Kinetic Inductance Detectors for the OLIMPO experiment: design and pre-flight characterization
A. Paiella, A. Coppolecchia, L. Lamagna, P. A. R. Ade, E. S. Battistelli, M. G. Castellano, I. Colantoni, F. Columbro, G. D'Alessandro, P. de Bernardis, S. Gordon, S. Masi, P. Mauskopf, G. Pettinari, F. Piacentini, G. Pisano, G. Presta, C. Tucker
PP repared for submission to JCAP
Kinetic Inductance Detectors for theOLIMPO experiment: design andpre–flight characterization
A. Paiella, a , b , A. Coppolecchia, a , b L. Lamagna, a , b P. A. R. Ade, c E. S. Battistelli, a , b M. G. Castellano, d I. Colantoni, d , e F. Columbro, a , b G. D’Alessandro, a , b P. de Bernardis, a , b S. Gordon, f S. Masi, a , b P. Mauskopf, f , g G. Pettinari, d F. Piacentini, a , b G. Pisano, c G. Presta a , b and C. Tucker c a Dipartimento di Fisica,
Sapienza
Università di Roma,P.le A. Moro 2, 00185 Roma, Italy b Istituto Nazionale di Fisica Nucleare, Sezione di Roma,P.le A. Moro 2, 00185 Roma, Italy c School of Physics and Astronomy, Cardi ff University,Cardi ff CF24 3YB, UK d Istituto di Fotonica e Nanotecnologie – CNR,Via Cineto Romano 42, 00156 Roma, Italy e current address : School of Cosmic Physics, Dublin Institute for Advanced Studies,31 Fitzwilliam Place, D02 XF86, Dublin, Ireland f School of Earth and Space Exploration, Arizona State University,Tempe, AZ 85287, USA g Department of Physics, Arizona State University,Tempe, AZ 85257, USA Corresponding author. a r X i v : . [ a s t r o - ph . I M ] A p r -mail: [email protected] Abstract.
We designed, fabricated, and characterized four arrays of horn–coupled, lumped elementkinetic inductance detectors (LEKIDs), optimized to work in the spectral bands of the balloon–borneOLIMPO experiment. OLIMPO is a 2 . ff ect. OLIMPO will also validate the LEKID technology in a repre-sentative space environment. The corrected focal plane is filled with di ff raction limited horn-coupledKID arrays, with 19, 37, 23, 41 active pixels respectively at 150, 250, 350, and 460 GHz.Here we report on the full electrical and optical characterization performed on these detectorarrays before the flight. In a dark laboratory cryostat, we measured the resonator electrical parameters,such as the quality factors and the electrical responsivities, at a base temperature of 300 mK. Themeasured average resonator Q s are 1 . × , 7 . × , 1 . × , and 1 . × for the 150, 250,350, and 460 GHz arrays, respectively. The average electrical phase responsivities on resonanceare 1 . / pW, 1 . / pW, 2 . / pW, and 2 . / pW; the electrical noise equivalent powers are45 aW / √ Hz, 160 aW / √ Hz, 80 aW / √ Hz, and 140 aW / √ Hz, at 12 Hz. In the OLIMPO cryostat, wemeasured the optical properties, such as the noise equivalent temperatures (NET) and the spectralresponses. The measured NET RJ s are 200 µ K √ s, 240 µ K √ s, 240 µ K √ s, and 340 µ K √ s, at 12 Hz;under 78, 88, 92, and 90 mK Rayleigh–Jeans blackbody load changes respectively for the 150, 250,350, and 460 GHz arrays. The spectral responses were characterized with the OLIMPO di ff erentialFourier transform spectrometer (DFTS) up to THz frequencies, with a resolution of 1 . Keywords:
CMBR detectors – CMBR experiments – Sunyaev–Zel’dovich e ff ect ontents ffi ciency 22 S parameter 26B Electrical responsivity in Fit Range and Precision measurements of the cosmic microwave background anisotropy, polarization and spectrum,require the development of sensitive low temperature detectors, scalable to form large arrays. Ki-netic Inductance Detectors are easily replicable in large (thousands of pixels) arrays, intrinsicallymultiplexable, and represent a very promising technology for this sector.A lumped element kinetic inductance detector consists of a high–Q LC resonant circuit, wherethe inductor acts also as the radiation absorber [1, 2]. The principle of operation of KIDs is based onthe kinetic inductance, L k , dependence on the relative density of paired (Cooper pairs) and unpaired(quasiparticles) charge carriers. Photons with energy greater than the binding energy ( h ν > ∆ )break the Cooper pairs, inducing an increase of quasiparticle density n qp , and, consequently, an in-crease of the kinetic inductance. This produces a shift of the resonant frequency ν r , and a change of– 1 –he quality factor Q of the resonator. These are measured by monitoring the amplitude and the phaseof a microwave bias signal, transmitted through a feedline coupled to the resonator (see fig. 1). C c,f C C c,g L g L k R s P h a s e ν r Bias frequency A m p li t ud e δAδϕ δAδϕ DarkIlluminated
Figure 1 . Top panel : Design ( left panel ) and equivalent circuit ( right panel ) of a kinetic inductance detector,capacitively coupled to a feedline and to the ground. C c , f (highlighted in red ) is the coupling capacitor betweenthe KID and the feedline (highlighted in brown ), while C c , g (highlighted in magenta ) is the coupling capacitorbetween the KID and the ground (highlighted in cyan ). The KID is composed of a capacitor, C (highlightedin blue ), a geometric and a kinetic inductance, L g and L k (highlighted in green ), and a residual resistance, R s ,due to the non–zero detector temperature, namely to the residual quasiparticles. Both R s and L k depend onthe superconducting material, and the geometric parameters of the detector design. Bottom–left panel : Biasfrequency dependence of the resonance amplitude and phase. The RLC circuit loads the feedline, producinga dip in its transmission ( blue lines ). The quasiparticles, produced by photons, increase both L k and R s . Thisshifts the resonance to lower frequencies, due to L k , and makes it broader and shallower, due to R s ( red lines ). Bottom–right panel : Polar representation of the resonance. In the polar plane the resonance is a circle ( blueline ), which changes its center and decreases its radius when quasiparticles are produced ( red line ). KIDs, therefore, exploit the phenomenon of superconductivity not only in the detection mech-anism, but also in the readout scheme. High quality factor values can be obtained since the super-conductor film has very low residual resistance, and allow thousands of kinetic inductance detectors,each with slightly di ff erent resonant frequency, to be read out using the same feedline.In this paper, we describe the design, the fabrication process, and the electrical and opticalcharacterization of the four horn–coupled LEKID arrays of the OLIMPO experiment. OLIMPO ( Os-servatorio nel Lontano Infrarosso Montato su Pallone Orientabile , Far Infrared Observatory Mountedon a Pointed Balloon) is a balloon–borne telescope designed to study the sky in the mm and sub–mmregions of the electromagnetic spectrum, with high angular resolution (matched to the typical angularscales of rich and nearby galaxy clusters) and sensitivity [3]. This experiment uses a 2 . plus He cryostat, and a Hesub–K refrigerator. OLIMPO is equipped with a di ff erential Fourier transform spectrometer (DFTS)[4, 5], with a maximum resolution ∆ ν = . ff ect [6]. For this reason its detectors cover four frequency bands matching thenegative, zero, and positive regions of the SZ spectrum. Apart from the lowest frequency bands,which have been used extensively by ground–based telescopes in the best observation sites, see e.g.[7–9], in the other bands atmospheric transmission is very low at ground level, and only space–basedexperiments can carry out sensitive measurements of the SZ e ff ect [10, 11], as demonstrated by thePlanck satellite [12–14]. The strength of OLIMPO consists in the possibility to perform low resolu-tion spectroscopy ( ∆ ν = ff ect along with broad band photometric measurements.These features allow to constrain all the main parameters of the intracluster plasma with low degen-eracy and optimal control of the foreground contamination [15].Moreover, OLIMPO will o ff er the opportunity to qualify the KID technology in a representativenear–space environment, in view of future space missions [16, 17].This paper is structured as follows: Section 2 describes the detector design, starting from therequirements (2.1), and presenting the results of the optical and the electrical simulations (2.2 and2.3); Section 3 summarizes the fabrication process of the LEKID arrays; Section 4 describes theexperimental setup composed of the dark cryogenic system for the electrical characterization (4.1),the OLIMPO cryostat and optical system for the optical characterization (4.2), and the readout chain(4.3); Section 5 summarizes the results of the electrical (5.1) and optical characterization (5.2) per-formed on the four LEKID arrays: the measurements of resonator quality factors (5.1.1), electricalresponsivity and noise equivalent power (5.1.2), optical responsivity and noise equivalent tempera-ture (5.2.1), spectral response (5.2.2), and optical e ffi ciency (5.2.3). Section 6 contains the concludingremarks. The design of the OLIMPO detector arrays has optimized the main characteristics of LEKIDs (high–Q RLC resonator coupled to a feedline, lumped element circuit, e ffi cient absorption for incomingphotons) given the base temperature and the optical system of OLIMPO, which constrained the sizeof the focal planes, the horn apertures, and the spectral bands.In order to perform properly, KIDs have to be cooled well below the critical temperature of thesuperconducting film, T c , usually T (cid:46) T c /
6. The base temperature of the OLIMPO refrigerator is300 mK, which means that T c (cid:38) .
80 K. On the other hand, as we said, only radiation with energy, h ν ,greater than the Cooper pair binding energy, 2 ∆ , can break Cooper pairs and then can be detected: h ν > ∆ . Since the 150 GHz spectral band starts from 135 GHz (lower limit of the full width halfmaximum, see tab. 1), in order to be safe, is reasonable to consider 130 GHz as the minimum radiationfrequency detectable. Therefore, using ∆ = . k B T c , (2.1)from the BCS theory [18], where k B is the Boltzmann constant, the constraint h ν > ∆ translatesinto T c < .
77 K. The two constraints on the critical temperature are formally inconsistent: we prefer– 3 –o relax the one given by the base temperature, and therefore to satisfy the one given by the minimumdetectable radiation frequency.We choose aluminum for the superconducting film. In fact, Al has a bulk critical temperatureof 1 .
20 K, which increases to 1 .
40 K for tens of nm thick films. In addition, we choose silicon forthe dielectric substrate, for its mechanical, thermal, and electrical properties. This selection of mate-rials is common for LEKIDs detecting mm–waves. For such materials, performance and fabricationtechnologies have already been demonstrated [19–21].
OLIMPO is designed to operate from the stratosphere for about 15 days. Its e ff ectiveness relies onthe ability to achieve high signal–to–noise ratio measurements in relatively short integrations. Onthe other hand, the spectral coverage, and the need to switch between photometric and spectroscopicoptical configurations, determine changes in the radiative background which are larger than thosedue to the elevation changes of the telescope. The focal plane must therefore be populated withlarge–dynamic–range, photon–noise limited detectors in the expected in-flight radiative environment.Tab. 1 shows the target background limited performance (BLIP) of OLIMPO in both photometric andspectrometric configurations. OLIMPO configuration Photometric SpectrometricChannel [GHz] 150 250 350 460 150 250 350 460Background Power (cid:2) pW (cid:3) (cid:104) aW / √ Hz (cid:105)
65 140 90 140 110 260 160 240optical NET
CMB (cid:104) µ K √ s (cid:105)
110 110 850 3300 190 550 1400 5200optical NET RJ (cid:104) µ K √ s (cid:105)
60 30 70 60 110 60 120 110
Table 1 . Forecast for the photon–noise–limited performance of the OLIMPO experiment, for both photometricand spectrometric configurations, in the four measurement bands (a conservative 50% absorption e ffi ciencyfor the detector has been assumed): [135 , , , , ffi ciencies due to the transmission and emission of the entire filters chain. The detector arrays are coupled to the optical system by means of feed–horns. The size of theaberration–corrected focal plane is such that the 150 GHz and 250 GHz arrays must be fabricated ona 3 (cid:48)(cid:48) diameter wafer, while the 350 GHz and 460 GHz arrays can fit on 2 (cid:48)(cid:48) wafers. The apertures ofthe horns are such that the 150 GHz, 250 GHz, 350 GHz, and 460 GHz arrays can host a maximum of19, 37, 23, and 41 illuminated pixels, respectively. To these we added 4 dark pixels on the 150 GHzarray and 2 dark pixels on each of the other arrays.The last requirement concerns the resonant frequency of the detectors. We choose resonantfrequencies in the hundreds of MHz range in order to have reasonably large capacitors, so that wecan have a uniform current distribution at the resonant frequency along the inductors, thus reducingTLS (two–level system) noise [22].For the OLIMPO experiment, we decided to use two readout signal chains and electronics forthe four arrays corresponding to approximately 60–70 detectors per readout chain. Each readoutchain consists of two coaxial lines, one for carrying the readout bias tones into the detectors and one– 4 –or carrying the signals transmitted through the feedline at each KID frequency after amplificationby a cryogenic low noise amplifier. We discarded the hypothesis to read out the four arrays indepen-dently because the thermal load of four independent readout chains would become significant for theOLIMPO cryostat: the thermal load introduced by four cryogenic amplifiers would negatively a ff ectthe hold time of the cryostat and the temperature of the amplifier, degrading its performance. On theother hand, we discarded the hypothesis to use only one readout system as well, in order to avoidlarge signal losses transmitted through the arrays, and to provide a minimum level of redundancy.In order to combine two arrays in the same readout line, we avoid overlaps in the resonantfrequencies among the detectors in both arrays. In addition, in order to evenly divide the detectorsbetween the two readout lines, we paired together the 150 GHz and 460 GHz arrays and the 250 GHzand 350 GHz arrays. Optical simulations were performed using ANSYS HFSS to optimize the absorber and radiationcoupler geometry and size, the illumination configuration (front or back), and the thicknesses of thesubstrate and the superconducting film.In non–polarimetric experiments as OLIMPO, the absorber geometry is optimized to absorbboth polarizations of the incoming radiation: a good choice is the Hilbert fractal curve of ordergreater than or equal to the III; see fig. 2. The Hilbert curve fills the absorbing area uniformly. Thisallows the detector to be sensitive to the two polarizations, with no preferential direction in absorption[23]. s h w h s h w h Figure 2 . Geometry of the inductor section optimized to absorb both polarizations of the incoming radiation:Hilbert fractal curve of the III ( left panel ) and IV ( right panel ) order.
In general, radiation couplers are composed of two or three elements: a horn or planar antenna,a mode–filtering waveguide, and possibly a transition element, such as a flare, or a choke, or both ofthem, to ensure e ffi cient power transfer to the detector. In our case, a horn antenna is used to couplethe output of the cryogenic reimaging optics to the detector waveguide. The waveguide is the opticalcomponent selecting the modes and the lowest frequency of the radiation to be detected. The flareand the choke placed at the end of the waveguide have the main task of reducing the optical cross–talkbetween adjacent detectors.For each frequency band of the OLIMPO experiment, we investigated • two di ff erent absorber geometries: the Hilbert fractal curve of the III and IV order, with di ff er-ent size (di ff erent values of s h and w h , referring to fig. 2); – 5 – three di ff erent radiation couplers: waveguide, flared waveguide, or choked waveguide, withdi ff erent size; • two illumination configurations: front–illuminated or back–illuminated; • di ff erent Si wafer and Al film thicknesses, t S i and t Al respectively (for the front illuminatedconfiguration the Si wafer thickness coincides with the backshort distance); • di ff erent distances between the radiation coupler and the absorber for the front illuminatedconfiguration, and di ff erent distance of the backshort for the back illuminated configuration, d .The configurations are optimized and selected by maximizing the absorbance in the four spec-tral bands of OLIMPO, and minimizing the losses through the lateral surfaces of the Si wafer and the“vacuum” space between the radiation coupler and the absorber for the front illuminated configura-tion, or between the absorber and the backshort for the back illuminated configuration. Minimizingthe losses corresponds to minimizing the optical cross–talk between adjacent detectors.The left panel of fig. 3 shows the HFSS design of the 350 GHz detector system in the frontilluminated configuration (or in the back illuminated configuration): a circular flared waveguide,the “vacuum” space between the radiation coupler and the absorber (or the Si substrate), the IVorder Hilbert absorber, and the Si substrate (or the “vacuum” space between the absorber and thebackshort). The right panel of fig. 3 shows the results of the optical simulations of the four OLIMPOchannels. The absorbance, integrated over the spectral band, is 94% for the 150 GHz channel, 71%for the 250 GHz channel, and 82% for both the 350 GHz channel and the 460 GHz channel. Thelosses, integrated over the spectral band, are lower than the 2% for the 150 GHz channel, 19% for the250 GHz channel, 5% for the 350 GHz channel, and 3% for the 460 GHz channel. Radiation Frequency [GHz]0 . . . . . . . A b s o r p t i o n
130 150 1700 . . . . . . . L o ss
200 250 300 330 350 370 420 460 500
VacuumSilicon
Figure 3 . Left panel : HFSS design of a IV order Hilbert absorber, for the 350 GHz channel of OLIMPO, cou-pled to the radiation through a circular flared waveguide.
Right panel : Frequency dependence of the absorption( top panels ) and the losses ( bottom panels ) for the OLIMPO channels. The red lines are for the “vacuum” andthe blue lines are for the silicon.
The results described above refer to the detector system configurations collected in tab. 2. Sim-ulations suggest that the best absorber is a front–illuminated IV order Hilbert, with the characteristic– 6 –ength s h scaling with the observed radiation wavelength. For the 150 and the 250 GHz channels, itis possible to obtain high absorbance and low losses by constraining mainly the distance between thewaveguide end and the absorber, without the need of a transition element. On the other hand, for the350 and the 460 GHz channels the transition element becomes important to reduce the losses, whichcannot be reduced significantly by decreasing d . Channel Radiation Illumination t Si d Absorber Waveguide Flare[GHz] Coupler (cid:2) µ m (cid:3) (cid:2) µ m (cid:3) Hilbert t Al w h s h d wg h wg d f h f order [nm] (cid:2) µ m (cid:3) (cid:2) µ m (cid:3) [mm] [mm] [mm] [mm]150 Waveguide Front 135 450 IV 30 2 162 1.4 6250 Waveguide Front 100 350 IV 30 2 132 1.0 5350 Flared Front 310 250 IV 30 2 72 0.60 2 1.0 7waveguide460 Flared Front 135 150 IV 30 2 52 0.44 2 0.8 2waveguide Table 2 . Optimized parameters values for each OLIMPO channel. The table collects information about theradiation coupler geometry and size: the waveguide diameter d wg , and height h wg , the flare diameter d f , andheight h f ; the illumination configuration, the silicon wafer thickness t S i , the distance between the radiationcoupler and the absorber d , the absorber geometry and size: the aluminum film thickness t Al , and w h and s h defined in fig. 2. The results of the optical simulations over these detector systems are shown in the right panel of fig. 3. After fixing the geometry and the size of the absorber, we have to complete the design of the detectorsby choosing the size of the capacitor, the bias coupling and the feedline. The resonator to feedlineand resonator to ground couplings are two capacitors, as shown in the top panels of fig. 1. Electricalsimulations are used to tune the feedline impedance and the resonant frequency, verify the lumpedcondition, constrain the coupling quality factor, and minimize the electrical cross–talk.The electrical cross–talk between adjacent resonators in the frequency domain can be minimizedby suitably spacing the resonant frequencies. As we are going to see in Subsec. 4.3, we use a readoutelectronics, based on a ROACH2 board, characterized by a total bandwidth of 512 MHz. In orderto populate a band of 512 MHz with 66 (150 /
460 GHz line) or 64 (250 /
350 GHz line) detectors, weneed to separate their resonant frequencies by a maximum of 7 . ff ects, which could bepresent in the real device and are not included in the simulations.The coupling quality factor Q c , which is a measure of the electrical losses external to the res-onator, constrains the detector dynamics. Larger Q c values correspond to smaller detector dynamicsand higher sensitivity. The OLIMPO requirements, described in Subsec. 2.1, translate into Q c ofabout 1 . × . A first generation of detectors had been built to have Q c < × , with t Al =
40 nm.These detectors had indeed a huge dynamic range, but the responsivity was low [24]. Given the ca-pacitance of each detector C , the coupling capacitance can be obtained from [20] C c = (cid:115) C πν r Q c Z f l , (2.2)where ν r is the resonant frequency, Q c = . × , and Z f l is the feedline impedance.– 7 –lectrical simulations were performed with the SONNET software, whose input is the layoutof the detector, including the feedline, the coupling capacitors, and the ground planes. For each arraywe simulated the first, second, and last pixels in order to be sure that the lumped condition is verifiedfor all the resonators (if the lumped condition is verified for the first and the last pixel, we can assumethat it is verified for all the pixels), and control the spacing between the first two pixels and betweenthe last and the first pixel of the arrays on the same readout line.Fig. 4 displays the SONNET results for the transmission scattering parameter S of the threesimulated pixels of each array: the 150 /
460 GHz line in the left panel , and the 250 /
350 GHz line inthe right panel . Tab. 3 collects the results of the simulations: frequency ranges, bandwidths, spacingof the resonators of the four arrays, and percentage non–uniformity in the current distribution alongthe inductor.
150 200 250 300 350 400 450
Bias Frequency [MHz] − − − − − − − − − − − − − S [ d B ] pixel 1pixel 2last pixel Array (23 pix.)Array (43 pix.)
150 200 250 300 350 400
Bias Frequency [MHz] − − − − − − − − − − − − S [ d B ] pixel 1pixel 2last pixel Array (39 pix.)Array (25 pix.) Figure 4 . Bias frequency dependence of the transmission scattering parameter S for three simulated pixelsof the 150 and the 460 GHz arrays ( left panel ), and of the 250 and 350 GHz arrays ( right panel ).Channel Table 3 . Results of the SONNET simulations: frequency ranges, bandwidths, spacing of the resonators of thefour arrays, and percentage non–uniformity in the current distribution along the inductor.
The lumped element condition is verified if the current distribution, at the resonant frequency,is uniform in the inductor and null in the capacitor. We consider this condition satisfied if the currentvariation between any two points along the inductor is always lower than 20%. As an example, fig. 5shows the current distribution for the first and the last pixels of the 250 GHz array. – 8 – Figure 5 . Current distribution from SONNET for the first ( left panel ) and the last ( right panel ) pixels of the250 GHz array. The current is null in the capacitors and is uniform in the inductors. The maximum non–uniformity along the inductors is about 4% for the first pixel, and about 10% for the last pixel.
Our detectors are fabricated in the ISO5 / ISO6 clean room of the Istituto di Fotonica e Nanotecnologie(IFN) of the Consiglio Nazionale delle Ricerche (CNR).The layout of the KID array is first realized by electron beam lithography (EBL) on the poly-methyl methacrylate (PMMA) film uniformly deposited on the Si wafer: the electron irradiationchemically modified the PMMA structure that is then developed in a solution (1:1) of methyl isobutylketone (MIBK) and isopropyl alcohol (IPA). A thin aluminium film is subsequently deposited byelectron–gun evaporation on the substrate patterned with PMMA. The aluminium deposition rate( ∼
10 A / s) and final thickness ( ∼
30 nm) have been controlled during the deposition by a quartz micro–balance and checked afterwards with a mechanical profilometer. Finally, the excess metal, depositedon the residual PMMA, is removed by a lift–o ff process [25].The detectors are fabricated on high-quality (FZ method) intrinsic Si(100) wafers, with highresistivity ( ρ >
10 k Ω cm), double side polished. The face of the Si wafer opposite to that where thedetectors have been realized is metalized with 200 nm of Al. This film acts as a backshort for theincoming radiation.Fig. 6 shows the pictures of the four OLIMPO detector arrays, mounted in their holders bymeans of four Teflon washers 100 µ m thick, and their horn arrays. Both the sample holders and thehorn arrays are made of ergal alloy (aluminum 7075), ensuring good thermalization, reducing thepower losses through the horn arrays, and minimizing the interactions between the holders and thedetectors. The experimental setup for the electrical characterization is composed of a dark (no optical system,blanked detectors) laboratory cryogenic system and its readout electronics, while for the optical char-acterization is composed of the OLIMPO cryostat and its optical system and flight readout electronics.– 9 –
150 GHz 250 GHz 350 GHz 460 GHz
Figure 6 . Pictures of the four OLIMPO detector arrays mounted in their holders by means of four Teflonwashers 100 µ m thick, and the horn arrays (including the waveguides and the flares where present). Clockwisefrom top left : the 150 GHz, 250 GHz, 460 GHz, and 350 GHz arrays.
The cryogenic system is composed of a Sumitomo 062B pulse tube cryocooler (PTC), a He / Hesorption fridge, and a custom dilution refrigerator. The PTC features two temperature stages: oneat 45 K and the other at 3 . He / He fridge, mounted on the coldest stage of the pulse tubecryocooler, provides other two temperature stages: one at 1 K and the other at 350 mK. The lastcooling stage, anchored on the coldest stage of the He / He fridge, is provided by a single–shotminiature He / He dilution refrigerator, whose mixing chamber can reach about 136 mK, under anoptical loading of about 14 µ W [26].The detector array in its holder is mounted on the coldest stage, with the horn entrance aperturesclosed by an aluminum foil to perform dark test. The sample holder is equipped with a heater and athermometer to perform temperature sweeps and to reproduce the flight operating conditions (in theOLIMPO cryostat the detectors work at 300 mK).
The cryogenic system of OLIMPO consists of a wet N plus He cryostat, coupled to a He sub–K refrigerator, able to cool at about 300 mK, for about 16 days, the four detector arrays in theirholders and their horn arrays, thanks to a gold–plated electrolytic tough pitch (ETP) copper link. Thetemperatures of liquid N and He are 77 K and 4 . He bath is 1 . ffi ciently the He and to reducethe emission of the optics box ( left panel of fig. 7). A copper vapor He cooled intermediate shieldfurther reduces the radiative thermal input on the He stage. In nominal thermal load conditions theregime temperature of this shield is about 30 K. – 10 –he cryostat window is a disk of high density polyethylene (HDPE) [27], with antireflectioncoating. The part of the OLIMPO optical system placed inside the cryostat is composed of a filterchain (see the right panel of fig. 7), three cold reimaging aluminum mirrors and the radiation couplers.
150 GHz array 350 GHz array 460 GHz array 250 GHz array He fridge gold-plated ETP copper link
200 400 600 800 1000
Frequency [GHz] . . . . . . . T r a n s m i ss i o n Low Pass
Low Pass
Low Pass
Low Pass
Band Pass
Low Pass
Band Pass
Low Pass
Low Pass
Band PassTotal OLIMPO bands
Figure 7 . Left panel : Picture of the optics box where the detector arrays, the He fridge, and the gold–platedETP copper link are indicated.
Right panel : Transmission spectra of the filters mounted in the OLIMPOcryostat. The dotted lines are the transmission spectra of the common filters to the four arrays: 1 THz low passfilter, in fuchsia , mounted on the N shield at 77 K; 750 GHz low pass filter, in blue , mounted on the vapor Heshield at 30 K; 630 GHz low pass filter, in green , mounted on the optics box shield at 1 . color dashed and solid lines are the transmission spectra of the filters mounted on the horn holders: di ff erent colors representdi ff erent detector arrays (in red the 150 GHz band, in goldenrod the 250 GHz band, in gray the 350 GHz band,and in purple the 460 GHz band), dashed lines are for the low pass filters, and solid lines are for band passfilters. The black solid line represents the total transmission spectra of the OLIMPO bands obtained by theconvolution of all the spectra on the same optical path (for the 250 GHz band the lower cut–o ff is given by the190 GHz dichroic filter). Our readout channels (a single one for the test cryostat, two for the OLIMPO cryostat) are composedof a bias line (input to the KID array) and a readout line (output of the KID array). The lines aremade of stainless steel, Cu–Ni, and Nb–Ti coaxial cables with SMA connectors, and are run fromthe room–temperature connectors on the vacuum–jacket shell of the cryostat all the way down to thecoldest stage. The signal on the input line is attenuated by three cryogenic attenuators ( −
10 dB each).The signal on the output line is amplified by a cryogenic low noise amplifier (LNA), developed byArizona State University (ASU), mounted on the 3 . Heshield at 30 K. All these components form the cold electronics .The readout channel is completed by a room–temperature electronics which generates a biassignal as the superposition of the tones matching the nominal resonant frequencies of all the KID pix-els, and monitors the signal transmitted by each of the KID pixels when their resonances are shiftedby the radiation flux. We use a ROACH2 board , including a MUSIC DAC / ADC board . Since the http://thz.asu.edu/products.html https://casper.berkeley.edu/wiki/ROACH2 https://casper.berkeley.edu/wiki/MUSIC_Readout – 11 –esonances of the OLIMPO KIDs extend to frequencies higher than 256 MHz, our room–temperatureelectronics (see fig. 8) includes up–conversion and down–conversion microwave components as de-scribed below. To/From Cryostat Clock/LO from Valon Bias of the microwave components R O A C H I Q d e m o du l a t o r A D C / D A C b o a r d Low Pass filters A m p li f i e r s Power splitters (180 (cid:113) phase shifter) P o w e r s p li tt e r ( (cid:113) ph a s e s h i f t e r ) I Q m o du l a t o r B i a s t ee s ROACH–2 boardADC/DAC boardADCDAC L P fi l t e r L P fi l t e r L P fi l t e r L P fi l t e r π phaseshifter π phaseshifter Bias teeBias teeBias teeBias tee IQ mixermodulatorIQ mixerdemodulator powersplitter Amp.1Amp.2LO from Valon From/To Cryostat Room–temperature Readout Electronics
Figure 8 . Photo ( left panel ) and block diagram ( right panel ) of the laboratory OLIMPO readout room–temperature electronics : this includes a ROACH2 ( red solid box ), a MUSIC DAC / ADC board ( cyan solidbox ), three power splitters ( violet solid boxes ), two room–temperature amplifiers ( blue solid boxes ), an IQmodulator ( red dotted box ), four bias tees ( green solid boxes ), four low pass filters ( cyan dotted boxes ), an IQdemodulator ( orange solid box ), and a frequency synthesizer (not shown).
The baseband bias signals (in phase, I , and in quadrature, Q ) output by the DACs are cleanedby low pass filters ( Mini Circuits SLP − + ), and up–converted by an IQ mixer modulator ( Ana-log Devices ADL 5385 ). The local oscillator (LO) is a frequency synthesizer model
Valon tech-nology 5009 . Its reference signal is split by a power splitter (
Mini Circuits ZFRSC − − S + ) andsupplies the modulator cited above and the demodulator described below. The ADL 5385
IQ mixerrequires as input the I and Q signals and their 180 ◦ phase shifts (obtained by means of a Mini CircuitsZFSCJ − − − S + ); all the input signals are o ff set positive by means of four bias tees ( Mini CircuitsZFBT − − − FT + ). The up–converted signal output of the ADL 5385 is connected to the biasline input of the cryostat.The signal from the readout line output of the cryostat is amplified by two room–temperatureamplifiers (
Mini Circuits ZX60 − P103LN + and ZX60 − + ), and input to the IQ mixer demod-ulator ( Analog Devices ADL 5387 ) to be down–converted to the baseband. The baseband I and Q demodulator outputs are low–passed (via Mini Circuits SLP − + filters) and input to the ADCs ofthe MUSIC board. The converted signal is processed by the FPGA to measure the amplitudes of the I ad Q signals transmitted by all the KID pixels. The FPGA firmware has been developed by ASU, andis able to generate up to 1000 tones over an up–converted 512 MHz bandwidth, with a demodulatedoutput sampling rate up to about 1 kHz [28]. – 12 – Results
Here we describe the electrical characterization of the four OLIMPO detector arrays. Each arrayhas been individually cooled inside the dark cryostat, and characterized at both the base temperatureand 300 mK. Because of the di ff erent geometry, volume and mass of the sample holders, due to thedi ff erent mounting needs of the holders in the OLIMPO cryostat, the base temperature reached isdi ff erent for the four channels: 185 mK, 168 mK, 155 mK, and 255 mK for the 150, 250, 350, and460 GHz holders, respectively.For each array we measured the transmission S scattering parameter, identifying the resonantfrequencies and establishing, through a bias power sweep, the optimal bias power at the base temper-ature. From these measurements, shown in fig. 9, we found also the frequency ranges, bandwidthsand average spacing of the resonators of the four arrays. These values are collected in tab. 4 and theyare in good agreement with the results of the simulations described in Subsec. 2.3. Channel Operating Optimal Resonant frequenciespixels Bias Power Range Bandwidth Spacing[GHz] [dBm] [MHz] [MHz] [MHz]150 20 /
23 (87%) −
90 [146; 267] 121 6250 34 /
39 (87%) −
79 [150; 335] 185 5.5350 23 /
25 (92%) −
96 [362; 478] 116 5460 43 /
43 (100%) −
99 [288; 487] 199 4.5
Table 4 . Number of operating pixels, optimal bias powers, and frequency ranges, bandwidths and averagespacing of the resonators of the four arrays.
The quality factors have been estimated through the procedure described in appendix A. This anal-ysis was performed both at the base temperature, and at around 300 mK (operating temperature ofOLIMPO). The values of the quality factors averaged, for each array, over all the detectors are col-lected in tab. 5.
Channel Temperature Average Q s[GHz] [mK] Q Q i
150 185 2 . × . ×
300 1 . × . ×
250 168 1 . × . ×
295 7 . × . ×
350 155 3 . × . ×
300 1 . × . ×
460 255 2 . × . ×
310 1 . × . × Table 5 . Array–average of the quality factors for the base and the OLIMPO cryostat–like temperatures. – 13 – − − I × − [DAQ unit] − − − Q × − [ D A Q un i t ]
140 160 180 200 220 240 260
Bias Frequency [MHz] A m p li t u d e × − [ D A Q un i t ]
140 160 180 200 220 240 260
Bias Frequency [MHz] − − − P h a s e [ r a d ] − − I × − [DAQ unit] − − Q × − [ D A Q un i t ]
150 200 250 300
Bias Frequency [MHz] A m p li t u d e × − [ D A Q un i t ]
150 200 250 300
Bias Frequency [MHz] − − − P h a s e [ r a d ] − − − I × − [DAQ unit] − − − Q × − [ D A Q un i t ]
360 380 400 420 440 460 480
Bias Frequency [MHz] . . . . . . . A m p li t u d e × − [ D A Q un i t ]
360 380 400 420 440 460 480
Bias Frequency [MHz] − − − P h a s e [ r a d ] − − I × − [DAQ unit] − − Q × − [ D A Q un i t ]
300 350 400 450 500
Bias Frequency [MHz] A m p li t u d e × − [ D A Q un i t ]
300 350 400 450 500
Bias Frequency [MHz] − − − P h a s e [ r a d ] Figure 9 . S parameter of the resonances of the four OLIMPO detector arrays. Left panels : Complex S parameter in the IQ plane. Central panels : Amplitude of the bias signal transmitted across the array.
Rightpanels : Phase of the bias signal transmitted across the array.
First row : 150 GHz array at 185 mK. The biassignal is composed of 20 tones with power P bias = −
90 dBm each, sweeping in a frequency range of 400 kHzaround the resonant frequencies.
Second row : 250 GHz array at 168 mK. The bias signal is composed of34 tones with power P bias = −
79 dBm each, sweeping in a frequency range of 400 kHz around the resonantfrequencies.
Third row : 350 GHz array at 155 mK. The bias signal is composed of 23 tones with power P bias = −
96 dBm each, sweeping in a frequency range of 400 kHz around the resonant frequencies.
Fourthrow : 460 GHz array at 255 mK. The bias signal is composed of 43 tones with power P bias = −
99 dBm each,sweeping in a frequency range of 400 kHz around the resonant frequencies. – 14 –n accordance with the design, the total quality factors are dominated by the coupling qualityfactors.
The electrical phase responsivity is given by R ϑ = − η pb τ qp ∆ Q δ x δ N qp , (5.1)where η pb is the pair–breaking e ffi ciency, τ qp is the quasiparticle lifetime, ∆ is half Cooper pairbinding energy, x = (cid:0) ν r − ν r , (cid:1) /ν r , is the dimensionless resonant frequency shift, and δ x /δ N qp is thetemperature responsivity.According to the BCS theory, at temperatures T (cid:28) T c the Cooper pair binding energy is linkedto the critical temperature of the superconductor by eq. (2.1), and the number of quasiparticles, N qp ,is linked to the superconductor temperature by equation N qp = V N (cid:112) π k B T ∆ e − ∆ / ( k B T ) , (5.2)where V is the volume of the absorber ( V
150 GHz = . µ m − , V
250 GHz = . µ m − , V
350 GHz = . µ m − , and V
460 GHz = . µ m − ), and N is the density of states at the Fermi surface, whichfor aluminum is N = . × J − µ m − .For the estimation of the electrical phase responsivity, we assume η pb = .
57 [29–31]. Fromthe signal spikes due to the interaction between the detectors and cosmic rays we measured thequasiparticle lifetime τ qp = (30 . ± . µ s at 300 mK. We measured the critical temperature T c = (1 . ± . ff erent thermal loads of theirholders, the points of the temperature sweeps are di ff erent array by array. Fig. 10 collects the plots ofthe temperature sweeps in amplitude of one detector per array. In these plots, the temperatures of thesweeps for each array are indicated.Fig. 11 shows the measured trends for the dimensionless resonant frequency shift versus thenumber of quasiparticles (or equivalently versus temperature) for all the resonators of the four ar-rays. Due to low–level nonlinearity in the response over the whole temperature range we explored, asingle linear fit is not adequate to reproduce the entire curve. Therefore, for each detector array, weconsidered three fit ranges. Specifically, Fit Range includes all the temperatures explored with thesweep; Fit Range includes the temperatures where the responsivity is maximum; and Fit Range starts from the OLIMPO base temperature. Tab. 6 specifies, in detail, the bounds in temperatureof the fit ranges for each detector array.The results for the Fit Range and are described in appendix B. Fig. 12 shows the fitresults in the Fit Range , for all the detectors of the OLIMPO detector arrays. For the 250 GHzarray, as shown in the top–right panel , the resonances corresponding to the pixels 9 and 22 disappearat 370 mK.The electrical phase responsivity has been obtained through eq. (5.1), where we used the Q values measured at around 300 mK. The array–average electrical phase responsivity result to be1 .
35 rad / pW, 1 .
49 rad / pW, 2 .
09 rad / pW, and 2 .
14 rad / pW for the 150, 250, 350, and 460 GHz arraysrespectively.In order to estimate the electrical NEP, we measured the phase noise spectrum for the four ar-rays. We measured the noises at a modulation frequency of 12 Hz and at a temperature of 300 mK,– 15 – . − . − . − . . . Frequency shift [MHz] − − − − − − − A m p li t u d e [ d B ] . . . . . . . . . . . . . . . − . − . − . − . − . − . . . Frequency shift [MHz] − − − − A m p li t u d e [ d B ] . . . . . . . . . . . . . − . − . . Frequency shift [MHz] − − − − − − A m p li t u d e [ d B ] . . . . . . . . . . . . . . . . . . . − . − . − . − . − . . . Frequency shift [MHz] − − − − − − A m p li t u d e [ d B ] . . . . . . . . . Figure 10 . Amplitude of the bias signal transmitted across the resonators for di ff erent temperatures of thearrays. Top–left panel : 2 nd pixel of the 150 GHz array. Top–right panel : 31 st pixel of the 250 GHz array. Bottom–left panel : 19 th pixel of the 350 GHz array. Bottom–right panel : 40 th pixel of the 460 GHz array.Channel Fit range[GHz] Table 6 . Definition of the fit ranges.
Fit Range : all the temperatures. Fit Range : temperature where theresponsivity is maximum. Fit Range : OLIMPO cryostat-like temperatures. which are the typical operating conditions in the OLIMPO receiver. The noises and the correspond-ing NEPs are collected in tab. 7, where the quoted uncertainties reflect the pixel variability over thearrays. These NEPs result lower than the BLIP NEPs of the OLIMPO experiment for both photo-metric and spectrometric configuration (see tab. 1), and are encouraging for the next step: the opticalcharacterization in the OLIMPO cryostat. – 16 – N qp × − − − − − ( ν r − ν r , ) / ν r , [ pp m ] [185;387]mK Fit Range [185;284]mK
Fit Range [300;387]mK
Fit Range [185;387]mK
Fit Range [185;284]mK
Fit Range [300;387]mK . . . . . Temperature [mK] . . . . . . . N qp × − − − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] [168;370]mK Fit Range [168;265]mK
Fit Range [295;370]mK
Fit Range [168;370]mK
Fit Range [168;265]mK
Fit Range [295;370]mK . . . . . . Temperature [mK] . . . . . N qp × − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] [155;365]mK Fit Range [155;291]mK
Fit Range [300;365]mK
Fit Range [155;365]mK
Fit Range [155;291]mK
Fit Range [300;365]mK . . . . Temperature [mK] . . . . . . . . . . N qp × − − − − − ( ν r − ν r , ) / ν r , [ pp m ] [255;373]mK Fit Range [255;293]mK
Fit Range [310;373]mK
Fit Range [255;373]mK
Fit Range [255;293]mK
Fit Range [310;373]mK . . . . Temperature [mK]
Figure 11 . Trends of (cid:16) ν r − ν r , (cid:17) /ν r , with the number of quasiparticles, N qp . ν r , is the resonant frequencyat the base temperature. The color dots with the error bars are the measured data, for which di ff erent colorsindicate di ff erent resonators. The color areas define the di ff erent ranges where the linear fits are performedin order to estimate the temperature responsivity δ x /δ N qp . Top–left panel : 150 GHz array.
Top–right panel :250 GHz array.
Bottom–left panel : 350 GHz array.
Bottom–right panel : 460 GHz array.Channel Average Noise Average NEP[GHz] (cid:104) rad / √ Hz (cid:105) (cid:104) aW / √ Hz (cid:105)
150 6 . × − . ± . . × − ± . × − . ± . . × − ± Table 7 . Array–average of the phase noise and electrical noise equivalent power measure at 12 Hz. – 17 – N qp × − − − − − − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . Temperature [mK] . . . . . . N qp × − − − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . . Temperature [mK] . . . . . . . . . N qp × − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . Temperature [mK] . . . . . . . . N qp × − − − − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . Temperature [mK]
Figure 12 . Fractional frequency shift as a function of bath temperature for all the four arrays. Here, thetemperatures varies from approximately 300 to 400 mK (
Fit Range in tab. 6). The dots with the errorbars are the measured data, and the solid lines are the linear fit results. Di ff erent colors indicate di ff erentresonators. Top–left panel : 150 GHz array, fit range [300; 387] mK.
Top–right panel : 250 GHz array, fit range[295; 370] mK.
Bottom–left panel : 350 GHz array, fit range [300; 365] mK.
Bottom–right panel : 460 GHzarray, fit range [310; 373] mK.
Here we report the results of the optical measurements performed on the detector arrays in theOLIMPO cryostat. OLIMPO is equipped with two independent readout chains: the first one servesthe 150 GHz array and the 460 GHz array, and the second serves the 250 GHz array and the 350 GHzarray.In all the optical measurements, as well as in the flight configuration of the experiment, wechoose to adopt the convention to normalize the readout signals to unity after o ff setting and rotatingthem in the I – Q plane in order to maximize the relative contribution from Q to the signal. This oper-ation is performed at the client–level stage of the readout chain. It has the advantage of maximizingthe sensitivity to smallest variations of the resonance circle, and to maximize the dynamics of thephase signal. For small variations of the resonance circle, the Q fluctuations coincide with the phasefluctuations. – 18 – .2.1 Optical Responsivity and NET In order to reproduce a radiative background comparable to the one expected on the detectors at about40 km of altitude, we inserted, in front of the cryostat window, a neutral density filter (NDF) withabout 0.01 transmittance ( t NDF ), and a drilled plate , designed in such a way to have a transmittanceranging from 0.04 to 0.05 for incident radiation from 150 to 460 GHz.The NDF is a thin layer of polypropylene 4 µ m thick with a 14 nm gold deposition. The drilledplate consists of an aluminum disk 5 mm thick, 100 mm in diameter, populated with 2 mm diameterholes, placed on the vertices of equilateral triangles (8 mm side). The transmittance of the drilledplate , t dp , has been measured for the four channels and the results are reported in tab. 8.Under this background, the 150 GHz and the 250 GHz arrays reached a temperature of about290 mK, while the 350 GHz and the 460 GHz arrays reached a temperature of about 320 mK.The optical signal has been obtained by alternating at the cryostat window two blackbodies atdi ff erent temperatures (room–temperature and 77 K). This produces Rayleigh–Jeans signals rangingfrom 78 to 92 mK (including the e ff ect of the NDF and the drilled plate ). The optical signals, ∆ T RJ ,for each channel are reported in tab. 8. Channel [GHz] t dp [%] ∆ T RJ [mK]150 3 . ± .
03 77 . ± . . ± .
05 88 . ± . . ± .
03 92 . ± . . ± .
03 90 . ± . Table 8 . Measured transmittance of the drilled plate and total optical signals at the cryostat window for thefour detector arrays, produced alternating two blackbodies (room-temperature and 77 K), attenuated by a NDFand a drilled plate . The optical signals are evaluated as ∆ T RJ = (285 K −
77 K) t NDF t dp . Both blackbodies fill the beam of the optical system. The signal modulation has been performedby means of a large chopper, with an adjustable modulation frequency ranging from 5 to 12 Hz. Forthe signal measurements, the modulation frequency has been set at 12 Hz. The left panels of fig. 13show the 1 s time streams of the ∆ T RJ signals, modulated at 12 Hz, and read out in the I and Q channels, for one representative pixel of each array.The noise measurements have been performed by closing the cryostat window with a metalmirror, and acquiring 50 s long signal time streams for the I and Q channels. The noise spectra areobtained by performing the Fourier transforms of the these time streams. The resulting noise spectraare shown in the right panels of fig. 13.From these measurements, the noise equivalent temperatures for the I and Q channels in theRayleigh–Jeans approximation (NET RJ ), referred to the cryostat window, can be easily obtained fromthe ratio between the noises at 12 Hz, n I and n Q , and the responsivities, R I and R Q . The responsivity isthe ratio between the peak–to–peak of the measured modulated signal and the temperature di ff erenceof the two blackbody sources ∆ T RJ .In order to maximize the signal, we defined a combined signal, ∆ S comb , as ∆ S comb = ∆ I cos α + ∆ Q sin α , (5.3)where α = arctan ( ∆ Q / ∆ I ), and to which we can associate a combined responsivity, R comb , definedas R comb = R I cos α + R Q sin α . (5.4)– 19 – . . . . . . Time [s] − . − . − . . . . . S i g n a l [ r a d ] I Q − − Frequency [Hz] − − − − N o i s e h r a d / √ H z i I Q . . . . . . Time [s] − . − . − . . . . . S i g n a l [ r a d ] I Q − − Frequency [Hz] − − − − N o i s e h r a d / √ H z i I Q . . . . . . Time [s] − . − . − . . . . . S i g n a l [ r a d ] I Q − − Frequency [Hz] − − − − N o i s e h r a d / √ H z i I Q . . . . . . Time [s] − . − . − . . . . . S i g n a l [ r a d ] I Q − − Frequency [Hz] − − − − N o i s e h r a d / √ H z i I Q
Figure 13 . Left column : 1 s time streams of the ∆ T RJ optical signal, modulated at 12 Hz, read out in the I ( redsolid line ) and Q ( blue dashed line ) channels for one pixel per array. Right column : noise spectra of the I ( redsolid line ) and Q ( blue dashed line ) channels (one pixel per array), obtained from 50 s long signal time streams,with the cryostat window closed by a mirror. First row : 8 th pixel of the 150 GHz array. Second row : 7 th pixelof the 250 GHz array. Third row : 17 th pixel of the 350 GHz array. Fourth row : 7 th pixel of the 460 GHz array. – 20 –he noise associated to ∆ S comb is obtained by performing the Fourier transforms of the 50 s longcombined signal time stream.Tab. 9 collects the optical responsivity and NET RJ averaged over all the the detectors of eacharray. Channel average R [rad / K] average NET RJ (cid:104) µ K √ s (cid:105) [GHz] Q combined Q combined150 0 . ± .
018 0 . ± .
019 212 ±
25 201 ± . ± .
024 0 . ± .
024 261 ±
32 243 ± . ± .
022 0 . ± .
021 259 ±
12 243 ± . ± .
022 0 . ± .
024 403 ±
29 336 ± Table 9 . Array–averages of the optical responsivity and noise equivalent temperature in the Rayleigh–Jeansapproximation, referred to the cryostat window.
The spectral response of the four detector arrays has been measured by using the OLIMPO di ff erentialFourier Transform spectrometer [4]. A high–pressure mercury vapor lamp ( Philips HPK–125 ) andan Eccosorb sheet have been used as the thermal Rayleigh–Jeans sources. The scan amplitude of themoving mirrors has been set in such a way that the DFTS resolution was ∆ ν = . / s toavoid source drift systematic and a triangular apodization has been implemented to the interferogramsto avoid spectral distortions due to the data analysis.Fig. 14 reports the spectra measured for the central pixels of each array, corrected for theRayleigh–Jeans spectrum of the source, and normalized to the peak signals.The FWHM of these spectra, and the e ff ective frequencies for a CMB spectrum, an interstellardust spectrum, and a SZ spectrum are collected in tab. 10. The e ff ective frequencies are calculated as ν e f f , i = (cid:82) ∆ ν ν B i ( T i , ν ) e ( ν ) d ν (cid:82) ∆ ν B i ( T i , ν ) e ( ν ) d ν (5.5)where i = CMB or dust or SZ, B CMB = BB ( T CMB , ν ) with T CMB = .
725 K [33], B dust ∼ ν α BB ( T dust , ν )with α = . T d =
20 K [34], B SZ = B CMB x e x e x − (cid:20) x cotanh (cid:18) x (cid:19) − (cid:21) (5.6)with x = h ν k B T CMB , (5.7) BB ( T , ν ) is the blackbody spectrum, and e ( ν ) is the spectral response. – 21 –
20 130 140 150 160 170 180
Frequency [GHz] . . . . . . N o r m a li z e d s p e c t r u m
200 250 300
Frequency [GHz] . . . . . . N o r m a li z e d s p e c t r u m
320 330 340 350 360 370 380
Frequency [GHz] . . . . . . N o r m a li z e d s p e c t r u m
400 420 440 460 480 500 520
Frequency [GHz] . . . . . . N o r m a li z e d s p e c t r u m Figure 14 . Measured spectral response for the central pixels of each detector array. The spectra are normalizedto the peak and corrected for the spectrum of the source (a high–pressure mercury vapor lamp
Philips HPK–125 ). Top–left panel : 150 GHz channel.
Top–right panel : 250 GHz channel.
Bottom–left panel : 350 GHzchannel.
Bottom–right panel : 460 GHz channel.Channel FWHM ν e f f , CMB ν e f f , dust ν e f f , SZ [GHz] [GHz] [GHz] [GHz] [GHz]150 25 151.0 153.4 150.1250 90 244.8 264.8 269.1350 30 350.8 353.4 352.3460 60 460.1 469.7 463.4 Table 10 . FWHM of the measured spectra reported in fig. 14 and e ff ective frequencies for a CMB spectrum,an interstellar dust spectrum, and a SZ spectrum. ffi ciency In order to estimate the optical e ffi ciency, ε , of OLIMPO (excluding the primary and the secondarymirrors), we compare the electrical phase responsivity R elec ϑ with the optical one R optQ . Since in thecentered–rotated resonance circle readout scheme Q coincides with the phase, converting R optQ from– 22 –rad / K] to [rad / W], and dividing it by R elec ϑ , we obtain the optical e ffi ciency: ε = R optQ R elec ϑ (5.8)The electrical responsivity reported in Subsubsec. 5.1.2 has been measured in dark conditions,and is thus overestimated with respect to the one in working conditions. For this reason the e ffi ciencyresults reported here should be considered as lower limits for the real e ffi ciency.The conversion of R optQ from [rad / K] to [rad / W] is given by R optQ (cid:34) radW (cid:35) = R optQ (cid:34) radK (cid:35) dTdP RJ , (5.9)with dP RJ dT = k B ∆ ν , (5.10)where ∆ ν is the FWHM, which values are collected in tab. 10. Using eq. (5.9) and (5.10), the valuesof the average R optQ in [rad / K] collected in tab. 9 can be converted in [rad / W], shown in tab. 11, withtogether the optical NEPs, referred to the cryostat window.
Channel average R opt (cid:2) rad / pW (cid:3) average NEP (cid:104) aW / √ Hz (cid:105) [GHz] Q combined Q combined150 0 . ± .
026 0 . ± .
028 207 ±
25 196 ± . ± .
010 0 . ± .
010 866 ±
105 808 ± . ± .
027 0 . ± .
026 303 ±
14 284 ± . ± .
013 0 . ± .
014 857 ±
68 787 ± Table 11 . Array–averages of the optical responsivity in [rad / W] and noise equivalent power, referred to thecryostat window.
Comparing R optQ and R elec ϑ , we obtain the optical e ffi ciencies for the four spectral bands. Thevalues are shown in tab. 12. Channel [GHz] R optQ (cid:2) rad / pW (cid:3) R elec ϑ (cid:2) rad / pW (cid:3) ε [%]150 0 . ± .
026 1 . ± . > ± . ± .
010 1 . ± . > ± . ± .
027 2 . ± . > ± . ± .
013 2 . ± . > ± Table 12 . Array–average of the optical e ffi ciency, given by the ratio between the optical responsivity and theelectrical responsivity measured in dark conditions. These measurements confirm the high sensitivity to mm-wave radiation of the four OLIMPOKID arrays and a reasonable e ffi ciency of the entire receiver.– 23 –rom the measured e ffi ciencies and NETs we can forecast a high precision spectroscopic mea-surement of the SZ spectrum in rich clusters of galaxies. Assuming that the noise performance mea-sured here is achieved also during the flight, and the typical optical e ffi ciency is 15% for all arrays,we have simulated a typical measurement of a rich cluster of galaxies ( τ th = .
005 and T e = . ∆ ν = Figure 15 . Expected sensitivity of the spectral observation of a rich cluster of galaxies with the OLIMPODFTS. The solid line represents the sum of thermal SZ brightness ( dashed line ) and dust continuum ( dottedline ). The filled regions represent the expected ± σ confidence intervals for the measured spectral data,based on the noise equivalent powers measured here and assuming an optical e ffi ciency of the telescope + spectrometer + receiver system of 15%. We assumed a DFTS resolution of 5 GHz. The confidence intervalswiden at both edges of each observation band, due to the reduced transmission of the band-selection filters atcut-on and cut-o ff . We have considered a 24–hours long integration on a cluster with τ th = . T e = . . / sr at 150 GHz.We have considered only the center pixel of each array, pointing at the center of the cluster, since the otherpixels will observe either the outskirts of the cluster, or the blank sky in the surrounding regions. In this paper we described the design, fabrication, electrical and optical characterization of the fourdetector arrays of the OLIMPO experiment. These detectors are front illuminated, horn–coupled, AlLEKIDs deposited on Si wafers. Optical and electrical simulations have brought to the definition– 24 –f the entire detector systems, from the waveguide to the backshort, through the optical transitionelement, the absorber, the capacitor, the feedline, the coupling between the detector and the feedline,and the dielectric substrate.The electrical characterization has been performed in the laboratory with a dark setup based ona dilution cryostat, with a replica of the OLIMPO room–temperature electronics . Measurements ofthe quasiparticle lifetime, of the critical temperature of the aluminum film, of the resonator qualityfactors, of the temperature responsivities, and of the phase noises were used to estimate the electricalNEPs. We obtained an average electrical NEP at 12 Hz lower than the estimated BLIP NEP of thespectrometric configuration of OLIMPO, for all the detector arrays.The characterization of the detectors has been completed with the optical tests, performed afterthe integration of the arrays in the OLIMPO cryostat. We measured the NET RJ s under realisticloading conditions, by measuring signal time–streams and noise spectral densities. We characterizedthe spectral responses by using the OLIMPO DFTS, with a resolution a 1 . ffi ciency of the OLIMPO receiver comparing the optical and the electrical responsivities.Given the measured performance, we forecast a high precision spectroscopic measurement ofthe SZ spectrum in rich clusters of galaxies, which looks really promising. Acknowledgments
We acknowledge the Italian Space Agency (ASI) for funding the OLIMPO experiment, and organiz-ing the 2018 launch campaign. We thank Giorgio Amico for manufacturing the array sample holders.We are grateful to Angelo Cruciani for useful suggestions and discussions.– 25 –
Fit of the complex S parameter In order to estimate the electrical properties of the resonators, each resonance circle (complex S parameter) can be fit to the equation [35] S ( ν r ) = a − Q e j φ / Q c + j Q ν − ν r ν r , (A.1)where a is a complex constant accounting for the gain and phase shift through the system, Q is thetotal quality factor, and φ takes into account the rotation of the resonance circle due to the impedancemismatches in proximity of the resonance. The total and the coupling quality factors are linked to theinternal quality factor, Q i , through the equation1 Q = Q i + Q c . (A.2)As an example, fig. 16 shows the results of the complex fit through eq. (A.1) of the resonancecircle of the first pixel of the 150 GHz array at 185 mK and 300 mK. − − I × − [DAQ unit] Q × − [ D A Q un i t ] fitdata .
10 146 .
15 146 .
20 146 .
25 146 .
30 146 . Bias Frequency [MHz] A m p li t u d e × − [ D A Q un i t ] fitdata .
10 146 .
15 146 .
20 146 .
25 146 .
30 146 . Bias Frequency [MHz] − . . . . . . . . P h a s e [ r a d ] fitdata − − − I × − [DAQ unit] − − − − − Q × − [ D A Q un i t ] fitdata .
05 146 .
10 146 .
15 146 .
20 146 .
25 146 . Bias Frequency [MHz] A m p li t u d e × − [ D A Q un i t ] fitdata .
05 146 .
10 146 .
15 146 .
20 146 .
25 146 . Bias Frequency [MHz] − . − . − . − . − . − . P h a s e [ r a d ] fitdata Figure 16 . Fit result for the first pixel of the 150 GHz array at 185 mK, in the top panels , and at 300 mK, inthe bottom panels . The fit function, eq. (A.1), is overplotted in red to the measured data in black ( dots with the error bars ) for the IQ circle, in the left panel , the amplitude, in the central panel , and the phase, in the rightpanel . – 26 – Electrical responsivity in
Fit Range and For completeness, in this appendix we report the estimate of the electrical phase responsivity in the
Fit Range and .Fig. 17 and 18 show the fit results in the Fit Range and Fit Range respectively, for allthe detectors of the OLIMPO detector arrays. The electrical phase responsivity has been obtainedthrough eq. (5.1), where we used the Q values measured at the base temperatures. We used the valuesof τ qp measured at 300 mK, hence the R ϑ calculated here have to be considered lower limits, becausethe value of τ qp at 300 mK is theoretically lower than those at the base temperatures. Tab. 13 collectsthe electrical phase responsivity averaged, for each array, over all the detectors. N qp × − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . Temperature [mK] . . . . . . . N qp × − − − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . . Temperature [mK] . . . . . N qp × − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . Temperature [mK] . . . . . . . . . . N qp × − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . Temperature [mK]
Figure 17 . Fractional frequency shift as a function of bath temperature for all the four arrays. Here, thetemperatures varies from approximately 200 to 400 mK (
Fit Range in tab. 6). The dots with the errorbars are the measured data, and the solid lines are the linear fit results. Di ff erent colors indicate di ff erentresonators. Top–left panel : 150 GHz array, fit range [185; 387] mK.
Top–right panel : 250 GHz array, fit range[168; 370] mK.
Bottom–left panel : 350 GHz array, fit range [155; 365] mK.
Bottom–right panel : 460 GHzarray, fit range [255; 373] mK. – 27 – . . . . . . N qp × − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . Temperature [mK] .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 . N qp × − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . Temperature [mK] .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 .
30 0 . N qp × − − − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . . . Temperature [mK] .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 . N qp × − − − − − − ( ν r − ν r , ) / ν r , [ pp m ] . . . . . . Temperature [mK]
Figure 18 . Fractional frequency shift as a function of bath temperature for all the four arrays. Here, thetemperatures varies from approximately 200 to 300 mK (
Fit Range in tab. 6). The dots with the errorbars are the measured data, and the solid lines are the linear fit results. Di ff erent colors indicate di ff erentresonators. Top–left panel : 150 GHz array, fit range [185; 284] mK.
Top–right panel : 250 GHz array, fit range[168; 265] mK.
Bottom–left panel : 350 GHz array, fit range [155; 291] mK.
Bottom–right panel : 460 GHzarray, fit range [255; 293] mK.Channel average R ϑ (cid:2) rad / pW (cid:3) [GHz] Fit Range . ± .
26 2 . ± .
31 1 . ± . . ± .
30 6 . ± .
42 1 . ± . . ± .
63 10 . ± . . ± . . ± .
27 6 . ± .
30 2 . ± . Table 13 . Array–average of the electrical phase responsivity in the three fit ranges.
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