that composethe device. With respect of this last figure, a long-pass filterat 4000 is installed in the device in order to avoid contam-ination from the second order. Moreover the VPHG, whichdisperses the light in the range 5500 - 8000 , has been de-signed to suppress as much as possible the contribution fromthe second order, which remains outside the spectral range.As highlighted in the previous sections, an importanteffect that has to be taken into account is that the diffractedintensity will be dimmed as light gradually passes throughthe VPHG layers but, in this configuration, thanks to theprecise design process, this effect is minimized. Indeed, foreach grating layer, a specific value of ∆ n, d and slanting angle φ was chosen in order to ensure the compatibility betweenthe efficiency curves.In the hypothesis that the sequence is first the REDgrating and second the BLUE grating, the wavelengths thatare diffracted by the RED grating (dotted green in Figure 6),are then transmitted through the BLUE layer with the re-sulting efficiency plotted in solid green. On the other hand,the wavelengths that have to be diffracted by the BLUEgrating, must firstly pass though the RED layer, with a re-sulting efficiency that is plotted in solid blue.After accounting for all of these effects, the obtainedefficiency curve for the multiplexed dispersive element is re- MNRAS000 , 1–12 (2017) pectral multiplexing using stacked VPHGs - Part I Table 1.
Parameters of the stacked grating composing the two-multiplexed device for OSIRIS, with prisms’ apex angle of 36.0 ° .grating l/mm λ range λ centr . R . dispersion[nm] [nm] @ λ centr al [˚A/ px]blue 2 1500 400-558 475 2232 0.52red 2 1000 550-800 675 2086 0.78 d i ff r a c t i on e ff i c i en cy Figure 6.
Diffraction efficiencies of the gratings composing themultiplexed element. The dotted lines refer to the single layerefficiencies (1st and 2nd diffraction orders), while the solid linesreferto the corrected efficiencies (labelled ”eaten”) at the exit ofthe multiplexed element, due to the reciprocal interference of thedispersive layers. Vertical lines identify the wavelength boundariesof the spectra in the CCD for each VPHG. ”Blue 2” is a VPHGwith ∆ n = 0.038 and d = 6 µ m while ”Red 2” with ∆ n = 0.024, d= 12 µ m and φ = 0.5 o . ported in Figure 7. The bump in the central region is dueto light diffracted by both gratings and that falls on thedetector in different places.Finally we remind that the efficiencies presented in thesimulations do not take into consideration the material ab-sorptions or the reflection losses that could arise to the pres-ence of interfaces inside the device. Nevertheless we expectthat these effects could be negligible at this level and are ofthe order of few percent points. S4 0954 +
65 is a bright BL Lac object identified for the firsttime by Walsh et al. (1984) which exhibits all the proper-ties of its class. In particular, the source presents a strongvariability in optical, with R apparent magnitudes usuallyranging between 15 and 17 (Raiteri et al. 1999), linear polar-isation (Morozova et al. 2014) and a radio map that shows acomplex jet-like structure. This BL Lac has recently caughtattention since it was detected with the Cherenkov telescopeMAGIC with a 5- σ significance (Mirzoyan 2015). The de-termination of redshift of BL Lac objects (in particular forTeV sources) is mandatory to assess their cosmological roleand evolution, which appears to be controversial due to red-shift incompleteness (Ajello et al. 2014) and to properly un-derstand their radiation mechanism and energetics (see e.gFalomo et al. (2014) and references therein). When BL Lacs μm] d i ff r a c t i on e ff i c i en cy Figure 7.
Blue line: overall efficiency of the two-multiplexingdispersive element. Green lines: single grating efficiencies of thespectra that are reaching the detector’s focal plane. Vertical linesidentify detector’s boundaries. are detected at TeV regime, the knowledge of their distanceis unavoidable since they could be exploited as a probe of theExtragalactic Background Light (EBL, see e.g Dom´ınguezet al. (2011), Franceschini et al. (2008)) allowing to under-stand how extremely high energy photons propagate fromthe source to the Earth and interact with the EBL through γ - γ absorption. Unfortunately, the determination of the red-shift of BL Lacs has proven to be difficult (see e.g. Shawet al. (2013), Landoni et al. (2013), Massaro et al. (2016))since their very faint spectral features are strongly diluted bytheir non-thermal emission (see the review of Falomo et al.(2014)).In the era of 10 m class telescopes (like the GTC), theresearch in this field has reached the so called ”photon star-vation regime” since the only way to significantly increasethe SNR is the adoption of extremely large aperture tele-scope (like ELT) (Landoni et al. 2013).On the other end, one can greatly increase the reso-lution of the secured spectra, maintaining a high SNR, de-creasing the minimum Equivalent Width (EW min ), allowingto measure fainter spectral features (see e.g. Sbarufatti et al.(2006), Shaw et al. (2013)).In particular, S4 0954 +
65 has been observed by Lan-doni et al. (2015b) after its outburst on the night of Febru-ary 28th, 2015. The object was observed with two grisms(R1000B and R1000R) in order to ensure a spectral cover-age from 4200 to ∼ (cid:48)(cid:48) with aresolution of R ∼ z = . (Stickel et al. 1993; Lawrence et al. 1996) and to infer a lowerlimit to the distance of z ≥ . thanks to EW min ∼ . ˚Aand SNR > MNRAS , 1–12 (2017)
A. Zanutta & M. Landoni et al.
Figure 8.
Two-Multiplexed grating case: Simulation of the S4 0954+65 spectrum (magenta) and comparison with the real observedspectrum (solid blue) secured with R1000B+R GRISMS. Spectral regions where telluric absorptions are severe are shaded and notincluded in the analysis. Bottom right box reports the comparison of the histograms of EW min between the observed spectrum in feb.2015 (shaded blue) and the one obtained with the new dispersing device. Top left box reports the SNR of the spectrum of S4 0954+65obtained with the new device (magenta) and the one estimated with GRISMs R2500 (cyan).
Considering the case of GTC and OSIRIS, the onlyavailable opportunity is to observe the target with theGRISMs R2500. Unfortunately these gratings possess a verynarrow spectral range so in order to ensure the wavelengthcoverage similar to the required (4000 - 8000 ˚A), one mustcollect four different spectra. This turns out in a telescopeallocation time of about 2 hrs (including overheads).By the adoption of the two VPHG multiplexed device,the observer is able to collect simultaneously two spectrawith a whole spectral range from 4000 to 8000 ˚A with a res-olution of approximately 2000. The simulated spectra ob-tained with this device is reported in Figure 8 along withthe comparison of the R1000B+R observed one.We also report the distribution of minimum detectableEquivalent Width, estimated following the recipes detailedin Sbarufatti et al. (2005) (histogram in the bottom rightcorner of Figure 8).The detectable EW min on the spectrum simulated byassuming the new dispersing element is 0.03, which is a fac-tor of 5 lower than the compared one. This turns in a lowerlimit to the redshift of z (cid:38) . putting the source at a plau-sible redshift region where the absorption from the EBL be-comes severe and making this TeV object an excellent probefor the study of the EBL through absorption.In this figure we also report the expected SNR obtainedwith our device (solid magenta in the top left box), andthe one simulated assuming the currently available R2500devices at the GTC. For the science cases that require a wide spectral range witha moderate resolution, nowadays the only possibility to fulfillthe requirements is to adopt an echelle grating based instru-ment, which is capable to secure wide wavelength ranges in areasonable number of shots . Otherwise according to OSIRISGRISMs specifications, in the GTC manual, up to six differ-ent setups (and exposures) are required to obtain the sameresult just in terms of spectral range, since the maximumresolution is approximately R max = .In this section we present a possible application of mul-tiplexed VPHGs, aiming to refurbish the dispersive elementsof OSIRIS at GTC, in order to reach the closest possible per-formance with respect to UV and VIS arm of X-SHOOTER.In order to cover a wide spectral range with a reso-lution of approximately 4500, we have designed two mul-tiplexed dispersive elements, each one composed by threestacked layers, therefore they will produce on the detectorthree spectra for each single exposure. With these two de-vices together, in just two exposures, we can cover a rangefrom 3500 to 10000 .While the number of dispersive layers could be theoret-ically further increased, due to complexities in calculations,possible transparency issues and manufacturing alignment,in this work we decided to set the limit to three elements. The first (of two) multiplexed device will be responsible forthe dispersion of the light in the range 3500 – 6000 , there-
MNRAS000
MNRAS000 , 1–12 (2017) pectral multiplexing using stacked VPHGs - Part I Table 2.
Parameters of the BLUE stacked grating composing thethree multiplexed device for OSIRIS, with prisms’ apex angle of52.3 ° .grating l/mm λ centr . λ range R . dispersion[nm] [nm] @ λ centr al [˚A/ px]BLUE 3.1 2850 385 354-425 4339 0.24BLUE 3.2 2400 460 411-498 4430 0.29BLUE 3.3 1980 550 493-600 4346 0.35 d i ff r a c t i on e ff i c i en cy wavelength [μm]0.35 0.4 0.45 0.5 0.55 0.6 Figure 9.
Multiplexing dispersive element designed for the BLUEband. Blue line: overall efficiency, green lines: single layer ef-ficiencies of the VPHGs. In the same way explained for thetwo-multipexed case, vertical lines identify detector’s boundaries.”Blue 3.1” possess ∆ n = 0.055, d = 4 µ m, ”Blue 3.2” ∆ n = 0.037,d = 6 µ m and φ = -0.2 o , ”Blue 3.3” ∆ n = 0.035, d = 7.5 µ m. fore hereafter it will be identified as the BLUE device. It iscomposed by three dispersing layers, each of them generat-ing the peaks in the summed efficiency displayed in Figure9 (solid blue curve). For this case, we did not report theplot with the contributions that generate the overall effi-ciency, since the general procedure is the same that in thetwo-multiplexed case. As highlighted in the previous case,the vertical solid lines identify the size of the detector withrespect to each spectra: since the total range will appear di-vided in three parts, the upper is displayed with solid blueboundaries, the central with green and the lower with red.As some small portions of the range will overlap, bumps inefficiency in the regions between the peaks appear.In Table 2, we report the specifications of the three grat-ings that have been designed for this BLUE element alongwith the calculated resolution and dispersion that is achiev-able integrating this device in the OSIRIS spectrograph. This second multiplexed device will be responsible to dis-perse the light in the spectral range from 6000 to 10000 ,therefore hereafter it will be identified as the RED device.Figure 10 (solid blue curve) reports the overall efficiencycurve that can be produced by the three dispersing layerscomposing this device.In Table 3, we report the specifications of the gratingsthat have been designed for this RED element along with
Table 3.
Parameters of the RED stacked grating composing thethree multiplexed device for OSIRIS, with prisms’ apex angle of55.1 ° .grating l/mm λ centr . λ range R . dispersion[nm] [ o ] @ λ centr al [˚A/ px]RED 3.1 1750 655 605-721 4825 0.39RED 3.2 1480 775 707-846 4851 0.46RED 3.3 1240 920 843-1000 4814 0.55 d i ff r a c t i on e ff i c i en cy wavelength [μm]0.65 0.7 0.75 0.8 0.85 0.9 0.95 Figure 10.
Multiplexing dispersive element designed for theRED band. Blue line: overall efficiency, green lines: single layerefficiencies of the VPHGs. In the same way explained for thetwo-multipexed case, vertical lines identify detector’s boundaries.”Red 3.1” possess ∆ n = 0.055, d = 6 µ m, ”Red 3.2” ∆ n = 0.044,d = 10 µ m and φ = -0.5 o , ”Red 3.3” ∆ n = 0.038, d = 12 µ m. the calculated resolution and dispersion that is achievableintegrating this device in the OSIRIS spectrograph. The study of the Intergalactic and Circumgalactic medium(IGM and CGM) is a powerful tool to investigate the prop-erties of the cool (and clumpy) gaseous halos between theobserver and the source, that lies at a certain z . The only wayto investigate the IGM or the CGM is through absorptionlines imprinted in the spectra of distant QSO, as demon-strated in the last few years by e.g Prochaska et al. (2014);Landoni et al. (2016b); L´opez et al. (2016) since its surfacebrightness is extremely faint to be probed directly, and onlyfew examples are know to succeed in the detection of emis-sion of Ly- α lines in the CGM (e.g Arrigoni Battaia et al.(2015)). This research field is actively growing and, recently,has begun to probe not only the physical state and the chem-ical composition of the IGM but also the three-dimensionaldistribution of the gas allowing scientists to build up an ac-tual tomography of the cool Universe between backgroundquasars and the Earth. For example, in this context one ofthe most recent and successfully survey is the CLAMATOsurvey (Lee et al. 2014). In this projects, authors aims toto collect spectra for 500 background Lyman-Break galaxies(LBGs) in ∼ − Mpc) . MNRAS , 1–12 (2017) A. Zanutta & M. Landoni et al.
The key step in these spectroscopic studies is the avail-ability of moderate-high resolving power (R ∼ µ m) at R > t exp = s for each grating aQSO (template taken from L´opez et al. (2016)) at redshiftz = 3.78 with m R ∼ . The overall obtained spectrum isreported in Figure 11. In particular the solid blue line corre-sponds to emission spectrum of the quasar secured with theBLUE multiplexed device. The absorption lines, imprintedby Lyman- α intervening systems and used to probe the IGM,are clearly detected and resolved in most of the cases. Thesolid red line, instead, report the spectrum recorded withthe RED multiplexed device where emission line from C IVand C III] are visibile. Results reported in Figure 11 areobtained with a total integration time of about 400s while,by comparison, to obtain the same results at half resolutionwith grisms available at GTC-OSIRIS would require morethan 1000s, since it should be observed four times with 4different gratings.As highlighted in the previous paragraphs, the X-SHOOTER spectrograph is able to obtain similar resultswith a broader band in a single snapshot. Although thisoutcome is obviously outside the capabilities of our proposedsolution, the multiplexing VPHG allows to cover in just twosnapshot a comparable quality (in terms of R, SNR and spec-tral range) in the UV and visible band. Therefore, the inte-gration of such element in a facility like OSIRIS would allowto scientifically compete with key-science projects that re-quire spectroscopic capabilities otherwise available only withmajor instrument commissioning. We have demonstrated the theoretical feasibility and the ad-vantages of an innovative dispersive element, able to greatlyincrease the performances of the existing spectrograph atthe state of the art 10 m telescope GTC. Thanks to theadvantages derived by the adoption of the photopolymericmaterial considered in the simulations, we achieved to in-crease by at least a factor of two in terms of resolution (andthus in the spent observing time), without changes in theoptical layout of the spectroscopic instrument. We have alsoshown that in the case of the three-multiplexed VPHG, it ispossible to reach with GTC OSIRIS, approximately the per-formances of the UV and VIS arm of X-SHOOTER (whenoperating in medium resolution) in just two exposures ofthe same target. Even though in this work we have selectedGTC OSIRIS for the simulations, the philosophy behind thismultiplexing design could be applied to almost every focal reducer spectrograph, donating the discussed advantages toall the instruments, allowing them to handle scientific casesthat would be otherwise out of reach for these facilities. Inthe forthcoming second part of this work, we will realizeand integrate the multiplexed device in a spectrograph forscience verification, focusing on the observational cases high-lighted in the simulations in this paper.
ACKNOWLEDGEMENTS
This work was partly supported by the European Commu-nity (FP7) through the OPTICON project (Optical InfraredCo-ordination Network for astronomy) and by the INAFthrough the TECNO-INAF 2014 “Innovative tools for highresolution and infrared spectroscopy based on non-standardvolume phase holographic gratings”.
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